Abstract:
Embodiments of cognitive radio technology can recover and utilize under-utilized portions of statically-allocated radio-frequency spectrum. A plurality of sensing methods can be employed. Transmission power control can be responsive to adjacent channel measurements. Digital pre-distortion techniques can enhance performance. Embodiments of a high dynamic range transceiver architecture can be employed.

Description:
PRIORITY 
       [0001]    This application is related to and claims priority under 35 U.S.C. 119(e) to U.S. Provisional Patent Application No. 60/890,801 filed on Feb. 20, 2007 entitled “SYSTEM AND METHOD FOR COGNITIVE RADIO” by Haiyun Tang the complete content of which is hereby incorporated by reference. 
     
    
     STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH AND DEVELOPMENT 
       [0002]    This invention was made with Government support under contract FA8750-05-C-0067 awarded by the Air Force. The Government has certain rights in the invention. 
     
    
     BACKGROUND 
       [0003]    1. Field of the Invention 
         [0004]    The inventions herein described relate to systems and methods for cognitive radio. 
         [0005]    2. Description of the Related Art 
       Spectrum Utilization Problems 
       [0006]    A recent study by the FCC Spectrum Task Force [United States&#39; Federal Communications Commission (FCC), “Report of the spectrum efficiency working group,” November 2002 found that while the available spectrum becomes increasingly scarce, the assigned spectrum is significantly underutilized. This imbalance between spectrum scarcity and spectrum underutilization is especially inappropriate in this Information Age, when a significant amount of spectrum is needed to provide ubiquitous wireless broadband connectivity, which is increasingly becoming an indispensable part of everyday life. 
         [0007]    Static spectrum allocation over time can also result in spectrum fragmentation. With lack of an overall plan, spectrum allocations in the US and other countries over the past several decades can appear to be random. Despite some efforts to serve best interests at the time, this leads to significant spectrum fragmentation over time. The problem is exacerbated at a global level due to a lack of coordinated regional spectrum assignments. In order to operate under such spectrum conditions, a device can benefit from operational flexibility in frequency and/or band shape; such properties can help to maximally exploit local spectrum availability. 
         [0008]    To address the above problems, an improved radio technology is needed that is capable of dynamically sensing and locating unused spectrum segments, and, communicating using these spectrum segments while essentially not causing harmful interference to designated users of the spectrum. Such a radio is generally referred to as a cognitive radio, although strictly speaking, it may perform only spectrum cognition functions and therefore can be a subtype of a broad-sense cognitive radio [J. M. III, “Cognitive radio for flexible mobile multimedia communications,”  Mobile Networks and Applications , vol. 6, September 2001.] that learns and reacts to its operating environment. Key aspects of a cognitive radio can include: Sensing: a capability to identify used and/or unused segments of spectrum. Flexibility: a capability to change operating frequency and/or band shape; this can be employed to fit into unused spectrum segments. Non-interference: a capability to avoid causing harmful interference to designated users of the spectrum. 
         [0009]    Such a cognitive radio technology can improve spectrum efficiency by dynamically exploiting underutilized spectrum, and, can operate at any geographic region without prior knowledge about local spectrum assignments. It has been an active research area recently. 
       FCC Spectrum Reform Initiatives 
       [0010]    FCC has been at the forefront of promoting new spectrum sharing technologies. In April 2002, the FCC issued an amendment to Part 15 rules that allows ultra-wideband (UWB) underlay in the existing spectrum [FCC, “FCC first report and order: Revision of part 15 of the commission&#39;s rules regarding ultra-wideband transmission systems,”  ET Docket No.  98-153, April 2002]. In June 2002, the FCC established a Spectrum Policy Task Force (SPTF) whose study on the current spectrum usage concluded that “many portions of the radio spectrum are not in use for significant periods of time, and that spectrum use of these ‘white spaces’ (both temporal and geographic) can be increased significantly”. SPTF recommended policy changes to facilitate “opportunistic or dynamic use of existing bands.” In December 2003, FCC issued the notice of proposed rule making on “Facilitating Opportunities for Flexible, Efficient and Reliable Spectrum Use Employing Cognitive Radio Technologies” [FCC, “Facilitating opportunities for flexible, efficient, and reliable spectrum use employing cognitive radio technologies,”  ET Docket No.  03-108, December 2003] stating that “by initiating this proceeding, we recognize the importance of new cognitive radio technologies, which are likely to become more prevalent over the next few years and which hold tremendous promise in helping to facilitate more effective and efficient access to spectrum.” 
         [0011]    While both UWB and cognitive radio are considered as spectrum sharing technologies, their approaches to spectrum sharing are substantially different. UWB is an underlay (below noise floor) spectrum sharing technology, while cognitive radio is an overlay (above noise floor) and interlay (between primary user signals) spectrum sharing technology as shown in  FIG. 1 . Through sensing combined with operational flexibility, a cognitive radio can identify and make use of spectral “white spaces” between primary user signals. Because a cognitive user signal resides in such “white spaces”, high signal transmission power can be permitted as long as signal power leakage into primary user bands does not embody harmful interference. 
       Broadcast TV Bands 
       [0012]    Exemplary broadcast TV bands are shown in Graph  200  of  FIG. 2 . Each TV channel is 6 MHz wide. Between 0 and 800 MHz, there are a total of 67 TV channels (Channels 2 to 69 excluding Channel 37 which is reserved for radio astronomy). The NPRM [FCC, May 2004, op. cit.] excludes certain channels for unlicensed use: Channels 2-4, which are used by TV peripheral devices, and Channels 52-69, which are considered for future auction. Among the channels remaining, Channels 5-6, 7-13, 21-36, and 38-51 are available for unlicensed use in all areas. Unlicensed use in Channels 14-20 is allowed only in areas where they are not used by public safety agencies [FCC, May 2004, op. cit.]. 
         [0013]    It can be appreciated that Channels 52-69 are currently used by TV broadcasters and it is not clear if/when they will be vacated. There is significant interference in the lower channels 5-6 and 7-13. Based on these considerations, the spectrum segment 470-806 MHz covering TV channels 14-69 can be of particular interest. 
       Spectrum Opportunity in the TV Bands 
       [0014]    Spectrum opportunity can be a direct result of incumbent system inefficiency. In TV bands, a signal from a TV tower can cover an area with a radius of tens of kilometers. TV receivers can be sensitive to interference such that TV cell planning may be very conservative to ensure there is essentially no co-channel interference. This can leave a substantial amount of “white spaces” between co-channel TV cells as illustrated in the Map  300  of  FIG. 3 . Those “white spaces” can constitute an opportunistic region for cognitive users on a particular TV channel. Each TV channel may have a differently shaped opportunistic region. The total spectrum opportunity at any location can comprise the total number of opportunistic regions covering the location. A measurement in one locality shows an average spectrum opportunity in TV channels 14-69 of about 28 channels; that can be expressed as an equivalent bandwidth of approximately 170 MHz. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0015]      FIG. 1  graph of spectrum sharing technologies: UWB and cognitive radio  FIG. 2  graph of exemplary television channel bands 
           [0016]      FIG. 3  map of television co-channel coverage areas and opportunistic region 
           [0017]      FIG. 4  diagram of a cognitive radio system 
           [0018]      FIG. 5  DTV signal Data Field Sync segment 
           [0019]      FIG. 6  NTSC signal video (V), chroma (C), and audio (A) carriers 
           [0020]      FIG. 7  graph: Simulated NTSC signal sensing gain contours 
           [0021]      FIG. 8  diagram: false detection probability and loss detection probability. 
           [0022]      FIG. 9  graph: Sensing error floor contours 
           [0023]      FIG. 10  diagram: hidden terminal problem. 
           [0024]      FIG. 11  diagram: relations between various signal power level definitions. 
           [0025]      FIG. 12  graph: PD/PS and P0/P1 for interference-free operation 
           [0026]      FIG. 13  diagram: hidden terminal problem in shadowing environment. 
           [0027]      FIG. 14  graph: Hidden terminal probability with sensing information sharing 
           [0028]      FIG. 15  graph: Critical mass for a specified HTP in a shadowing environment. 
           [0029]      FIG. 16  radio signal coverage areas at different data rates. 
           [0030]      FIG. 17  ATSC Data Frame format 
           [0031]      FIG. 18  diagram: ATSC signal sensing 
           [0032]      FIG. 19  diagram: auto-correlation processing. 
           [0033]      FIG. 20  diagram: NTSC signal sensing 
           [0034]      FIG. 21  diagram: Energy sensing 
           [0035]      FIG. 22  diagram: Combined sensing methods 
       
    
    
     DETAILED DESCRIPTION 
       [0036]      FIG. 4  depicts an embodiment of a cognitive radio system in block diagram. A transceiver  401  can be coupled to and/or in communication with one or more antennae  402 . Baseband signal processing can be provided by elements of a baseband processor  403 . Elements of a baseband processor  403  can comprise a sensing processor  404 , a transmit power control element  405 , and a pre-distortion element  406 . In some embodiments a pre-distortion element  406  can be coupled to and/or in communication with a transceiver  401 . In some embodiments a transmit power control element can be coupled to and/or in communication with a transceiver  401 . In some embodiments a collective sensing element  407  can be coupled to and/or in communication with a baseband processor  403  and/or elements comprising a baseband processor. 
         [0037]    In some embodiments transceiver  401  can comprise transceiver and/or transmitter and/or receiver mechanisms disclosed herein. In some embodiments sensing element  404  can comprise one or more sensing mechanisms as described herein. By way of example and not limitation these sensing mechanisms can include energy sensing, National Television Systems Committee (NTSC) signal sensing, and/or Advanced Television Systems Committee (ATSC) signal sensing. In some embodiments a collective sensing element  407  can provide collective sensing mechanisms as described herein. 
         [0038]    In some embodiments transmit power control  405  can support adaptive transmit power control mechanisms described herein. In some embodiments pre-distortion element  406  can provide digital pre-distortion mechanisms as described herein. 
         [0039]    In some embodiments baseband processor  403  can support additional processing mechanisms as described herein. By way of example and not limitation these mechanisms can include filtering and/or digital mixing. 
       Sensing for TV Band Adaptive Spectrum System 
       [0040]    Sensing methods can generally be separated into two categories: 1) energy sensing and 2) phase sensing. Energy sensing can measure spectrum energy of a target signal and can be a fundamental sensing method when nothing else is known about the target signal. In some embodiments, a received signal can be transformed to a frequency domain in order to perform an energy sensing operation. Some embodiments can employ a fast Fourier transform (FFT) and/or any other known and/or convenient transformation to a frequency domain. Signal energies in specified frequency ranges can subsequently be measured. 
         [0041]    In some embodiments and/or circumstances phase sensing can achieve better performance than energy sensing. Phase sensing can require that a target signal contains one or more known signal patterns. Phase sensing can be achieved by correlating a received signal with one or more known patterns. In some embodiments of a TV-band cognitive radio system, the incumbent signal can contain known signal patterns. In some embodiments an incumbent signal can be a Digital Television (DTV) signal and/or an NTSC signal and/or any other known and/or convenient signal organized as a channel and/or having adjacent channels. In some embodiments specified performance levels can be achieved through the use of phase sensing techniques. The terms phase sensing, waveform sensing, and/or signal sensing can be considered substantially identical as discussed herein. 
       DTV Signal Sensing: 
       [0042]    A broadcast DTV signal can contain a Data Field Sync [ATSC, “Digital television standard ,” ATSC Digital Television Standard , August 2001] segment of 832 symbols (at a symbol period 0.186 μs and/or a sampling frequency of 5.38 MHz) occurring every 24.2 ms. The diagram  500  of  FIG. 5  shows the format of a DTV Data Field Sync segment that contains a 511-element PN sequence and three 63-element PN sequences, all of which can be specified and/or known. 
         [0043]    A PN sequence can have useful correlation properties. A PN sequence correlated with any rotated version of itself can produce a result of −1, except when two PN sequences are aligned, in which case the result is equal to the PN sequence length. A PN sequence can be cyclically extended to create an infinite sequence s(n). It follows that 
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A sensing metric M(m) can be generated by correlating a received signal with a known PN sequence
 
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                       · 
                       
                         
                           
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                               c 
                                
                               
                                 ( 
                                 m 
                                 ) 
                               
                             
                              
                           
                           2 
                         
                         
                           
                             ∑ 
                             
                               n 
                               = 
                               
                                 - 
                                 ∞ 
                               
                             
                             ∞ 
                           
                            
                           
                               
                           
                            
                           
                             
                                
                               
                                 c 
                                  
                                 
                                   ( 
                                   n 
                                   ) 
                                 
                               
                                
                             
                             2 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Rake combining can be employed to eliminate the factor 
         [0000]    
       
         
           
             
               
                 
                   
                     
                        
                       
                         c 
                          
                         
                           ( 
                           m 
                           ) 
                         
                       
                        
                     
                     2 
                   
                   
                     
                       ∑ 
                       
                         n 
                         = 
                         
                           - 
                           ∞ 
                         
                       
                       ∞ 
                     
                      
                     
                         
                     
                      
                     
                       
                          
                         
                           c 
                            
                           
                             ( 
                             n 
                             ) 
                           
                         
                          
                       
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
         [0000]    in equation (7). A sensing gain over a nominal symbol SNR can then be N c . For example, a 63-element PN sequence can be used for sensing, wherein a sensing gain can be calculated 
         [0000]      10 log 10 (63)=18 dB  (9)
 
         [0044]    In some embodiments, a sensing gain of more than 20 dB can be achieved when a 511-element PN sequence is employed. 
       ATSC Signal Sensing: Signal Sensing: 
       [0045]    The format of the Data Field Sync segment (one in each Data Field of 313 832-symbol segments) can be as shown in diagram  500  of  FIG. 5 . The Data Field Sync segment contains 4 binary-modulated pseudo-random sequence, i.e. one PN511 and 3 PN63. These are intended for ATSC receiver channel equalization. 
         [0046]    When coherently combined, the PN sequences can provide significant coding gain over a nominal symbol SNR and can be employed for some embodiments with reliable low-threshold ATSC signal detection. For example, a PN63 sequence can provide about 10*log 10(63)=18 dB gain over nominal SNR and a PN511 sequence can provide about 10*log 10(511)=27 dB gain over a nominal SNR. 
         [0047]    Diagram  1800  of  FIG. 18  depicts an embodiment of a detailed block diagram for an ATSC signal sensing algorithm for an input signal y(n)  1801 , and providing a sensing result  1838 . An algorithm is based on the use of the PN sequences PN63 and PN511 in the ATSC Data Field Sync segment. The algorithm can be described as comprising essentially two distinct parts, an upper part  1851  and a lower part  1852 . The upper part  1851  can compute a signal auto-correlation using the 3 repeated PN63 sequences (refer to Data Field Sync segment format in  FIG. 5 ). The auto-correlation can generate a frequency offset estimation that can be used to compensate the input signal so that signal cross-correlation with known PN63 and/or PN511 sequences can be performed as shown in the lower part  1852 . 
         [0048]    An auto-correlation operation can be expressed in the following formula: 
         [0000]    
       
         
           
             
               
                 
                   
                     J 
                      
                     
                       ( 
                       n 
                       ) 
                     
                   
                   = 
                   
                     
                       ∑ 
                       
                         l 
                         = 
                         
                           n 
                           - 
                           62 
                         
                       
                       n 
                     
                      
                     
                         
                     
                      
                     
                       
                         
                           y 
                           * 
                         
                          
                         
                           ( 
                           
                             l 
                             - 
                             63 
                           
                           ) 
                         
                       
                        
                       
                         y 
                          
                         
                           ( 
                           l 
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Here y(l) is a received signal and y(l−63) is an input signal delayed by 63 sampling cycles; it is the output of a 63-element delay line Delay 63  1802 . Conjugation, multiplication, and summing operations of Equation (10) can be performed by the respectively corresponding modules Conjugate  1804 , Multiply  1806 , and Running Sum 63  1808 . J is the output of Running Sum 63  1808 . 
         [0049]    An auto-correlation magnitude |J(n)| curve can be expected to have a plateau when the input y(n) enters the PN63 region within the Data Field Sync segment, as illustrated in  FIG. 19  where |J(n)| is shown as the thicker curve. The auto-correlation magnitude |J(n)| normalized by the average signal power can be compared against a predefined threshold in order to determine whether such a situation has occurred. 
         [0050]    An average signal power can be computed by elements of diagram  1800 , including a Magnitude Square  1810  module and an Averaging  1812  module. An average signal power can be expressed as: 
         [0000]    
       
         
           
             
               
                 
                   
                     P 
                      
                     
                       ( 
                       n 
                       ) 
                     
                   
                   = 
                   
                     
                       1 
                       N 
                     
                      
                     
                       
                         ∑ 
                         
                           l 
                           = 
                           
                             n 
                             - 
                             
                               ( 
                               
                                 N 
                                 - 
                                 1 
                               
                               ) 
                             
                           
                         
                         n 
                       
                        
                       
                         
                            
                           
                             y 
                              
                             
                               ( 
                               l 
                               ) 
                             
                           
                            
                         
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
         [0000]    A direct implementation of averaging in Equation (11) can be achieved employing numerous techniques well known in the art. In a reduced hardware implementation embodiment, an Infinite Impulse Response (IIR) with a forgetting factor 1/N can be employed. The HR filter output can serve as a close approximation to an actual running sum output. Operation of an averaging IIR filter embodiment can be expressed as: 
         [0000]    
       
         
           
             
               
                 
                   
                     P 
                      
                     
                       ( 
                       n 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         1 
                         N 
                       
                        
                       
                         
                            
                           
                             y 
                              
                             
                               ( 
                               n 
                               ) 
                             
                           
                            
                         
                         2 
                       
                     
                     + 
                     
                       
                         ( 
                         
                           1 
                           - 
                           
                             1 
                             N 
                           
                         
                         ) 
                       
                        
                       
                         P 
                          
                         
                           ( 
                           
                             n 
                             - 
                             1 
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where P(n−1) is the IIR filter output for the sampling cycle immediately previous. It can be appreciated that averaging depth N is a parameter common to a plurality of implementations. In some embodiments, a relatively large N can be employed in order to achieve specified performance criteria for computation of average power. For example, N can be chosen to be 500. 
         [0051]    An Autocorr. Threshold  1814  module can compare normalized auto-correlation magnitude, i.e.: 
         [0000]    
       
         
           
             
               
                 
                   
                      
                     
                       J 
                        
                       
                         ( 
                         n 
                         ) 
                       
                     
                      
                   
                   
                     P 
                      
                     
                       ( 
                       n 
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
         [0000]    against a specified pre-defined threshold, e.g. 0.45. A threshold can be specified such that values exceeding the threshold indicate a specified reasonable confidence of entering a PN63 region of a Data Field Sync segment, whereupon a peak search operation can follow. 
         [0052]    A Peak Search  1822  operation can be controlled by two time stamps: peak search start p0  1816  and peak search end p1  1818 . These time stamps can be generated by a Control Timer  1820  module. In the event that an autocorrelation threshold is exceeded at sampling index n, a requirement can follow that: 
         [0000]        p 0 ≧n   (14)
 
         [0000]    A p0  1816  value can typically be chosen to be equal to n. The duration between time stamps: 
         [0000]        T   PS   =p 1 −p 0  (15)
 
         [0000]    can be specified to be long enough so that it can cover a plateau region of normalized auto-correlation magnitude as shown in diagram  1900 . For example, T PS  can be chosen to be twice the PN63 length, i.e. 126. 
         [0053]    Between the two time stamps p0 and p1, a Peak Search  1822  module can be activated in order to search for an auto-correlation J(n) that corresponds to a maximum normalized auto-correlation magnitude, as expressed in Equation (13). This maximum auto-correlation can be used to estimate a frequency offset and/or to generate a phase increment in order to derotate an input signal in order to compensate for a frequency offset. Taking into account frequency offset, the auto-correlation can be expressed as: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       y 
                        
                       
                         ( 
                         n 
                         ) 
                       
                     
                      
                     
                       J 
                        
                       
                         ( 
                         n 
                         ) 
                       
                     
                   
                   = 
                   
                     
                        
                       
                         j2πρ 
                         · 
                         63 
                       
                     
                      
                     
                       
                         ∑ 
                         
                           l 
                           = 
                           
                             n 
                             - 
                             62 
                           
                         
                         n 
                       
                        
                       
                         
                           
                             y 
                             * 
                           
                            
                           
                             ( 
                             
                               l 
                               - 
                               63 
                             
                             ) 
                           
                         
                          
                         
                           y 
                            
                           
                             ( 
                             l 
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
           
         
       
     
         [0000]    with per sample frequency offset ρ=Δf c T s  where Δf c  is the frequency offset and T s  is the sampling period. Referring to diagram  1900 , for a maximum J(n) (within the plateau region) it can be expected that 
         [0000]        y ( l− 63)= y ( l )  (17)
 
         [0000]    if noise is neglected. Thus Equation (16) becomes: 
         [0000]    
       
         
           
             
               
                 
                   
                      
                     
                       j2πρ 
                       · 
                       63 
                     
                   
                   = 
                   
                     
                       J 
                        
                       
                         ( 
                         n 
                         ) 
                       
                     
                     
                       
                         ∑ 
                         
                           l 
                           = 
                           
                             n 
                             - 
                             62 
                           
                         
                         n 
                       
                        
                       
                         
                            
                           
                             y 
                              
                             
                               ( 
                               l 
                               ) 
                             
                           
                            
                         
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   18 
                   ) 
                 
               
             
           
         
       
     
         [0000]    and a frequency offset per sample can be estimated: 
         [0000]    
       
         
           
             
               
                 
                   
                     2 
                      
                     πρ 
                   
                   = 
                   
                     
                       arg 
                        
                       
                         [ 
                         
                           J 
                            
                           
                             ( 
                             n 
                             ) 
                           
                         
                         ] 
                       
                     
                     63 
                   
                 
               
               
                 
                   ( 
                   19 
                   ) 
                 
               
             
           
         
       
     
         [0000]    The above computation can be performed by the Phase Incre. Comp.  1824  module. The module can generate an incrementing phase factor: 
         [0000]        e   −j2πρn   (20)
 
         [0000]    that can be used to compensate input signal samples y(n)  1801  for frequency offset when (complex) multiplied by this factor. The complex multiplier  1826  can perform this multiplication on a delayed version of the input signal. 
         [0054]    ATSC signal sensing can be performed by correlating compensated input signal samples with known PN sequence patterns. PN511 and/or PN63 can be used for such correlation. In order for correlation to be performed after frequency offset is computed, a start time of such correlation c0 can be required to satisfy: 
         [0000]        c 0 ≧p 1  (21)
 
         [0055]    In some embodiments a delay element Delay X  1828  can be provided between input signal samples and complex multiplier  1826  employed for frequency offset compensation. This delay element can ensure that frequency offset compensation will not be missed on the target PN sequence pattern. 
         [0056]    In one example, the desired PN sequence pattern can be PN511, referring to diagram  1900 . Assuming that the start of PN511 is n0, a length X of the delay element Delay X  1828  can be required to satisfy: 
         [0000]        X≧c 0 −n 0 ≧p 1 −n 0 =T   PS +( p 0 −n 0)  (22)
 
         [0000]    Assuming that p0 occurs before the end of a third PN63, then a maximum distance between p0 and n0 can be 511+63×3=700. The length of the delay element can be required to be at least: 
         [0000]        X=T   PS +700  (23)
 
         [0000]    If the desired PN sequence is the third PN63, a maximum distance between p0 and n0 is 63, and thus a required length of delay element can be: 
         [0000]        X=T   PS +63  (24)
 
         [0057]    Note that as discussed previously, PN511 can give higher coding gain than PN63 (27 dB versus 18 dB). However, if a desired coding gain is less than 18 dB, the third PN63 can be selected as the target correlation pattern in order to minimize computational complexity. 
         [0058]    Compensated signal samples can be piped through a shift register Shift Register Y  1830  whose size can be equal to the length of a target PN sequence, e.g. 511 for PN511 and 63 for PN63. A signal pattern in the shift register can then be correlated with a target PN sequence to generate a sensing metric for thresholding, i.e. 
         [0000]    
       
         
           
             
               
                 
                   
                     M 
                      
                     
                       ( 
                       n 
                       ) 
                     
                   
                   = 
                   
                     
                       ∑ 
                       
                         l 
                         = 
                         0 
                       
                       
                         Y 
                         - 
                         1 
                       
                     
                      
                     
                         
                     
                      
                     
                       
                         s 
                          
                         
                           ( 
                           
                             n 
                             - 
                             l 
                           
                           ) 
                         
                       
                       · 
                       
                         b 
                          
                         
                           ( 
                           
                             Y 
                             - 
                             1 
                             - 
                             l 
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   25 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Here s(n−l) is the l-th element of the shift register and b(l) is the l-th element of the PN sequence. Y can be take on the value of 511 or 63, depending on the PN sequence used. Equation (25) can be implemented by modules Shift Register Y  1830 , vector multiplier  1832 , PN_Y  1834 , and Sum Y  1836 . PN_Y  1834  can provide a PN sequence to the vector multiplier  1832 . Sum Y  1836  can perform a summing operation on input provided by the vector multiplier  1832  and provide a result to a Sensing Threshold  1840  module. 
         [0059]    Power of an averaged sensing metric normalized by an average signal power, i.e.: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                        
                       
                         
                           1 
                           Y 
                         
                          
                         
                           M 
                            
                           
                             ( 
                             n 
                             ) 
                           
                         
                       
                        
                     
                     2 
                   
                   
                     P 
                      
                     
                       ( 
                       n 
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   26 
                   ) 
                 
               
             
           
         
       
     
         [0000]    can then be compared with a threshold to determined ATSC signal presence. For example, such a threshold could have a value of 0.25. Threshold comparisons can be performed by the Sensing Threshold  1840  module. 
         [0060]    Sensing Threshold  1840  module can be activated between times represented by time stamps s0  1842  and s1  1844 ; these time stamps can be generated by a Control Timer  1820  module. For example, s0 can be chosen to be p1, and, s1 can be chosen to ensure that a desired PN sequence completely passes through the shift register. 
       NTSC Signal Sensing: 
       [0061]    A NTSC (analog TV) signal can contain narrowband video, chroma, and audio carriers. Video, chroma, and audio carriers can be located at 1.25 MHz, 4.83 MHz, 5.75 MHz from the left band edge respectively, as depicted in the diagram  600  of  FIG. 6 . 
         [0000]    Since a video carrier can have significantly higher power than other carriers in the composite signal, some embodiments of NTSC signal sensing can be based on video carrier sensing; hence chroma and audio carriers are neglected in the following analysis. A transmitted TV signal can be approximated in the following form: 
         [0000]    
       
         
           
             
               
                 
                   
                     s 
                      
                     
                       ( 
                       n 
                       ) 
                     
                   
                   = 
                   
                     
                       
                          
                         
                           j2π 
                            
                           
                               
                           
                            
                           
                             kv 
                             N 
                           
                            
                           n 
                         
                       
                       
                          
                         
                           Video 
                            
                           
                               
                           
                            
                           Carrier 
                         
                       
                     
                     + 
                     
                       μ 
                        
                       
                           
                       
                        
                       
                         
                           x 
                            
                           
                             ( 
                             n 
                             ) 
                           
                         
                         
                            
                           Data 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   27 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where μ is the modulation index [A. B. Carlson,  Communication Systems.    
         [0062]    Electrical and Electronic Engineering Series, McGraw-Hill, third ed., 1986]. Data signal samples x can be assumed to be independent with unit power, i.e. 
         [0000]        E[x ( n ) x *( m )]=δ( n−m )  (28)
 
         [0063]    A sensing operator can be applied to a received signal in order to generate a sensing metric: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           M 
                            
                           
                             ( 
                             m 
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             
                               
                                 1 
                                 N 
                               
                                
                               
                                 
                                   ∑ 
                                   
                                     n 
                                     = 
                                     
                                       
                                         - 
                                         N 
                                       
                                       / 
                                       2 
                                     
                                   
                                   
                                     
                                       N 
                                       / 
                                       2 
                                     
                                     - 
                                     1 
                                   
                                 
                                  
                                 
                                     
                                 
                                  
                                 
                                    
                                   
                                     
                                       - 
                                       j2π 
                                     
                                      
                                     
                                         
                                     
                                      
                                     
                                       
                                         L 
                                         v 
                                       
                                       N 
                                     
                                      
                                     
                                       ( 
                                       
                                         n 
                                         - 
                                         m 
                                       
                                       ) 
                                     
                                   
                                 
                               
                             
                             
                                
                               
                                 NTSC 
                                  
                                 
                                     
                                 
                                  
                                 sensing 
                                  
                                 
                                     
                                 
                                  
                                 operator 
                               
                             
                           
                            
                           
                             y 
                              
                             
                               ( 
                               n 
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                              
                             
                               j2π 
                                
                               
                                 
                                   L 
                                   v 
                                 
                                 N 
                               
                                
                               m 
                             
                           
                            
                           
                             1 
                             N 
                           
                            
                           
                             
                               ∑ 
                               
                                 n 
                                 = 
                                 
                                   
                                     - 
                                     N 
                                   
                                   / 
                                   2 
                                 
                               
                               
                                 
                                   N 
                                   / 
                                   2 
                                 
                                 - 
                                 1 
                               
                             
                              
                             
                               
                                  
                                 
                                   
                                     - 
                                     j2π 
                                   
                                    
                                   
                                       
                                   
                                    
                                   
                                     
                                       L 
                                       v 
                                     
                                     N 
                                   
                                    
                                   n 
                                 
                               
                               [ 
                               
                                 
                                   
                                     ∑ 
                                     
                                       p 
                                       = 
                                       
                                         - 
                                         ∞ 
                                       
                                     
                                     ∞ 
                                   
                                    
                                   
                                       
                                   
                                    
                                   
                                     
                                       c 
                                        
                                       
                                         ( 
                                         p 
                                         ) 
                                       
                                     
                                      
                                     
                                       s 
                                        
                                       
                                         ( 
                                         
                                           n 
                                           - 
                                           p 
                                         
                                         ) 
                                       
                                     
                                   
                                 
                                 + 
                                 
                                   z 
                                    
                                   
                                     ( 
                                     n 
                                     ) 
                                   
                                 
                               
                               ] 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   29 
                   ) 
                 
               
             
           
         
       
     
         [0000]    It can be appreciated that such a sensing operator can be essentially equivalent to an FFT-based narrowband filter. A multipath delay spread can be assumed to be time-limited; it follows that c(p) can be nonzero only when 
         [0000]      | p|&lt;L   (30)
 
         [0000]    Terms can be considered 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       1 
                       N 
                     
                      
                     
                       
                         ∑ 
                         
                           n 
                           = 
                           
                             
                               - 
                               N 
                             
                             / 
                             2 
                           
                         
                         
                           
                             N 
                             / 
                             2 
                           
                           - 
                           1 
                         
                       
                        
                       
                           
                       
                        
                       
                         
                            
                           
                             
                               - 
                               j 
                             
                              
                             
                                 
                             
                              
                             2 
                              
                             
                                 
                             
                              
                             π 
                              
                             
                               
                                 k 
                                 v 
                               
                               N 
                             
                              
                             n 
                           
                         
                          
                         
                           
                             ∑ 
                             
                               p 
                               = 
                               
                                 - 
                                 ∞ 
                               
                             
                             ∞ 
                           
                            
                           
                               
                           
                            
                           
                             
                               c 
                                
                               
                                 ( 
                                 p 
                                 ) 
                               
                             
                              
                             
                               s 
                                
                               
                                 ( 
                                 
                                   n 
                                   - 
                                   p 
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                   
                   = 
                   
                     
                       
                         ∑ 
                         
                           
                              
                             p 
                              
                           
                           &lt; 
                           L 
                         
                         
                             
                         
                       
                        
                       
                           
                       
                        
                       
                         
                           c 
                            
                           
                             ( 
                             p 
                             ) 
                           
                         
                          
                         
                            
                           
                             
                               - 
                               j 
                             
                              
                             
                                 
                             
                              
                             2 
                              
                             
                                 
                             
                              
                             π 
                              
                             
                               
                                 k 
                                 v 
                               
                               N 
                             
                              
                             p 
                           
                         
                          
                         
                           1 
                           N 
                         
                          
                         
                           
                             ∑ 
                             
                               n 
                               = 
                               
                                 
                                   - 
                                   N 
                                 
                                 / 
                                 2 
                               
                             
                             
                               
                                 N 
                                 / 
                                 2 
                               
                               - 
                               1 
                             
                           
                            
                           
                             
                                
                               
                                 
                                   - 
                                   j 
                                 
                                  
                                 
                                     
                                 
                                  
                                 2 
                                  
                                 
                                     
                                 
                                  
                                 π 
                                  
                                 
                                   
                                     k 
                                     v 
                                   
                                   N 
                                 
                                  
                                 
                                   ( 
                                   
                                     n 
                                     - 
                                     p 
                                   
                                   ) 
                                 
                               
                             
                              
                             
                               s 
                                
                               
                                 ( 
                                 
                                   n 
                                   - 
                                   p 
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                     = 
                     
                       
                         
                           ∑ 
                           
                             
                                
                               p 
                                
                             
                             &lt; 
                             L 
                           
                           
                               
                           
                         
                          
                         
                             
                         
                          
                         
                           
                             c 
                              
                             
                               ( 
                               p 
                               ) 
                             
                           
                            
                           
                              
                             
                               
                                 - 
                                 j 
                               
                                
                               
                                   
                               
                                
                               2 
                                
                               
                                   
                               
                                
                               π 
                                
                               
                                 
                                   k 
                                   v 
                                 
                                 N 
                               
                                
                               p 
                             
                           
                            
                           
                             1 
                             N 
                           
                            
                           
                             
                               ∑ 
                               
                                 q 
                                 = 
                                 
                                   
                                     
                                       - 
                                       N 
                                     
                                     / 
                                     2 
                                   
                                   - 
                                   p 
                                 
                               
                               
                                 
                                   N 
                                   / 
                                   2 
                                 
                                 - 
                                 1 
                                 - 
                                 p 
                               
                             
                              
                             
                               
                                  
                                 
                                   
                                     - 
                                     j 
                                   
                                    
                                   
                                       
                                   
                                    
                                   2 
                                    
                                   
                                       
                                   
                                    
                                   π 
                                    
                                   
                                     
                                       k 
                                       v 
                                     
                                     N 
                                   
                                    
                                   q 
                                 
                               
                                
                               
                                 s 
                                  
                                 
                                   ( 
                                   q 
                                   ) 
                                 
                               
                             
                           
                         
                       
                       = 
                       
                         
                           
                             
                               ∑ 
                               
                                 
                                    
                                   p 
                                    
                                 
                                 &lt; 
                                 L 
                               
                               
                                   
                               
                             
                              
                             
                                 
                             
                              
                             
                               
                                 c 
                                  
                                 
                                   ( 
                                   p 
                                   ) 
                                 
                               
                                
                               
                                  
                                 
                                   
                                     - 
                                     j 
                                   
                                    
                                   
                                       
                                   
                                    
                                   2 
                                    
                                   
                                       
                                   
                                    
                                   π 
                                    
                                   
                                     
                                       k 
                                       v 
                                     
                                     N 
                                   
                                    
                                   p 
                                 
                               
                                
                               
                                 { 
                                 
                                   
                                     1 
                                     N 
                                   
                                    
                                   
                                     
                                       ∑ 
                                       
                                         q 
                                         = 
                                         
                                           
                                             
                                               - 
                                               N 
                                             
                                             / 
                                             2 
                                           
                                           - 
                                           p 
                                         
                                       
                                       
                                         
                                           
                                             - 
                                             N 
                                           
                                           / 
                                           2 
                                         
                                         - 
                                         1 
                                       
                                     
                                      
                                     
                                       
                                         + 
                                         
                                           1 
                                           N 
                                         
                                       
                                        
                                       
                                         
                                           ∑ 
                                           
                                             q 
                                             = 
                                             
                                               
                                                 - 
                                                 N 
                                               
                                               / 
                                               2 
                                             
                                           
                                           
                                             
                                               N 
                                               / 
                                               2 
                                             
                                             - 
                                             1 
                                           
                                         
                                          
                                         
                                           
                                             - 
                                             
                                               1 
                                               N 
                                             
                                           
                                            
                                           
                                             ∑ 
                                             
                                               q 
                                               = 
                                               
                                                 
                                                   N 
                                                   / 
                                                   2 
                                                 
                                                 - 
                                                 p 
                                               
                                             
                                             
                                               
                                                 N 
                                                 / 
                                                 2 
                                               
                                               - 
                                               1 
                                             
                                           
                                         
                                       
                                     
                                   
                                 
                                 } 
                               
                                
                               
                                  
                                 
                                   
                                     - 
                                     j 
                                   
                                    
                                   
                                       
                                   
                                    
                                   2 
                                    
                                   
                                       
                                   
                                    
                                   π 
                                    
                                   
                                     
                                       k 
                                       v 
                                     
                                     N 
                                   
                                    
                                   q 
                                 
                               
                                
                               
                                 s 
                                  
                                 
                                   ( 
                                   q 
                                   ) 
                                 
                               
                             
                           
                           ≈ 
                           
                             
                               ∑ 
                               
                                 
                                    
                                   p 
                                    
                                 
                                 &lt; 
                                 L 
                               
                               
                                   
                               
                             
                              
                             
                                 
                             
                              
                             
                               
                                 c 
                                  
                                 
                                   ( 
                                   p 
                                   ) 
                                 
                               
                                
                               
                                  
                                 
                                   
                                     - 
                                     j 
                                   
                                    
                                   
                                       
                                   
                                    
                                   2 
                                    
                                   
                                       
                                   
                                    
                                   π 
                                    
                                   
                                     
                                       k 
                                       v 
                                     
                                     N 
                                   
                                    
                                   p 
                                 
                               
                                
                               
                                 1 
                                 N 
                               
                                
                               
                                 
                                   ∑ 
                                   
                                     q 
                                     = 
                                     
                                       
                                         - 
                                         N 
                                       
                                       / 
                                       2 
                                     
                                   
                                   
                                     
                                       N 
                                       / 
                                       2 
                                     
                                     - 
                                     1 
                                   
                                 
                                  
                                 
                                   
                                      
                                     
                                       
                                         - 
                                         j 
                                       
                                        
                                       
                                           
                                       
                                        
                                       2 
                                        
                                       
                                           
                                       
                                        
                                       π 
                                        
                                       
                                         
                                           k 
                                           v 
                                         
                                         N 
                                       
                                        
                                       q 
                                     
                                   
                                    
                                   
                                     s 
                                      
                                     
                                       ( 
                                       q 
                                       ) 
                                     
                                   
                                 
                               
                             
                           
                         
                         = 
                         
                           
                             NC 
                              
                             
                               ( 
                               
                                 k 
                                 v 
                               
                               ) 
                             
                           
                            
                           
                             S 
                              
                             
                               ( 
                               
                                 k 
                                 v 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   31 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where an approximation can be taken assuming 
         [0000]        N&gt;&gt;L&gt;|p|   (32)
 
         [0000]    and for a channel frequency response C(k v ) and a spectral signal value S(k v ) at a video carrier frequency 
         [0000]    
       
         
           
             f 
             = 
             
               
                 k 
                 v 
               
               
                 NT 
                 s 
               
             
           
         
       
     
         [0000]    where: 
         [0000]    
       
         
           
             
               
                 
                   
                     C 
                      
                     
                       ( 
                       
                         k 
                         v 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       1 
                       N 
                     
                      
                     
                       
                         ∑ 
                         
                           n 
                           = 
                           
                             
                               - 
                               N 
                             
                             / 
                             2 
                           
                         
                         
                           
                             N 
                             / 
                             2 
                           
                           - 
                           1 
                         
                       
                        
                       
                           
                       
                        
                       
                         
                           c 
                            
                           
                             ( 
                             n 
                             ) 
                           
                         
                          
                         
                            
                           
                             
                               - 
                               j 
                             
                              
                             
                                 
                             
                              
                             2 
                              
                             
                                 
                             
                              
                             π 
                              
                             
                               
                                 k 
                                 v 
                               
                               N 
                             
                              
                             n 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   33 
                   ) 
                 
               
             
             
               
                 
                   
                     S 
                      
                     
                       ( 
                       
                         k 
                         v 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       1 
                       N 
                     
                      
                     
                       
                         ∑ 
                         
                           n 
                           = 
                           
                             
                               - 
                               N 
                             
                             / 
                             2 
                           
                         
                         
                           
                             N 
                             / 
                             2 
                           
                           - 
                           1 
                         
                       
                        
                       
                           
                       
                        
                       
                         
                           s 
                            
                           
                             ( 
                             n 
                             ) 
                           
                         
                          
                         
                            
                           
                             
                               - 
                               j 
                             
                              
                             
                                 
                             
                              
                             2 
                              
                             
                                 
                             
                              
                             π 
                              
                             
                               
                                 k 
                                 v 
                               
                               N 
                             
                              
                             n 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   34 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Similarly, spectral noise Z(k v ) at a frequency k v  can be expressed as 
         [0000]    
       
         
           
             
               
                 
                   
                     Z 
                      
                     
                       ( 
                       
                         k 
                         v 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       1 
                       N 
                     
                      
                     
                       
                         ∑ 
                         
                           n 
                           = 
                           
                             
                               - 
                               N 
                             
                             / 
                             2 
                           
                         
                         
                           
                             N 
                             / 
                             2 
                           
                           - 
                           1 
                         
                       
                        
                       
                           
                       
                        
                       
                         
                           z 
                            
                           
                             ( 
                             n 
                             ) 
                           
                         
                          
                         
                            
                           
                             
                               - 
                               j 
                             
                              
                             
                                 
                             
                              
                             2 
                              
                             
                                 
                             
                              
                             π 
                              
                             
                               
                                 k 
                                 v 
                               
                               N 
                             
                              
                             n 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   35 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Given the definitions above, a sensing metric M(m) can be expressed as 
         [0000]    
       
         
           
             
               
                 
                   
                     M 
                      
                     
                       ( 
                       m 
                       ) 
                     
                   
                   = 
                   
                     
                        
                       
                         j 
                          
                         
                             
                         
                          
                         2 
                          
                         
                             
                         
                          
                         π 
                          
                         
                             
                         
                          
                         
                           
                             k 
                             v 
                           
                           N 
                         
                          
                         m 
                       
                     
                      
                     
                       [ 
                       
                         
                           
                             NC 
                              
                             
                               ( 
                               
                                 k 
                                 v 
                               
                               ) 
                             
                           
                            
                           
                             S 
                              
                             
                               ( 
                               
                                 k 
                                 v 
                               
                               ) 
                             
                           
                         
                         + 
                         
                           Z 
                            
                           
                             ( 
                             
                               k 
                               v 
                             
                             ) 
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   36 
                   ) 
                 
               
             
           
         
       
     
         [0000]    S(k v ) can be further expanded using equation (27): 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             S 
                              
                             
                               ( 
                               
                                 k 
                                 v 
                               
                               ) 
                             
                           
                           = 
                             
                            
                           
                             
                               1 
                               N 
                             
                              
                             
                               
                                 ∑ 
                                 
                                   n 
                                   = 
                                   
                                     
                                       - 
                                       N 
                                     
                                     / 
                                     2 
                                   
                                 
                                 
                                   
                                     N 
                                     / 
                                     2 
                                   
                                   - 
                                   1 
                                 
                               
                                
                               
                                   
                               
                                
                               
                                 
                                   [ 
                                   
                                     
                                        
                                       
                                         j 
                                          
                                         
                                             
                                         
                                          
                                         2 
                                          
                                         
                                             
                                         
                                          
                                         π 
                                          
                                         
                                           
                                             k 
                                             v 
                                           
                                           N 
                                         
                                          
                                         n 
                                       
                                     
                                     + 
                                     
                                       μ 
                                        
                                       
                                           
                                       
                                        
                                       
                                         x 
                                          
                                         
                                           ( 
                                           n 
                                           ) 
                                         
                                       
                                     
                                   
                                   ] 
                                 
                                  
                                 
                                    
                                   
                                     
                                       - 
                                       j 
                                     
                                      
                                     
                                         
                                     
                                      
                                     2 
                                      
                                     
                                         
                                     
                                      
                                     π 
                                      
                                     
                                       
                                         k 
                                         v 
                                       
                                       N 
                                     
                                      
                                     n 
                                   
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           = 
                             
                            
                           
                             1 
                             + 
                             
                               μ 
                                
                               
                                   
                               
                                
                               
                                 X 
                                  
                                 
                                   ( 
                                   
                                     k 
                                     v 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   where 
                 
               
               
                 
                   ( 
                   37 
                   ) 
                 
               
             
             
               
                 
                   
                     X 
                      
                     
                       ( 
                       
                         k 
                         v 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       1 
                       N 
                     
                      
                     
                       
                         ∑ 
                         
                           n 
                           = 
                           
                             
                               - 
                               N 
                             
                             / 
                             2 
                           
                         
                         
                           
                             N 
                             / 
                             2 
                           
                           - 
                           1 
                         
                       
                        
                       
                           
                       
                        
                       
                         
                           x 
                            
                           
                             ( 
                             n 
                             ) 
                           
                         
                          
                         
                            
                           
                             
                               - 
                               j 
                             
                              
                             
                                 
                             
                              
                             2 
                              
                             
                                 
                             
                              
                             π 
                              
                             
                               
                                 k 
                                 v 
                               
                               N 
                             
                              
                             n 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   38 
                   ) 
                 
               
             
           
         
       
     
         [0000]    A sensing metric M(m) can then be expressed as 
         [0000]    
       
         
           
             
               
                 
                   
                     M 
                      
                     
                       ( 
                       m 
                       ) 
                     
                   
                   = 
                   
                     
                        
                       
                         j 
                          
                         
                             
                         
                          
                         2 
                          
                         
                             
                         
                          
                         π 
                          
                         
                           
                             k 
                             v 
                           
                           N 
                         
                          
                         m 
                       
                     
                     [ 
                     
                       
                         
                           NC 
                            
                           
                             ( 
                             
                               k 
                               v 
                             
                             ) 
                           
                         
                         
                            
                           Signal 
                         
                       
                       + 
                       
                         
                           
                             μ 
                              
                             
                                 
                             
                              
                             NC 
                              
                             
                               ( 
                               
                                 k 
                                 v 
                               
                               ) 
                             
                              
                             
                               X 
                                
                               
                                 ( 
                                 
                                   k 
                                   v 
                                 
                                 ) 
                               
                             
                           
                           + 
                           
                             Z 
                              
                             
                               ( 
                               
                                 k 
                                 v 
                               
                               ) 
                             
                           
                         
                         
                            
                           Noise 
                         
                       
                     
                     ] 
                   
                 
               
               
                 
                   ( 
                   39 
                   ) 
                 
               
             
           
         
       
     
         [0064]    Note that in some embodiments a NTSC data signal can be considered as noise when sensing is performed, since it is not being decoded. Since a data signal and noise are independent, a total sensing metric noise power can be expressed as: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         μ 
                         2 
                       
                        
                       
                         N 
                         2 
                       
                        
                       
                         
                            
                           
                             C 
                              
                             
                               ( 
                               
                                 k 
                                 v 
                               
                               ) 
                             
                           
                            
                         
                         2 
                       
                        
                       
                         E 
                          
                         
                           [ 
                           
                             
                                
                               
                                 X 
                                  
                                 
                                   ( 
                                   
                                     k 
                                     v 
                                   
                                   ) 
                                 
                               
                                
                             
                             2 
                           
                           ] 
                         
                       
                     
                     + 
                     
                       E 
                        
                       
                         [ 
                         
                           
                              
                             
                               Z 
                                
                               
                                 ( 
                                 
                                   k 
                                   v 
                                 
                                 ) 
                               
                             
                              
                           
                           2 
                         
                         ] 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   where 
                 
               
               
                 
                   ( 
                   40 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                           
                             E 
                              
                             
                               [ 
                               
                                 
                                    
                                   
                                     X 
                                      
                                     
                                       ( 
                                       
                                         k 
                                         v 
                                       
                                       ) 
                                     
                                   
                                    
                                 
                                 2 
                               
                               ] 
                             
                           
                           = 
                             
                            
                           
                             E 
                             [ 
                             
                               
                                  
                                 
                                   
                                     1 
                                     N 
                                   
                                    
                                   
                                     
                                       ∑ 
                                       
                                         n 
                                         = 
                                         
                                           
                                             - 
                                             N 
                                           
                                           / 
                                           2 
                                         
                                       
                                       
                                         
                                           N 
                                           / 
                                           2 
                                         
                                         - 
                                         1 
                                       
                                     
                                      
                                     
                                       
                                         x 
                                          
                                         
                                           ( 
                                           n 
                                           ) 
                                         
                                       
                                        
                                       
                                          
                                         
                                           
                                             - 
                                             j 
                                           
                                            
                                           
                                               
                                           
                                            
                                           2 
                                            
                                           π 
                                            
                                           
                                             
                                               k 
                                               v 
                                             
                                             N 
                                           
                                            
                                           n 
                                         
                                       
                                     
                                   
                                 
                                  
                               
                               2 
                             
                             ] 
                           
                         
                       
                     
                     
                       
                         
                           = 
                             
                            
                           
                             
                               1 
                               
                                 N 
                                 2 
                               
                             
                              
                             
                               
                                 ∑ 
                                 
                                   n 
                                   , 
                                   
                                     m 
                                     = 
                                     
                                       
                                         - 
                                         N 
                                       
                                       / 
                                       2 
                                     
                                   
                                 
                                 
                                   
                                     N 
                                     / 
                                     2 
                                   
                                   - 
                                   1 
                                 
                               
                                
                               
                                 
                                    
                                   
                                     
                                       - 
                                       j2 
                                     
                                      
                                     
                                         
                                     
                                      
                                     π 
                                      
                                     
                                       
                                         k 
                                         v 
                                       
                                       N 
                                     
                                      
                                     
                                       ( 
                                       
                                         n 
                                         - 
                                         m 
                                       
                                       ) 
                                     
                                   
                                 
                                  
                                 
                                   E 
                                    
                                   
                                     [ 
                                     
                                       
                                         x 
                                          
                                         
                                           ( 
                                           n 
                                           ) 
                                         
                                       
                                        
                                       
                                         
                                           x 
                                           * 
                                         
                                          
                                         
                                           ( 
                                           m 
                                           ) 
                                         
                                       
                                     
                                     ] 
                                   
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           = 
                             
                            
                           
                             1 
                             N 
                           
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     and 
                      
                     
                         
                     
                      
                     similarly 
                   
                 
               
               
                 
                   ( 
                   41 
                   ) 
                 
               
             
             
               
                 
                   
                     E 
                      
                     
                       [ 
                       
                         
                            
                           
                             Z 
                              
                             
                               ( 
                               
                                 k 
                                 v 
                               
                               ) 
                             
                           
                            
                         
                         2 
                       
                       ] 
                     
                   
                   = 
                   
                     
                       σ 
                       2 
                     
                     N 
                   
                 
               
               
                 
                   ( 
                   42 
                   ) 
                 
               
             
           
         
       
     
         [0000]    An NTSC data signal power can be expressed 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           E 
                            
                           
                             [ 
                             
                               
                                  
                                 
                                   
                                     
                                       c 
                                        
                                       
                                         ( 
                                         n 
                                         ) 
                                       
                                     
                                     ⊗ 
                                     μ 
                                   
                                    
                                   
                                       
                                   
                                    
                                   
                                     x 
                                      
                                     
                                       ( 
                                       n 
                                       ) 
                                     
                                   
                                 
                                  
                               
                               2 
                             
                             ] 
                           
                         
                         = 
                           
                          
                         
                           
                             μ 
                             2 
                           
                            
                           
                             
                               ∑ 
                               
                                 n 
                                 = 
                                 
                                   - 
                                   ∞ 
                                 
                               
                               ∞ 
                             
                              
                             
                                 
                             
                              
                             
                               
                                  
                                 
                                   c 
                                    
                                   
                                     ( 
                                     n 
                                     ) 
                                   
                                 
                                  
                               
                               2 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             μ 
                             2 
                           
                            
                           
                             
                               ∑ 
                               
                                 
                                    
                                   n 
                                    
                                 
                                 &lt; 
                                 L 
                               
                               
                                   
                               
                             
                              
                             
                                 
                             
                              
                             
                               
                                  
                                 
                                   c 
                                    
                                   
                                     ( 
                                     n 
                                     ) 
                                   
                                 
                                  
                               
                               2 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             μ 
                             2 
                           
                            
                           
                             
                               ∑ 
                               
                                 n 
                                 = 
                                 
                                   
                                     - 
                                     N 
                                   
                                   / 
                                   2 
                                 
                               
                               
                                 
                                   N 
                                   / 
                                   2 
                                 
                                 - 
                                 1 
                               
                             
                              
                             
                                 
                             
                              
                             
                               
                                  
                                 
                                   c 
                                    
                                   
                                     ( 
                                     n 
                                     ) 
                                   
                                 
                                  
                               
                               2 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   43 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Using an inverse fast Fourier transform (IFFT),
 
the NTSC data signal power can further be expressed as
 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             μ 
                             2 
                           
                            
                           
                             
                               ∑ 
                               
                                 n 
                                 = 
                                 
                                   
                                     - 
                                     N 
                                   
                                   / 
                                   2 
                                 
                               
                               
                                 
                                   N 
                                   / 
                                   2 
                                 
                                 - 
                                 1 
                               
                             
                              
                             
                                 
                             
                              
                             
                               
                                  
                                 
                                   c 
                                    
                                   
                                     ( 
                                     n 
                                     ) 
                                   
                                 
                                  
                               
                               2 
                             
                           
                         
                         = 
                           
                          
                         
                           
                             μ 
                             2 
                           
                            
                           
                             
                               ∑ 
                               
                                 n 
                                 = 
                                 
                                   
                                     - 
                                     N 
                                   
                                   / 
                                   2 
                                 
                               
                               
                                 
                                   N 
                                   / 
                                   2 
                                 
                                 - 
                                 1 
                               
                             
                              
                             
                               
                                 [ 
                                 
                                   
                                     ∑ 
                                     
                                       k 
                                       = 
                                       
                                         
                                           - 
                                           N 
                                         
                                         / 
                                         2 
                                       
                                     
                                     
                                       
                                         N 
                                         / 
                                         2 
                                       
                                       - 
                                       1 
                                     
                                   
                                    
                                   
                                     
                                       C 
                                        
                                       
                                         ( 
                                         k 
                                         ) 
                                       
                                     
                                      
                                     
                                        
                                       
                                         j 
                                          
                                         
                                             
                                         
                                          
                                         2 
                                          
                                         
                                             
                                         
                                          
                                         π 
                                          
                                         
                                           
                                             k 
                                             v 
                                           
                                           N 
                                         
                                          
                                         n 
                                       
                                     
                                   
                                 
                                 ] 
                               
                                
                               
                                 [ 
                                 
                                   
                                     ∑ 
                                     
                                       l 
                                       = 
                                       
                                         
                                           - 
                                           N 
                                         
                                         / 
                                         2 
                                       
                                     
                                     
                                       
                                         N 
                                         / 
                                         2 
                                       
                                       - 
                                       1 
                                     
                                   
                                    
                                   
                                     
                                       
                                         C 
                                         * 
                                       
                                        
                                       
                                         ( 
                                         l 
                                         ) 
                                       
                                     
                                      
                                     
                                        
                                       
                                         
                                           - 
                                           j 
                                         
                                          
                                         
                                             
                                         
                                          
                                         2 
                                          
                                         
                                             
                                         
                                          
                                         π 
                                          
                                         
                                           l 
                                           N 
                                         
                                          
                                         n 
                                       
                                     
                                   
                                 
                                 ] 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             μ 
                             2 
                           
                            
                           
                             
                               ∑ 
                               
                                 k 
                                 = 
                                 
                                   
                                     - 
                                     N 
                                   
                                   / 
                                   2 
                                 
                               
                               
                                 
                                   N 
                                   / 
                                   2 
                                 
                                 - 
                                 1 
                               
                             
                              
                             
                               
                                 ∑ 
                                 
                                   l 
                                   = 
                                   
                                     
                                       - 
                                       N 
                                     
                                     / 
                                     2 
                                   
                                 
                                 
                                   
                                     N 
                                     / 
                                     2 
                                   
                                   - 
                                   1 
                                 
                               
                                
                               
                                 
                                   C 
                                    
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                                  
                                 C 
                                 * 
                                 
                                   ( 
                                   l 
                                   ) 
                                 
                                  
                                 
                                   
                                     ∑ 
                                     
                                       n 
                                       = 
                                       
                                         
                                           - 
                                           N 
                                         
                                         / 
                                         2 
                                       
                                     
                                     
                                       
                                         N 
                                         / 
                                         2 
                                       
                                       - 
                                       1 
                                     
                                   
                                    
                                   
                                      
                                     
                                       j 
                                        
                                       
                                           
                                       
                                        
                                       2 
                                        
                                       
                                           
                                       
                                        
                                       π 
                                        
                                       
                                         
                                           k 
                                           - 
                                           l 
                                         
                                         N 
                                       
                                        
                                       n 
                                     
                                   
                                 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             μ 
                             2 
                           
                            
                           
                             
                               ∑ 
                               
                                 k 
                                 = 
                                 
                                   
                                     - 
                                     N 
                                   
                                   / 
                                   2 
                                 
                               
                               
                                 
                                   N 
                                   / 
                                   2 
                                 
                                 - 
                                 1 
                               
                             
                              
                             
                               
                                 ∑ 
                                 
                                   l 
                                   = 
                                   
                                     
                                       - 
                                       N 
                                     
                                     / 
                                     2 
                                   
                                 
                                 
                                   
                                     N 
                                     / 
                                     2 
                                   
                                   - 
                                   1 
                                 
                               
                                
                               
                                 
                                   C 
                                    
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                                  
                                 C 
                                 * 
                                 
                                   ( 
                                   l 
                                   ) 
                                 
                                  
                                 N 
                                  
                                 
                                     
                                 
                                  
                                 
                                   δ 
                                    
                                   
                                     ( 
                                     
                                       k 
                                       - 
                                       l 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             μ 
                             2 
                           
                            
                           N 
                            
                           
                             
                               ∑ 
                               
                                 k 
                                 = 
                                 
                                   
                                     - 
                                     N 
                                   
                                   / 
                                   2 
                                 
                               
                               
                                 N 
                                 / 
                                 2 
                               
                             
                              
                             
                                 
                             
                              
                             
                               
                                  
                                 
                                   C 
                                    
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                                  
                               
                               2 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   44 
                   ) 
                 
               
             
           
         
       
     
         [0000]    A data signal SNR can then be expressed as 
         [0000]    
       
         
           
             
               
                 
                   SNR 
                   = 
                   
                     
                       
                         E 
                          
                         
                           [ 
                           
                             
                                
                               
                                 
                                   
                                     c 
                                      
                                     
                                       ( 
                                       n 
                                       ) 
                                     
                                   
                                   ⊗ 
                                   μ 
                                 
                                  
                                 
                                     
                                 
                                  
                                 
                                   x 
                                    
                                   
                                     ( 
                                     n 
                                     ) 
                                   
                                 
                               
                                
                             
                             2 
                           
                           ] 
                         
                       
                       
                         E 
                          
                         
                           [ 
                           
                             
                                
                               
                                 z 
                                  
                                 
                                   ( 
                                   n 
                                   ) 
                                 
                               
                                
                             
                             2 
                           
                           ] 
                         
                       
                     
                     = 
                     
                       
                         
                           μ 
                           2 
                         
                          
                         N 
                          
                         
                           
                             ∑ 
                             
                               k 
                               = 
                               
                                 
                                   - 
                                   N 
                                 
                                 / 
                                 2 
                               
                             
                             
                               N 
                               / 
                               2 
                             
                           
                            
                           
                               
                           
                            
                           
                             
                                
                               
                                 C 
                                  
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                                
                             
                             2 
                           
                         
                       
                       
                         σ 
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   45 
                   ) 
                 
               
             
           
         
       
     
         [0000]    A SNR of the a metric expressed in Equation (39) can then be expressed 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             SNR 
                             M 
                           
                           = 
                             
                            
                           
                             
                               
                                 N 
                                 2 
                               
                                
                               
                                 
                                    
                                   
                                     C 
                                      
                                     
                                       ( 
                                       
                                         k 
                                         v 
                                       
                                       ) 
                                     
                                   
                                    
                                 
                                 2 
                               
                             
                             
                               
                                 
                                   μ 
                                   2 
                                 
                                  
                                 
                                   N 
                                   2 
                                 
                                  
                                 
                                   
                                      
                                     
                                       C 
                                        
                                       
                                         ( 
                                         
                                           k 
                                           v 
                                         
                                         ) 
                                       
                                     
                                      
                                   
                                   2 
                                 
                                  
                                 
                                   E 
                                    
                                   
                                     [ 
                                     
                                       
                                          
                                         
                                           X 
                                            
                                           
                                             ( 
                                             
                                               k 
                                               v 
                                             
                                             ) 
                                           
                                         
                                          
                                       
                                       2 
                                     
                                     ] 
                                   
                                 
                               
                               + 
                               
                                 E 
                                  
                                 
                                   [ 
                                   
                                     
                                        
                                       
                                         Z 
                                          
                                         
                                           ( 
                                           
                                             k 
                                             v 
                                           
                                           ) 
                                         
                                       
                                        
                                     
                                     2 
                                   
                                   ] 
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           = 
                             
                            
                           
                             
                               
                                 N 
                                 2 
                               
                                
                               
                                 
                                    
                                   
                                     C 
                                      
                                     
                                       ( 
                                       
                                         k 
                                         v 
                                       
                                       ) 
                                     
                                   
                                    
                                 
                                 2 
                               
                             
                             
                               
                                 
                                   μ 
                                   2 
                                 
                                  
                                 N 
                                  
                                 
                                   
                                      
                                     
                                       C 
                                        
                                       
                                         ( 
                                         
                                           k 
                                           v 
                                         
                                         ) 
                                       
                                     
                                      
                                   
                                   2 
                                 
                               
                               + 
                               
                                 
                                   σ 
                                   2 
                                 
                                 N 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           = 
                             
                            
                           
                             
                               
                                 N 
                                 2 
                               
                                
                               
                                 
                                    
                                   
                                     C 
                                      
                                     
                                       ( 
                                       
                                         k 
                                         v 
                                       
                                       ) 
                                     
                                   
                                    
                                 
                                 2 
                               
                             
                             
                               
                                 
                                   μ 
                                   2 
                                 
                                  
                                 N 
                                  
                                 
                                   
                                      
                                     
                                       C 
                                        
                                       
                                         ( 
                                         
                                           k 
                                           v 
                                         
                                         ) 
                                       
                                     
                                      
                                   
                                   2 
                                 
                               
                               + 
                               
                                 
                                   
                                     μ 
                                     2 
                                   
                                    
                                   
                                     
                                       ∑ 
                                       
                                         k 
                                         = 
                                         
                                           
                                             - 
                                             N 
                                           
                                           / 
                                           2 
                                         
                                       
                                       
                                         N 
                                         / 
                                         2 
                                       
                                     
                                      
                                     
                                         
                                     
                                      
                                     
                                       
                                          
                                         
                                           C 
                                            
                                           
                                             ( 
                                             k 
                                             ) 
                                           
                                         
                                          
                                       
                                       2 
                                     
                                   
                                 
                                 SNR 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           = 
                             
                            
                           
                             
                               1 
                               
                                 μ 
                                 2 
                               
                             
                              
                             
                               
                                 N 
                                 · 
                                 SNR 
                               
                               
                                 SNR 
                                 + 
                                 η 
                               
                             
                           
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   where 
                 
               
               
                 
                   ( 
                   46 
                   ) 
                 
               
             
             
               
                 
                   η 
                   = 
                   
                     
                       
                         ∑ 
                         
                           k 
                           = 
                           
                             
                               - 
                               N 
                             
                             / 
                             2 
                           
                         
                         
                           N 
                           / 
                           2 
                         
                       
                        
                       
                           
                       
                        
                       
                         
                            
                           
                             C 
                              
                             
                               ( 
                               k 
                               ) 
                             
                           
                            
                         
                         2 
                       
                     
                     
                       N 
                        
                       
                         
                            
                           
                             C 
                              
                             
                               ( 
                               
                                 k 
                                 v 
                               
                               ) 
                             
                           
                            
                         
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   47 
                   ) 
                 
               
             
           
         
       
     
         [0000]    It follows that a sensing gain can be expressed 
         [0000]    
       
         
           
             
               
                 
                   
                     10 
                      
                     
                         
                     
                      
                     
                       log 
                       10 
                     
                      
                     
                       
                         SNR 
                         M 
                       
                       SNR 
                     
                   
                   = 
                   
                     10 
                      
                     
                         
                     
                      
                     
                       
                         log 
                         10 
                       
                        
                       
                         ( 
                         
                           
                             1 
                             
                               μ 
                               2 
                             
                           
                            
                           
                             N 
                             
                               SNR 
                               + 
                               η 
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   48 
                   ) 
                 
               
             
           
         
       
     
         [0065]    In some embodiments, a sensing gain can decrease with an increasing SNR. In some embodiments this property can be neglected since at high SNR, sensing can be relatively successful essentially regardless of a sensing gain value. A factor η can be a measure of multipath fading on a video carrier. When the fading is significant, the sensing gain can become smaller. The graph  700  of  FIG. 7  shows sensing gain contours at different SNRs and fading levels η where N=256 and μ=0.875 (TV video signal modulation index according to [A. B. Carlson, op. cit.]). It can be appreciated that sensing gain can increase with increasing N. In some fading environments, a narrowband fade could be larger than 30 dB [T. S. Rappaport,  Wireless Communications Principles and Practice . Prentice-Hall, 1996]. Rather than simply increasing the correlation depth N in order to ameliorate this effect, it can be advantageous in some embodiments to share sensing information with other users. In some embodiments, multipath fading can be a local phenomenon whose effects can be statistically reduced by combining sensing results from different locations. 
       Energy Sensing: 
       [0066]    Energy sensing can be employed as a fundamental method of signal detection in some embodiments; any information-conveying signal has finite energy. In some embodiments, energy-based sensing can suffer from a drawback of a longer convergence time as compared to phase-based sensing, as discussed herein regards DTV and NTSC signal sensing. Energy-based sensing can achieve salutary specified performance levels under the conditions of a high SNR, in some embodiments. Furthermore, in some embodiments energy-based sensing can be used to estimate a SNR. A received signal y(n) can be expressed as 
         [0000]        y ( n )= x ( n )+ z ( n )  (49)
 
         [0000]    A sequence of signal samples x(n) can be assumed to be independent, in order to simplify derivation. Correlation between signal samples x(n)s, e.g. due to multipath channel memory effect, can (only) improve sensing performance. Since the noise sample z(n)s are independent, the received signal sample y(n)s are independent.
 
Consider a signal energy S obtained by averaging:
 
         [0000]    
       
         
           
             
               
                 
                   S 
                   = 
                   
                     
                       1 
                       
                         N 
                         B 
                       
                     
                      
                     
                       
                         ∑ 
                         
                           n 
                           = 
                           1 
                         
                         
                           N 
                           B 
                         
                       
                        
                       
                           
                       
                        
                       
                         
                            
                           
                             y 
                              
                             
                               ( 
                               n 
                               ) 
                             
                           
                            
                         
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   50 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where N B  can be an averaging buffer size. Since |y(n)| 2  can be a sequence of independent and identically distributed (IID) random variables with mean and variance, it follows that: 
         [0000]        E[|y ( n )| 2 ]=μ  (51)
 
         [0000]        E[|y ( n )| 4 ]=σ 2   (52)
 
         [0000]    Assuming N B &gt;&gt;1, according to the central limit theorem, S can be approximated as a Gaussian random variable with mean μ S  and variance σ S   2 : 
         [0000]    
       
         
           
             
               
                 
                   
                     μ 
                     S 
                   
                   = 
                   μ 
                 
               
               
                 
                   ( 
                   53 
                   ) 
                 
               
             
             
               
                 
                   
                     σ 
                     S 
                     2 
                   
                   = 
                   
                     
                       σ 
                       2 
                     
                     
                       N 
                       B 
                     
                   
                 
               
               
                 
                   ( 
                   54 
                   ) 
                 
               
             
           
         
       
     
         [0000]    PFD vs. PLD:
 
When there is no signal present, i.e. x(n)=0, the result of averaging can be expressed:
 
         [0000]    
       
         
           
             
               
                 
                   
                     S 
                     0 
                   
                   = 
                   
                     
                       1 
                       
                         N 
                         B 
                       
                     
                      
                     
                       
                         ∑ 
                         
                           n 
                           = 
                           1 
                         
                         
                           N 
                           B 
                         
                       
                        
                       
                           
                       
                        
                       
                         
                            
                           
                             z 
                              
                             
                               ( 
                               n 
                               ) 
                             
                           
                            
                         
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   55 
                   ) 
                 
               
             
           
         
       
     
         [0000]    When there is a signal present, the result of the averaging can be expressed 
         [0000]    
       
         
           
             
               
                 
                   
                     S 
                     1 
                   
                   = 
                   
                     
                       1 
                       
                         N 
                         B 
                       
                     
                      
                     
                       
                         ∑ 
                         
                           n 
                           = 
                           1 
                         
                         
                           N 
                           B 
                         
                       
                        
                       
                           
                       
                        
                       
                         
                            
                           
                             y 
                              
                             
                               ( 
                               n 
                               ) 
                             
                           
                            
                         
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   56 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where y(n) is given by Equation (49). A threshold S T  can be used to determine whether a signal is present. A value of (averaged) signal energy exceeding the threshold can correspond to the presence of a signal. A value of (averaged) signal energy not exceeding the threshold can correspond to the absence of a signal. 
         [0067]    As illustrated in the graph  800  of  FIG. 8 , a probability of false detection (PFD) is the probability that the sensing indicates signal presence (i.e. energy average of Equation (50) above threshold) when there is noise but essentially no signal present. A probability of loss detection (PLD) is the probability that sensing indicates absence of a signal (i.e. energy average Equation (50) below threshold) when there is a signal present. A threshold can be set relatively high, thus reducing PFD at the expense of increased PLD. The threshold can be set relatively low, thus reducing PLD at the expense of increased PFD. Thus an optimal threshold S T  can be selected at an operating point where PFD is essentially equal to PLD. 
       Sensing Error Floor Calculation: 
       [0068]    A sensing error floor (SEF) can be defined as the PFD, or equivalently PLD, at an optimal threshold. A general expression for a sensing error floor can be derived. Referring to  FIG. 8 , a PFD can be expressed using a Q function: 
         [0000]    
       
         
           
             
               
                 
                   PFD 
                   = 
                   
                     Q 
                      
                     
                       ( 
                       
                         
                           
                             S 
                             T 
                           
                           - 
                           
                             μ 
                             
                               S 
                               0 
                             
                           
                         
                         
                           σ 
                           
                             S 
                             0 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   57 
                   ) 
                 
               
             
           
         
       
     
         [0000]    and a PLD can be expressed using a Q function: 
         [0000]    
       
         
           
             
               
                 
                   PLD 
                   = 
                   
                     
                       1 
                       - 
                       
                         Q 
                          
                         
                           ( 
                           
                             
                               
                                 S 
                                 T 
                               
                               - 
                               
                                 μ 
                                 
                                   S 
                                   1 
                                 
                               
                             
                             
                               σ 
                               
                                 S 
                                 1 
                               
                             
                           
                           ) 
                         
                       
                     
                     = 
                     
                       Q 
                        
                       
                         ( 
                         
                           - 
                           
                             
                               
                                 S 
                                 T 
                               
                               - 
                               
                                 μ 
                                 
                                   S 
                                   1 
                                 
                               
                             
                             
                               σ 
                               
                                 S 
                                 1 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   58 
                   ) 
                 
               
             
           
         
       
     
         [0000]    using a symmetry property of the Q function. (A Q-function can be defined as the complement of a standard normal cumulative distribution function.) At the sensing error floor, the PFD is equal to the PLD, i.e. 
         [0000]    
       
         
           
             
               
                 
                   
                     Q 
                      
                     
                       ( 
                       
                         
                           
                             S 
                             T 
                           
                           - 
                           
                             μ 
                             
                               S 
                               0 
                             
                           
                         
                         
                           σ 
                           
                             S 
                             0 
                           
                         
                       
                       ) 
                     
                   
                   = 
                   
                     
                       
                         Q 
                          
                         
                           ( 
                           
                             - 
                             
                               
                                 
                                   S 
                                   T 
                                 
                                 - 
                                 
                                   μ 
                                   
                                     S 
                                     1 
                                   
                                 
                               
                               
                                 σ 
                                 
                                   S 
                                   1 
                                 
                               
                             
                           
                           ) 
                         
                       
                       ⇒ 
                       
                         
                           
                             S 
                             T 
                           
                           - 
                           
                             μ 
                             
                               S 
                               0 
                             
                           
                         
                         
                           σ 
                           
                             S 
                             0 
                           
                         
                       
                     
                     = 
                     
                       - 
                       
                         
                           
                             S 
                             T 
                           
                           - 
                           
                             μ 
                             
                               S 
                               1 
                             
                           
                         
                         
                           σ 
                           
                             S 
                             1 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   59 
                   ) 
                 
               
             
           
         
       
     
         [0000]    which leads to a solution of the threshold 
         [0000]    
       
         
           
             
               
                 
                   
                     S 
                     T 
                   
                   = 
                   
                     
                       
                         
                           μ 
                           
                             S 
                             0 
                           
                         
                          
                         
                           σ 
                           
                             S 
                             1 
                           
                         
                       
                       + 
                       
                         
                           μ 
                           
                             S 
                             1 
                           
                         
                          
                         
                           σ 
                           
                             S 
                             0 
                           
                         
                       
                     
                     
                       
                         σ 
                         
                           S 
                           0 
                         
                       
                       + 
                       
                         σ 
                         
                           S 
                           1 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   60 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Substituting from Equation (60) for S T  in Equation (57), the sensing error floor can be expressed 
         [0000]    
       
         
           
             
               
                 
                   SEF 
                   = 
                   
                     Q 
                      
                     
                       ( 
                       
                         
                           
                             μ 
                             
                               S 
                               1 
                             
                           
                           - 
                           
                             μ 
                             
                               S 
                               0 
                             
                           
                         
                         
                           
                             σ 
                             
                               S 
                               0 
                             
                           
                           + 
                           
                             σ 
                             
                               S 
                               1 
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   61 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Using Equations (53) and (54), the sensing error floor can be further expressed as 
         [0000]    
       
         
           
             
               
                 
                   
                     SEF 
                     = 
                     
                       
                         Q 
                         ( 
                         
                           
                             
                               μ 
                               1 
                             
                             - 
                             
                               μ 
                               0 
                             
                           
                           
                             
                               
                                 σ 
                                 0 
                               
                               
                                 
                                   N 
                                   B 
                                 
                               
                             
                             + 
                             
                               
                                 σ 
                                 1 
                               
                               
                                 
                                   N 
                                   B 
                                 
                               
                             
                           
                         
                         ) 
                       
                       = 
                       
                         Q 
                         ( 
                         
                           
                             
                               N 
                               B 
                             
                           
                            
                           
                             
                               
                                 μ 
                                 1 
                               
                               - 
                               
                                 μ 
                                 0 
                               
                             
                             
                               
                                 σ 
                                 0 
                               
                               + 
                               
                                 σ 
                                 1 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   where 
                 
               
               
                 
                   ( 
                   62 
                   ) 
                 
               
             
             
               
                 
                   
                     μ 
                     0 
                   
                   = 
                   
                     E 
                      
                     
                       [ 
                       
                         
                            
                           
                             z 
                              
                             
                               ( 
                               n 
                               ) 
                             
                           
                            
                         
                         2 
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   63 
                   ) 
                 
               
             
             
               
                 
                   
                     σ 
                     0 
                   
                   = 
                   
                     
                       E 
                        
                       
                         [ 
                         
                           
                             ( 
                             
                               
                                 
                                    
                                   
                                     z 
                                      
                                     
                                       ( 
                                       n 
                                       ) 
                                     
                                   
                                    
                                 
                                 2 
                               
                               - 
                               
                                 μ 
                                 0 
                               
                             
                             ) 
                           
                           2 
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   64 
                   ) 
                 
               
             
             
               
                 
                   
                     μ 
                     1 
                   
                   = 
                   
                     E 
                      
                     
                       [ 
                       
                         
                            
                           
                             y 
                              
                             
                               ( 
                               n 
                               ) 
                             
                           
                            
                         
                         2 
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   65 
                   ) 
                 
               
             
             
               
                 
                   
                     σ 
                     1 
                   
                   = 
                   
                     
                       E 
                        
                       
                         [ 
                         
                           
                             ( 
                             
                               
                                 
                                    
                                   
                                     y 
                                      
                                     
                                       ( 
                                       n 
                                       ) 
                                     
                                   
                                    
                                 
                                 2 
                               
                               - 
                               
                                 μ 
                                 1 
                               
                             
                             ) 
                           
                           2 
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   66 
                   ) 
                 
               
             
           
         
       
     
         [0000]    (For simplicity, in the following derivations, the sample index n is omitted.) The noise power can be assumed to be 
         [0000]      μ 0   =E[|z|   2   ]=P   N   (67)
 
         [0000]    The noise covariance can be expressed 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             σ 
                             0 
                             2 
                           
                           = 
                             
                            
                           
                             E 
                              
                             
                               [ 
                               
                                 
                                   ( 
                                   
                                     
                                       
                                          
                                         z 
                                          
                                       
                                       2 
                                     
                                     - 
                                     
                                       μ 
                                       0 
                                     
                                   
                                   ) 
                                 
                                 2 
                               
                               ] 
                             
                           
                         
                       
                     
                     
                       
                         
                           = 
                             
                            
                           
                             E 
                              
                             
                               [ 
                               
                                 
                                   
                                      
                                     z 
                                      
                                   
                                   4 
                                 
                                 - 
                                 
                                   2 
                                    
                                   
                                     μ 
                                     0 
                                   
                                    
                                   
                                     
                                        
                                       z 
                                        
                                     
                                     2 
                                   
                                 
                                 + 
                                 
                                   μ 
                                   0 
                                   2 
                                 
                               
                               ] 
                             
                           
                         
                       
                     
                     
                       
                         
                           = 
                             
                            
                           
                             
                               E 
                                
                               
                                 [ 
                                 
                                   
                                      
                                     z 
                                      
                                   
                                   4 
                                 
                                 ] 
                               
                             
                             - 
                             
                               μ 
                               0 
                               2 
                             
                           
                         
                       
                     
                     
                       
                         
                           = 
                             
                            
                           
                             
                               ( 
                               
                                 
                                   α 
                                   
                                     complex 
                                     - 
                                     gaussian 
                                   
                                 
                                 - 
                                 1 
                               
                               ) 
                             
                              
                             
                               P 
                               N 
                               2 
                             
                           
                         
                       
                     
                     
                       
                         
                           = 
                             
                            
                           
                             
                               ( 
                               
                                 2 
                                 - 
                                 1 
                               
                               ) 
                             
                              
                             
                               P 
                               N 
                               2 
                             
                           
                         
                       
                     
                     
                       
                         
                           = 
                             
                            
                           
                             P 
                             N 
                             2 
                           
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   where 
                 
               
               
                 
                   ( 
                   68 
                   ) 
                 
               
             
             
               
                 
                   
                     α 
                     
                       complex 
                       - 
                       gaussion 
                     
                   
                   = 
                   
                     
                       E 
                        
                       
                         [ 
                         
                           
                              
                             z 
                              
                           
                           4 
                         
                         ] 
                       
                     
                     
                       
                         { 
                         
                           E 
                            
                           
                             [ 
                             
                               
                                  
                                 z 
                                  
                               
                               2 
                             
                             ] 
                           
                         
                         } 
                       
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   69 
                   ) 
                 
               
             
           
         
       
     
         [0000]    The signal power can be assumed to be 
         [0000]        P   S   =E[|x|   2 ]  (70)
 
         [0000]    so that 
         [0000]      μ 1   =E[|y|   2   ]=E[|x|   2   ]+E[|z|   2   ]=P   S   +P   N   (71)
 
         [0000]    Finally, the covariance 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           σ 
                           1 
                           2 
                         
                         = 
                           
                          
                         
                           E 
                            
                           
                             [ 
                             
                               
                                 ( 
                                 
                                   
                                     
                                        
                                       y 
                                        
                                     
                                     2 
                                   
                                   - 
                                   
                                     μ 
                                     1 
                                   
                                 
                                 ) 
                               
                               2 
                             
                             ] 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             E 
                              
                             
                               [ 
                               
                                 
                                    
                                   y 
                                    
                                 
                                 4 
                               
                               ] 
                             
                           
                           - 
                           
                             μ 
                             1 
                             2 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   72 
                   ) 
                 
               
             
           
         
       
     
         [0000]    E[|y| 4 ] can be expanded as 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           E 
                            
                           
                             [ 
                             
                               
                                  
                                 y 
                                  
                               
                               4 
                             
                             ] 
                           
                         
                         = 
                           
                          
                         
                           E 
                            
                           
                             [ 
                             
                               
                                 { 
                                 
                                   
                                     ( 
                                     
                                       x 
                                       + 
                                       z 
                                     
                                     ) 
                                   
                                    
                                   
                                     ( 
                                     
                                       
                                         x 
                                         * 
                                       
                                       + 
                                       
                                         z 
                                         * 
                                       
                                     
                                     ) 
                                   
                                 
                                 } 
                               
                               2 
                             
                             ] 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           E 
                            
                           
                             [ 
                             
                               
                                 ( 
                                 
                                   
                                     
                                        
                                       x 
                                        
                                     
                                     2 
                                   
                                   + 
                                   
                                     
                                        
                                       z 
                                        
                                     
                                     2 
                                   
                                   + 
                                   
                                     xz 
                                     * 
                                   
                                   + 
                                   
                                     zx 
                                     * 
                                   
                                 
                                 ) 
                               
                               2 
                             
                             ] 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           E 
                           [ 
                           
                             
                               
                                  
                                 x 
                                  
                               
                               4 
                             
                             + 
                             
                               
                                  
                                 z 
                                  
                               
                               4 
                             
                             + 
                             
                               
                                 
                                   x 
                                   2 
                                 
                                  
                                 
                                   ( 
                                   
                                     z 
                                     * 
                                   
                                   ) 
                                 
                               
                               2 
                             
                             + 
                             
                               
                                 
                                   ( 
                                   
                                     x 
                                     * 
                                   
                                   ) 
                                 
                                 2 
                               
                                
                               
                                 z 
                                 2 
                               
                             
                             + 
                             
                               2 
                                
                               
                                 
                                    
                                   x 
                                    
                                 
                                 2 
                               
                                
                               
                                 
                                    
                                   z 
                                    
                                 
                                 2 
                               
                             
                             + 
                           
                         
                       
                     
                   
                   
                     
                       
                           
                          
                         
                           
                             2 
                              
                             
                               
                                  
                                 x 
                                  
                               
                               2 
                             
                              
                             
                               xz 
                               * 
                             
                           
                           + 
                           
                             2 
                              
                             
                               
                                  
                                 x 
                                  
                               
                               2 
                             
                              
                             
                               x 
                               * 
                             
                              
                             z 
                           
                           + 
                           
                             2 
                              
                             x 
                              
                             
                               
                                  
                                 z 
                                  
                               
                               2 
                             
                              
                             
                               z 
                               * 
                             
                           
                           + 
                           
                             2 
                              
                             
                               x 
                               * 
                             
                              
                             
                               
                                  
                                 z 
                                  
                               
                               2 
                             
                              
                             z 
                           
                           + 
                           
                             2 
                              
                             
                               
                                  
                                 x 
                                  
                               
                               2 
                             
                              
                             
                               
                                  
                                 z 
                                  
                               
                               2 
                             
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   73 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Assuming E[x]=E[z]=0 all terms involving the first-order of x and z in equation (73) can vanish after an expectation operation. Since z is a complex Gaussian random variable, i.e. z=u+jv, it follows that 
         [0000]        E[z   2   ]=E[u   2   −v   2 ]+2 jE[u]E[v]= 0 =E [( z *) 2 ]  (74)
 
         [0000]    and thus all terms involving the second-order of z in equation (73) can vanish after expectation. Equation (73) can then be simplified to: 
         [0000]        E[|y|   4   ]=E[|x|   4   ]+E[|z|   4 ]+4 E[|x|   2 ]4 E[|z|   2 ]  (75)
 
         [0000]    For a complex Gaussian random variable z, 
         [0000]        E[|z|   4 ]=2 {E[|z|   2 ]} 2 =2 P   n   2   (76)
 
         [0000]      For 
         [0000]        E[|x|   4   ]=α{E[|x|   2 ]} 2   =αP   S   2   (77)
 
         [0000]    Equation (75) can be expressed as 
         [0000]        E[|y|   4   ]=αP   S   2 +2 P   N   2 +4 P   N   P   S   (78)
 
         [0000]    Substituting the above in equation (72) and using equation (71), it follows that 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           σ 
                           1 
                           2 
                         
                         = 
                           
                          
                         
                           
                             E 
                              
                             
                               [ 
                               
                                 
                                    
                                   y 
                                    
                                 
                                 4 
                               
                               ] 
                             
                           
                           - 
                           
                             μ 
                             1 
                             2 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             α 
                              
                             
                                 
                             
                              
                             
                               P 
                               S 
                               2 
                             
                           
                           + 
                           
                             2 
                              
                             
                               P 
                               N 
                               2 
                             
                           
                           + 
                           
                             4 
                              
                             
                               P 
                               N 
                             
                              
                             
                               P 
                               S 
                             
                           
                           - 
                           
                             
                               ( 
                               
                                 
                                   P 
                                   N 
                                 
                                 + 
                                 
                                   P 
                                   S 
                                 
                               
                               ) 
                             
                             2 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               ( 
                               
                                 α 
                                 - 
                                 1 
                               
                               ) 
                             
                              
                             
                               P 
                               S 
                               2 
                             
                           
                           + 
                           
                             2 
                              
                             
                               P 
                               N 
                             
                              
                             
                               P 
                               S 
                             
                           
                           + 
                           
                             P 
                             N 
                             2 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   79 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Using equations (67) (68) (71), and (79), the sensing error floor SEF of equation (62) can be alternatively expressed as 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         SEF 
                         = 
                           
                          
                         
                           Q 
                           [ 
                           
                             
                               
                                 N 
                                 B 
                               
                             
                              
                             
                               
                                 P 
                                 S 
                               
                               
                                 
                                   P 
                                   N 
                                 
                                 + 
                                 
                                   
                                     
                                       
                                         ( 
                                         
                                           α 
                                           - 
                                           1 
                                         
                                         ) 
                                       
                                        
                                       
                                         P 
                                         S 
                                         2 
                                       
                                     
                                     + 
                                     
                                       2 
                                        
                                       
                                         P 
                                         N 
                                       
                                        
                                       
                                         P 
                                         S 
                                       
                                     
                                     + 
                                     
                                       P 
                                       N 
                                       2 
                                     
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           Q 
                           [ 
                           
                             
                               
                                 N 
                                 B 
                               
                             
                              
                             
                               SNR 
                               
                                 1 
                                 + 
                                 
                                   
                                     
                                       
                                         ( 
                                         
                                           α 
                                           - 
                                           1 
                                         
                                         ) 
                                       
                                        
                                       
                                         SNR 
                                         2 
                                       
                                     
                                     + 
                                     
                                       2 
                                       · 
                                       SNR 
                                     
                                     + 
                                     1 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   80 
                   ) 
                 
               
             
           
         
       
     
         [0000]    αs for some typical types of signals are shown in the following table: 
         [0000]                                                                  Type   Example   α                                        Gaussian   White noise, OFDM   2               signal               Uniform   Quantization noise   1.4           Amplitude-modulated   64 QAM   1.38           Amplitude-modulated   16 QAM   1.32           Phase-modulated   BPSK, QPSK, 8-PSK   1                        
Assuming α=2, a SEF can be simplified to
 
         [0000]    
       
         
           
             
               
                 
                   SEF 
                   = 
                   
                     Q 
                      
                     
                       ( 
                       
                         
                           
                             N 
                             B 
                           
                         
                          
                         
                           SNR 
                           
                             SNR 
                             + 
                             2 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   81 
                   ) 
                 
               
             
           
         
       
     
         [0069]    The graph  900  of  FIG. 9  shows the sensing error floor contours at various SNRs and averaging buffer sizes. Note that the error floor is expressed in dB units, e.g. −20 dB corresponding to an SEF of 0.01. When SNR&lt;&lt;1, the argument of the Q function in equation (81) can be approximated as 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       N 
                       B 
                     
                   
                    
                   
                     SNR 
                     2 
                   
                 
               
               
                 
                   ( 
                   82 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Thus, in some embodiments a linear decrease in SNR can be met by a quadratic increase in buffer size N B  in order to maintain a specified SEF value. When SNR&gt;&gt;1, the argument of the Q function in equation (81) can be approximated as √{square root over (N B )} independent of SNR. 
       Energy-Based Sensing: 
       [0070]    Energy-based sensing is a generic sensing method that can apply to many classes of signals, since any information-bearing signals have essentially nonzero energy. Energy-based sensing can work well when a noise signal is far smaller in energy than a target signal. However, in some embodiments, the reliability of energy-based sensing can be significantly impaired when the target signal power approaches the noise floor. In addition, since energy sensing does not differentiate signal types, energy-based sensing can be susceptible to false detection, e.g. due to impulse noise and/or other types of radio activity. 
         [0071]    In an embodiment of energy-based sensing, average signal power within a specified target channel can be computed. Signal power can then be compared to a noise floor and can be thresholded to determine signal presence. The computation can also lead to a channel SNR estimation that can be useful elsewhere. 
         [0072]    A block diagram  2100  for some embodiments of energy sensing is depicted in  FIG. 21 . The upper branch of the graph illustrates computation of signal power in a target channel. A filter block  2102  can essentially provide a significant information-bearing portion of signal spectrum while removing an unreliable portion of the signal spectrum (e.g. channel edges which can be contaminated by signal leakages from adjacent channels). For a signal after the filter y(n), a target channel signal power can be computed as: 
         [0000]    
       
         
           
             
               
                 
                   
                     P 
                      
                     
                       ( 
                       n 
                       ) 
                     
                   
                   = 
                   
                     
                       1 
                       N 
                     
                      
                     
                       
                         ∑ 
                         
                           l 
                           = 
                           
                             n 
                             - 
                             
                               ( 
                               
                                 N 
                                 - 
                                 1 
                               
                               ) 
                             
                           
                         
                         n 
                       
                        
                       
                         
                            
                           
                             y 
                              
                             
                               ( 
                               l 
                               ) 
                             
                           
                            
                         
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   83 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where N corresponds (again) to averaging depth. Equation (83) can be implemented by Magnitude Square  2104  and Averaging  2106  modules. Magnitude Square  2104  can perform a power computation function |y(l)| 2  as shown in Equation (83) and whose implementations are discussed herein. Averaging  2106  can perform an averaging function whose implementations are discussed herein and particularly regarding diagrams  1800 . 
         [0073]    A key part of an energy sensing algorithm can be computation of noise power. A target signal power can be compared against a computed noise power. For a TV signal, noise power can be computed using a reference channel that contains essentially no signal transmission. In the TV band, Channel 37 is typically reserved for astronomy observations; typically essentially no signal transmission occurs. This channel can be used as a reference channel. Signal power computation on the reference channel can be essentially the same as that for the target channel, as shown in the lower branch of the graph. The reference channel power can be computed as: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       P 
                       0 
                     
                      
                     
                       ( 
                       n 
                       ) 
                     
                   
                   = 
                   
                     
                       1 
                       N 
                     
                      
                     
                       
                         ∑ 
                         
                           l 
                           = 
                           
                             n 
                             - 
                             
                               ( 
                               
                                 N 
                                 - 
                                 1 
                               
                               ) 
                             
                           
                         
                         n 
                       
                        
                       
                         
                            
                           
                             
                               y 
                               0 
                             
                              
                             
                               ( 
                               l 
                               ) 
                             
                           
                            
                         
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   84 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where y 0 (n) is an input signal on the reference channel after filtering. A sensing decision can be made by comparing target channel signal power P(n) against the reference channel signal power P 0 (n) using a specified threshold. A signal-to-noise ratio can be computed as: 
         [0000]    
       
         
           
             
               
                 
                   
                     SNR 
                      
                     
                       ( 
                       n 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         P 
                          
                         
                           ( 
                           n 
                           ) 
                         
                       
                       - 
                       
                         
                           P 
                           0 
                         
                          
                         
                           ( 
                           n 
                           ) 
                         
                       
                     
                     
                       
                         P 
                         0 
                       
                        
                       
                         ( 
                         n 
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   85 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Threshold or Div.  2108  can provide a sensing result by comparing and/or thresholding the averaged power of a target channel signal (provided by Averaging  2106 ) with an averaged power of a reference channel. A signal processing chain comprising Filter  2112 , Magnitude Square  2114 , and Averaging  2116  can provide a static and/or a dynamic averaged power for a reference channel. A dynamic averaged power can also be otherwise specified and/or computed as discussed herein. Filter  2112  can provide filtering for a reference channel as Filter  2102  does for a target channel. Magnitude Square  2114  and Averaging  2116  modules can provide power computation and averaging to the reference channel signal path as are provided to the target channel signal path by the corresponding modules  2104   2106 . In some embodiments Threshold or Div.  2108  module can provide a SNR result as specified in Equation (85). 
       System and Network Layer Analysis: 
       [0074]    Some important system and network layer techniques are herein described that can be used in order to facilitate TV-band cognitive radio operation. For example, since TV receivers are typically passive, reactive interference control by detecting their presence is essentially not possible in some embodiments. Instead, a proactive approach can be taken through collective sensing by networked cognitive users in order to reduce interference in a statistical sense. To maximize the potential of cognitive user transmission while limiting adjacent channel interference to TV users, a cognitive user transmission power can be controlled adaptively based on signal power measurements of adjacent TV channels. A hidden terminal probability analysis can quantify a TV-band hidden terminal probability, and is described herein. Collective sensing can help reduce hidden terminal probability, and is described herein. Rate and range adaptation to optimize system throughput under various field conditions is described herein. Also herein described are embodiments of collective sensing and adaptive transmission power control in a TV-band cognitive radio system. 
       Hidden Terminal Probability Analysis 
       [0075]    Instances of a hidden terminal can pose a significant challenge to some embodiments of a TV-band cognitive system. In a TV-band cognitive radio system, TV stations and TV receivers can be primary users. Since TV receivers typically do not transmit, detecting the presence of a TV receiver is not straightforward. The hidden terminal problem in a TV-band cognitive system can alternatively be addressed in a statistical fashion. First, the hidden terminal problem can be quantified in terms of a hidden terminal probability (HTP). A mechanism is herein described to then reduce hidden terminal probability through sensing information sharing amongst cognitive users; this approach is called collective sensing. 
         [0076]    A uniform propagation loss model is described herein, wherein signal propagation loss can increase monotonically with distance. A case of shadowing is herein described, where propagation loss can depend on propagation distance and/or environmental attenuation. 
       HTP With No Shadowing: 
       [0077]    A signal transmission from a primary user U 1    1002  to another primary user U 2    1004  in a propagation environment with uniform propagation loss is depicted in the diagram  1000  of  FIG. 10 . d 0    1006  can represent a maximum distance within which a primary user can detect another primary user. d 1    1008  can be a maximum distance within which a cognitive user can detect a primary user. d 2    1010  can be a maximum distance within which a transmission from a cognitive user can be considered harmful to a primary user. 
         [0078]    As depicted in the illustration, for a signal transmission from U 1  to U 2 , a cognitive user who appears in the marked hidden terminal region A 1    1012  cannot detect U 1  and can create harmful interference to U 2  upon choosing to transmit. A worst case interference, i.e. the largest A 1 , can result when U 2  is at a maximum distance d 0  from U 1 . 
         [0079]    Assuming a cognitive user area density of ρ, the hidden terminal probability—the probability that at least one cognitive user appearing in the interference region A 1 , can be expressed 
         [0000]        P   HT =1 −e   −ρA     1     (86)
 
         [0000]    as derived herein. Referring to  FIG. 10 , in order to completely eliminate the interference can require that 
         [0000]        d   1   ≧d   0   +d   2   (87)
 
         [0000]    in which case A 1 =0 and P HT =0.
 
In a log-distance path loss model [T. S. Rappaport, op. cit.], loss from a transmitter to a receiver at a distance r away can be expressed as
 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       L 
                       _ 
                     
                      
                     
                       ( 
                       r 
                       ) 
                     
                   
                   = 
                   
                     
                       K 
                        
                       
                         ( 
                         
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                           0 
                         
                         ) 
                       
                     
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                           r 
                           
                             r 
                             0 
                           
                         
                         ) 
                       
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                   ( 
                   88 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Here α is the path loss exponent characteristic of the propagation environment; r 0  is the distance from the transmitter to a close-in reference point; and K (r 0 ) is the loss from the transmitter to the reference point. For simplicity, the primary user and cognitive user can be assumed to have essentially the same r 0  and K(r 0 ). It can be appreciated that such assumptions can effectively be equivalent to assuming that a TV station transmitter has the same elevation as a cognitive user transmitter. Under these assumptions, a TV signal path loss can be significantly overestimated. 
         [0080]    As illustrated in the diagram  1100  of  FIG. 11 , primary user transmission power is P 0    1102 ; cognitive user transmission power is P 1    1104 ; a primary user decoding threshold power is P D    1106 ; a cognitive user sensing power can be P S    1108 ; and a harmful interference threshold power level can be P H    1110 . Since losses for the distances d 0  d 1  d 2  (figure elements  1112   1114   1116 , respectively) can be expressed: 
         [0000]          L   ( d   0 )= P   0   /P   D   (89)
 
         [0000]          L   ( d   1 )= P   0   /P   S   (90)
 
         [0000]          L   ( d   2 )= P   1   /P   H   (91)
 
         [0000]    An interference free condition of Equation (87) can be restated as: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
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                                 D 
                               
                               
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                                 H 
                               
                             
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                   92 
                   ) 
                 
               
             
           
         
       
     
         [0081]    Note that a sensing gain  1118  P D /P S  can measure cognitive user sensing performance against primary user decoding performance. P 0 /P 1  can be a measure of primary user and cognitive user transmission power difference  1120 . The graph  1200  of  FIG. 12  plots sensing gain P D /P S    1118  values against transmission power difference P 0 /P 1    1120  required in order to achieve an interference-free condition of Equation (92), assuming that P D /P H =30 dB. Curves  1220   1225   1230   1235   1240   1245   1250  are shown for path loss exponent α values of 2.0 2.5 3.0 3.5 4.0 4.5 5.0, respectively. 
         [0082]      FIG. 12  illustrates an embodiment in which a typical TV station transmission power is approximately 100 kW and a cognitive user&#39;s maximum transmission power is approximately 1 W (P 0 /P 1 =50 dB). In some embodiments an 8 dB P D /P S  can ensure essentially interference-free operation under the conditions of typical path loss exponents. 
       HTP in Shadowing Environment: 
       [0083]    A typical propagation environment can be non-uniform. Receivers disposed at essentially equivalent distances from a particular transmitter can simultaneously experience different received signal strengths from that transmitter. Variations can depend on signal paths between transmitter and receivers. This effect is called shadowing. The log-distance path loss of Equation (88) can be expressed in dB form 
         [0000]          L     dB ( r )= K   dB ( r   0 )−10α log 10   r   0 +10α log 10   r   (93)
 
         [0000]    and an actual loss at a particular receiver can be modeled as 
         [0000]        L   dB ( r )=   L     dB ( r )+ X   σ   dB   (94)
 
         [0000]    where  L   dB (r) is considered as an average path loss while a zero-mean Gaussian random variable X σ   dB  with standard deviation a can account for the effect of shadowing [T. S. Rappaport, op. cit.]. 
         [0084]    A signal transmission from primary user U 1    1002  to primary user U 2    1004  is depicted in the diagram  1300  of  FIG. 13 . Given a distance between U 1  and U 2  of r, a distance between a potentially interfering cognitive user and U 2  of Δ, and a distance between U 1  and the cognitive user of r′, it can follow that due to the transmission power difference between U 1  and the cognitive user, r&gt;&gt;Δ and 
         [0000]          L   ( r )≈   L   ( r +Δ)≧   L   ( r ′)≧   L   ( r )             L   ( r ′)≈   L   ( r )  (95)
 
         [0085]    In some embodiments a potentially interfering cognitive user can experience essentially the same path loss for a signal coming from U 1  as for a signal coming from U 2 . In another case, U 2  can be at a cell edge, i.e. r=d 0 . Signal path loss from U 1  to a cognitive user can then be expressed 
         [0000]          L     dB ( d   0 )+ X   σ   dB   (96)
 
         [0000]    Successful sensing of the signal by the cognitive user can require 
         [0000]        P   0   dB   −[  L     dB ( d   0 )+ X   σ   dB   ]&gt;P   S   dB             X   σ   dB   &lt;P   D   dB   −P   S   dB    
         [0000]    with a sensing success probability of 
         [0000]    
       
         
           
             
               
                 
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                   = 
                   
                     
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                             - 
                             
                               
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                   ( 
                   97 
                   ) 
                 
               
             
           
         
       
     
         [0000]    (P D  and P S  are in dB units and Γ is a probability value between 0 and 1.) Because of shadowing, the interference region can extend beyond d 2  (from U 2 ), with interference probability decreasing with increasing distance from U 2 . An effective interference region A 1    1302  around U 2  can be assumed (for simplicity): 
         [0000]        A   1   =πd   1   2   (98)
 
         [0000]    noting that d 1    1304  can be on the same order as d 2  for this assumption. A cognitive user that is located in effective interference region A 1  and that does not successfully sense a signal from U 1  can be identified as a hidden terminal. 
         [0086]    Given cognitive user density ρ, sensing success probability Γ, and effective interference region A 1 , a hidden terminal probability in the case of shadowing can be expressed 
         [0000]        P   HT =1 −e   −ρA     1     (1−Γ)   (99)
 
         [0000]    as derived herein. For a resulting constant A 1 =πd 1   2˜πd   2   2 , an essentially zero HTP thus corresponds to Γ=1. Such a constraint could require essentially infinite sensing gain P D /P S  to meet a specified performance criterion. For a finite P D /P s , HTP in Equation (99) is monotonic with cognitive user density ρ. As ρ increases, HTP can exceed a tolerable specified performance level.
 
HTP with Sensing Information Sharing:
 
         [0087]    In some embodiments the above dilemma can result from sensing being performed by a lone local cognitive user. If a user happens to experience severe shadowing, the user may not be able to detect a primary user signal even with relatively large sensing gain. As cognitive user density increases, such a situation can become more likely and can result in increased interference to a primary user. 
         [0088]    This system behavior can be addressed in some embodiments by employing sensing information sharing between cognitive users. As an increasing number of cognitive users share their sensing results, the probability of shadowing can be reduced exponentially, and hidden terminal probability can be similarly reduced. This approach can be called collective sensing by a cognitive user network. 
         [0000]    Referring to  FIG. 13 , all cognitive users in an area A C    1306  around U 2  and defined by radius d C    1308 , 
         [0000]        A   C   =πd   C   2   (100)
 
         [0000]    can share their sensing information so that a cognitive user located in A 1    1302  transmits only under the condition that essentially none of the cognitive users in A C    1306  sense a signal from U 1    1002 . Assuming A C ≧A 1 , a hidden terminal probability can be expressed 
         [0000]        P   HT   =e   −ρA     C     Γ [1− e   −ρA     1     (1−Γ)]   (101)
 
         [0000]    as derived herein. 
         [0089]    Comparing Equation (101) with Equation (99), the factor e −ρA     C     Γ —a result of sensing information sharing—can help to drive down HTP as ρ increases. This effect is shown in the graph  1400  of  FIG. 14  under the assumption of A 1 =A C . Γ can be calculated using Equation (97); a shadowing environment can be characterized by using a random Gaussian variable Xf with σ=11.8 dB based on an urban cellular measurement [T. S. Rappaport, op. cit.]. 
         [0090]    Graph  1400  depicts HTP value curves  1402 ,  1404 ,  1406 ,  1408 , and  1410  corresponding to specified sensing gains of 0 dB, 5 dB, 10 dB, 15 dB, and 20 dB, respectively, varying with the quantity of cognitive users sharing information ρA C . 
         [0091]    Graph  1400  shows that an arbitrarily low HTP can be achieved in some embodiments by enlisting an adequate number of cognitive users ρA C  in sharing their sensing information. A target HTP can be achieved by requiring a threshold number of cognitive user participants. This threshold can be called the critical mass of collective sensing. The critical mass M C  of collective sensing, cognitive user participants can be defined as 
         [0000]        M   C   =ρA   C   (102)
 
         [0000]    such that Equation (101) achieves a predefined HTP. Graph  1500  of  FIG. 15  depicts the M C s required to achieve an HTP of 10 −4  in a shadowing environment with σ=11.8 dB for varying values of sensing gain P D /P S  and area ratio A C /A 1 . For example, when A C /A 1 =2 and P D /P S =10 dB, a critical mass of 11 cognitive users can achieve a target HTP of 10 −4    
       Rate Coverage Area: 
       [0092]    Supporting system rates as discussed above can require different SNRs. A coverage area (i.e. cell size) for a particular data rate can be defined as an area around a transmitter where a received signal SNR is above a required SNR level corresponding to the data rate. 
         [0093]    A log-normal path loss model of Equation (88) can be used to calculate a coverage area. A cognitive transmitter can be assumed to have a clearance of 10 meters (noting the same clearance is used in the TV-band per the NPRM [FCC, May 2004, op. cit.]. Within the clearance distance, signal propagation can follow a free-space propagation model. Signal power at the edge of a clearance region can be calculated as 
         [0000]    
       
         
           
             
               
                 
                   
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                   ( 
                   103 
                   ) 
                 
               
             
           
         
       
     
         [0000]    which is also known as the Friis free-space equation [T. S. Rappaport, op. cit.], and where c is the speed of light. Signal power loss from a transmitter to an edge of the clearance region can be expressed 
         [0000]    
       
         
           
             
               
                 
                   
                     
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         [0000]    For example, K (r 0 ) is 48 dB if r 0 =10 m and f=600 MHz. Signal propagation beyond the clearance region can follow a log-normal path loss model as shown in Equation (88), and signal power at a distance r away from the transmitter can be expressed 
         [0000]        P   dB ( r )= P   TX   dB   −K   dB ( r   0 )−α( r   dB   −r   0   dB )  (105)
 
         [0000]    noting the distance is expressed in dB units as well. Successful reception can be achieved for signal power exceeding a threshold V T . The coverage area radius can be expressed 
         [0000]    
       
         
           
             
               
                 
                   
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         [0000]    where a decoding threshold is expressed as 
         [0000]    
       
      
       V 
       T 
       dB 
       =N 
       0 
       dB 
       +NF+SNR 
       T 
       dB  
      
     
         [0000]    and where N 0 =−106 dBm is the thermal noise in a 6 MHz TV channel; NF is the receiver noise figure; and SNR T  is the SNR threshold for successful decoding. SNR thresholds for various data rates are described previously. 
         [0094]    Graph  1600  of  FIG. 16  shows signal coverage areas at different data rates assuming a carrier frequency of 600 MHz, a clearance radius of 10 m, transmission power of 30 dBm (1 W), a path loss exponent α=3.3, and a receiver noise figure of 8 dB. It can be appreciated that these coverage areas can be derived based on additive white gaussian channel (AWGN) SNRs and that areas can shrink if multipath margin is included in the SNRs. Notably, relative coverage area sizes can be independent of transmission power. 
       Collective Sensing: 
       [0095]    Collective sensing can be key to reducing hidden terminal problems in a TV-band cognitive system as discussed herein. Collective sensing can be employed in some embodiments as described herein following. 
         [0096]    Essentially all cognitive users considered in an embodiment can be required to periodically, e.g. every 10 seconds, broadcast their sensing results. A broadcast message from each cognitive user can include its SNR estimates and/or DTV and/or NTSC signal sensing outcomes on all TV channels. In some embodiments, such a broadcast message can be transmitted using a lowest data rate that has a largest coverage area, as shown in  FIG. 16 . 
         [0097]    Each cognitive user in an embodiment can also “listen” to (receive and respond to) messages from potentially all of the other cognitive users in the embodiment. In order to transmit and/or otherwise use a TV channel, a cognitive user must collect negative sensing results on the target TV channel from at least M C  cognitive users where M C  is a critical mass corresponding to a specified level of hidden terminal probability as discussed regards Equation (102). For example, suppose a harmful interference level P H  (as shown in  FIG. 11 ) is at the noise floor. Since sensing results can be shared using the lowest data rate with a required SNR of −11 dB, an area ratio between the sensing result sharing region and potential interference region can be expressed as approximately 
         [0000]        A   C   dB   −A   1   dB −2( r   C   dB   −r   I   dB )≈2·10/3.3.6 dB  (107)
 
         [0000]    corresponding to A C /A 1 =4 in linear scale. Using sensing methods as discussed herein, a sensing gain P D /P S  of 15 dB can be achieved. Referring to  FIG. 15 , a required critical mass for 10 −4  HTP is then 9. 
       ATSC Signal Sensing: ATSC Frame Format: 
       [0098]    An ATSC data transmission can be organized into Data Frames as shown in diagram  1700  of  FIG. 17 . Each Data Frame contains two Data Fields, each containing 313 Data Segments. The first Data Segment of each Data Field is a unique training sequence that can typically be used for channel equalization in a receiver. 
         [0099]    The remaining 312 Data Segments carry data. Each Data Segment encodes a 188-byte transport stream packet and its associated 20 Reed Solomon FEC bytes. Each data segment consists of 832 8-VSB symbols and each symbol is a 8-level signal carrying 3 bits of information. The first 4 symbols of the Data Segment corresponding to the first (sync) byte of the 188-byte transport stream are transmitted in binary form and provide segment synchronization. The remaining 828 symbols can carry a total of 828*3=2484 bits of information. Since the symbols are ⅔ trellis coded, the equivalent number of data bits carried in the 828 symbols can be 2484*2/3=1656 or 207 data bytes, e.g. 187 transport stream bytes plus 20 RS FEC bytes. Notably, the first byte of a 188-byte transport packet is transmitted in the first 4 symbols of a Data Segment for segment sync. 
       NTSC Signal Sensing: 
       [0100]    An NTSC (analog TV) signal can contain narrowband video, chroma, and audio carriers. These carriers can be at 1.25 MHz, 4.83 MHz, and 5.75 MHz from the left band edge, respectively. These relationships are illustrated in diagram  600  of  FIG. 6 . NTSC signal sensing can be based on detecting narrowband NTSC video and audio carriers. An FFT-based narrowband filter scheme can be used in order to detect video and audio carriers, as illustrated in diagram  2000  of  FIG. 20 . 
         [0101]    A FFT size can be selected so as to be large enough to enable resolution of video and audio carriers. For example, for a 6 MHz TV channel, an FFT size of 256 or bigger can be used. As shown in diagram  2000 , an input signal spectrum can be obtained by transforming a time-domain input signal to frequency domain using FFT. Bins around a video carrier can be extracted, and bins around an audio carrier can be extracted. Module FFT  2002  can perform an FFT operation on an input signal. 
         [0102]    The number of bins taken for detecting the video and/or audio carriers can be specified, and can depend on channel bandwidth and FFT size. The number of bins taken can be specified to be large enough so that the probability of missing a target carrier is minimized. A missing carrier can occur if there is frequency offset between transmitter and receiver. For example, for a system that uses a 1024-point FFT over a 6 MHz channel bandwidth, the subcarrier spacing can be 5.86 kHz. It follows that in some embodiments of detection, 10 bins each around the video and audio carriers can be specified. Modules  2010   2020   2030  can be employed to extract video carrier, midband, and audio carrier bins, respectively. 
         [0103]    In order to detect either video or audio carriers, power on each extracted bin can be evaluated, and an average over the bins taken. Magnitude Square modules  2012   2022   2032  can provide a magnitude-squared-based power measurement for video carrier, midband, and audio carrier signals, respectively. The power measurements can be bin-averaged by Averaging (over bins) modules  2014   2024   2034  (again respectively). The resulting bin-averaged power(s) can each be averaged again over a predefined number of symbols, e.g. 10, in order to improve sensing reliability. The bin-averaged power measurements can be symbol-averaged by Averaging (over symbols) modules  2016   2026   2036  (again respectively). Averaging processes can use implementations discussed herein and/or any other known and/or convenient averaging technique. In some embodiments, for averaging over a small number of elements, a running sum approach can be advantageously employed. 
         [0104]    Averaged video and audio carrier powers can be appropriately normalized before thresholding for detection. An average power over bins in the center of a TV channel can be used as a basis for normalization, based on  FIG. 6 . According to  FIG. 6 , bins in the center of a TV channel can be relatively free of narrowband carriers, and, their average power can be a relatively accurate reflection of average power over the whole channel. Video and audio carrier powers can be expected to exceed average power over mid-band bins by a margin. The margin value can, by way of non-limiting example, be 10 dB. Further, comparing normalized video and audio carriers with such a threshold can enable a determination of the presence of a NTSC signal. If the video and audio carriers each exceed such a threshold, a positive NTSC signal detection result can apply. If the carriers do not exceed a threshold, a negative NTSC signal detection result can apply. A threshold  2004  module can perform a comparison between video carrier power and midband power, providing a NTSC signal detection result to an AND  2008  module. A threshold  2006  module can perform a comparison between audio carrier power and midband power, providing a NTSC signal detection result to an AND  2008  module. An AND  2008  module can be employed to logically combine the result of signal detection results from threshold  2004  and threshold  2006  in order to provide a combined NTSC signal detection result. An AND  2008  module can perform specified logic and/or other operations (such as time-based operations) on provided input results in order to provide one or more combined results. 
         [0105]    Diagram  2200  of  FIG. 22  depicts some embodiments of combined sensing methods for cognitive radio. 
         [0106]    A cognitive radio unit CR  2201  can comprise a phase sensing element  2204 , an energy sensing element  2205 , and a collective sensing element  2206 . Phase sensing element  2204  and energy sensing element  2205  can be adapted to provide sensing functions as discussed herein, employing phase sensing techniques and energy sensing techniques, respectively. Phase sensing element  2204  and energy sensing element  2205  can be adapted to communicate and/or cooperate with each other, that is, interoperate, according to a specified physical layer  2203 . A cognitive radio unit CR  2201  can further comprise a collective sensing element  2206 . A collective sensing element  2206  can interoperate with other sensing elements according to a specified network and protocol layer  2202 . As depicted in Diagram  2200 , phase sensing  2204  and/or energy sensing  2205  elements can also interoperate with other sensing elements according to a specified network and protocol layer  2202 . 
         [0107]    As illustrated in Diagram  2200 , a second cognitive radio unit CR  2211  can be substantially similar in architecture to CR  2201 . CR  2211  can comprise a phase sensing element  2214 , an energy sensing element  2215 , and a collective sensing element  2216 . Phase sensing element  2214  and energy sensing element  2215  can be adapted to interoperate according to a specified physical layer  2213 . A collective sensing element  2216  can interoperate with other sensing elements according to a specified network and protocol layer  2212 . Phase sensing  2214  and/or energy sensing  2215  elements can also interoperate with other sensing elements according to a specified network and protocol layer  2212 . 
         [0108]    Sensing elements in a first cognitive radio unit CR1  2201  can interoperate with sensing elements in a second cognitive radio unit CR2  2211  according to one or more specified network and protocol layers. In some embodiments, a specified network and protocol layer  2202  can be the same network and protocol layer  2212 . 
         [0109]    Physical layer sensing can comprise phase sensing and/or energy sensing. In some embodiments physical layer sensing can be advantageously combined with collective sensing, through utilization of network and protocol layer(s). 
         [0110]    Sensing decisions for individual and/or multiple cognitive radio units  2201   2211  can be determined collectively through combining physical layer sensing results from a plurality of nearby cognitive radio units. In some embodiments, a collective sensing result can be determined as a weighted average of physical layer sensing results from nearby cognitive radio units. A weighting for a physical layer sensing result can be based on a specified and/or measured distance between a cognitive radio unit and another cognitive radio unit and/or a specified location; a specified location can be the location of a physical layer sensing process. That is, in some embodiments a weighting can be responsive to measured and/or specified locations and/or distances: between cognitive radio units, between a cognitive radio unit and a specified location, and/or between specified locations. In some embodiments, a distance metric can be based on a measurement of radio signal strength detected from a specified cognitive radio unit. 
         [0111]    By way of non-limiting examples, communications for collective sensing and between two or more cognitive radio units  2201   2211  can be achieved through one or more of a specified cognitive radio channel, a cellular link, a WiFi link, an Ethernet link, and/or any other known and/or convenient wired and/or wireless communication systems. By way of non-limiting examples, such communications can be adapted for a wide-area network (WAN) and/or any other known and/or convenient technology for network communications. 
       Hidden Terminal Probability Derivations: 
     Hidden Terminal Probability: 
       [0112]    A large number N ∞  of cognitive users can be assumed to be randomly distributed over a large area A ∞ , covering the area of interest A. The probability of no user appearing in A, i.e. all users appearing outside A, can be expressed: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             P 
                             0 
                           
                            
                           
                             ( 
                             A 
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             ( 
                             
                               1 
                               - 
                               
                                 A 
                                 
                                   A 
                                   ∞ 
                                 
                               
                             
                             ) 
                           
                           
                             N 
                             ∞ 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             [ 
                             
                               
                                 ( 
                                 
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                                     A 
                                     
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                                 ∞ 
                               
                               
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                               - 
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                              
                             
                                 
                             
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                             A 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   108 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where 
         [0000]    
       
         
           
             ρ 
             = 
             
               
                 N 
                 ∞ 
               
               
                 A 
                 ∞ 
               
             
           
         
       
     
         [0000]    is the cognitive user area density. The probability of one or more cognitive users appearing in A is 
         [0000]        P   1+ ( A )=1 −P   0 ( A )=1 −e   −ρA   (109)
 
         [0000]    The probability of k users appearing in A can be calculated as 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
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                   ( 
                   110 
                   ) 
                 
               
             
           
         
       
     
       HTP in Shadowing Environment: 
       [0113]    The probability that k users appear in an effective interference region A 1  can be expressed 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         ( 
                         
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                   111 
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         [0114]    The probability that all k users have successfully sensed the signal from U 1  can be expressed as 
         [0000]      Γ k   (112)
 
         [0115]    The probability that at least one user has not successfully sensed the signal from U 1  can be expressed as 
         [0000]      1−Γ k   (113)
 
         [0000]    This can represent an interference probability, given k users are inside the interference region A 1 . An overall HTP can then be expressed 
         [0000]    
       
         
           
             
               
                 
                   
                     
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         [0000]    HTP with Sensing Information Sharing: 
         [0116]    For any k users appearing in A 1 , interference can occur when all k users are not sensing a signal from U 1 , in combination with all users appearing in the area A C -A 1  not sensing a signal from U 1 . The total HTP can be expressed 
         [0000]    
       
         
           
             
               
                 
                   
                     
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         [0117]    In the foregoing specification, the embodiments have been described with reference to specific elements thereof. It will, however, be evident that various modifications and changes may be made thereto without departing from the broader spirit and scope of the embodiments. For example, the reader is to understand that the specific ordering and combination of process actions shown in the process flow diagrams described herein is merely illustrative, and that using different or additional process actions, or a different combination or ordering of process actions can be used to enact the embodiments. For example, specific reference to NTSC and/or ATSC and/or DTV embodiments are provided by way of non-limiting examples. Systems and methods herein described can be applicable to any other known and/or convenient channel-based communication embodiments; these can comprise single and/or multiple carriers per channel and can comprise a variety of specified channel bandwidths. The specification and drawings are, accordingly, to be regarded in an illustrative rather than restrictive sense.