Abstract:
An approach is provided for correlation of a signal over time and frequency. The signal is correlated with a bit sequence over time instances and certain frequency offsets, wherein sub-segments of the signal are correlated with sub-segments of the bit sequence to generate a correlation factor associated with each signal sub-segment. The correlation factors are coherently combined to generate a final correlation factor, wherein a respective phase shift (for each frequency offset) is applied to each correlation factor to generate a set of frequency adjusted correlation factors, and the frequency adjusted correlation factors of a respective set are combined to generate the final correlation factor over the signal sub-segments, resulting in the matrix of final correlation factors over time and frequency. A signal parameter estimation is performed, based on the matrix of final correlation factors, to determine a highest correlation value for the signal over the frequency offsets.

Description:
RELATED APPLICATIONS 
     This application is a continuation, and claims the benefit of the filing date under 35 U.S.C. §120, of U.S. patent application Ser. No. 13/018,670 (filed 1, Feb. 2011), the entirety of which is incorporated herein by reference. 
    
    
     BACKGROUND 
     In some communications systems, a goal is the detection of a signal with some unknown parameters in noise. For example, in a burst-mode transmission, the start of the burst is often marked using some recognizable signal, or “Unique Word” (UW). This signal will typically arrive at the receiver with unknown (to a greater or less extent) timing, as well as unknown phase and frequency. The signal will also have been subjected to various impairments, such as additive white Gaussian noise (AWGN). 
       FIG. 1  illustrates a block diagram of a conventional communication system  100 . 
     Communication system  100  includes a transmitter  102  and a receiver  104 . 
     Receiver  104  receives information from transmitter  102  via a communication channel  106 . Transmitter transmits a transmitted signal  108 . Impairments to the reception of transmitted signal  108  by receiver  104  are generated by conditions denoted as impairment sources  110  external to transmitter  102  and receiver  104 . Non-limiting examples of impairments include atmospheric noise, solar noise, cosmic noise, thermal noise, white noise, Gaussian noise and Doppler effect. Impairment sources  110  generate and inject impairments as denoted by an impairment  112 . Interference by impairments  112  to transmitted signal  108  is modeled as additive as denoted by a noise addition element  114 . Noise addition element  114  adds transmitted signal  108  and impairments  112  to generate a noisy signal  116 . Receiver  104  receives and processes noisy signal  116 . In order to receive and process noisy signal  116 , receiver  104  performs processing steps, non-limiting examples of which include filtering, mixing and correlation. 
       FIG. 2  illustrates an example communications protocol  200  that is transmitted by conventional transmitter  102  ( FIG. 1 ). 
     Communications protocol  200  includes a plurality of frames with a sampling denoted as a frame  204  and a frame  206 . 
     Frame  204  and frame  206  are configured with respect to an x-axis  202  with units of time and resolution of seconds. 
     Transmission of frame  204  initiates at a time  208  and terminates at a time  210 . Transmission of frame  206  initiates at a time  212  and terminates at a time  214 . 
     Frame  204  includes a unique word  216  and a payload  218 . Unique word provides a mechanism for receiver  104  to synchronize with frame  204 . Payload  218  includes data and information desired by transmitter  102  to be received and processed by receiver  104 . Transmission of unique word  216  initiates at time  208  and terminates at a time  220 . Transmission of payload  218  initiates at time  220  and terminates at time  210 . 
     Unique word  216  includes a plurality of symbols with a sampling denoted as a symbol  222  and a symbol  224 . Transmission of symbol  222  initiates at time  208  and terminates at a time  226 . Transmission of symbol  224  initiates at a time  228  and terminates at time  220 . Payload  218  includes a plurality of symbols with a sampling denoted as a symbol  230  and a symbol  232 . Transmission of symbol  230  initiates at time  220  and terminates at a time  234 . Transmission of symbol  232  initiates at a time  236  and terminates at time  210 . 
     Receiver  104  receives unique word  216  followed by payload  218 . Receiver  104  knows in advance the symbol structure of unique word  216  and seeks to find unique word  216  by performing a correlation operation. Once a threshold has been met for the correlation operation, receiver  104  determines a starting time for the first symbol received of unique word  216 , as denoted by time  208 . Once receiver has determined the starting time for the initial symbol received, receiver  104  has also determined the initial time of reception for frame  204 , as denoted by time  208 . Receiver then uses the determination of time for initial reception of frame  204 , as denoted by time  208 , to synchronize and process the symbols of payload  218 . 
       FIG. 3  illustrates a graph  302 , a graph  304  and a graph  306  for explaining a conventional continuous correlation operation  300 . 
     Conventional continuous correlation operation  300  may be described by the following:
 
∫y(t−τ)x*(t)dt  (1)
 
     For equation (1), x and y represent general complex-valued signals and τ represents an estimate for the starting time of the received signal. 
     Graph  302  describes the characteristic of x or equation (1), graph  304  describes the characteristic of y of equation (1) and graph  306  describes the result of performing a correlation operation between x and y or graph  302  and graph  304 . 
     Graph  302  includes an x-axis  308  with units of time in increments of seconds and a y-axis  310  with units of height. A function  312  initiates at a time  314  and terminates at a time  316 . Function  312  has a height as designated by a height  318 . 
     Graph  304  includes an x-axis  320  with units of time in increments of seconds and a y-axis  322  with units of height. A function  324  initiates at a time  326  and terminates at a time  328 . Function  324  has a height as designated by a height  330 . 
     Graph  306  includes an x-axis  332  with units of time in increments of seconds and a y-axis  334  with units of height. A function  336  represents the correlation of function  312  of graph  302  with function  324  of graph  304  as described by equation (1). Function  336  initiates at a time  338  and increases linearly to a point  340  at a time  342  with a maximum value as denoted by a maximum value  344 . Following this, function  336  decreases linearly and terminates at a time  346  with a height of zero. A threshold value as denoted by a threshold height  350  crosses function  336  at a point  348  with x-axis  332  value as represented by a time  352  and also at a point  354  with x-axis  332  value as represented by a time  356 . 
     For receiver  104 , threshold height  350  represents a condition of a potential match between a received signal and an expected signal, as denoted between time  352  and time  356 , with point  340  representing an exact match between a received signal and an expected signal. Receiver  104  uses correlation to determine when a received signal has matched an expected signal and then uses the timing information to decode and process received information from a received signal. 
     In the case of AWGN in particular, it is well known that a signal can be optimally detected by computing the correlation between the known transmitted signal and the received signal, and finding the value of time τ which maximizes the magnitude of the correlation as given by the following equation: 
     
       
         
           
             
               
                 
                   
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     Where x and y in equation (2) are in general complex-valued signals and τ is the estimate of the starting time of the received signal. The variable x describes a sequence of predetermined symbols of a unique word and variable y represents a received sequence of symbols. 
     Typically digital sampled signals are being processed, and the correlation is replaced by the summation as shown below: 
     
       
         
           
             
               
                 
                   
                     
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     For equation (3), T represents a sampling period. 
     In addition to unknown timing and phase, a received signal may also have unknown frequency offset, within a range. The frequency offset will cause a phase shift over the length of the received signal. This will cause the correlation to be reduced or negatively affected. The reduction in correlation may be described as: 
     
       
         
           
             
               
                 
                   
                     
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     For equation (4), f represents a frequency offset and T represents the length of time for the correlation. As may be observed, if the frequency offset relative to the correlation length becomes large, the peak value of the correlation may be reduced and as a result of the reduction in correlation, the detection performance may be degraded. 
     Three solutions to problems applying correlation to received signals with a frequency offset have been applied. One solution is nearly optimal, but highly complex. The other two solutions are less complicated, but experience suboptimal performance. 
     The first solution discussed may be referred to as a “brute force” approach where a search is performed over time and frequency. Instead of performing a single correlation as shown above, a bank of correlators may be used. The input to each correlator may be referred to as a signal y which has been frequency shifted by some increment. The maximization is taken over all the correlation magnitude values. In the limit of continuous time and frequency, this may be described as equivalent to: 
     
       
         
           
             
               
                 
                   
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     Typically, a discrete time and frequency approximation to (5) may be used as shown below: 
     
       
         
           
             
               
                 
                   
                     
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     For equation (6), mF represents some multiple of frequency sampling interval F. While this approach may perform well, it has replaced a single correlation with a bank of correlations, one for each discrete frequency. 
       FIG. 4  illustrates a block diagram of a conventional brute force receiver portion  400 . 
     Brute force receiver portion  400  includes a plurality of correlators with a sampling denoted as a correlator  402 , a correlator  404  and a correlator  406 , a plurality of magnitude portions with a sampling denoted as a magnitude portion  408 , a magnitude portion  410  and a magnitude portion  412  and a maximum calculation portion  414 . 
     Correlator  402 , correlator  404  and correlator  406  receive a signal via a communication channel  416  from external to brute force receiver portion  400 . Furthermore, correlator  402  receives a signal  418  representing a discrete frequency offset denoted as 1F. Correlator  404  receives a signal  426  representing a discrete frequency offset denoted as 2F. Correlator  406  receives a signal  432  representing a discrete frequency offset denoted as mF, where m represents a value of maximum increment for frequency offset F. 
     Magnitude portion  408  receives a signal  420  from correlator  402 . Magnitude portion  410  receives a signal  428  from correlator  404 . Magnitude portion  412  receives a signal  434  from correlator  406  and output a signal  424 . 
     Correlator  402 , correlator  404  and correlator  406  receives a signal via communication channel  416  for processing via a correlation algorithm. Magnitude portion  408 , magnitude portion  410  and magnitude portion  412  receives correlated signals from correlator  402 , correlator  404  and correlator  406 , respectively, for performing a magnitude calculation. Finally, maximum calculation portion  414  receives a signal which has had a correlation calculation and magnitude calculation performed via a signal  422 , a signal  430  and a signal  436 . Maximum calculation portion  414  determines which received signal has the largest magnitude. The signal with the largest magnitude and a value larger than a certain threshold may then be processed for timing information for retrieving received data information as received via communication channel  416 . 
     While application of the brute force correlation method may perform well, it has replaced a single correlation with a bank of correlations, one for each discrete frequency. In other words, a correlator may search for the entire Unique Word over all frequencies and all times. Application of the brute force correlation method is very expensive to implement, especially in environments where size, weight, power consumption and power dissipation are considered a premium, such as in satellite or military applications. 
     A second approach for processing a correlation of a received signal is to break the correlation into shorter correlation intervals, and then combine the outputs of these subintervals non-coherently as shown below: 
     
       
         
           
             
               
                 
                   
                     
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       FIG. 5  illustrates a block diagram of a conventional non-coherent receiver portion  500 . 
     Conventional non-coherent receiver portion  500  includes a unique word portion  504 , a plurality of sub-correlators with a sampling denoted as a sub-correlator  506 , a sub-correlator  508  and a sub-corrclator  510 , a plurality of delay portions with a sampling denoted as a delay portion  512 , a delay portion  514  and a delay portion  516 , a plurality of magnitude portions with a sampling denoted as a magnitude portion  518 , a magnitude portion  520  and a magnitude portion  522  and a summation portion  524 . 
     Sub-correlator  506  receives a signal from a communication channel  526  and receives a signal  552  from unique word portion  504 . Magnitude portion  518  receives a signal  528  from sub-correlator  506 . Delay portion  512  receives a signal from communication channel  526 . Sub-correlator  508  receives a signal  532  from delay portion  512  and a signal  550  from unique word portion  504 . Magnitude portion  520  receives a signal  534  from sub-correlator  508 . Delay portion  514  receives signal  532  from delay portion  512 . Delay portion  516  receives a signal  538  generated from a plurality of delay portions. Sub-correlator  510  receives a signal from delay portion  516  via a signal  540  and from unique word portion  504  via a signal  548 . Magnitude portion  522  receives a signal  542  from sub-correlator  510 . Summation portion  524  receives a signal from magnitude portion  518  via a signal  530 , from magnitude portion  520  via a signal  536 , from magnitude portion  522  via a signal  544  and from a plurality of other magnitude portions not shown. 
     Unique word portion  504  includes a plurality of unique word sub-portions with a sampling denoted as a unique word sub-portion  554 , a unique word sub-portion  556  and a unique word sub-portion  558 . Unique word sub-portion  554  includes a plurality of symbols with a sampling denoted as a symbol  560  and a symbol  562 . Unique word sub-portion  556  includes a plurality of symbols with a sampling denoted as a symbol  564  and a symbol  566 . Unique word sub-portion  558  includes a plurality of symbols with a sampling denoted as a symbol  568  and a symbol  570 . 
     Unique word portion  504  is configured with respect to an x-axis  502  with units of time and resolution of seconds. Unique word portion  504  represents a predetermined sequence of symbols to be received in order to perform synchronization, decoding and processing. Symbols of unique word sub-portions correspond to a relation with respect to x-axis  502  for order of transmission and arrival. For example symbol  560  of unique word sub-portion  554  may be considered the first symbol to be received for a frame of data provided from a transmitter, whereas, symbol  570  of unique word sub-portion  558  may be considered the last received symbol for the unique word portion of a frame with payload symbols to follow. 
     Sub-correlator  506  receives a signal via communication channel  526  and performs a correlation of the received signal with the symbols received from unique word sub-portion  558 . Sub-correlator  508  receives a delayed signal from communication channel  526  via delay portion  512  and performs a correlation of the delayed received signal with the symbols of unique word sub-portion  556 . Sub-correlator  510  receives a multiplied delayed signal from communication channel  526  and performs a correlation of the delayed received signal with the symbols of unique word sub-portion  554 . 
     Magnitude portion  518  receives a signal from sub-correlator  506  and performs a magnitude calculation. Magnitude portion  520  receives a signal from sub-correlator  508  and performs a magnitude calculation. Magnitude portion  522  receives a signal from sub-correlator  510  and performs a magnitude calculation. Summation portion  524  receives a set of magnitude calculations from magnitude portion  518 , magnitude portion  520 , magnitude portion  522  and a plurality of other magnitude portions not shown and performs a summation calculation. The summation calculation may be compared to threshold in order to determine if a unique word has been received as denoted by the configuration of unique word portion  504 . Once the threshold has been achieved, the signal received via communication channel  526  may then be processed for timing information for retrieving received data information as received via communication channel  526 . 
     With the conventional non-coherent receiver approach, a single correlator may be required, however the drawback is that the performance of the correlator in noisy conditions is degraded due to the non-coherent summation performed for the sub-correlations. 
     A third approach for processing a correlation of a received signal is to apply differential detection. For differential detection, a differential detection operation is performed on the received sequence of symbols to form a new sequence described as:
 
y′ i =y i y* i−1   (8)
 
     The new sequence is then correlated with an expected differential sequence described as:
 
x′ i x=x i x* i−1   (9)
 
       FIG. 6  illustrates a block diagram of a conventional differential detection receiver portion  600 . 
     Conventional differential detection receiver portion  600  includes a delay  602 , a differential portion  604 , a unique word portion  606 , a delay  608 , a differential portion  610  and a correlator  612 . 
     Delay  602  receives a signal via a communication channel  614 . Differential portion  604  receives a signal from communication channel  614  and a delayed version of the signal from delay  602  via a signal  616 . Delay  608  receives a signal  620  from unique word portion  606 . Differential portion  610  receives a signal  622  from unique word portion  606  and a delayed or shifted version of unique word from delay  608  via a signal  624 . Correlator portion  612  receives a received differential signal from differential portion  604  via a signal  618  and an expected differential signal from differential portion  610  via a signal  626 . Correlator  612  provides a signal external to conventional differential detection receiver portion  600  via signal  618 . 
     Unique word portion  606  provides storage for an expected unique word to be received via communication channel  614 . Delay  608  provides a delayed or shifted version of unique word portion  606 . Differential portion  610  performs a differential operation on the unique word stored in unique word portion  606  and a delayed or shifted version of the unique word stored in unique word portion  606 . Delay  602  provides a delayed version of the signal received via communication channel  614 . Differential portion  604  performs a differential operation on the signal received via communication channel  614  and the delayed version of the signal received from delay  602 . Correlator  612  performs a correlation operation on the differential operation performed on the unique word stored in unique word portion  606  and the differential operation performed on the signal received via communication channel  614  and the delayed version of the signal received via communication channel  614 . 
     Signal  628  generated by correlator  612  is compared to a threshold in order to determine if a unique word has been received as denoted by the configuration of unique word portion  606 . Once the threshold has been achieved, the signal received via communication channel  614  is then processed for timing information for retrieving received data information as received via communication channel  614 . 
     An advantage of the conventional differential detection approach is that it is inherently insensitive to issues related to frequency offsets. However, the drawback to this approach is it can suffer a significant performance loss due to the differential detection step. Furthermore, the losses due to differential detection increase as the signal-to-noise ratio decreases. 
     What is needed is a system and method for optimally or near optimally detecting and decoding information embedded in a signal without necessitating a large numbcr of correlator banks for implementation. 
     BRIEF SUMMARY 
     The present invention provides a system and method for nearly optimal performance for searching a signal over both time and frequency, and for decoding and processing information embedded within the received signal. 
     In accordance with an aspect of the present invention, a system and method is provided for use with a frequency band including a transmission frequency and a received frequency. The transmission frequency includes a transmission signal having a transmitted unique word therein. The received frequency includes a received signal having a received unique word therein, wherein the received unique word had been received at a received time and at a received phase. The system includes a first sub-correlator, a second sub-correlator and a discrete Fourier transform device. The first sub-correlator can perform a first correlation of only a first portion of the received unique word with a corresponding first portion of the transmitted unique word over a plurality of instances of time and can output a first plurality of sub-correlation values. The second sub-correlator can perform a second correlation of only a second portion of the received unique word with a corresponding second portion of the transmitted unique word over the plurality of instances of time and can output a second plurality of sub-correlation values. The discrete Fourier transform device can perform a discrete Fourier transform over a plurality of frequencies within the frequency hand on the first plurality of sub-correlation values and can perform a discrete Fourier transform over the plurality of frequencies within the frequency band on the second plurality of sub-correlation values. The first portion of the received unique word is different from the second portion of the received unique word 
     Additional advantages and novel features of the invention are set forth in part in the description which follows, and in part will become apparent to those skilled in the art upon examination of the following or may be learned by practice of the invention. The advantages of the invention may be realized and attained by means of the instrumentalities and combinations particularly pointed out in the appended claims. 
    
    
     
       BRIEF SUMMARY OF THE DRAWINGS 
       The accompanying drawings, which are incorporated in and form a part of the specification, illustrate an exemplary embodiment of the present invention and, together with the description, serve to explain the principles of the invention. In the drawings: 
         FIG. 1  illustrates a block diagram of a conventional communication system; 
         FIG. 2  illustrates a conventional transmission of a communications protocol by a transmitter as shown in  FIG. 1 ; 
         FIG. 3  illustrates a conventional continuous correlation operation; 
         FIG. 4  illustrates a block diagram of a conventional brute force receiver portion; 
         FIG. 5  illustrates a block diagram of a conventional non-coherent receiver portion; 
         FIG. 6  illustrates a block diagram of a conventional differential detection receiver portion; 
         FIG. 7  illustrates a block diagram of an example communication receiver portion, in accordance with an aspect of the present invention; 
         FIG. 8  illustrates a detailed version of an example data recovery portion as shown in  FIG. 7 , in accordance with an aspect of the present invention; 
         FIG. 9  illustrates a detailed version of an example sub-correlator portion as shown in  FIG. 8 , in accordance with an aspect of the present invention; 
         FIG. 10  illustrates a detailed version of an example digital Fourier transform DFT portion as shown in  FIG. 8 , in accordance with an aspect of the present invention; 
         FIG. 11  illustrates a detailed version of an example phase-shift portion as shown in  FIG. 10 , in accordance with an aspect of the present invention; 
         FIG. 12  illustrates a detailed version of an example magnitude portion as shown in  FIG. 8 , in accordance with an aspect of the present invention; 
         FIG. 13  illustrates a detailed version of an example data processor as shown in  FIG. 8 , in accordance with an aspect of the present invention; 
         FIG. 14  illustrates an example matrix of magnitude information as calculated by a data recovery portion as shown in  FIGS. 7-8 , in accordance with an aspect of the present invention; and 
         FIGS. 15A-B  illustrate an example method for operation of a data processor as shown in  FIG. 8  and  FIG. 13 , in accordance with an aspect of the present invention. 
     
    
    
     DETAILED DESCRIPTION 
     Generally a demodulator receives a waveform and outputs either hard decisions, i.e., binary 1 and binary 0, or outputs soft decisions, values determined to be either a binary 1 and binary 0. In particular, a burst-mode demodulator includes two functions: first, it estimates parameters needed to decode a signal, e.g., time of the burst, frequency of the burst, phase, etc.; and then 2) using the estimates, there is a demodulation process, e.g, similar to a continuous mode demodulation. Aspects of the present invention are drawn to the first function of a burst-mode demodulator, i.e., estimating parameters of the burst. 
     An aspect of the present invention provides nearly optimal performance for searching a signal over both time and frequency. A correlation operation may be performed between the received signal and a predetermined unique word. In the prior art brute force method discussed above, an entire received unique word is correlated over a plurality of time instances and over a plurality of frequencies. On the contrary, in accordance with the present invention, the unique word is divided into segments. Then, each segment is correlated over the plurality of time instances as a plurality of sub-correlations. The plurality of sub-correlations is then correlated over the plurality of frequencies by way of a discrete Fourier transform (DFT). Consequently, the entire unique word is only correlated once over the plurality of time instances and over the plurality of frequencies. Furthermore, the result of the phase shift and DFT performed for the sub-correlations may be considered a matrix of complex-values organized by time and frequency. 
     In other embodiments of the present invention, a method and system will be described for performing a magnitude calculation for the results following the performance of the DFT as described for the first embodiment and for determining time and frequency offset to provide for decoding information embedded in a received signal. 
     The matrix of real-valued magnitude information organized by time and frequency may be stored for processing. The stored information may be retrieved and processed. Non-limiting example of processing performed may include threshold detection and matrix operations. For determination of a matrix element with a magnitude value greater than a threshold, a time and frequency offset may be ascertained. 
     Further processing may include examining neighboring values of the element of the matrix with the maximum value for purposes of further refining the time and frequency offset. For a determination of significant neighboring values to the maximum value, an interpolation may be performed for ascertaining a more accurate representation for the time and frequency offset. 
     The resulting time and frequency offset information may be used for decoding the embedded information located within the received signal. The decoded information may be delivered for a use of some purpose. 
     Initial discussion will focus on explaining the time element of the present invention. The output of the correlator at time j may be described as: 
     
       
         
           
             
               
                 
                   
                     c 
                     j 
                   
                   = 
                   
                     
                       ∑ 
                       n 
                       
                           
                       
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         y 
                         
                           n 
                           + 
                           j 
                         
                       
                       ⁢ 
                       
                         x 
                         n 
                         * 
                       
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
     Where x and y in equation (10) are generally complex-valued. The variable x may describe a sequence of predetermined symbols of a unique word and variable y may represent a received sequence of symbols. Equation (10) may describe the discrete correlation of y and x as denoted by the summation of the sequence of y multiplied by the sequence of x. 
     The discussion for frequency will now be considered as described by: 
     
       
         
           
             
               
                 
                   
                     c 
                     
                       j 
                       , 
                       k 
                     
                   
                   = 
                   
                     
                       ∑ 
                       n 
                       
                           
                       
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         y 
                         
                           n 
                           + 
                           j 
                         
                       
                       ⁢ 
                       
                         x 
                         n 
                         * 
                       
                       ⁢ 
                       
                         ⅇ 
                         
                           
                             - 
                             ⅈ2π 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           nkF 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
     For equation (11), F may describe a frequency increment, j may represent a time index and k may represent a frequency index. 
     The summation calculation as performed by equation (11) may be broken up into summations of smaller intervals as described by: 
     
       
         
           
             
               
                 
                   
                     c 
                     
                       j 
                       , 
                       k 
                       , 
                       l 
                     
                   
                   = 
                   
                     
                       ∑ 
                       
                         n 
                         = 
                         
                           lL 
                           - 
                           1 
                         
                       
                       
                         
                           
                             ( 
                             
                               l 
                               + 
                               1 
                             
                             ) 
                           
                           ⁢ 
                           L 
                         
                         - 
                         1 
                       
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         y 
                         
                           n 
                           + 
                           j 
                         
                       
                       ⁢ 
                       
                         x 
                         n 
                         * 
                       
                       ⁢ 
                       
                         ⅇ 
                         
                           
                             - 
                             ⅈ2π 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           nkF 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
     For equation (12), l may represent an index over the subintervals. 
     The complete correlation for each time and frequency may be described as the summation over all of the smaller intervals as described by: 
     
       
         
           
             
               
                 
                   
                     c 
                     
                       j 
                       , 
                       k 
                     
                   
                   = 
                   
                     
                       ∑ 
                       l 
                       
                           
                       
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       c 
                       
                         j 
                         , 
                         k 
                         , 
                         l 
                       
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
     The substitution of equation (12) into equation (13) may be described as: 
     
       
         
           
             
               
                 
                   
                     c 
                     
                       j 
                       , 
                       k 
                     
                   
                   = 
                   
                     
                       ∑ 
                       l 
                       
                           
                       
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         ∑ 
                         
                           n 
                           = 
                           
                             lL 
                             - 
                             1 
                           
                         
                         
                           
                             
                               ( 
                               
                                 l 
                                 + 
                                 1 
                               
                               ) 
                             
                             ⁢ 
                             L 
                           
                           - 
                           1 
                         
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         
                           y 
                           
                             n 
                             + 
                             j 
                           
                         
                         ⁢ 
                         
                           x 
                           n 
                           * 
                         
                         ⁢ 
                         
                           ⅇ 
                           
                             
                               - 
                               ⅈ2π 
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             nkF 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
           
         
       
     
     For equation (14), l may operate as an index over the subintervals. 
     The length of each subinterval for equation (14), as denoted by L, may be chosen small enough such that the change in phase factor e −i2πnkF  over the interval may be considered as small. Furthermore, since the contribution of the phase factor is very small for small subintervals, the phase factor may be removed from the inner summation to the outer summation as described by: 
     
       
         
           
             
               
                 
                   
                     c 
                     
                       j 
                       , 
                       k 
                     
                   
                   = 
                   
                     
                       ∑ 
                       l 
                       
                           
                       
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         ⅇ 
                         
                           
                             - 
                             ⅈ2π 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           klLF 
                         
                       
                       ⁢ 
                       
                         
                           ∑ 
                           
                             n 
                             = 
                             
                               lL 
                               - 
                               1 
                             
                           
                           
                             
                               
                                 ( 
                                 
                                   l 
                                   + 
                                   1 
                                 
                                 ) 
                               
                               ⁢ 
                               L 
                             
                             - 
                             1 
                           
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           
                             y 
                             
                               n 
                               + 
                               j 
                             
                           
                           ⁢ 
                           
                             x 
                             n 
                             * 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
           
         
       
     
     Taking into account the change in phase between the subintervals may be considered as 2πkLF, equation (15) may be further simplified as described by: 
     
       
         
           
             
               
                 
                   
                     c 
                     
                       j 
                       , 
                       k 
                     
                   
                   = 
                   
                     
                       ∑ 
                       l 
                       
                           
                       
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         ⅇ 
                         
                           
                             - 
                             ⅈ2π 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           klLF 
                         
                       
                       ⁢ 
                       
                         c 
                         
                           j 
                           , 
                           0 
                           , 
                           l 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
           
         
       
     
     The length of the subcorrelation, as denoted by L, may be chosen small enough such that the loss as described by equation (4) may be considered acceptably small. This approach may produce a similar result as described previously with respect to the brute force approach, albeit with a small loss as described by equation (4). Furthermore, the result of this approach may operate using a single correlator instead of a bank of correlators as used for the brute force approach. 
     Equation (16) has the form of a discrete Fourier transform (DFT). Thus, a DFT may be performed for the results generated from performing the subinterval correlations. 
     In summary, the correlation sequence x and input sequence y are divided into l segments of length L. The correlation calculation for the segments may be considered a vector of length M (i.e. r xy (j), j=0 . . . M−1). The DFT may be applied over the l segments for each time index j. The resulting output of the DFT may be considered a 2-dimensional complex-valued matrix over time and frequency. For signals with unknown phase, a magnitude calculation may be performed for the output of the DFT, resulting in a 2-dimensional matrix of real-valued magnitudes over time and frequency. The resulting 2-dimensional matrix may be processed dependant upon the application. For example, to find the highest correlation magnitude over time and frequency, the 2-dimensional matrix may be searched for the highest value of magnitude. 
     A more detailed discussion for an exemplary embodiment of the present invention will now be described with respect to  FIGS. 7-15 . 
       FIG. 7  illustrates a block diagram of an example communication receiver portion  700 , in accordance with an aspect of the present invention. 
     Communication receiver portion  700  includes a filter portion  702 , a parameter estimator  704  and a demodulator portion  706 . Each of the elements of communication receiver portion  700  are illustrated as individual devices, however, in some embodiments of the present invention at least two of filter portion  702 , parameter estimator  704  and demodulator portion  706  may be combined as a unitary device. 
     Filter portion  702  may receive a communication signal via a communication channel  708 . Parameter estimator  704  may receive information from filter portion  702  via a signal  710 . Demodulator portion  706  may receive information from parameter estimator  704  via a signal  712 . 
     Filter portion  702  may receive a communication signal via communication channel  708  and perform a filtering function or functions on the received communication signal. Non-limiting examples of filtering which may be performed include band pass, high pass and low pass. 
     Parameter estimator  704  may receive the filtered signal from filter portion  702  and perform a demodulation function or functions. Non-limiting examples of demodulation which may be performed include Amplitude, Frequency and Phase-shift Demodulation. 
     Demodulator portion  706  receives the demodulated signal from parameter estimator  704 , performs processing for data recovery and receives recovered data and information via a signal  712 . Non-limiting examples of processes which may be applied include mixing, correlating, delaying, matching, multiplying, performing magnitude calculations, phase shifting, performing summation calculations, performing matrix operations, performing DFT calculations, performing complex conjugate calculations and performing interpolation calculations. 
     Communication receiver portion  700  may receive a communication signal via communication channel  708  and process the received signal such that the transmitted signal may be recovered and transmitted via signal  714 . 
       FIG. 8  illustrates a detailed version of example parameter estimator  704  and demodulator portion  706  ( FIG. 7 ), in accordance with an aspect of the present invention. 
     Parameter estimator  704  includes a unique word portion  804 , plurality of correlators with a sampling denoted as a sub-correlator portion  806 , a sub-correlator portion  808  and a sub-correlator portion  810 , a plurality of delay portions with a sampling denoted as a delay portion  812 , a delay portion  814  and a delay portion  816 , a DFT portion  818 , a plurality of magnitude portions, with a sampling denoted as a magnitude portion  820 , a magnitude portion  822  and a magnitude portion  824  and a signal parameter estimator  826 . Each of the elements of parameter estimator  704  are illustrated as individual devices, however, in some embodiments of the present invention at least two of unique word portion  804 , plurality of correlators with a sampling denoted as sub-correlator portion  806 , sub-correlator portion  808  and sub-correlator portion  810 , plurality of delay portions with a sampling denoted as delay portion  812 , delay portion  814  and delay portion  816 , DFT portion  818 , plurality of magnitude portions, with a sampling denoted as magnitude portion  820 , magnitude portion  822  and magnitude portion  824  and signal parameter estimator  826  may be combined as a unitary device. 
     Sub-correlator portion  806  may receive information via a signal  828  generated external to parameter estimator  704  and receive a signal  860  from unique word portion  804 . Sub-correlator portion  806  may then correlate signal  828  with signal  860  to generate signal  836 . Delay portion  812  may receive information via signal  828 . Sub-correlator portion  808  may receive a signal  830  from delay portion  812  and a signal  858  from unique word portion  804 . Sub-correlator portion  808  may then correlate signal  830  with signal  858  to generate signal  838 . Delay portion  814  may receive signal  830  from delay portion  812  and provide an output signal  831  to other delay portions (not shown). Delay portion  816  may receive a signal  832  from other delay portions (not shown). Sub-correlator portion  810  may receive a signal  834  from delay portion  816  and a signal  856  from unique word portion  804 . Sub-correlator portion  810  may then correlate signal  834  with signal  856  to generate signal  840 . DFT portion  818  may receive a signal  836  from sub-correlator portion  806 , a signal  838  from sub-correlator portion  808 , a signal  840  from sub-correlator portion  810  and a plurality of signals from other sub-correlator portions (not shown). Magnitude portion  820  may receive a signal  842  from DFT portion  818 . Magnitude portion  822  may receive a signal  844  from DFT portion  818 . Magnitude portion  824  may receive a signal  846  from DFT portion  818 . A plurality of other magnitude portions (not shown) may receive signals from DFT portion  818 . Signal parameter estimator  826  may receive a signal  848  from magnitude portion  820 , a signal  850  from magnitude portion  822 , a signal  852  from magnitude portion  824  and a plurality of signals from other magnitude portions (not shown). Signal parameter estimator  826  may provide signal  712  for external connection from parameter estimator  704 . 
     Unique word portion  804  includes a plurality of unique word sub-portions with a sampling denoted as a unique word sub-portion  862 , a unique word sub-portion  864  and a unique word sub-portion  866 . Unique word sub-portion  862  includes a plurality of symbols with a sampling denoted as a symbol  868  and a symbol  870 . Unique word sub-portion  864  includes a plurality of symbols with a sampling denoted as a symbol  872  and a symbol  874 . Unique word sub-portion  866  includes a plurality of symbols with a sampling denoted as a symbol  876  and a symbol  878 . 
     Unique word portion  804  may be configured with respect to an x-axis  802  with units of time and resolution of seconds. Unique word portion  804  may represent a predetermined sequence of symbols to be received in order to perform synchronization, decoding and processing. Symbols of unique word sub-portions correspond to a relation with respect to x-axis  502  for order of transmission and arrival. For example symbol  868  of unique word sub-portion  862  may be considered the first symbol to be received for a frame of data provided from a transmitter, whereas, symbol  878  of unique word sub-portion  866  may be considered the last received symbol for the unique word portion of a frame with a payload of symbols to follow. 
     Sub-correlator portion  806  may receive signal  828  and perform a correlation of the received signal with the symbols received from unique word sub-portion  866 . Sub-correlator portion  808  may receive a delayed signal  828  via delay portion  812  and perform a correlation of the delayed signal with the symbols provided by unique word sub-portion  864 . Sub-correlator portion  810  may receive a multiply delayed signal of signal  828  via a plurality of delays and perform a correlation of the delayed received signal with the symbols provided by unique word sub-portion  862 . A plurality of other correlators (not shown) may receive a plurality of delayed signals (not shown) of signal  828  via a plurality of delays (not shown) and perform a correlation of the delayed received signals with the symbols provided by unique word sub-portions (not shown). 
     DFT portion  818  may received the correlated signals from sub-correlator portion  806 , sub-correlator portion  808  and sub-correlator portion  810  and from a plurality of other correlators (not shown) and perform a DFT operation on the received signals. 
     Magnitude portion  820 , magnitude portion  822 , magnitude portion  824  and a plurality of other magnitude portions (not shown) may receive signals from DFT portion  818  and perform a magnitude calculation on the received signals. 
     Signal parameter estimator  826  may receive the signals from magnitude portion  820 , magnitude portion  822 , magnitude portion  824  and a plurality of other magnitude portions (not shown) and perform processing functions. Non-limiting examples of the processing functions performed by signal parameter estimator  826  include threshold calculations, threshold comparisons, time related calculations, frequency related calculations, interpolation calculations and decoding operations. Signal  712  output from signal parameter estimator  826  may include estimates of parameters needed to demodulate the received signal. Non-limiting examples of parameters includes signal timing and frequency. Demodulator  706  may then use the estimates within signal  712  to demodulate unique word  804  and the payload to output signal  714 . 
     Demodulator portion  706  may receive a signal containing information and perform correlations of sub-portions of the received signal with sub-portions of a unique word. A DFT portion may receive the results of the sub-correlation operations and perform a DFT operation. Magnitude portions may receive the results of the DFT operation and perform magnitude calculations. A data processor portion may receive the magnitude calculations and perform processing of the magnitude information to recover data information from the received signal. 
       FIG. 9  illustrates a detailed version of example sub-correlator portion  806  ( FIG. 8 ), in accordance with an aspect of the present invention. 
     Sub-correlator portion  808  ( FIG. 8 ), sub-correlator portion  810  ( FIG. 8 ) and a plurality of sub-correlator portions (not shown) may also be described by the illustration of  FIG. 9 . 
     Sub-correlator portion  806  includes a multiplier portion  902  and a summation portion  904 . Each of the elements of sub-correlator portion  806  are illustrated as individual devices, however, in some embodiments of the present invention at least two of multiplier portion  902  and summation portion  904  may be combined as a unitary device. 
     Multiplier portion  902  may receive a data signal  906  and a unique word signal  908  generated external to sub-correlator portion  810 . Summation portion  904  may receive a signal  910  from multiplier portion  902  and provide a signal  912  for external connection from sub-correlator portion  806 . 
     Multiplier portion  902  may perform a multiplication operation of information received from data signal  906  with information received from unique word signal  908 . Summation portion  904  may receive the multiplication information generated by multiplier portion  902  and perform a summation operation. 
     Sub-correlator portion  806  may receive data information and unique word information and perform a multiplication of the received information. Furthermore, sub-correlator portion  806  may perform a summation calculation for the information generated from the multiplication operation. 
       FIG. 10  illustrates a detailed version of example DFT portion  818  ( FIG. 8 ), in accordance with an aspect of the present invention. 
     DFT portion  818  includes a plurality of phase-shift portions, with a sampling denoted as a phase-shift portion  1002 , a phase-shift portion  1004 , a phase-shift portion  1006 , a plurality of phase-shift coefficients, with a sampling denoted as a phase-shift coefficient  1008 , a phase-shift coefficient  1010  and a phase-shift coefficient  1012 . Each of the elements of DFT portion  818  are illustrated as individual devices, however, in some embodiments of the present invention at least two of phase-shift portion  1002 , phase-shift portion  1004 , phase-shift portion  1006 , a plurality of phase-shift coefficients, with a sampling denoted as phase-shift coefficient  1008 , phase-shift coefficient  1010  and phase-shift coefficient  1012  may be combined as a unitary device. 
     Phase-shift portion  1002  may receive a signal  1014  generated from external to DFT portion  818 , receive a phase-shift coefficient from phase-shift coefficient  1008  via a signal  1016  and provide a signal  1018  for connection external to DFT portion  818 . Phase-shift portion  1002  may receive a signal  1020  from generated external to OFT portion  818 , receive a phase-shift coefficient from phase-shift coefficient  1010  via a signal  1022  and provide a signal  1024  for connection external to DFT portion  818 . Phase-shift portion  1006  may receive a signal  1026  generated from external to DFT portion  818 , receive a phase-shift coefficient from phase-shift coefficient  1012  via a signal  1028  and provide a signal  1030  for connection external to DFT portion  818 . A plurality of phase-shift portions (not shown) may receive a plurality of signals generated from external to DFT portion  818  (not shown), may receive a plurality of phase-shift coefficients from a plurality of phase-shift coefficient portions (now shown) via a plurality of signals (now shown) and provide a plurality of signals (not shown) for connection external to OFT portion  818 . 
     Phase-shift portion  1002 , phase-shift portion  1004 , phase-shift portion  1006  and a plurality of phase-shift portions (not shown) may perform a phase shift as denoted by a received phase-shift coefficient, perform a DFT for a received signal and deliver the results of the combined phase-shift and DFT operation external to OFT portion  818 . 
     DFT portion  818  may receive a plurality of signals delivering sub-correlations performed between sub-signals and unique word sub-portions. Furthermore, a plurality of differing phase shift operations and DFT operations may be applied to the received sub-correlations for generating a plurality of signals  842 ,  844  and  846 . 
       FIG. 11  illustrates a detailed version of example phase-shift portion  1002  ( FIG. 10 ), in accordance with an aspect of the present invention. 
     Phase-shift portion  1004  ( FIG. 10 ), phase-shift portion  1006  ( FIG. 10 ) and a plurality of phase-shift portions (not shown) may also be described by the illustration of  FIG. 11 . 
     Phase-shift portion  1002  includes a coefficient select portion  1102 , a coefficients portion  1104 , a multiplier portion  1106  and a summation portion  1108 . Each of the elements of phase-shift portion  1002  are illustrated as individual devices, however, in some embodiments of the present invention at least two of coefficient select portion  1102 , coefficients portion  1104 , multiplier portion  1106  and summation portion  1108  may be combined as a unitary device. 
     Coefficient select portion  1102  may receive a signal  1110  generated external to phase-shift portion  1002  and may receive a signal  1112  from coefficients portion  1104 . Multiplier portion  1106  may receive a signal  1114  generated external to phase-shift portion  1002  and a signal  1116  from coefficient select portion  1102 . Summation portion  1108  may receive a signal  1118  from multiplier portion  1106  and generate a signal  1120  for delivery external to phase-shift portion  1002 . 
     Coefficient select portion  1102  may receive a coefficient indication from external to phase-shift portion  1002  for selecting a group of coefficients from coefficients portion  1104  for delivery to multiplier portion  1106 . Multiplier portion  1106  may receive the selected group of coefficients from coefficient select portion  1102  and receive a sub-correlation calculation generated external to phase-shift portion  1002  and perform a multiplication of the received signal with the selected group of coefficients. Summation portion  1108  may receive the multiplication calculation performed by multiplier portion  1106  and provide the summation result external to phase-shift portion  1002 . 
       FIG. 12  illustrates a detailed version of example magnitude portion  820  ( FIG. 8 ), in accordance with an aspect of the present invention. 
     Magnitude portion  822  ( FIG. 8 ), magnitude portion  824  ( FIG. 8 ) and a plurality of magnitude portions (not shown) may also be described by the illustration of  FIG. 12 . 
     Magnitude portion  822  includes a complex conjugate portion  1202  and a multiplier portion  1204 . Each of the elements of magnitude portion  822  are illustrated as individual devices, however, in some embodiments of the present invention at least two of complex conjugate portion  1202  and multiplier portion  1204  may be combined as a unitary device. 
     Complex conjugate portion  1202  may receive a signal  1206  generated external to magnitude portion  822 . Multiplier portion  1204  may receive signal  1206  generated external to magnitude portion  822 , a signal  1208  from complex conjugate portion  1202  and provide a signal  1210  for delivery external to complex conjugate portion  1202 . 
     Magnitude portion  822  may receive a signal generated from external to magnitude portion  822 , perform a complex conjugate operation for the received signal, perform a multiplication operate of the received signal and the complex conjugate calculation to generate a magnitude calculation for the received signal. Furthermore, the magnitude calculation may be provided for delivery external to magnitude portion  822 . 
     As an example, magnitude portion  822  may receive a value of (2+j3) in order to determine the magnitude. Complex conjugate portion  1202  may calculate the complex conjugate for (2+j3) denoted as (2−j3). Multiplier portion  1204  may then multiply (2+j3)*(2−j3) and generate a magnitude value of 13 for delivery external to magnitude portion  822 . 
       FIG. 13  illustrates a detailed version of example signal parameter estimator  826  ( FIG. 8 ), in accordance with an aspect of the present invention. 
     Signal parameter estimator  826  includes a processor portion  1302  and a memory portion  1304 . Each of the elements of signal parameter estimator  826  are illustrated as individual devices, however, in some embodiments of the present invention at least two of processor portion  1302  and memory portion  1304  may be combined as a unitary device. 
     Processor portion  1302  may receive a plurality of signals containing magnitude information, with a sampling denoted as a signal  1308 , a signal  1310  and a signal  1312 , and receive a signal  1306  containing information for decoding. Processor portion  1302  may communicate bi-directionally with memory via a communication channel  1314 . 
     Processor portion  1302  may receive the plurality of signals containing magnitude information and store the magnitude information in memory portion  1304 . Processor may retrieve magnitude information from memory portion  1304  for processing. Processor portion  1302  may perform threshold calculations and comparisons for the magnitude information in order to determine the receipt and match for a unique word. Furthermore, processor portion  1302  may use the determination of a unique word match for determining synchronization information and phase information for decoding information received via signal  1306  for deliver external to signal parameter estimator  826  via a signal  1316 . 
     Non-limiting examples of the processing functions performed by signal parameter estimator  826  include threshold calculations, threshold comparisons, time related calculations, frequency related calculations, interpolation calculations and decoding operations. 
       FIG. 14  illustrates an example matrix  1402  of magnitude information as calculated by example parameter estimator  704  ( FIGS. 7-8 ), in accordance with an aspect of the present invention. 
     Matrix  1402  includes a plurality of row information with a sampling denoted as a row  1404 , a row  1406 , a row  1408 , a row  1401  and a row  1412  and a plurality of column information with a sampling denoted as a column  1414 , a column  1416 , a column  1418 , a column  1420 , a column  1422 , a column  1424  and a column  1426 . 
     The rows of matrix  1402  may be organized by frequency offset as determined by a plurality of phase-shill coefficients with a sampling denoted, referring to  FIG. 10 , as phase-shift coefficient  1008 , phase-shift coefficient  1010  and phase-shift coefficient  1012 . The columns of matrix  1402  may be organized with respect to time with the information depicted in column  1414  as being received prior to information received in other columns and with the information depicted in column  1426  as being received after information received in other columns. 
     The magnitude information as depicted in matrix  1402  may indicate a frequency offset and moment of time for synchronization with an expected unique word for a received signal. For example, the largest value of magnitude as depicted in matrix  1402  is the value of eight located at the intersection of row  1406  and column  1422 . For this example, the time and frequency offset may be determined as being with respect to the frequency offset of row  1406  and with respect to the timing of column  1422 . 
     Furthermore, the exact time and frequency for synchronization may not occur at exactly the intersection of row  1406  and column  1422 . A case of inexact synchronization may be observed by significant, but lower magnitude, values located adjacent to the largest magnitude value. For example, the next largest magnitude values of matrix  1402  are located in adjacent positions to the largest magnitude value of 8. The significant but lesser magnitude values may be observed as a value of 7 located at the intersection of row  1404  and column  1422  and by a value 6 located at the intersection of row  1406  and column  1420 . A more accurate representation for the time and frequency for synchronization may be determined by performing an interpolation calculation between the largest value of magnitude and lesser valued adjacent magnitude values. For example, the true frequency offset may be considered as between the frequency offset as denoted by column  1422  and column  1420  and the true time offset may be considered as between the time offset as denoted by row  1404  and row  1406 . 
       FIGS. 15A-B  illustrate an exemplary method  1500  for operation of signal parameter estimator  826 , in accordance with an aspect of the present invention. 
     Starting with  FIG. 15A , in the example embodiment, method  1500  starts (S 1502 ) and signal parameter estimator  826  may receive and store a matrix of information as depicted, by the exemplary embodiment as illustrated in  FIG. 14  (S 1504 ). 
     Returning to  FIG. 13 , processor portion  1302  may receive magnitude information via a plurality of signals with a sampling denoted as signal  1308 , signal  1310  and signal  1312 . Processor portion  1302  may then store received magnitude information in memory portion  1304  via communication channel  1314 . 
     Matrix of magnitude information may be retrieved and examined by processor portion  1302  (S 1506 ). 
     Processor portion  1302  may retrieve matrix of magnitude information from memory portion  1304  via communication channel  1314  and examine the elements of the retrieved matrix for magnitude elements of the matrix exceeding a predetermined threshold. 
     For a determination of not finding a value of the matrix greater than the predetermined threshold, execution of method  1500  returns to receiving and storing matrix information (S 1504 ). 
     For a determination of finding a value of the matrix greater than the predetermined threshold (S 1508 ), a determination for the frequency offset and time offset is made (S 1510 ) based upon the respective row and column of the matrix for an element or elements exceeding the predetermined threshold. 
     For example, returning to  FIG. 14 , the magnitude value of 8 located as the cross section of row  1406  and column  1422 , as depicted in exemplary matrix  1402 , may be considered as having the maximum value of all of the elements of the matrix and surpassing a threshold value of 5. Furthermore, the frequency offset may be determined approximately as being with respect to row  1406  and the time offset may be determined approximately as being with respect to column  1422 . 
     After determining a maximum magnitude for a matrix of information, the magnitude of neighboring elements to the maximum magnitude for the matrix may be examined for significance in order to determine if a more accurate estimate for the time and frequency offset may be ascertained (S 1512 ). 
     As illustrated in  FIG. 15B , for a determination of significant neighboring elements of the maximum magnitude value (S 1514 ), an interpolated value for the time and/or frequency offset may be calculated (S 1516 ). 
     For example, returning to  FIG. 14 , the magnitude value of 7 located at the cross section of row  1404  and column  1422  may be considered greater than a threshold of 5. Furthermore, the magnitude value of 6 located at the cross section of row  1406  and column  1420  may be considered greater than a threshold of 5. Based on this a more accurate approximation for the frequency offset may be determined via interpolation as being located between the frequency as indicated by row  1404  and row  1406 . Furthermore, a more accurate approximation for the time offset may be determined via interpolation as being located between the time as indicated by column  1420  and column  1422 . Any known method for interpolation calculation may be used for determining more accurate approximations for the time and frequency offset. 
     After determining a time and frequency offset, the received signal may be processed for decoding the embedded symbols (S 1518 ). 
     For example, returning to  FIG. 2 , consider frame  204 . The starting time of frame  204 , as denoted by time  208 , may be determined, as well as any frequency offset. Using the time and frequency information derived from processing unique word  216 , signal parameter estimator  826 , as illustrated in  FIG. 8 , may determine the start time of payload  218 , as denoted by time  220 . Furthermore, signal parameter estimator  826  may determine the starting time and frequency offset for each symbol of payload  218 . Furthermore, having determined the starting time and frequency offset for each symbol, signal parameter estimator  826  may determine the value of each symbol resident within payload  218 . Furthermore, signal parameter estimator  826  may transmit decode information external to communication receiver portion  700 . 
     After decoding information embedded in a signal, it may be determined whether method  1500  continues execution (S 1520 ). 
     For a determination of continuation of method  1500 , execution of method  1500  returns to receiving and storing matrix information (S 1504 ) ( FIG. 15A ). 
     For a determination of cessation of method  1500 , method  1500  terminates (S 1522 ) ( FIG. 15B ). 
     A data processor may receive a matrix of magnitude information, store information, retrieve information, process information, examine information, determine a time and frequency offset, perform interpolation operations to determine a more accurate representation of the time and frequency offset and use time and frequency offset to perform processing and decoding of information embedded within a received signal. 
     In accordance with an aspect of the present invention, a system and method has been described for receiving an encoded signal containing impairments and for providing filtering, demodulation and processing for the near optimal recovery of the encoded information embedded within the received signal. 
     The foregoing description of various preferred embodiments of the invention have been presented for purposes of illustration and description. It is not intended to be exhaustive or to limit the invention to the precise forms disclosed, and obviously many modifications and variations are possible in light of the above teaching. The example embodiments, as described above, were chosen and described in order to best explain the principles of the invention and its practical application to thereby enable others skilled in the art to best utilize the invention in various embodiments and with various modifications as are suited to the particular use contemplated. It is intended that the scope of the invention be defined by the claims appended hereto.