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.

Description:
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 x n , captured signals y n  at the destination  120  may be represented as:
 
 y   n   =a   0   ·x   n   +f ( x   n−K     1     , . . . ,x   n−1   ,x   n+1   , . . . ,x   n+K     2   )+ω n .  (1)
 
where a 0  represents a gain factor associated with the channel 130, f(x n−K     1   , . . . X n+K     2   ) is a functional representation that relates the ISI to the symbols, X n−K     1   , . . . X n+K     2   , causing ISI corruption and ω n  represents corruption from other sources. In linear systems, equation 2 may reduce to:
 
                   y   n     =       x   n     +       ∑           i   =       ⁢     -     K   1                   i   ≠       ⁢   0             K   2       ⁢           ⁢       a   i     ·     x     n   -   i           +     ω   n               (   2   )               
where a −K     1   , . . . a K     2    represent the values of the impulse response of the channel. In accordance to common practice, the values a i  have been normalized by the value of a 0  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 y n  that is very likely to be located within a decision region of a corresponding source symbol x n  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 y n  from a decision region of the symbol x n  from which it originated. 
   According to an embodiment of the present invention, identification of a signal y n  as “reliable” may be carried out using a reliability factor R n  given by: 
                   R   n     =       ∑           i   =       ⁢     -     K   1                   i   ≠       ⁢   0             K   2       ⁢            y     n   -   i            ·     c   l                 (   3   )               
where the c i  are constants representing any priori knowledge of the ISI effect that may be available. Generally, if nothing is known about the ISI, then the c l &#39;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 c i &#39;s may be given values reflecting this information. If the reliability factor of a sample y n  is less than a predetermined limit value, designated “d lim ” herein, the sample may be designated as a “reliable symbol.”
 
   Where samples on only one side of a candidate sample y n  contribute to the ISI, the reliability factor of the sample y n  may be determined using: 
                   R   n     =       ∑     i   =   1     K     ⁢            y     n   -   i            ·       c   i     .                 (   4   )               
where K=K 2  in equation 3. In respect to the forgoing reliability factors (equations (3) and (4)) the y n &#39;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   ≠       ⁢   0             K   2       ⁢           y     1     n   -   l       2     +     y     2     n   -   l       2         .     c   i                 (   5   )               
where y 1     n−i     2  and y 2     n−2     2  respectively represent values of y n−i  in the first and second dimensions.
 
   In another embodiment, the reliability factor R n  may be calculated based on the constellation symbols that are closest to the captured samples. Each captured sample y n  will be closest to one constellation point p n  from the constellation
 
 p   n   ={CP   p :min( CP−y   n )}  (6)
 
where CP is the set of all possible received constellation points.
 
   In this embodiment, reliability factors may be determined from the constellation points p n  according to one of: 
                     R   n     =       ∑           i   =       ⁢     -     K   1                   i   ≠       ⁢   0             K   2       ⁢            p     n   -   i            ·     c   i           ,     
     ⁢       R   n     =         ∑     i   =   1     K     ⁢              p     n   -   i            ·     c   i       ⁢           ⁢   or   ⁢           ⁢     R   n         =       ∑           i   =       ⁢     -     K   1                   i   ≠       ⁢   0             K   2       ⁢           p     1     n   -   l       2     +     p     2     n   -   l       2         ·     c   i                     (   7   )               
These formulae simply are an extension of equations 3–5 substituting p n−i  for y n−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 y n  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 y n  may be designated as a reliable symbol (box  1030 ). Otherwise, the sample y n  is not reliable. 
   The predetermined threshold d lim  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 d lim =(K 1 +K 2 )·d min  where d min  is half the distance between two constellation points that are closest together. This threshold is appropriate for the case where 
               1          a   0            ⁢       ∑       i   =     -     K   1           i   ≠   0         K   2       ⁢           ⁢          a   i              ≤   1.         
Experiments have shown, however, that operation can be maintained using the same threshold when
 
   
     
       
         
           
             
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   The threshold d lim  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 d lim , 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 d lim  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 d lim  value may be increased. Or, if the rate of detected symbols exceeds a second rate threshold, the d lim  value may be decreased. 
   In other embodiments, samples may be identified as reliable symbols based not only on reliability factors of the samples R n  but also may be based on the values of the sample itself (y n , p n ). In a given application, reliability factors of a plurality of candidate samples (say, y 1 , y 2 , y 3 ) each may be at or near the threshold (R n (y n )≈d lim , ∀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 R n  but also on the sample values y n  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 d lim  and if the sample value y n  (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 y n  is a reliable symbol. For operation of the method, an index variable i may be set to −K 1  and a reliability counter R n  may be set to zero (R n =0) (box  2010 ). The method may begin by adding to reliability counter R n  the value of a sample y n−i  (R n =R n +|y n−i |) (box  2020 ). Thereafter, if the reliability counter R n  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 y n . 
   If at box  2030  the reliability counter R n  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 y n  itself (box  2060 ), the index value may be incremented again. Otherwise, the method  2000  may determine whether i is greater than K 2  (box  2070 ). If so, then the candidate sample y n  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 y n−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., c i =1 for all i). When knowledge of the channel is available and c l  values may be determined for one or more i, then at box  2020  the reliability counter R n  may increment according to R n =R n +c i ·|y n−i | (shown as bracketed text in box  2020 ). 
   In this way, the method of operation  2000  examines the neighboring samples of y n  (K 1  precursors and K 2  postcursors) to see if y n  meets the criterion for being a reliable symbol. 
   When a destination captures a plurality of samples y n , 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 y j , by itself exceeds the reliability threshold then none of the neighboring symbols y i , i=j−K 1  to j+K 2 , 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 y n  that does not include y j  in its group of surrounding samples. In this embodiment, although the value of y j  may disqualify neighboring samples from being reliable symbols, y j  itself may be a reliable symbol. The method  2000  may operate on y j  to determine whether it is a reliable symbol. 
   Additionally, the surrounding samples may be selected, as a sub-set of the full range i=−K 1  to K 2  and the associated surrounding samples be examined. If a sequence of, say, three samples y j  to Y j+2  have values that would cause the reliability limit d lim  to be exceeded, then any sample y l  having the sequence of samples within the −K 1  to K 2  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 k 1  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 c l  is available. The method  3000  may initialize an index value i to −K 1  (box  3010 ). The method may determine whether the absolute value of a symbol Y n−i  occurs within a predetermined limit (box  3020 ). If not, the method terminate for candidate symbol y n ; it will not be designated as a reliable symbol (box  3030 ). If the value of y n−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&gt;K 2  (box  3060 ). If so, the sample y n  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&#39;s reliability may be calculated for the Q domain without regard for the sample&#39;s I value and also calculated for the I domain without regard for the sample&#39;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 y n−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 p n−i  substituting for the y n−i  as discussed above. 
   Alternatively, reliable symbols may be identified according to one or more of the techniques described in the Applicant&#39;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 Y RS  of reliable symbols, Y n ∈Y RS , a data decoder in a destination  120  may generate decoded symbols {circumflex over (x)} n  to be the constellation point closest to y n . The decoded symbol {circumflex over (x)} n  may be the destination&#39;s estimate of the source data symbol x n . 
   The foregoing embodiments find application in applications in which captured samples y n  do not exhibit phase offset with respect to the source symbols x n . Of course, in some applications, it may be expected that the captured samples y n  will exhibit a phase offset with respect to their source symbols x n . Where captured samples y n  exhibit a phase rotation with respect to the source symbols x n , a “reliable symbol” may be defined alternately as a sample y n  that is likely to be observed in the annular constellation ring of its source symbol x n . Restated, ISI corruption is unlikely to push the source symbol x n  from its constellation ring when observed as the captured sample y n  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   ⁢           ⁢     (     y     n   -   i       )         ·     c   i           ,           (   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 y n exhibit phase offset with respect to their source symbols x n . In this case, the threshold d lim  may be set according to half the width of the annular ring in which the captured sample y n  is observed. 
   In one embodiment a subset of the total range of power levels of y n  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 x n  from received non-reliable captured samples that are not reliable symbols (y n ∉Y RS ). 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 Y RS ∈Y RS  from a sequence of captured samples y n . The reliable symbol detector  310  may output the reliable symbols Y RS  and their surrounding samples (labeled y, in  FIG. 7 ) to the adaptation unit  320 . Based upon y RS  and y 1 , 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 M ISI , representing the ISI metrics. Based upon the ISI metrics, M ISI , the symbol decoder  330  may generate decoded symbols {circumflex over (x)} n  from the captured samples y n , for all n, regardless of whether the sample y n  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 Y RS  from a sequence Y of captured samples (Step  3010 ). Using this set of reliable symbols Y RS  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)} n from 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 y n . 
   Perhaps the simplest embodiment of equalizer is the subtractive equalizer. In the subtractive equalizer, the adaptation unit  320  estimates the channel ISI coefficients â i . Using the estimated coefficients â i  the symbol decoder  330  may estimate source symbols, {circumflex over (x)} n , by decoding y′ n  where: 
                   y   n   ′     =       y   n     -       ∑     i   =   1       K   2       ⁢         a   ^     i     ·       x   ^       n   -   i                     (   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 y n . 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 M isi . 
   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   =(   H     T     H   ) −1     H     T   δ   (11)
 
where:  â  is a vector of the ISI coefficient estimates; H is an N×M matrix, with N&gt;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 (K 1 =0,K 2 =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 a 1  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 = (   H     t     WH   ) −1     H     T     W   δ     (14)
 
where  W  is a diagonal N×N matrix of reliability weights w i,i  (w i,i =0 for all i≠j). In one such embodiment, the reliability weights w i,i  may be obtained as:
 
 w   i,i   =f ( R   i )  (15)
 
where R i  is the reliability factor associated with an i th  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 (a i , i=·K 1  to K 2 , i≠0) and also no a priori knowledge of the channel gain (a 0 ). 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)} 1   max  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)} i   1  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 M J  is the number of points along the J th  axis of the constellation and q J  is the index along a J th  axis of the constellation.
 
   Revising the Estimated Constellation Points 
   Returning to the regular case, an improved, {circumflex over (p)} 2   q , 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, s q  is a set of reliable symbols that are associated with the constellation point q as defined by Equation 18 and {y n   q  } are the set of sample values which are reliable symbols and are associated with the q th  estimated constellation point. Equation 18 defines a set of constellation point estimates for use in channel gain estimation. The channel gain a 0  may be estimated as a ratio of the first constellation point estimate {circumflex over (p)} 2   1  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 y n  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 d n . 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.