Abstract:
The present invention provides a novel technique for improving the performance of equalizers by reducing the effects of error propagation in equalizers that use a Viterbi Decoder. Methods and systems are described that can improve the performance of equalizers by reducing the effects of error propagation in equalizers that use a Viterbi Decoder. Systems and methods of symbol correction in prediction decision feedback equalization (“pDFE”) architectures are described. Systems are described that include one or more enhanced Viterbi decoders together with novel methods of symbol correction to obtain better system performance. Systems and methods are described that utilize dual pDFEs and can use a blending algorithm to reduce errors in symbol decoding. Dual pDFEs are described that include forward and backward Viterbi decoders wherein the backward Viterbi decoded may operate on time reversed data blocks and with some degree of latency. Forward and backward Viterbi decoders can generate different decoded symbols from the same equalized data. A blending algorithm is described for weighting results based on reliability of the respective decoded symbols. A forward-backward blender can additionally increase performance of the second pDFE by blending long delayed trellis symbols from the first Viterbi decoder with symbols output by the second Viterbi decoder.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application is a continuation of U.S. patent application Ser. No. 11/405,352, entitled “DUAL PDFE SYSTEM WITH FORWARD-BACKWARD VITERBI” and filed on Apr. 17, 2006, (U.S. Pat. No. 7,697,604), and is related to U.S. application Ser. No. 11/405,349, entitled “REDUCING EQUALIZER ERROR PROPAGATION WITH A LOW COMPLEXITY SOFT OUTPUT VITERBI DECODER” filed on Apr. 17, 2006, (U.S. Pat. No. 7,697,642), which applications are incorporated herein by reference and for all purposes. 
     
    
     BACKGROUND OF THE INVENTION 
       [0002]    1. Field of the Invention 
         [0003]    The present invention relates to decoding of trellis-encoded signals and more particularly to systems and methods of symbol correction in predictive decision feedback equalization architectures. 
         [0004]    2. Description of Related Art 
         [0005]    Since the adoption of the Advanced Television Systems Committee (“ATSC”) digital television (“DTV”) standard in 1996, there has been an ongoing effort to improve the design of receivers built for the ATSC DTV signal as described in the ATSC standard A/54 (see U.S. patent application publication 20050163209 for . . . ). Designers face major obstacles in designing receivers that might achieve good reception is the presence of multipath interference in the channel. Multipath interference affects the ability of the receiver to correctly decode transmitted symbols. Therefore, designers often add equalizers to receivers in order to cancel the effects of multipath interference and thereby improve signal reception. 
         [0006]    Referring to  FIG. 1 , in the ATSC DTV transmission system, data is transmitted in frames  10 . Each frame  10  is composed of 2 fields  11  and  12 , each field  11  and  12  having 313 segments, and each segment having 832 symbols. The first four symbols in each segment are segment sync symbols  13  having the sequence [+5, −5, −5, +5]. The first segment in each field is a field sync segment  14  and  15 . 
         [0007]    Referring to figure shown in more detail in  FIG. 2 , field sync  20  comprises segment sync  21 , a 511 symbol pseudo noise (PN511) sequence  22 , a 63 symbol pseudo noise (PN63) sequence  23 , a second PN63 sequence  24 , a third PN63 sequence  25 , and a 128 symbol sequence  26  composed of various mode, reserved, and precode symbols. The four PN sequences  22 - 25  are composed of symbols from the set {+5, −5}. In alternate fields, the three PN63 sequences  23 - 25  are the same. In the remaining fields, the first PN63  23  and third PN63  25  are the same while the second PN63  24  is inverted. 
         [0008]    As shown in  FIG. 3 , subsequent 312 segments  30  of the field  11  and  12  (referred to as data segments) are structured such that 828 symbols  32  following the four segment sync symbols  31  are trellis encoded by a 12 phase trellis encoder described in detail in ATSC standard A/54. This results in 8 level symbols derived from the alphabet {−7 −5 −3 −1 +1 +3 +5 +7}. 
         [0009]    Consider now an 8T-VSB transmitter such as is illustrated in  FIG. 4 . Input data  40  is first randomized  41 , Reed-Solomon byte wise encoded  42 , and then byte interleaved  43 . Next the data is trellis encoded by a 12-phase trellis encoder  44 . A multiplexer  45  adds the segment sync symbols and the field sync symbols to the trellis coded data at the appropriate times in the frame. Then, a pilot is inserted  46  by adding a DC level to the baseband signal and a modulator  47  modulates the resulting symbols to IF. Finally a RF upconverter  48  converts the signal for RF transmission as a vestigial sideband (VSB) signal at a symbol rate of 10.76 MHz. 
         [0010]    Now consider a baseband model of the transmission channel fed by the above transmitter. The transmitted signal has a root raised cosine spectrum with a nominal bandwidth of 5.38 MHz and an excess bandwidth of 11.5% centered at one fourth of the symbol rate (i.e., 2.69 MHz). Thus the transmitted pulse shape q(t) is complex and given by 
         [0000]        q ( t )= e   jπF     s     t/2   q   RRC ( t ), 
         [0000]    where F s  is the symbol frequency, and q RRC (t) is a real square root raised cosine pulse with an excess bandwidth of 11.5% of the channel. The pulse q(t) is referred to as the “complex root raised cosine pulse”. For the 8T-VSB system, the transmitter pulse shape q(t) and the receiver matched filter pulse shape q*(−t) are identical since q(t) is conjugate-symmetric. Thus the raised cosine pulse p(t), referred to as the “complex raised cosine pulse”, is given by 
         [0000]        p ( t )= q ( t )* q *(− t ) 
         [0000]    where * denotes convolution, and * denotes complex conjugation. The transmitted baseband signal of data rate 1/T symbols/sec can be represented as: 
         [0000]    
       
         
           
             
               
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         [0000]    where {I k εA≡{a 1 , . . . , a 8 }⊂R 1 } is the transmitted data sequence, which is a discrete 8-ary sequence taking values on the real 8-ary alphabet A. The physical channel between the transmitter and receiver is denoted c(t) and can be described by: 
         [0000]    
       
         
           
             
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         [0011]    where {c k (τ)}⊂C 1 , L ha  and L hc  are the number of maximum anti-casual and casual multipath delays, τ k  multipath delay, and δ(t) is the Dirac delta function. Hence, the overall channel impulse response is: 
         [0000]    
       
         
           
             
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         [0012]    In the 8T-VSB receiver block diagram depicted in  FIG. 5 , tuner  50  and IF filter  51  demodulate an RF signal to baseband. Timing and synchronization recovery is performed  52  and any NTSC interference is rejected  53 . Data is then equalized  54  and sent through a phase tracker  55  and trellis decoded  56 , de-interleaved  57 , Reed-Solomon decoded  58 , and finally de-randomized  59 . The matched filter output y(t) in the receiver prior to equalization is: 
         [0000]    
       
         
           
             
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         [0000]    denotes the complex (colored) noise process after the pulse matched filter, with η(t) being a zero-mean white Gaussian noise process with spectral density σ n   2  per real and imaginary part. Sampling the matched filter output y(t) at the symbol rate produces the discrete time representation of the overall communication system according to the following equation: 
         [0000]        y[n]≡y ( t )| t=nt   =ΣI   k   h[n−k]+v[n]   
         [0013]    Broadcast television channels are a relatively severe multipath environment due to a variety of conditions encountered in the channel and at the receiver. Only 728 symbols of a VSB field sync segment are known a priori and can be used as a training sequence for an adaptive equalizer. The channel is not known a priori, so the equalizer in the receiver must be able to adaptively identify and combat the various channel conditions. Since multipath signals in the broadcast channel may arrive many symbols after the main signal, the decision feedback equalizer (DFE) is invariably used in 8T-VSB applications. Another DFE structure that is well known is the noise predictive decision feedback equalizer (pDFE). Although both DFEs and pDFEs are good at combating multipath channels, both have the problem of error propagation. Error propagation occurs when there are errors in the feedback path. This, in turn, feeds erroneous data into the decision device resulting in incorrect symbol decisions. For 8T-VSB applications, the most commonly used decision device is the Viterbi Decoder. Therefore it is important to mitigate the effects of error propagation. 
         [0014]    Since the 8T-VSB symbols are convolutionally coded, they may be decoded in the receiver with a Viterbi decoder [ATSC Standard A/54, U.S. Pat. No. 5,600,677, U.S. Pat. No. 5,583,889]. The Viterbi Algorithm (VA) for maximum likelihood sequence estimation of transmitted symbols corrupted by white noise is very well known (see “The Viterbi Algorithm”, G. D. Forney, Jr., Proc. IEEE, vol. 61, pp. 268-278, March 1973, “Digital Communications—Fundamentals and Applications”, Bernard Sklar, Prentice-Hall, 1988). The decoder may equivalently provide estimates of the encoded bit pairs or estimates of the mapped 8 level symbols, the later being utilized in the context of an equalizer. As is well known, the VA requires a path history memory for each state and involves add, compare, select operations based on trellis path metrics determined from sums of Euclidean distance branch metrics. As time advances, the most likely trellis paths (as indicated by the lowest path metrics) into each state of the trellis are saved, the rest are discarded. If the decoding algorithm searches back sufficiently deep in the trellis path memory, the result of discarding less likely paths—leaving only survivor paths—is a single surviving branch which defines the most likely symbol (hard symbol decision) at that prior point in time. At shallower path memory trace back depths (closer to the present time), there is a higher likelihood of multiple surviving branches with symbol probabilities proportional to the corresponding path metrics. 
       BRIEF SUMMARY OF THE INVENTION 
       [0015]    The present invention provides a novel technique for improving the performance of equalizers by reducing the effects of error propagation in equalizers that use a Viterbi Decoder. Systems and methods of symbol correction in predictive decision feedback equalization (“pDFE”) architectures are provided. More particularly, embodiments of the invention are described that include one or more enhanced Viterbi decoders together with novel methods of symbol correction to obtain better system performance. Embodiments of the invention utilize dual pDFEs and, in some embodiments, a blending algorithm reduces errors in symbol decoding. 
         [0016]    Dual pDFEs are described that include forward and backward Viterbi decoders. The backward Viterbi decoder typically operates on time reversed data blocks and with a degree of latency. Under certain conditions, forward and backward Viterbi decoders can generate different decoded symbols from the same equalized data. The potential for unequal results typically increases under heavy multipath conditions. In certain embodiments, a blending algorithm is provided for weighting results based on reliability of the respective decoded symbols. A forward-backward blender can additionally increase performance of the second pDFE by blending long delayed trellis symbols from the first Viterbi decoder with symbols output by the second Viterbi decoder. 
         [0017]    The present invention provides a novel technique for improving the performance of equalizers by reducing the effects of error propagation in equalizers that use a Viterbi Decoder. The foregoing and other aspects of various embodiments of the present invention will be apparent through examination of the following detailed description thereof in conjunction with the accompanying drawings. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0018]    The present invention is illustrated by way of example, and not limitation, in the figures of the accompanying drawings in which like references denote similar elements, and in which: 
           [0019]      FIG. 1  depicts a frame in an ATSC DTV transmission system; 
           [0020]      FIG. 2  depicts a field sync segment in a frame in an ATSC DTV transmission system; 
           [0021]      FIG. 3  depicts a data segment in a frame in an ATSC DTV transmission system; 
           [0022]      FIG. 4 . illustrates an 8T-VSB transmitter; 
           [0023]      FIG. 5  shows an 8T-VSB receiver block diagram; 
           [0024]      FIG. 6  illustrates predictive decision feedback equalization as included in certain embodiments of the invention; 
           [0025]      FIG. 7  depicts an example of an embodiment of the invention comprising dual pDFEs; 
           [0026]      FIG. 8  illustrates the relationship between data blocks in the embodiment illustrated in  FIG. 7 ; and 
           [0027]      FIG. 9  depicts an 8-state trellis diagram for an 8T-VSB system. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0028]    Embodiments of the present invention will now be described in detail with reference to the drawings, which are provided as illustrative examples so as to enable those skilled in the art to practice the invention. Notably, the figures and examples below are not meant to limit the scope of the present invention. Wherever convenient, the same reference numbers will be used throughout the drawings to refer to same or like parts. Where certain elements of these embodiments can be partially or fully implemented using known components, only those portions of such known components that are necessary for an understanding of the present invention will be described, and detailed descriptions of other portions of such known components will be omitted so as not to obscure the invention. Further, the present invention encompasses present and future known equivalents to the components referred to herein by way of illustration. 
         [0029]    Certain embodiments provide systems and methods of symbol correction in pDFE architectures. Certain of the methods and systems described can also be applied to conventional decision feedback equalization (“DFE”) architectures. Thus, it will be appreciated that systems and methods described in the context of pDFE architectures in this description can be applied to DFE architectures. Descriptions in the context of pDFE architectures permit a more complete yet efficient discussion of certain aspects of the invention. 
         [0030]    Embodiments of the invention include two or more Viterbi decoders. Viterbi decoders typically implement a Viterbi algorithm (“VA”) that can be described as follows for an S state trellis with a path memory of length M for each state that holds a sequence of state transitions and associated branch metrics:
       At each time increment n
           For each trellis state k
               Calculate the Euclidean branch metric for each branch into state k from all possible prior states at time (n−1)   Add the above branch metrics to the associated path metrics for each possible prior state at time (n−1)   Choose the path into state k at time n with the best path metric and store the path and the metric in the path memory associated with state k (overwriting the previous stored path)   
               Decode symbol
               Examine path memory back to time (n−M); if M is large enough, the path memories for each of the S states will show the same state transition at time (n−M) and hence indicate the same symbol; choose that symbol as the hard decision   If the state transitions for time (n−M) are not the same, choose the state transition (and hence the symbol) corresponding to the path that has the best path metric from time (n−M) to time n   
               
               
 
         [0039]    In certain embodiments, Viterbi decoders can be adapted to output an M+1 long vector of symbol decisions with delays ranging from zero (corresponding to a time t n ) to M (corresponding to a time t n−m ) as follows. For each time increment n, the Viterbi decoder updates the metrics and returns a vector of symbols whose length is M+1, where M will be referred to as the trace back depth. Deep trace back depth symbols can be more accurate than shallow trace back depth symbols. As will be explained subsequently, trellis decoders may use this advantage in the feedback path of an adaptive equalizer. For a given time n, it is beneficial to update all M+1 symbols in the equalizer feedback path such that M trace back depth symbols will overwrite M previously decoded symbols in the feedback path, thus updating symbol decisions for times t n−M  through t n . This updating of more accurate symbols helps to reduce error propagation in the equalizer feedback path. 
         [0040]    Referring to  FIG. 6 , an example of a pDFE architecture is illustrated. A feed forward filter  61  performs block based frequency domain filtering on data received at an input  60  to provide filtered input  62 . Typically, frequency domain filter  61  is block based and filtered input  62  consequently comprises a block of symbols. Summing element  63  adds filtered input  62  to noise prediction output  69  received from feedback filter  68 . The summed output is then provided to Viterbi decoder  64 . Viterbi decoder  64  provides the pDFE output  65 . pDFE output  65  may be added to filtered input  62  using summer  66  to provide an error signal  67  representing differences between filtered input  62  and pDFE output  65 . Error signal  67  is applied to feedback filter  68 , which typically comprises a noise predictor. The noise predictor in the feedback loop can estimate colored (non-white) noise from error signal  67 . Adder  63  may then subtract the estimated colored noise in noise prediction output  69  from the equalized data  62 , thereby helping Viterbi decoder  64  to make better decisions. 
         [0041]    In certain embodiments, Viterbi Decoder  64  can store metrics for a plurality of states including a smallest metric obtained, a previous state, and a current state. As discussed above, the metrics are typically used to configure or adjust a Viterbi algorithm that requires a path history memory for each state. The metrics can be based on trellis path metrics determined from sums of Euclidean distance branch metrics. The condition of the plurality of stored metrics is used to determine which symbol is decoded. If a delay is incurred, Viterbi Decoder  64  may be able to correct some symbols using trace back depth decoding. 
         [0042]    Referring now to  FIG. 7 , certain embodiments of the invention provide improved performance using two or more pDFEs, shown generally at  70  and  72 . In the example depicted in  FIG. 7 , a system comprising two pDFEs  70  and  72  receives an input  700  and produces an optimized output  724 . First pDFE  70  typically performs in the manner described above for the pDFE of  FIG. 6  using forward Viterbi decoder  704 . Second pDFE  72  comprises backward Viterbi decoder  722 , second feedback filter  727  and forward-backward blender  723 . Frequency domain filter  701  is typically block based and Viterbi decoder  704  can be configured to output a signal  705  comprising a block of symbols. These symbols can then be flipped using hardware or software flipping component  720  to provide a reversed order set of symbols. The reversed order set of symbols can be stored in general alignment with symbols provided at the output  724  of backward Viterbi decoder  722 . Both forward and backward decoded symbols can then be provided to forward-backward blender  723  for processing using a blending algorithm. 
         [0043]    Referring now to  FIGS. 7 and 8 , second pDFE  72  can be configured to operate on a signal comprising a time reversed data block that may incur some latency. In  FIG. 8 , F 1  represents a first block of data  81  for first pDFE  70 , F 2  the second block of data  82  for first pDFE  70 , F 3  the third block of data  83  for first pDFE  70 , and so on. Similarly, B 1  represents the first block of data  88  for second pDFE  72 , B 2  the second block of data  87  for second pDFE  72 , B 3  the third block of data  86  for second pDFE  72 , and so on. F blocks  80  are observable at signal  702  which is provided to flipping component  729 . B blocks  85  are observable at signal  749  output by flipping component  729 . Thus, B 1   88 , B 2   87  and B 3   86  are the flipped data of F 1   81 , F 2   82  and F 3   83 , respectively. In order for B 2   87  to be processed in second pDFE  72 , a latter portion (typically, one half) of F 1   81 , all of F 2   82 , and all of F 3   83  must be decoded from first pDFE  70 . The symbols from the last half of F 3   83  are used to preload the feedback filter  727 . Then the backward Viterbi decoder decodes half of B 3   86 , all of B 2   87 , and half of B 1   88  as shown in  FIG. 8 . It will be appreciated that, in some examples, the system may operate with fewer decoded symbols from first pDFE  70  such that latency is reduced; however, operation with fewer decoded symbols can result in degraded system performance. 
         [0044]    Prior to decoding symbols in second pDFE  72 , corresponding metric values received from first Viterbi decoder  704  can be used to initialize the metric values  730  for backward Viterbi decoder  722 . Additionally, decoded symbols  731  provided by first pDFE  70  can be used to preload noise predictor  727  of second pDFE  72 . 
         [0045]    of the latterly-defined system  72  of  FIG. 7  can be better understood by considering the following example with reference to  FIGS. 4 and 8 . Using a block length of 512 symbols, the latter half of symbols from F 3   83  preload the noise predictor symbols for second pDFE  72 . Second pDFE  72  can then begin decoding 1024 symbols (256 symbols of B 3   86 , 512 symbols of B 2   87 , and 256 symbols of B 1   88 ), of which only the middle 512 symbols of B 2   87  are typically output as backward decoded symbols. The remaining 512 symbols are decoded for optimizing the middle 512 symbols. It will be appreciated that backward Viterbi decoder  722  operates similarly to first Viterbi decoder  704 , except that it decodes in the backward direction as visualized on a trellis diagram (see  FIG. 9 ). This backwards action generates symbols  724  that may differ from symbols  705  generated by first Viterbi Decoder  704  output using the same equalized data  702 . The potential for unequal results increases under heavy multipath conditions. 
         [0046]    Having obtained symbols from forward Viterbi decoder  704  and backward Viterbi decoder  722 , symbols from F 2   82  and the corresponding symbols obtained by the backward Viterbi Decoder  722  from B 2   87  are typically sent to forward-backward blender  723 . Forward-backward blender  723  can increase performance of the second pDFE  722  by blending long delayed trellis symbols from the first Viterbi Decoder  704  with symbols output by the second Viterbi decoder  722 . In certain embodiments, forward-backward blender  723  operates to select an output symbol from forward Viterbi decoder  704 , backward Viterbi Decoder  722  or from a blended combination of forward Viterbi decoder  704  and backward Viterbi Decoder  722 . 
         [0047]    The operation of forward-backward blender  723  can be best understood in consideration of certain generalities of 8-state trellis decoding.  FIG. 9  shows an 8-state trellis diagram for an 8T-VSB system. In  FIG. 9 , at any given time instant n, there are 8 states and their corresponding survivor paths. When trace back depth decoding occurs at time n, the state with the lowest metric traces back its survivor path to decode the symbols. The lowest metric state at time n+1 may or may not contain the lowest metric state from time n. A main survivor path jump is identified when the lowest metric state at time n+1 contains the lowest metric state from time n. A main survivor path jump can occur under poor channel conditions. When a main survivor path jump occurs, a tally of differing symbols between the old survivor path and the new survivor path is taken. Unreliability of the sequence of decoded symbols increases with the size of the tally. This tally is typically taken every time a survivor path jump occurs. 
         [0048]    Referring again to  FIGS. 7 and 8 , forward-backward blender  723  can execute a blending algorithm that is dependent on the tallies of the survivor path jumps in a plurality of Viterbi decoders. When a survivor path jump is identifiable, the difference between the common symbols in the survivor path at time n and the survivor path at time n+1 is tallied. Tallies are obtained for both forward decoder  704  and backward decoder  702 . For each block, the tallies of each trellis decoder are summed up and represent an unreliability value. For example, in the 8T-VSB system, there are 12 trellis decoders and 12 unreliability values may be maintained for each block. Each unreliability value is the sum of the tallies for the corresponding trellis decoder. Thus, for every block, the unreliability of the decoded symbols of each trellis decoder is determined by the tallies. The forward-backward blending algorithm between forward Viterbi decoded symbols  705  and backward Viterbi decoded symbols  724  can be based upon this unreliability. If the unreliability of the symbols  705  obtained from forward Viterbi decoder  704  is a large value and the unreliability of symbols  724  from backward Viterbi decoder  722  is a small value, then, greater weight is given to symbols  724  obtained from backward Viterbi decoder  722 . Similarly, if the unreliability of symbols  705  from forward Viterbi decoder  704  is a small value while the unreliability of the symbols  724  from backward Viterbi decoder  722  is a large value, greater weight is given to symbols  705  obtained from forward Viterbi decoder  704 . On the other hand, if both the forward and backward Viterbi symbols unreliabilities are a similar value, then equal weighting can be given to both sets of symbols. For example, if scalar weighting factor a is associated with symbols  705  and scalar weighting factor b is associated with symbols  724 , then a and b can be selected depending on the unreliability values as shown in Table 1. In Table 1, “&lt;&lt;,” “&gt;&gt;” and “˜=” denote “much less than,” “much greater than” and “approximately equal to,” respectively. The symbols received from blender  723  are the sum of a*forward_Viterbi_symbols and b*backward_Viterbi_symbols. 
         [0000]    
       
         
               
               
               
               
             
               
               
               
               
               
             
           
               
                   
                 TABLE 1 
               
               
                   
                   
               
               
                   
                 Fwd Viterbi 
                 Fwd Viterbi 
                 Fwd Viterbi 
               
               
                   
                 symbols 
                 symbols 
                 symbols 
               
               
                   
                 unreliability &lt;&lt; 
                 unreliability &gt;&gt; 
                 unreliability ~= 
               
               
                   
                 Bkwd Viterbi 
                 Bkwd Viterbi 
                 Bkwd Viterbi 
               
               
                   
                 symbols 
                 symbols 
                 symbols 
               
               
                   
                 unreliability 
                 unreliability 
                 unreliability 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 a 
                 1.0 
                 0.0 
                 0.5 
               
               
                   
                 b 
                 0.0 
                 1.0 
                 0.5 
               
               
                   
                   
               
             
          
         
       
     
         [0049]    These blended symbols may also be used as the output symbols instead of  724 , although some may be a soft value. If a hard value is desired, one would choose the backward decoded symbol  724 . 
         [0050]    In simulations using a block size of 512 and a trace back depth of 16, six different channels were tested. In comparison to the basic pDFE system in  FIG. 6 , the dual pDFE of  FIG. 7  performs 0.1 dB better (SNR input can be 0.1 dB less) for AWGN, 0.4 dB better for Brazil A, 0.6 dB better for Brazil B, 1.0 dB better for Brazil C, 0.8 dB better for Brazil D, and 0.5 dB better for Brazil E. The AWGN channel has no multipath; only additive white Gaussian noise is introduced. 
         [0051]    It is apparent that the above embodiments may be altered in many ways without departing from the scope of the invention. Further, various aspects of a particular embodiment may contain patentably subject matter without regard to other aspects of the same embodiment. Additionally, various aspects of different embodiments can be combined together. Also, those skilled in the art will understand that variations can be made in the number and arrangement of components illustrated in the above diagrams. It is intended that the appended claims include such changes and modifications.