Abstract:
A multicarrier transceiver for communicating spatially multiplexed orthogonal frequency division multiplexed (OFDM) signals over two or more spatial channels in a wireless access network in accordance with an orthogonal frequency division multiple access technique with a plurality of antennas is generally disclosed herein. In some embodiments, the multicarrier transceiver comprises a matrix generator to generate a matrix for precoding transmission symbols based an indicator received from a receiving station, the indicator being based at least in part on channel characteristics. The multicarrier transceiver also includes a precoder to multiply the transmission symbols by the matrix for transmission on groups of subcarriers that comprise the OFDM signals using the antennas for transmission through two or more spatial channels, each of the two or more spatial channels to concurrently convey separate spatially multiplexed data streams over a same set of subcarriers.

Description:
RELATED APPLICATIONS 
       [0001]    This application is a continuation of U.S. patent application Ser. No. 12/245,050, filed Oct. 3, 2008, which is a continuation of U.S. patent application Ser. No. 10/654,037, filed Sep. 3, 2003, issued as U.S. Pat. No. 7,453,946, all of which are incorporated herein by reference in their entireties. 
     
    
     TECHNICAL FIELD 
       [0002]    Embodiments of the present invention pertain to wireless communications, and some embodiments pertain to systems using symbol-modulated orthogonal subcarrier communications. 
       BACKGROUND  
       [0003]    Orthogonal frequency division multiplexing is an example of a multi-carrier transmission technique that uses symbol-modulated orthogonal subcarriers to transmit information within an available spectrum. When the subcarriers are orthogonal to one another, they may be spaced much more closely together within the available spectrum than, for example, the individual channels in a conventional frequency division multiplexing (FDM) system. To achieve orthogonality, a subcarrier may have a null at the center frequency of the other subcarriers. Orthogonality of the subcarriers may help reduce inter-subcarrier interference within the system. Before transmission, the subcarriers may be modulated with a low-rate data stream. The transmitted symbol rate of the symbols may be low, and thus the transmitted signal may be highly tolerant to multipath delay spread within the channel. For this reason, many modern digital communication systems are using symbol-modulated orthogonal subcarriers as a modulation scheme to help signals survive in environments having multipath reflections and/or strong interference. 
         [0004]    Communication systems that use symbol-modulated orthogonal subcarrier communications may have reduced channel capacity due to multipath fading and other channel conditions. Thus, there are general needs for apparatus and methods that increase channel capacity, improve channel equalization and/or reduce the effects of multipath fading, especially in systems using symbol-modulated orthogonal subcarrier communications. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0005]    The appended claims are directed to some of the various embodiments of the present invention. However, the detailed description presents a more complete understanding of embodiments of the present invention when considered in connection with the figures, wherein like reference numbers refer to similar items throughout the figures and: 
           [0006]      FIG. 1  illustrates a wireless communication environment in which some embodiments of the present invention may be practiced; 
           [0007]      FIG. 2  is a block diagram of a communication node in accordance with some embodiments of the present invention; 
           [0008]      FIG. 3  illustrates a block diagram of a transceiver in accordance with some embodiments of the present invention; 
           [0009]      FIG. 4  illustrates a time-frequency structure of an orthogonal frequency division multiplexed packet suitable for use with some embodiments of the present invention; and 
           [0010]      FIG. 5  is a flow chart of a communication procedure in accordance with some embodiments of the present invention. 
       
    
    
     DETAILED DESCRIPTION 
       [0011]    The following description and the drawings illustrate some specific embodiments of the invention sufficiently to enable those skilled in the art to practice them. Other embodiments may incorporate structural, logical, electrical, process, and other changes. Examples merely typify possible variations. Individual components and functions are optional unless explicitly required, and the sequence of operations may vary. Portions and features of some embodiments may be included in or substituted for those of others. The scope of embodiments of the invention encompasses the full ambit of the claims and all available equivalents of those claims. 
         [0012]      FIG. 1  illustrates a wireless communication environment in which some embodiments of the present invention may be practiced. Communication environment  100  includes one or more wireless communication devices (WCD)  102  which may communicate with access point (AP)  104  over communication links  108 , which may be bi-directional links. WCDs  102  may include, for example, personal digital assistants (PDAs), laptop and portable commuters with wireless communication capability, web tablets, wireless telephones, wireless headsets, pagers, instant messaging devices, MP3 players, digital cameras, and other devices that may receive and/or transmit information wirelessly. WCDs  102  may communicate with AP  104  using a multi-carrier transmission technique, such as an orthogonal frequency division multiplexing (OFDM) technique that uses orthogonal subcarriers to transmit information within an assigned spectrum. WCDs  102  and AP  104  may also implement one or more communication standards, such as one of the IEEE 802.11a, b or g standards, the Digital Video Broadcasting Terrestrial (DVB-T) broadcasting standard, or the High performance radio Local Area Network (HiperLAN) standard. Other local area network (LAN) and wireless area network (WAN) communication techniques may also be suitable for communication over links  108 . 
         [0013]    In addition to facilitating communications between WCDs  102 , in some embodiments, AP  104  may be coupled with one or more networks  114 , such as an intranet or the Internet, allowing WCDs  102  to access such networks. For convenience, the term “downstream” is used herein to designate communications in the direction from AP  104  to WCDs  102  while the term “upstream” is used herein to designate communications in the direction from WCDs  102  to AP  104 , however, the terms downstream and upstream may be interchanged. WCDs  102  may support duplex communications utilizing different spectrum for upstream and downstream communications, although this is not a requirement. In some embodiments, upstream and downstream communications may share the same spectrum for communicating in both the upstream and downstream directions. Although  FIG. 1  illustrates point-to-multipoint communications, embodiments of the present invention are suitable to both point-to-multipoint and point-to-point communications. 
         [0014]    In some embodiments, a communication node (e.g., access point  104 ) of a wireless local area network (WLAN) may utilize multi-element array antenna  106  to estimate angle-of-arrival  110  (e.g., theta (θ)) for communication signals received over links  108  from one or more signal sources (e.g., WCDs  102 ). Angle  110  may be measured relative to end-fire direction  116  of the antenna  106 , although the scope of the invention is not limited in this respect. The signal sources may be wireless communication devices which communicate on symbol-modulated orthogonal subcarriers. Channel coefficients may be estimated from the angle-of-arrival for the one or more signal sources to increase channel capacity, improve channel equalization and/or reduce the effects of multipath fading. In some embodiments, the channel coefficients may be generated from one symbol modulated on a plurality of subcarriers received by different elements of antenna  106 . In some embodiments, AP  104  may provide communications within a range of up to 500 feet, and even greater, for wireless communication devices, although the scope of the invention is not limited in this respect. 
         [0015]    In some embodiments, beamforming coefficients may also be generated from the angle-of-arrival for improved reception and/or transmission of communication signals with the one or more signal sources using multi-element array antenna  106 . The beamforming coefficients may be used to direct the reception and/or transmission of signals in a direction of the particular signal source. The angle-of-arrival may be estimated by sampling the response from the antenna elements of the array for at least one symbol at the subcarrier frequencies, although the scope of the invention is not limited in this respect. The sampled symbol may be a training symbol having a known value. The sampling may be performed on the same symbol at all subcarrier frequencies after demodulation by a fast Fourier transform (FFT) although the scope of the invention is not limited in this respect. With beamforming, frequency reuse may be realized using space-division multiple access techniques. 
         [0016]    Multi-element array antenna  106  may be a phased-array antenna comprising at least two directional or omnidirectional antenna elements  112 . Elements  112  may comprise dipole antennas, monopole antennas, loop antennas, microstrip antennas or other type of antenna suitable for reception and/or transmission of RF signals which may be processed by AP  104 . In some embodiments, a beamformer may be used to control phasing between elements  112  to provide directional communications with WCDs  102 . In some embodiments, the phasing may be controlled at baseband, although the scope of the invention is not limited in this respect. 
         [0017]      FIG. 2  is a block diagram of a communication node in accordance with some embodiments of the present invention. Communication node  200  may be suitable for use as AP  104  ( FIG. 1 ), although other communication nodes may also be suitable. In some embodiments, communication node  200  may also be suitable for use as one or more of WCDs  102  ( FIG. 1 ), although the scope of the invention is not limited in this respect. 
         [0018]    Communication node  200  receives and/or transmits radio frequency (RF) communications with multi-element array antenna  202 . RF signals received from antenna  202  may be converted to baseband signals and eventually to data signals comprising a bit stream by transceiver  204 . Transceiver  204  may also convert data signals comprising a bit stream to baseband signals and RF signals for transmission by antenna  202 . Communication node  200  may also include signal separator  206  to separate received and transmitted communication signals. Communication node  200  may also include data processing portion  208  to process data signals received through transceiver  204  and generate data signals for transmission by transceiver  204 . Antenna  202  may comprise a plurality of antenna elements  212 , which may correspond to antenna elements  112  ( FIG. 1 ). Although signal separator  206  is illustrated as a separate element of node  200 , the present invention is not limited in this respect. In some embodiments, signal separator  206  may be part of antenna  202 , while in other embodiments, antenna  202  may comprise one set of antenna elements for transmission of signals, and another set of antenna elements for reception of signals eliminating the need for signal separator  206 . 
         [0019]    In some embodiments, communication node  200  may include interfaces  210  to wireline devices and wireline networks, such as to a personal computer, a server, or the Internet, for example. In these embodiments, communication node  200  may facilitate communications between WCDs  102  ( FIG. 1 ) and these wireline devices and/or networks. 
         [0020]      FIG. 3  illustrates a block diagram of a transceiver in accordance with some embodiments of the present invention. Transceiver  300  may be suitable for use as transceiver  204  ( FIG. 2 ) although other transceiver configurations may also be suitable. Transceiver  300  may include RF circuitry  302  to receive a signal from a signal source through a multi-element antenna having a plurality of antenna elements. The signal may comprise a plurality of subcarriers modulated with at least one symbol. Transceiver  300  may also include angle-of-arrival (AOA) estimator  304  to estimate an angle-of-arrival for a signal source from a subcarrier level of the symbol received by at least two of the antenna elements. Transceiver  300  may also include channel coefficient generator  306  to generate channel coefficients for communications received from the signal source based on the angle-of-arrival. The channel coefficients may compensate for at least some of the channel effects between a signal source and the access point. Transceiver  300  may also include channel equalizer  308  which may be responsive to the channel coefficients to provide equalized frequency-domain symbol-modulated subcarriers  310  resulting in improved reception. 
         [0021]    In some embodiments, transceiver  300  may further include beamformer coefficient generator  312  to generate beamforming coefficients for elements of the multi-element antenna based on the angle-of-arrival. The beamforming coefficients may be used to help direct the reception and/or transmission of signals in a direction of a particular signal source. In these embodiments, transceiver  300  may further include beamformer  314 . Beamformer  314  may change the directionality of the antenna based on the beamforming coefficients, and in some embodiments, beamformer  314  may change phasing of received and/or transmitted signals. In some embodiments, beamforming may be done prior to conversion to corresponding RF signals by RF circuitry  302  and transmission of the signals by the elements of the multi-element antenna. In some embodiments, beamformer  314  may change the directionality of the antenna by changing the phasing of baseband-level signals that comprise a plurality of symbol-modulated subcarriers for use in generating and/or receiving an orthogonal-frequency division multiplexed signal by RF circuitry  302  for transmission and/or reception by a multi-element antenna. With beamforming, frequency reuse may be realized using space-division multiple access techniques. 
         [0022]    In some embodiments, angle-of-arrival estimator  304  may include one or more processors and memory to generate an initial matrix (e.g., X) comprising demodulated pilot subcarriers for a symbol provided by FFT  328  corresponding to each of the antenna elements. The processor and memory may also generate a response matrix (e.g., A) substantially from the equation X=AD+N. In the equation, ‘D’ may represent a diagonal matrix having elements corresponding to the pilot subcarriers of the symbol, and ‘N’ may represent an uncorrelated noise matrix. The processor and memory may use a search function to identify a peak corresponding to the angle-of-arrival. The search function may be based on a decomposition of the response matrix. This is described in more detail below. 
         [0023]      FIG. 4  illustrates a time-frequency structure of an orthogonal frequency division multiplexed packet suitable for use with some embodiments of the present invention. Time-frequency structure  400  is an example of a packet in accordance with the IEEE 802.11(a) standard; however, other time-frequency structures for packets may be equally suitable for use with some embodiments of the present invention. As illustrated in structure  400 , symbols having known training values are crosshatched/shaded. Structure  400  illustrates a packet starting with ten short training symbols  402  modulated on twelve subcarriers  404 . These symbols may contain known pilot subcarriers. Short training symbols  402  are followed by two long training symbols  406  which are followed by data symbols  408 . Data symbols  408  may include four pilot subcarriers  410 . 
         [0024]    In some embodiments, angle-of-arrival estimator  304  ( FIG. 3 ) may estimate the angle-of-arrival based the antenna response for subcarriers  404  for one of training symbols  402  or based on one of training symbols  406 , although the scope of the invention is not limited in this respect. A training symbol may have known training values. In some embodiments, channel equalizer  308  ( FIG. 3 ) may provide equalized frequency-domain symbol-modulated subcarriers for subsequent data symbols (e.g., symbols  408 ) of a data packet received from the signal source. 
         [0025]    Referring back to  FIG. 3 , in some embodiments, RF receive circuitry  302  receives signals through a multi-element antenna, and generates serial symbol stream  320  representing symbols. In some embodiments, a packet may include short training symbols  402  ( FIG. 4 ) and long training symbols  406  ( FIG. 4 ) followed by data symbols  408  ( FIG. 4 ). In some embodiments, the received signal may have a carrier frequency ranging between 5 and 6 GHz, although embodiments of the present invention are equally suitable to carrier frequencies, for example, ranging between 2 and 20 GHz, and even greater. In some embodiments, a symbol-modulated signal may include up to a hundred or more subcarriers. The short training symbols may be transmitted on a portion of the subcarriers, and data symbols may contain one or more known pilot subcarriers although this is not a requirement. In some embodiments, the long training symbols may have a duration of approximately 4 microseconds and the short training symbols may have a duration of approximately one microsecond. In some embodiments, the signals may be infrared (IR) signals. 
         [0026]    The receiver portion of transceiver  300  may include serial to parallel (S/P) converter  322  to convert a symbol of serial symbol stream  320  into parallel groups of time-domain samples  324 . Cyclic-redundancy prefix (C/P) element  326  removes a cyclic-redundancy prefix from each symbol. Fast Fourier Transform (FFT) element  328  performs an FFT on parallel groups of time-domain samples  330  to generate frequency-domain symbol-modulated subcarriers  332  for use by equalizer  308  and angle-of-arrival estimator  304 . 
         [0027]    Angle-of-arrival estimator  304  may generate an angle-of-arrival estimate for a signal source which may be used by channel coefficient generator  306  for generating channel coefficients for use by equalizer  308  for improved demodulation of the subcarriers. In some embodiments, a channel estimator (not illustrated) may be used, in addition to generator  306 , to generate channel estimates for use by equalizer  308 . 
         [0028]    Equalizer  308  may perform a channel equalization on frequency-domain symbol-modulated subcarriers  332  provided by FFT element  328 . Equalizer  308  may generate equalized frequency-domain symbol-modulated subcarriers  310  using the channel coefficients provided by channel coefficient generator  306 . For example, equalization in the frequency domain may be performed by division of the frequency domain subcarriers  332  with complex values that represent the channel estimation. Accordingly, the magnitudes of equalized frequency-domain symbol-modulated subcarriers  332  may be normalized and the phases of equalized frequency-domain symbol-modulated subcarriers  310  may be aligned to a zero origin to allow for further processing by demapper  334 . 
         [0029]    Equalized frequency-domain symbol-modulated subcarriers  310  may be demapped by demapper  334  to produce a plurality of parallel symbols. Demapper  334  may demap the parallel symbols in accordance with a particular modulation order in which the transmitter modulated the subcarriers. Modulation orders, for example, may include binary phase shift keying (BPSK), which communicates one bit per symbol, quadrature phase shift keying (QPSK), which communicates two bits per symbol, 8-PSK, which communicates three bits per symbol, 16-quadrature amplitude modulation (16-QAM), which communicates four bits per symbol, 32-QAM, which communicates five bits per symbol, and 64-QAM, which communicates six bits per symbol. Modulation orders may also include differentially-coded star QAM (DSQAM). Modulation orders with lower and even higher communication rates may also be used. The parallel symbols from demapper  334  may be converted from a parallel form to a serial stream by parser  336 , which may perform a de-interleaving operation on the serial stream. Parser  336  generates decoded serial bit stream  338  for use by data processing elements (not illustrated). 
         [0030]    The transmitter portion of transceiver  300  may include parser  342  to encode serial bit-stream  340  to generate parallel symbols. Mapper  344  maps the parallel symbols to frequency-domain symbol-modulated subcarriers  346 . IFFT element  348  performs an inverse fast Fourier transform (IFFT) on frequency-domain symbol-modulated subcarriers  346  to generate parallel groups of time-domain samples  350 . CP circuit  352  adds a cyclic-redundancy prefix to each symbol, and parallel-to-serial (P/S) circuit  354  converts the parallel groups of time-domain samples  356  to serial symbol stream  358  for RF circuitry  302 . In accordance with embodiments, the length of the cyclic-redundancy prefix is greater than the length of intersymbol interference. 
         [0031]    Although communication node  200  ( FIG. 2 ) and transceiver  300  are illustrated as having several separate functional circuit elements, one or more of the functional elements may be combined and may be implemented by combinations of software-configured elements, such as processing elements including digital signal processors (DSPs), and/or other hardware elements and software. For example, circuit elements may comprise one or more processing elements such as microprocessors, DSPs, application specific integrated circuits (ASICs), and combinations of various hardware and logic circuitry for performing at least the functions described herein. 
         [0032]      FIG. 5  is a flow chart of a communication procedure in accordance with some embodiments of the present invention. Communication procedure  500  may be performed by a communication node, such as AP  104  ( FIG. 1 ) although other communication nodes may also be suitable for performing procedure  500 . In some embodiments, communication procedure  500  may be performed by communication devices, such as WCDs  102  ( FIG. 1 ). Although the individual operations of procedure  500  are illustrated and described as separate operations, one or more of the individual operations may be performed concurrently and nothing requires that the operations be performed in the order illustrated. 
         [0033]    In operation  502 , a signal comprising at least one symbol of a data packet comprising symbol-modulated subcarriers is received through a multi-element antenna from a signal source. In operation  504 , an FFT may be performed on parallel groups of time-domain samples that represent the symbol as received by the elements of the multi-element antenna. The FFT may generate frequency-domain symbol-modulated subcarriers for each antenna element. The symbol may be a training symbol having known training values. In operation  506 , an angle-of-arrival estimate is generated for the signal source. The angle-of-arrival may be relative to an end-fire direction of the multi-element antenna. The angle-of-arrival may be estimated based on the antenna response for the antenna elements for more than one subcarrier frequency of the symbol, although the scope of the invention is not limited in this respect. In operation  508 , channel coefficients may be generated from the angle-of-arrival estimate, and in operation  510 , the channel coefficients may be used for equalization of symbols, including data symbols, subsequently received from the signal source. In operation  512 , beamforming coefficients may be generated based on the angle-of-arrival, and in operation  514 , a communication signal comprising symbol-modulated subcarriers may be directionally transmitted to the signal source (e.g., in a direction of the signal source) using the beamforming coefficients. In some embodiments, a communication signal comprising symbol-modulated subcarriers may be directionally received from the signal source using the beamforming coefficients. 
         [0034]    In some embodiments, the operations of procedure  500  may be repeated or performed concurrently for one or more of a plurality of signal sources. In these embodiments, angles-of-arrival may be individually estimated for the different signal sources, and channel and beamforming coefficients may be generated for the different signal sources and used for communicating with the signal sources. Accordingly, increased channel capacity, improved channel equalization and/or reduced the effects of multipath fading may be achieved, although the scope of the invention is not limited in this respect. 
         [0035]    In some embodiments of the present invention, an angle-of-arrival may be estimated by angle-of-arrival estimator  304  ( FIG. 2 ) and channel coefficients may be generated by channel coefficient generator  306  ( FIG. 3 ) as illustrated in the following example. Consider an N-element adaptive antenna receiving J—user signals having J distinct directions θ 1 , . . . θ J , where the angles θ j  are measured with respect to end-fire direction  116  ( FIG. 1 ). In this example, let Q be number of subcarriers used to carry known pilot subsymbols transmission. The remaining (K-Q) subcarriers may be used for information bearing subsymbols. In this example, consider N&gt;Q. For the sake of generality, a single sample case is illustrated which may be further extended for multiple samples in which an average estimate may be obtained. In the single-sample case, the signals may be collected after demodulation by an FFT in the form of matrix, which may be described by the following equations. 
         [0000]        X=AD+N    (1)
 
         [0036]    In equation (1), X is a matrix in which the i th  column may correspond to the antenna-array response to the i th  subcarrier. D is a diagonal matrix whose elements may correspond to the known pilot symbols scaled by channel coefficients along with the phase shift. A is an array-response matrix for the subcarrier frequencies. m corresponds to the m th symbol. N may be a spatially and temporally uncorrelated noise matrix. 
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         [0000]        D= diag( p ( m,  0),  p ( m,  1), . . . ,  p ( m, Q− 1))   (4)
 
         [0000]        p ( m,  0)= s ( m,  0) h   0   e   −iδ     1     , . . . , p ( m, Q− 1)= s ( m, Q− 1) h   Q-1   e   −δ     Q-1      (5)
 
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                                 2 
                                  
                                 Q 
                               
                             
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                               ( 
                               
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                           … 
                         
                         
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                           … 
                         
                       
                       
                         
                           
                             
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                               ( 
                               
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                           … 
                         
                         
                           
                             
                               n 
                               NQ 
                             
                              
                             
                               ( 
                               
                                 m 
                                 , 
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                               ) 
                             
                           
                         
                       
                     
                     ] 
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
         [0037]    In some embodiments, equation (1) may be multiplied by unit vectors, e.g., e=[1 . . . 1] T  and shown as Xe=ADe+Ne which reduces to: 
         [0000]      x=Ap   (7)
 
         [0038]    where x=x 1 +x 2 + . . . +x Q-1  and p=p 1 +p 2 + . . . +p Q-1    
         [0000]      x ∈ span{A}  (8)
 
         [0039]    A matrix B may be formed. 
         [0000]        B=[A (θ) x]  where θ ∈(0, 2π).   (9)
 
         [0040]    The size of matrix B may be N(Q+1), where N≧(Q+1). 
         [0041]    Matrix B may become rank deficient (e.g., undetermined) when θ=θ true . The θ true  estimate can be found from the following QR-decomposition and search function. 
         [0000]        B (θ)= Q (θ) R (θ),   (10)
 
         [0042]    with search function as 
         [0000]    
       
         
           
             
               
                 
                   
                     G 
                      
                     
                       ( 
                       θ 
                       ) 
                     
                   
                   - 
                   
                     
                       max 
                        
                       
                         [ 
                         
                           1 
                           
                             
                               r 
                               
                                 
                                   ( 
                                   Q 
                                   ) 
                                 
                                  
                                 
                                   ( 
                                   Q 
                                   ) 
                                 
                               
                             
                              
                             
                               ( 
                               θ 
                               ) 
                             
                           
                         
                         ] 
                       
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
         [0043]    r Q,Q (θ) is the Q-th diagonal element of the upper triangular matrix R(θ). The search function G(θ) may have J-highest peaks that may correspond to the angle-of-arrival estimates, {circumflex over (θ)} 1 , . . . {circumflex over (θ)} J  of J-sources. Note that the estimates ({circumflex over (θ)} 1 , . . . {circumflex over (θ)} J ) may be obtained from processing of four pilot subcarriers that are spaced quite apart in the frequency spectrum. Such a property may provide a good approximation of the angle-of-arrival corresponding to the complete set of subcarriers in the OFDM. In other words the estimates may correspond to angle-of-arrival of broadband signal sources. 
         [0044]    Having obtained {circumflex over (θ)} ∈({circumflex over (θ)} 1 , . . . {circumflex over (θ)} J ), {circumflex over (θ)} may be substituted in the matrix A in equation (7) as 
         [0000]        {circumflex over (x)} = A ({circumflex over (θ)}) p.    (12)
 
         [0045]    Thus, in equation (12) p remains unknown, and may be obtained as follows: 
         [0000]        p=[A ({circumflex over (θ)}) A ({circumflex over (θ)})] −1   A   T ({circumflex over (θ)}) x    (13)
 
         [0046]    The k th element of p is p(m, k)=s(m, k)h k e −1δ     k   . Since s(m, k) is known, the channel estimation may be obtained as 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       h 
                       k 
                     
                      
                     
                        
                       
                         
                           - 
                            
                         
                          
                         
                             
                         
                          
                         
                           δ 
                           k 
                         
                       
                     
                   
                   = 
                   
                     
                       p 
                        
                       
                         ( 
                         
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                           , 
                           k 
                         
                         ) 
                       
                     
                     
                       s 
                        
                       
                         ( 
                         
                           m 
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                           k 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
           
         
       
     
         [0047]    where s(m, k), k=1, . . . , Q , are known pilot symbols. 
         [0048]    In the second stage, the next set of Q-subcarriers may be chosen to obtain the channel coefficients as, 
         [0000]        p=[A ({circumflex over (θ)}) A ({circumflex over (θ)})] −1   A   T ({circumflex over (θ)}) x,    (13)
 
         [0049]    where A({circumflex over (θ)}) corresponds to the columns as a function of next subset of subcarriers. This channel estimation process may be repeated for this next subset of subcarriers. 
         [0050]    In some embodiments, the estimation of angular information {circumflex over (θ)} of a signal source may be performed for only one sample. The angular estimate {circumflex over (θ)} may be repeatedly used for each subset of subcarrier matrices and accordingly the channel estimates for entire subcarrier channels may be found. For increased reliability, in some embodiments, the angular estimation may be performed for each sample and the average estimate can be obtained as follows: 
         [0000]      θ estimate =E[{circumflex over (θ)}].   (15)
 
         [0051]    In some embodiments, beamforming in the direction θ estimate  is performed to increase the channel capacity. With beamforming, frequency reuse may be realized using space-division multiple access techniques. The beamforming may be used for both reception and transmission. 
         [0052]    It is emphasized that the Abstract is provided to comply with 37 C.F.R. Section 1.72(b) requiring an abstract that will allow the reader to ascertain the nature and gist of the technical disclosure. It is submitted with the understanding that it will not be used to limit or interpret the scope or meaning of the claims. 
         [0053]    In the foregoing detailed description, various features are occasionally grouped together in a single embodiment for the purpose of streamlining the disclosure. This method of disclosure is not to be interpreted as reflecting an intention that the claimed embodiments of the subject matter require more features that are expressly recited in each claim. Rather, as the following claims reflect, inventive subject matter lies in less than all features of a single disclosed embodiment. Thus the following claims are hereby incorporated into the detailed description, with each claim standing on its own as a separate preferred embodiment.