# Patent

## Title
Reliable symbols as a means of improving the performance of information transmission systems

## Abstract

All practical communication channels impose some type of corruption on received data through inter-symbol interference (ISI). ISI corruption is particularly acute in high-order constellation transmission. Although ISI effects of high-order constellation transmission are very large on average, some symbols may be received that suffer relatively low levels of ISI. These symbols are “reliable symbols” and can be used to provide blind estimation of the ISI coefficients. Once the ISI effects of a channel are known, all captured signals may be corrected.

## Background
CROSS-REFERENCE TO RELATED APPLICATIONS
This application is a continuation-in-part of the following applications: U.S. patent application Ser. No. 09/836,281, filed Apr. 18, 2001, PCT/GB00/02634, filed Jul. 10, 2000 (which benefits from the priority of UK application 16938.3, also filed Jul. 10, 2000), and PCT/GB00/02648, filed Jul. 10, 2000 (which benefits from the priority of UK application 9926167.4, filed Nov. 4, 1999), the disclosures of which is incorporated herein by reference. Certain claims may benefit from the priority of these applications.


BACKGROUND
The present invention relates to a data processing technique that permits identification of reliable symbols in the presence of Inter-Symbol Interference (“ISI”) and other data correlated noise (collectively, “ISI”). Data correlated noise refers to a variety of phenomena in data processing systems in which a data signal interferes with itself at a destination. The present invention also relates to the use of reliable symbols to determine values of source symbols that are corrupted by ISI. The present invention finds application in systems where source symbols are members of high-order constellations. Previously, such systems have required the use of training symbols for operation in the presence of real-world ISI phenomenon.
FIG. 1 illustrates an exemplary data processing system 100 in which ISI may occur. A source 110 may generate a data signal X (herein, a “source data signal”). When delivered to a destination 120 as a received signal Y, the source data signal X may be corrupted by ISI sources 130. For example, multiple copies of a single data signal X may be captured at the destination 120, each copy being received with an unknown time shift and gain with respect to the other copies. Further, the time shifts and gains may vary over time.
ISI phenomena may be modeled mathematically. In the case where the data signal X is populated by a number of data symbols xn, captured signals yn at the destination 120 may be represented as:

yn=a0·xn+f(xn−K1, . . . ,xn−1,xn+1, . . . ,xn+K2)+ωn.  (1)

where a0 represents a gain factor associated with the channel 130, f(xn−K1, . . . Xn+K2) is a functional representation that relates the ISI to the symbols, Xn−K1, . . . Xn+K2, causing ISI corruption and ωn represents corruption from other sources. In linear systems, equation 2 may reduce to:





  
    
      
        
          y
          n
        
        =
        
          
            x
            n
          
          +
          
            
              ∑
              
                
                  
                    
                      i
                      =
                      
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                        -
                        
                          K
                          1
                        
                      
                    
                  
                
                
                  
                    
                      i
                      ≠
                      
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                  -
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          +
          
            ω
            n
          
        
      
    
    
      
        (
        2
        )
      
    
  




where a−K1, . . . aK2 represent the values of the impulse response of the channel. In accordance to common practice, the values ai have been normalized by the value of a0 in equation 2.

ISI may arise from a variety of real-world phenomena. Multipath is an example of ISI that occurs in wireless and other communication systems. In a wireless system 200, shown in FIG. 2, a base station 210 may transmit data addressed to a mobile station 220 over a region of space, typically a cell or a cell sector. The mobile station 220 may receive the signal via a direct line-of-sight path and also may receive copies of the data signal via other indirect paths. The indirect paths may be caused by reflections of the transmitted signal from structures in the transmission environment such as buildings, trucks, mountains and the like. At the mobile station 200, the directly received and indirectly received signals interfere with each other. The indirect transmissions, however, because they travel a longer propagation path before they reach the mobile station, are delayed with respect to the direct path signal.
ISI is seen as a serious impediment to the use of high-order constellations for data processing systems. A “constellation” represents a set of unique values that may be assigned to data symbols. Several examples are shown in FIG. 3. FIGS. 3 (a)–(c) illustrate constellations for amplitude shift keying (“ASK”) applications where symbols can take one of four, eight or sixteen unique values. When compared to a binary symbol constellation, use of these constellations yields data throughput increases by factors of 2 (four levels), 3 (eight levels) or 4 (sixteen levels). FIGS. 3 (d)–(f) illustrate constellations for quadrature amplitude modulation (“QAM”) applications where symbols can take one of four, sixteen or sixty-four unique values. When compared to a binary symbol constellation, use of these constellations yield data throughput increases of 2 (four levels), 4 (sixteen levels) and 6 (sixty-four levels). Thus, use of high-order constellations in data processing systems can yield increased throughput over binary systems within the same bandwidth.
The problem is that, when using high-order constellations, blind equalization (equalization without either an initial training sequence, or ‘refresher’ training sequences) is very hard to achieve because the detrimental effects of ISI increase with increasing constellation order.
There is a need in the art for a data transmission system that, in the presence of realistic levels of ISI, uses blind techniques to decode symbols from a high-order constellation.



BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 illustrates an exemplary data processing system in which IS may occur.
FIG. 2 illustrates an exemplary communication system in which ISI may occur due to multipath.
FIG. 3 illustrates various symbol constellations.
FIG. 4 illustrates a method of operation for detecting reliable symbols according to an embodiment of the present invention.
FIG. 5 illustrates a method of operation for detecting reliable symbols according to an embodiment of the present invention.
FIG. 6 illustrates another method of operation 3000 for detecting reliable symbols
FIG. 7 is a block diagram of a data decoder according to an embodiment of the present invention.
FIG. 8 illustrates a data decoding method of operation according to an embodiment of the present invention.
FIG. 9 is a block diagram of a data decoder according to another embodiment of the present invention.
FIG. 10 is a block diagram of a receiver structure according to an embodiment of the present invention.



DETAILED DESCRIPTION
Embodiments of the present invention identify reliable symbols from a sequence of captured signal samples at a destination. Although the ISI effects associated with high-order symbol constellation transmissions impose large signal corruption on average, some samples suffer relatively low levels of ISI. These samples are the reliable symbols. Having identified reliable symbols from a sequence of captured signal samples, it is possible to reliably estimate the actual source symbols for all captured signal samples.
Identification Of Reliable Symbols
A “reliable symbol” is a captured sample yn that is very likely to be located within a decision region of a corresponding source symbol xn transmitted from the source 110 at time n. At a destination 120, each constellation symbol is associated with a decision region that represents a set of all points that are closer to the respective symbol than to any other symbol in the constellation. FIG. 3(e) shows exemplary decision regions 140, 150 for symbols −1,−1 and 1,3 in the 16-level QAM constellation. For a reliable symbol, the combined ISI and additive noise effects and other channel and system impairments are unlikely to have pushed the captured sample yn from a decision region of the symbol xn from which it originated.
According to an embodiment of the present invention, identification of a signal yn as “reliable” may be carried out using a reliability factor Rn given by:




  
    
      
        
          R
          n
        
        =
        
          
            ∑
            
              
                
                  
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                    =
                    
                    ⁢
                    
                      -
                      
                        K
                        1
                      
                    
                  
                
              
              
                
                  
                    i
                    ≠
                    
                    ⁢
                    0
                  
                
              
            
            
              K
              2
            
          
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                y
                
                  n
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            ·
            
              c
              l
            
          
        
      
    
    
      
        (
        3
        )
      
    
  




where the ci are constants representing any priori knowledge of the ISI effect that may be available. Generally, if nothing is known about the ISI, then the cl's may all be set equal to 1. In other situations, additional information as to the nature of the channel 130 may be known and the ci's may be given values reflecting this information. If the reliability factor of a sample yn is less than a predetermined limit value, designated “dlim” herein, the sample may be designated as a “reliable symbol.”

Where samples on only one side of a candidate sample yn contribute to the ISI, the reliability factor of the sample yn may be determined using:




  
    
      
        
          R
          n
        
        =
        
          
            ∑
            
              i
              =
              1
            
            K
          
          ⁢
          
            
              
              
                y
                
                  n
                  -
                  i
                
              
              
            
            ·
            
              
                c
                i
              
              .
            
          
        
      
    
    
      
        (
        4
        )
      
    
  




where K=K2 in equation 3. In respect to the forgoing reliability factors (equations (3) and (4)) the yn's may be real for one-dimensional signal structures or complex for two-dimensional signal structures.

For systems using two-dimensional constellations, such as the QAM constellations shown in FIG. 3(d)–(f), the reliability factor may be determined using:




  
    
      
        
          R
          n
        
        =
        
          
            ∑
            
              
                
                  
                    i
                    =
                    
                    ⁢
                    
                      -
                      
                        K
                        1
                      
                    
                  
                
              
              
                
                  
                    i
                    ≠
                    
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              K
              2
            
          
          ⁢
          
            
              
                
                  y
                  
                    1
                    
                      n
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                +
                
                  y
                  
                    2
                    
                      n
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                      l
                    
                  
                  2
                
              
            
            .
            
              c
              i
            
          
        
      
    
    
      
        (
        5
        )
      
    
  




where y1n−i2 and y2n−22 respectively represent values of yn−i in the first and second dimensions.

In another embodiment, the reliability factor Rn may be calculated based on the constellation symbols that are closest to the captured samples. Each captured sample yn will be closest to one constellation point pn from the constellation

pn={CPp:min(CP−yn)}  (6)

where CP is the set of all possible received constellation points.

In this embodiment, reliability factors may be determined from the constellation points pn according to one of:




  
    
      
        
          
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            n
          
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              ∑
              
                
                  
                    
                      i
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            =
            
              
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                          -
                          
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                            1
                          
                        
                      
                    
                  
                  
                    
                      
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                      p
                      
                        2
                        
                          n
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        (
        7
        )
      
    
  




These formulae simply are an extension of equations 3–5 substituting pn−i for yn−i.

FIG. 4 is a flow diagram of a reliable symbol detection method 1000 according to an embodiment of the present invention. According to the method, reliable symbol detection may begin by calculating a reliability factor of a sample yn based on values of neighboring samples (box 1010). Thereafter, the method may determine whether the reliability factor is less than or equal to a predetermined threshold (box 1020). If so, the sample yn may be designated as a reliable symbol (box 1030). Otherwise, the sample yn is not reliable.
The predetermined threshold dlim may be determined based on the applications for which the identification method is to be used. In one embodiment, the threshold may be set to the value dlim=(K1+K2)·dmin where dmin is half the distance between two constellation points that are closest together. This threshold is appropriate for the case where




  
    
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  ≤
  1.




Experiments have shown, however, that operation can be maintained using the same threshold when





  
    
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    1.4
    .
  




The threshold dlim also may vary over time. If the predetermined threshold is increased, then an increased number of samples will be accepted as reliable symbols though, of course, all of these symbols will not be of the same reliability. Similarly, by decreasing the threshold dlim, the number of samples that are designated as reliable symbols will decrease. These symbols will be those symbols with lower reliability factors. During operations of a reliable symbol detection method, the threshold dlim may be varied to maintain a rate of detected reliable symbols at a desired value. For example, if a rate of detected symbols falls below a first rate threshold, the dlim value may be increased. Or, if the rate of detected symbols exceeds a second rate threshold, the dlim value may be decreased.
In other embodiments, samples may be identified as reliable symbols based not only on reliability factors of the samples Rn but also may be based on the values of the sample itself (yn, pn). In a given application, reliability factors of a plurality of candidate samples (say, y1, y2, y3) each may be at or near the threshold (Rn(yn)≈dlim, ∀n=1,2,3). In this case, the candidate samples may be prioritized according to the magnitude of the samples themselves, sorting either in ascending order of sample value or descending value of sample value as may be appropriate in a given application. Similarly, after equalization has begun and estimated source symbols {circumflex over (x)}n become available, prioritization among candidate samples may be made according to the magnitude of the estimated symbols. Additionally, identification of reliable symbols may be based not only upon reliability factors Rn but also on the sample values yn or estimated symbol values {circumflex over (x)}n themselves. In this embodiment, a sample may be designated as a reliable symbol if the reliability factor is less than a first threshold dlim and if the sample value yn (or symbol value {circumflex over (x)}n) is less than a second threshold value. In this embodiment, these two conditions are required to be met before a sample is designated as a reliable symbol.
FIG. 5 is a flow diagram of a method of operation 2000 to determine whether a candidate sample yn is a reliable symbol. For operation of the method, an index variable i may be set to −K1 and a reliability counter Rn may be set to zero (Rn=0) (box 2010). The method may begin by adding to reliability counter Rn the value of a sample yn−i (Rn=Rn+|yn−i|) (box 2020). Thereafter, if the reliability counter Rn exceeds a predetermined limit (box 2030), the candidate symbol may be disqualified as a reliable symbol (box 2040). In this case, operation of the method 2000 may cease for the candidate sample yn.
If at box 2030 the reliability counter Rn does not exceed the predetermined limit, the method may continue. The index value i may be incremented (box 2050). If i=0, if n-i points to the candidate symbol yn itself (box 2060), the index value may be incremented again. Otherwise, the method 2000 may determine whether i is greater than K2 (box 2070). If so, then the candidate sample yn is a reliable symbol (box 2080). Otherwise, the method may return to the operation at box 2020 and add to the reliability counter based on the value of the next sample yn−i.
The foregoing description of the method 2000 has presented operation when no a priori knowledge of the channel is available at the destination 120 (e.g., ci=1 for all i). When knowledge of the channel is available and cl values may be determined for one or more i, then at box 2020 the reliability counter Rn may increment according to Rn=Rn+ci·|yn−i| (shown as bracketed text in box 2020).
In this way, the method of operation 2000 examines the neighboring samples of yn (K1 precursors and K2 postcursors) to see if yn meets the criterion for being a reliable symbol.
When a destination captures a plurality of samples yn, each sample may be considered according to the method of FIG. 5 to determine whether the sample is a reliable symbol. Operation of the method 2000 can be accelerated in certain embodiments. If, for example, a sample, say yj, by itself exceeds the reliability threshold then none of the neighboring symbols yi, i=j−K1 to j+K2, can be reliable symbols. In this case, the method 2000 need not be operated upon these neighboring symbols. The procedure can advance by skipping ahead to examine the first sample yn that does not include yj in its group of surrounding samples. In this embodiment, although the value of yj may disqualify neighboring samples from being reliable symbols, yj itself may be a reliable symbol. The method 2000 may operate on yj to determine whether it is a reliable symbol.
Additionally, the surrounding samples may be selected, as a sub-set of the full range i=−K1 to K2 and the associated surrounding samples be examined. If a sequence of, say, three samples yj to Yj+2 have values that would cause the reliability limit dlim to be exceeded, then any sample yl having the sequence of samples within the −K1 to K2 window need not be considered under the method 2000 of FIG. 5.
An alternate embodiment finds application where ISI corruption is expected to be linear and caused by symbols from only one side of a candidate symbol, according to:




  
    
      
        
          y
          n
        
        =
        
          
            x
            n
          
          +
          
            
              ∑
              
                i
                =
                1
              
              
                K
                2
              
            
            ⁢
            
              
                a
                i
              
              ·
              
                x
                
                  n
                  -
                  i
                
              
            
          
          +
          
            ω
            n
          
        
      
    
    
      
        (
        8
        )
      
    
  




In such an embodiment, the iterative scan illustrated in FIG. 5 may simplify since k1 is equal to zero.

FIG. 6 illustrates another method of operation 3000 for detecting reliable symbols when ISI effects are expected to be linear and no knowledge of the coefficients cl is available. The method 3000 may initialize an index value i to −K1 (box 3010). The method may determine whether the absolute value of a symbol Yn−i occurs within a predetermined limit (box 3020). If not, the method terminate for candidate symbol yn; it will not be designated as a reliable symbol (box 3030). If the value of yn−i does occur within the predetermined limit, however, the method may increment i (box 3040). Thereafter, the method may determine whether i=0 (box 3050). If so, the method may return to box 3040 and increment i again. Thereafter, the method may determine whether i>K2 (box 3060). If so, the sample yn may be designated as a reliable symbol (box 3070). If not, the method may return to box 3020 for testing of other samples.
In QAM systems, there are several alternatives to detect reliable symbols. As shown in FIGS. 3 (d)–(f), QAM constellation points may be mapped as a two-dimensional coordinate space of in-phase data (“I”) and quadrature-phase data (“Q”). In the simplest embodiment, where ISI is known to corrupt I data and Q data independently of each other, reliability factors may be established independently for I and Q data. That is, any of the methods of FIG. 6 may be performed for independently I and Q data. A sample's reliability may be calculated for the Q domain without regard for the sample's I value and also calculated for the I domain without regard for the sample's Q value. It may occur that a symbol will be considered reliable for I but not for Q or vice versa. This is appropriate since this technique is to be used in circumstances where it is known that the ISI in each domain are independent.
The method of FIG. 6 finds application in other embodiments where ISI is not known to be real. In such a case, the predetermined limit may be based on rectangular “rings” of the constellation. With reference to FIG. 3(f), for example, a first constellation ring may include the set of (I,Q) constellation points: 1,1, 1,−1, −1,−1 and −1,1 (shown as 160 in FIG. 3 (f)). A second constellation ring may include the set of constellation points: 3,3, 3,1, 3,−1, 3,−3, 1,−3, −1,−3, −3,−3, −3,−1, −3,1, −3,3, −1,3 and 1,3 (shown as 170 in FIG. 3 (f)). Higher order constellations may have additional rings. In this embodiment, the method determines whether values of the samples yn−i occur within a predetermined rectangular ring or any lower-order ring.
In an embodiment, the methods of FIGS. 5 and 6 may be used with constellation points pn−i substituting for the yn−i as discussed above.
Alternatively, reliable symbols may be identified according to one or more of the techniques described in the Applicant's co-pending PCT patent application PCT/GB00/02634, entitled “Adaptive Blind Equaliser,” filed Jul. 10, 2000, the subject matter of which is incorporated herein by reference.
The foregoing discussion has described various embodiments for identification of reliable symbols in a captured signal stream. Reliable symbols may be decoded immediately without further processing. Thus, for the set YRS of reliable symbols, Yn∈YRS, a data decoder in a destination 120 may generate decoded symbols {circumflex over (x)}n to be the constellation point closest to yn. The decoded symbol {circumflex over (x)}n may be the destination's estimate of the source data symbol xn.
The foregoing embodiments find application in applications in which captured samples yn do not exhibit phase offset with respect to the source symbols xn. Of course, in some applications, it may be expected that the captured samples yn will exhibit a phase offset with respect to their source symbols xn. Where captured samples yn exhibit a phase rotation with respect to the source symbols xn, a “reliable symbol” may be defined alternately as a sample yn that is likely to be observed in the annular constellation ring of its source symbol xn. Restated, ISI corruption is unlikely to push the source symbol xn from its constellation ring when observed as the captured sample yn at the destination 120. The reliability factor of equation 3 may be applied in this embodiment, using observed power levels of the captured samples:




  
    
      
        
          
            R
            n
          
          =
          
            
              ∑
              
                
                  i
                  =
                  
                    -
                    
                      K
                      1
                    
                  
                
                
                  i
                  ≠
                  0
                
              
              
                K
                2
              
            
            ⁢
            
              
                
                  Power
                  ⁢
                  
                    
                  
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                    (
                    
                      y
                      
                        n
                        -
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                    )
                  
                
              
              ·
              
                c
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        ,
      
    
    
      
        (
        9
        )
      
    
  




and, equation 5 may be used.

Exemplary annular constellation rings are shown in FIG. 3(g). For any given symbol point (such as point (1,5)) there will be a plurality of symbols having the same distance from the constellation center. These symbols define a circle 180. Other constellation symbols define other circles, such as 190-1 and 190-2 in FIG. 3(g). Each circle may be associated with an annular ring (not shown) that includes all points in the constellation space that are closer to the circle than to any other circle in the constellation.
The methods of FIGS. 4 and 5 may find application when captured samples ynexhibit phase offset with respect to their source symbols xn. In this case, the threshold dlim may be set according to half the width of the annular ring in which the captured sample yn is observed.
In one embodiment a subset of the total range of power levels of yn may be used.
Use Of Reliable Symbols
In further embodiments of the present invention, reliable symbols may be used as a basis for decoding transmitted symbols xn from received non-reliable captured samples that are not reliable symbols (yn∉YRS). A description of these embodiments follows.
FIG. 7 is a block diagram of a data decoder 300 according to an embodiment of the present invention. The data decoder 300 may include a reliable symbol detector 310, an adaptation unit 320 and a symbol decoder 330. The reliable symbol detector 310 may identify a plurality of reliable symbols YRS∈YRS from a sequence of captured samples yn. The reliable symbol detector 310 may output the reliable symbols YRS and their surrounding samples (labeled y, in FIG. 7) to the adaptation unit 320. Based upon yRS and y1, the adaptation unit 320 may generate ISI metrics that characterize the ISI signal corruption 130 (FIG. 1). The adaptation unit 320 may output to the symbol decoder 330 data MISI, representing the ISI metrics. Based upon the ISI metrics, MISI, the symbol decoder 330 may generate decoded symbols {circumflex over (x)}n from the captured samples yn, for all n, regardless of whether the sample yn is a reliable symbol or not.
FIG. 8 illustrates a data decoding method 3000 according to an embodiment of the present invention. According to the method, a data decoder may identify a set of reliable symbols YRS from a sequence Y of captured samples (Step 3010). Using this set of reliable symbols YRS and their neighbors, the data decoder may estimate an ISI metric (Step 3020). Thereafter, using the ISI metric, the data decoder may decode symbols {circumflex over (x)}nfrom the sequence Y of captured samples (Step 3030).
Adaptation and symbol correction techniques per se are known. In communication applications, such techniques often are provided within channel equalizers. A variety of channel equalization techniques are known, including both time-domain equalizers and frequency-domain equalizers. At a high level, adaptation refers to the process by which the equalizer learns of the ISI corruption effects and symbol correction refers to a process by which the equalizer reverses the ISI effects to determine from the sequence of captured samples Y what the source symbol sequence X is most likely. However, for these existing techniques to work, in the presence of realistic level of ISI when operating with high-order constellations, it would be necessary to use an initializing training sequence and thereafter to use training sequences that are transmitted periodically. The use of the reliable symbols method overcomes this need. Any of a variety of known equalizers may be used with the reliable symbols technique and the adaptation process—the process by which the equalizer learns—can be rendered blind. Having learned what the ISI effects are based on the reliable symbols YRS, the equalizer may decode symbols {circumflex over (x)}n from all of the captured samples yn.
Perhaps the simplest embodiment of equalizer is the subtractive equalizer. In the subtractive equalizer, the adaptation unit 320 estimates the channel ISI coefficients âi. Using the estimated coefficients âi the symbol decoder 330 may estimate source symbols, {circumflex over (x)}n, by decoding y′n where:




  
    
      
        
          y
          n
          ′
        
        =
        
          
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            n
          
          -
          
            
              ∑
              
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                =
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                2
              
            
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                  a
                  ^
                
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                  ^
                
                
                  n
                  -
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        (
        10
        )
      
    
  




in which {circumflex over (x)}n−i represent prior decoded symbols. The equalizer may generate a decoded symbol {circumflex over (x)}n as the constellation symbol that is closest to y′n.

As noted, different types of equalizers can be used. A decision feedback equalizer (also “DFE”) may be incorporated within the symbol decoder 410 of the system 400 shown in FIG. 9. Conventionally a DFE is fed with information obtained from training sequences. In an embodiment employing reliable symbols, information may be fed to the adaptation unit 420. The adaptation unit 420 may update the tap settings of the DFE.
In this embodiment shown in FIG. 9, the reliable symbol detector 430 may identify reliable symbols from the captured samples yn. An output of the reliable symbol detector 430 may be an enabling input to the adaptation unit 420. When a reliable symbol is identified, the adaptation unit 420 may be enabled, causing it to revise its estimate of the ISI metrics Misi.
The foregoing embodiments have described use of reliable symbols to extend application of known adaptation processes to ISI estimation for high-order constellations in the presence of realistic levels of ISI without the use of training sequences. By extension, this use of reliable symbols permits data decoders to estimate high-constellation source symbols X from a sequence Y of captured samples. Advantageously, this use of reliable symbols may be made non-invasive in that it can be employed without changing known adaptation and symbol decoding processes in prior art equalization systems.
Estimation of Channel Coefficients Based on Reliable Symbols and Reliability
By way of illustration, a way in which reliable symbols can be used in ISI coefficient estimation will now be described briefly. Consider the estimation of one-dimensional ISI coefficients. After a sufficient number of reliable and their related surrounding samples have been identified, the estimation of the ISI coefficients may be obtained as the solution of a standard matrix equation:

â=(HTH)−1HTδ  (11)

where: â is a vector of the ISI coefficient estimates; H is an N×M matrix, with N>M, in which each row contains the M surrounding symbol estimates or alternatively, the corresponding M surrounding sample values for each reliable symbol, and N is the number of related detected reliable symbols (a larger N is required for lower signal to noise ratios); and δ is an N×1 vector that contains the distances of the N reliable symbols from their estimated origin points.

By way of example, consider the following situation: The ISI length is assumed to have two coefficients (K1=0,K2=2) and the estimation is based on four reliable symbols. Let it be assumed that they correspond to time indexes: 100, 250, 300 and 320. Then,




  
    
      
        
          δ
          _
        
        =
        
          
            {
            
              
                
                  y
                  100
                
                -
                
                  
                    x
                    ^
                  
                  100
                
              
              ,
              
                
                  y
                  250
                
                -
                
                  
                    x
                    ^
                  
                  250
                
              
              ,
              
                
                  y
                  300
                
                -
                
                  
                    x
                    ^
                  
                  300
                
              
              ,
              
                
                  y
                  320
                
                -
                
                  
                    x
                    ^
                  
                  320
                
              
            
            }
          
          T
        
      
    
    
      
        (
        12
        )
      
    
  
  
    
      
        
          H
          
            _
            _
          
        
        =
        
          {
          
            
              
                
                  
                    
                      x
                      ^
                    
                    98
                  
                  ,
                  
                    
                      x
                      ^
                    
                    99
                  
                
              
            
            
              
                
                  
                    
                      x
                      ^
                    
                    248
                  
                  ,
                  
                    
                      x
                      ^
                    
                    249
                  
                
              
            
            
              
                
                  
                    
                      x
                      ^
                    
                    298
                  
                  ,
                  
                    
                      x
                      ^
                    
                    299
                  
                
              
            
            
              
                
                  
                    
                      x
                      ^
                    
                    318
                  
                  ,
                  
                    
                      x
                      ^
                    
                    319
                  
                
              
            
          
          }
        
      
    
    
      
        (
        13
        )
      
    
  




Optionally, however, the performance of the ISI adaptation can be improved by integrating a reliability weight factor into the calculation of ISI metrics. Consider the case of a subtractive equalizer. In such an equalizer, an adaptation unit 320 may estimate channel coefficients a1 and generate an estimate of source symbols according to equation 11 above.

In an embodiment, an estimate â of a may include a weighting based on reliabilities associated with received signal values. In this embodiment an estimate â of a may proceed according to:

â=(HtWH)−1HTWδ  (14)

where W is a diagonal N×N matrix of reliability weights wi,i (wi,i=0 for all i≠j). In one such embodiment, the reliability weights wi,i may be obtained as:

wi,i=f(Ri)  (15)

where Ri is the reliability factor associated with an ith sample value, i being a member of the set of N sample values being used in the estimation process, and f(.) is a function that increases inversely with the associated reliability factor (e.g. as defined in equation 3).

Thus, symbols of varying degrees of reliability can be used with an appropriate reliability weighting.
In an embodiment, a destination may store captured samples in a buffer memory while reliable symbols are detected and while ISI estimation occurs. Thereafter, when the ISI metrics are available, the stored samples may be read from the memory and decoded. In this regard, provided the buffer memory is appropriately sized, all captured samples may be decoded.
Estimation of Constellation Symbols In View of Channel Gain
Successful signal detection in communication systems requires a-priori knowledge of the location of the received constellation points. Hard-decision and soft-decision detection processes use a distance between a received signal point and its associated received constellation point to decode symbols. Communication in the presence of an ISI channel results with the received extreme points being affected to such degree that they cannot be used simply to detect the position of the received constellation points. In fact, the received extreme points can reach as far as




  1
  +
  
    
      ∑
      i
    
    ⁢
    
      
      
        a
        i
      
      
    
  




times their nominal distance from the origin. In addition, with gaussian noise from other sources taken in account, this maximum distance from the origin can be increased further. The location of the received constellation points is the product of the location of transmitted constellation points and the channel gain.

In many communication applications, upon initial start up, a destination may have no a-priori knowledge of ISI coefficients (ai, i=·K1 to K2, i≠0) and also no a priori knowledge of the channel gain (a0). Under this condition, the estimation of received constellation points may be carried out in two stages. In a first stage, an initial estimation of the received constellation points may be made based on a small set of reliable symbols. In a second stage, a final estimation of received constellation points may be made using a larger set (possibly all) of the reliable symbols. These two stages are described below.
Initial Estimation of the Received Constellation Points
As described above, reliable symbols have the property that, when observed at the destination, they are closer to the source constellation point than to any other point in the constellation. This implies that the maximum distance from the reliable symbol to the source constellation point is at most half the distance between adjacent points in the received constellation.
The channel gain estimation may be made from reliable symbols. From a plurality of reliable symbols, those reliable symbols having the maximum magnitude along the constellation axes (e.g. the I and Q axes of a QAM constellation) may be chosen to be the initial maximum received constellation point in each axis. An initial constellation size may be determined from the magnitude of these maximally sized reliable symbols.
Let {circumflex over (P)}1max be the initial estimation of the value of the maximum of the received constellation point along an axis. For a regular constellation, one having the same number of symbols in each axis, an initial estimation {circumflex over (P)}i1 of the received constellation is:




  
    
      
        
          
            P
            ^
          
          1
          q
        
        =
        
          
            
              sign
              ⁡
              
                (
                q
                )
              
            
            ·
            
              
                
                  P
                  ^
                
                1
                max
              
              
                
                  M
                
                -
                1
              
            
            ·
            
              (
              
                
                  2
                  ⁢
                  
                    
                    q
                    
                  
                
                -
                1
              
              )
            
          
          :
          
            q
            ∈
            
              [
              
                
                  
                    -
                    
                      M
                    
                  
                  2
                
                ,
                
                  
                    M
                  
                  2
                
              
              ]
            
          
        
      
    
    
      
        (
        16
        )
      
    
  




where M is the number of points in the constellation and q is an integer index along an axis of the constellation. Equation 16 is appropriate for use when the constellation is square and the constellation points are regularly spaced. In general, when different symmetrical constellation shapes are used, the denominator in Equation 16 may be the number of constellation points for each axis, minus one, and q may be an appropriately valued index.

In an embodiment using a general constellation, the denominator in Equation 16 may be adjusted according to the number of constellation points for each axis:




  
    
      
        
          
            P
            ^
          
          
            1
            J
          
          q
        
        =
        
          
            
              sign
              ⁡
              
                (
                
                  q
                  J
                
                )
              
            
            ·
            
              
                
                  P
                  ^
                
                
                  1
                  J
                
                max
              
              
                
                  M
                  J
                
                -
                1
              
            
            ·
            
              (
              
                
                  2
                  ⁢
                  
                    
                    
                      q
                      J
                    
                    
                  
                
                -
                1
              
              )
            
          
          :
          
            
              q
              J
            
            ∈
            
              [
              
                
                  -
                  
                    M
                    J
                  
                
                ,
                
                  M
                  J
                
              
              ]
            
          
        
      
    
    
      
        (
        17
        )
      
    
  




where MJ is the number of points along the Jth axis of the constellation and qJ is the index along a Jth axis of the constellation.

Revising the Estimated Constellation Points
Returning to the regular case, an improved, {circumflex over (p)}2q, can be obtained from:




  
    
      
        
          
            
              P
              ^
            
            2
            q
          
          =
          
            
              
                P
                ^
              
              1
              q
            
            +
            
              
                (
                
                  
                    2
                    ⁢
                    
                      
                      q
                      
                    
                  
                  -
                  1
                
                )
              
              ·
              
                
                  
                    e
                    ^
                  
                  1
                
                :
                
                  q
                  ∈
                  
                    
                      [
                      
                        
                          
                            -
                            
                              M
                            
                          
                          2
                        
                        ,
                        
                          
                            M
                          
                          2
                        
                      
                      ]
                    
                    ⁢
                    
                      
                    
                    ⁢
                    where
                  
                
              
            
          
        
        ,
      
    
    
      
        (
        18
        )
      
    
  
  
    
      
        
          
            e
            ^
          
          1
        
        =
        
          
            1
            s
          
          ⁢
          
            
              ∑
              q
            
            ⁢
            
              
                1
                
                  
                    2
                    ⁢
                    
                      
                      q
                      
                    
                  
                  -
                  1
                
              
              ·
              
                
                  ∑
                  
                    n
                    ∈
                    
                      s
                      q
                    
                  
                
                ⁢
                
                  (
                  
                    
                      
                        P
                        ^
                      
                      1
                      q
                    
                    -
                    
                      y
                      n
                      q
                    
                  
                  )
                
              
            
          
        
      
    
    
      
        (
        19
        )
      
    
  




and where s is the number of detected reliable symbols, sq is a set of reliable symbols that are associated with the constellation point q as defined by Equation 18 and {ynq } are the set of sample values which are reliable symbols and are associated with the qth estimated constellation point. Equation 18 defines a set of constellation point estimates for use in channel gain estimation. The channel gain a0 may be estimated as a ratio of the first constellation point estimate {circumflex over (p)}21 to the magnitude of a smallest transmitted constellation point, e.g. +1. The estimation method described above can be generalized to the situation in which the constellation may be non symmetrical and the separation between points may be non-uniform.

FIG. 10 is a block diagram of a receiver structure 500 according to an embodiment of the present invention. The receiver 500 may include a demodulator 510, a memory 520 and a processor 530. FIG. 10 illustrates communication flow among the demodulator 510, the memory 520 and the processor 530, not actual electrical interconnections among these units.
The demodulator 510 captures a signal Y from the channel and generates captured samples yn therefrom. The channel may be an electric, magnetic, acoustic, or optical propagation medium. Demodulators 510 for capturing such signals are well-known. On account of the ISI, samples from the captured signal stream generally will have no detectable correspondence to the transmitted constellation. It may take any number of values between the constellation points (e.g. 6.3, 6.5, −3.1). Captured sample data may be stored in a buffer 522 in the memory 520.
The memory system 520 may be logically organized to perform storage functions that may be necessary for operation of the structure 500 as an equalizer. A first area 522 of the memory may store captured samples y′n for further processing. This area may double as the frame memory 250 and buffer 270 illustrated in FIG. 2. A second area 524 of the memory may store the decoded symbols dn. And, of course, a third area of memory 526 may store program instructions. The memory system 520 may be populated by electric, magnetic or optical memories or other storage elements which may be configured as a read-only memory (ROM) or random access memory (RAM).
As dictated by the instructions, operation of the processor 530 may be divided into logical units such as a reliable symbol detector 532, an adaptation unit 534 and a symbol decoder 536. The processor 530 may be a general purpose processor, a digital signal processor, an application-specific integrated circuit or a collection of processing elements. The processor 530 may generate data representing estimated source symbols {circumflex over (x)}n. These estimated source symbols may be output from the receiver structure 500 or, in an alternate embodiment, be returned to the memory 520 in a decoded symbol buffer 524 to await further processing, or both.
The foregoing discussion has presented techniques for identifying, from a sequence of captured samples, reliable symbols—samples that are likely to remain within the decision region of source symbols notwithstanding the presence of ISI corruption. Further, various data decoding techniques have been presented that permit ISI estimation to be carried out based on the identified reliable symbols and, therefore, permits decoding of all captured samples to occur. Additionally, the reliable symbol techniques permit equalization to occur as a “blind” process, without requiring use of training symbols to estimate the channel effect. The inventors have simulated transmission using 64-level QAM, 256-level QAM and 4096-level QAM. Use of these transmission constellations provides a 3 to 6-fold increase respectively in data transmission rates over 4-level QAM. Thus, the present invention contributes to data transmission systems having increased throughput without incurring expense in communication bandwidth.
Although the foregoing discussion refers to intersymbol interference as a source of data corruption affecting a source signal X, application of the present invention is not so limited. The present invention finds application in any situation in which data correlated noise occurs. References herein to “ISI” should be so construed.
Several embodiments of the present invention are specifically illustrated and described herein. However, it will be appreciated that modifications and variations of the present invention are covered by the above teachings and within the purview of the appended claims without departing from the spirit and intended scope of the invention.

## Claims

1. A channel gain estimation method for use in a communication system for transmitting symbols of a high order constellation, comprising:
identifying reliable symbols from a sequence of captured data samples recovered from a communication channel;
estimating a constellation size from a set of maximally-sized reliable symbols;
estimating a gain of the communication channel based on the estimated constellation size.

2. The channel gain estimation method of claim 1, further comprising estimating constellation points P^q within a square constellation with uniformly separated points according to:


P1^q=sign(q) (P1^max/(√M−1)) (2|q|−1), where

P1^max represents the estimated constellation size,
M represents an order of the constellation, and
q is an index provided along an axis of the constellation.

3. The channel gain estimation method of claim 1, further comprising estimating constellation points P1J^q within a general constellation according to:


P1J^q=sign(qj) (P1J^max/(√MJ−1)) (2|qJ|−1), where

P1J^max represents the estimated constellation size along a Jth axis,
MJ represents an order of the constellation along the Jth axis, and
qj is an index provided along the Jth axis of the constellation.

4. The channel gain estimation method of claim 1, further comprising revising the estimate of the constellation size based on additional reliable symbols.

5. The channel gain estimation method of claim 4, wherein the revising comprises estimating a second set of constellation points P2^q according to:


P2^q=P1^q+(|q|−1)·e1^, where



e1^=(1/s)Σq(1/(2|q|−1)Σn ∈sq(P1^q−ynq)



P1^q=sign(q) (P1^max/(√M−1)) (2|q|−1)

P1^max represents the estimated value of the magnitude of the maximum constellation point,
M represents an order of the constellation,
s is a number of detected reliable symbols,
sq is a set of reliable symbols that are associated with the constellation point q,
{n9} are the set of sample values which are reliable symbols that are associated with the qth estimated constellation point . . . and
q is an index provided along an axis of the constellation.

6. A reliable symbol identification method for use in a communication system for transmitting symbols of a high order constellation comprising:
calculating a reliability factor of a candidate sample from constellation points nearest to each of a plurality of other samples in proximity to the candidate sample, wherein the candidate sample and the plurality of other samples represent a data signal recovered from a communication channel,
if the reliability factor is less than a predetermined limit, designating the candidate sample as a reliable symbol.

7. The method of claim 6, wherein the reliability factor Rn of the candidate sample is given by:


Rn=Σi=−K1,i≠0K2(|Pn−i|ci, where

Pn−i is the value of a constellation point nearest to the sample yn−i which is in proximity to the candidate sample yn,
K1, K2 are numbers of samples adjacent to the candidate sample, and
ci, is a coefficient representing any prior knowledge of intersymbol interference effects.

8. The method of claim 6, wherein the reliability of a two-dimensional candidate sample yn is given by:


Rn=Σi=K1,i≠0K2√(P1n−i2+P2n−i2)·Ci, where

P1n−i and P2n−i respectively represent first and second dimensional values of a constellation point nearest to yn−i which is in proximity to the candidate sample yn,
K1, K2 are numbers of samples adjacent to the candidate sample, and
ci is a coefficient representing any prior knowledge of intersymbol interference effects.

9. The method of claim 6, further comprising, for any samples having similar reliability factors, prioritizing the samples based on the samples' values.

10. The method of claim 6, further comprising, for any sample having a reliability factor that is less than the predetermined limit, comparing the sample's value against a second threshold and, if the value exceeds the threshold, disqualifying the sample as a reliable symbol.

11. The method of claim 6 further comprising, for any samples having similar reliability factors, prioritizing the samples based on values of constellation points nearest to the samples.

12. The method of claim 6 further comprising, for any sample having a reliability factor that is less than the predetermined limit, comparing a value of a constellation point nearest to the sample to a second threshold and, if the value exceeds the threshold, disqualifying the sample as a reliable symbol.

13. A method of identifying reliable symbols for use in a communication system for transmitting symbols of a high order constellation, comprising:
for a candidate sample yn recovered from a communication channel:
iteratively, for i=−K1 to K2, i#0:
adding to a reliability factor a value derived from a constellation point nearest to a sample yn−i,
if the reliability factor exceeds a predetermined limit, disqualifying the candidate sample as a reliable symbol, and
otherwise, incrementing i and, if i=0, re-incrementing i for a subsequent iteration;
thereafter, unless the candidate symbol has been disqualified, designating the candidate sample as a reliable symbol.

14. The method of claim 13, wherein the adding adds a scaled value of the constellation point to the reliability factor, the value scaled in accordance with a predetermined coefficient ci, representing any prior knowledge of intersymbol interference effects.

15. The method of claim 13, the predetermined limit is (K1+K2) dmin where dmin is half a distance between two constellation points that are closest together in a governing constellation.

16. The method of claim 13, wherein the predetermined limit is the product of K1+K2 and half the width of an annular constellation ring associated with the candidate symbol.

17. A method of identifying reliable symbols for use in a communication system for transmitting symbols of a high order constellation, comprising:
for a candidate sample recovered from a communication channel:
determining whether any of a plurality of constellation points is within a predetermined threshold, where each of the plurality of constellation points is associated with samples neighboring the candidate sample also recovered from a communication channel,
if none of the constellation points exceed the threshold, designating the candidate sample as a reliable symbol.

18. The method of claim 17, wherein the neighboring samples occur in a first window adjacent to the candidate sample on one side of the candidate sample.

19. The method of claim 17, wherein the neighboring samples occur in a pair of windows that are adjacent to, and on either side of the candidate sample.