# Patent

## Title
Adaptive coefficient signal generator for adaptive signal equalizers with fractionally-spaced feedback

## Abstract

An adaptive coefficient signal generator for use in an adaptive signal equalizer with fractionally-spaced feedback. The signals representing the feedback tap coefficients are generated in conjunction with a timing interpolation parameter such that the fractionally-spaced feedback circuitry dynamically emulates symbol-spaced feedback circuitry.

## Background
RELATED APPLICATIONS
This is a continuation of U.S. patent application Ser. No. 10/322,024, filed on Dec. 17, 2002 now U.S. Pat. No. 7,039,104, which is a continuation-in-part of U.S. patent application Ser. No. 10/290,571, filed on Nov. 8, 2002 now U.S. Pat. No. 6,940,898.


BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to signal transmission and detection, and in particular, to techniques for compensating for signal distortions caused by signal dispersion and nonlinearities within the signal transmission media.
2. Description of the Related Art
Signal processing architectures for intersymbol interference (ISI) equalization as used for communications transmission and/or storage systems may be divided into two categories: discrete-time architecture and continuous-time architecture. Discrete-time architectures, commonly used in current systems, use a sampled approach to render the input continuous-time, analog waveform in discrete form. Typically, a high resolution A/D converter, which follows the analog anti-aliasing filter, is used as the sampler at the analog front end. Continuous-time architectures use an analog continuous-time approach which directly processes and equalizes the incoming analog waveform while remaining in the continuous time domain until the final data bit stream is generated.
At present, those signal processing architectures having a feedforward transversal filter and a feedback filter as their basic components are considered, and in particular, the following scenarios: discrete-time/continuous-time architectures with fractionally-spaced (i.e., tap spacing less than symbol-spaced) feedforward taps; continuous-time architecture with feedback that is nominally symbol-spaced; continuous-time/discrete-time architectures with fractionally-spaced feedback. For purposes of the presently claimed invention, the following discussion concerns “fat tap” adaptation to cover the continuous-time architecture with fractionally-spaced feedback; however, such discussion may be readily extended to cover the other scenarios as well.
Fractional-spaced feedforward filters have commonly been used either as stand-alone linear equalizers or in combination with Decision Feedback. Advantages of fractional-spaced versus symbol-spaced feedforward filters include: added robustness to constant or slowly varying sampling phase offset or sampling jitter; and improved signal-to-noise ratio (SNR) sensitivity, particularly in the absence of complete channel information, due to the role of the fractional-spaced filter as a combined adaptive matched filter and equalizer.
The adaptation technique for the tap coefficients have always implicitly assumed independence in the adaptation of the successive tap coefficients, which has been based on minimizing the mean squared error (MSE) as computed using the difference between the slicer input and output. This adaptation technique is referred to as LMSE (least mean squared error) or MMSE (minimized mean squared error) adaptation. It can be shown that the LMSE adaptation for both fractional feedforward or symbol spaced feedback at iteration k+1 reduces to the following coefficient update equations:

c(k+1)=c(k)+μe(k)s (discrete-time adaptation case)

where c(k) is the tap coefficient vector and e(k) the corresponding error at the kth iteration, s is the vector with components as the input waveform to the corresponding tap mixer and μ is a constant and is an adaptation parameter; and





  
    c
    _
  
  =
  
    
      ∫
      0
      t
    
    ⁢
    
      
        μ
        ·
        
          e
          ⁡
          
            (
            t
            )
          
        
      
      ⁢
      
        
          s
          _
        
        ⁡
        
          (
          t
          )
        
      
      ⁢
      
        
      
      ⁢
      
        d
        
          t
          ⁡
          
            (
            
              continuous
              ⁢
              
                -
              
              ⁢
              time
              ⁢
              
                
              
              ⁢
              adaptation
              ⁢
              
                
              
              ⁢
              case
            
            )
          
        
      
    
  




with similar terminology as above.

When continuous-time feedback is considered, a number of difficulties are encountered. For example, it is difficult and sometimes unfeasible to design precisely symbol-spaced, flat group delay filters. If the total group delay on the feedback path for canceling successive past symbols is even slightly different from the corresponding symbol period, the performance loss can be substantial. This may necessitate the need for using fractionally-spaced feedback filters. Fractionally-spaced feedback filters may also be needed to account for the slicer-induced jitter and/or the data bits pattern-specific group delays due to frequency dependent group delays of the slicer, mixer and any other analog/digital component on the feedback data path. Further when an equalizer with fractionally-spaced feedback taps is used, independent LMS adaptation of the successive feedback taps fails because of the strongly correlated nature of the fractional tap-spaced feedback data.
SUMMARY OF THE INVENTION
In accordance with the presently claimed invention, an adaptive coefficient signal generator for use in an adaptive signal equalizer with fractionally-spaced feedback generates signals representing feedback tap coefficients in conjunction with a timing interpolation parameter such that the fractionally-spaced feedback circuitry dynamically emulates symbol-spaced feedback circuitry. Advantages realized with the presently claimed invention include avoidance of a need for precisely symbol-spaced flat group delay filters, and the ability to account for slicer-induced jitter as well as variable group delays specific to certain data bit patterns due to frequency dependent group delays of various system elements (e.g., slicer(s) and mixer(s) in the feedback data path).
As will become evident from the following discussion, the presently claimed invention can be implemented and practiced in either the continuous time (e.g., analog) or discrete time (e.g., digital) domain. At the present point in time, data symbol rates less than one gigabit per second (1 Gb/s) can often be processed in either the continuous or discrete time domain, while data symbol rates greater than 1 Gb/s must generally be processed in the continuous time domain. However, as the applicable technology advances, it is expected that data symbol rates in excess of 1 Gb/s will also become more susceptible to processing in the discrete time domain as well. As will become further evident, the presently claimed invention benefits the host system or network by effectively increasing the signal-to-noise ratio (SNR), thereby reducing the bit error rate (BER) and, in turn, adding robustness (e.g., with respect to phase offsets or jitter among the data symbols). For example, in the case of a fiber optic network, such added performance and robustness will allow a longer network to be realized without a concomitant increase in network infrastructure.
In accordance with one embodiment of the presently claimed invention, an adaptive feedback coefficient signal generator for use in an adaptive signal equalizer with an adaptive filter responsive to a plurality of adaptive filter coefficient signals related to an error signal, with fractionally-spaced feedback and in which an equalization feedback signal adaptively equalizes an incoming data signal to form a pre-slicer data signal that is sliced to provide a post-slicer data signal includes signal multiplication circuitry, signal combining circuitry, signal integration circuitry, signal weighting circuitry and signal complement circuitry. First signal multiplication circuitry receives and multiplies a plurality of multiplicand signals to provide a plurality of product signals. The plurality of multiplicand signals includes: a first data signal corresponding to a post-slicer data signal and having a data symbol period associated therewith; a second data signal corresponding to the first data signal and delayed by a fraction of the data symbol period; an error signal corresponding to a difference between the post-slicer data signal and a pre-slicer data signal; a first adaptation control signal having a first value bounded by lower and upper values; and a second adaptation control signal having a second value related to a difference between a normalized value and the first value. The plurality of product signals includes: a first product signal corresponding to a product of the first data signal, the error signal and the first adaptation control signal; and a second product signal corresponding to a product of the second data signal, the error signal and the second adaptation control signal. The signal combining circuitry, coupled to the first signal multiplication circuitry, receives and combines the plurality of product signals to provide a combined signal. The signal integration circuitry, coupled to the signal combining circuitry, receives and integrates the combined signal to provide a third adaptation control signal. Second signal multiplication circuitry, coupled to the signal integration circuitry, receives and multiplies the first, second and third adaptation control signals to provide a plurality of adaptive feedback coefficient signals. The signal weighting circuitry, coupled to the first signal multiplication circuitry and the second signal multiplication circuitry, receives a plurality of weighted coefficient signals and in response thereto receives and weights a plurality of adaptive filter coefficient signals to provide the first adaptation control signal. The signal complement circuitry, coupled to the first signal multiplication circuitry, the second signal multiplication circuitry and the signal weighting circuitry, receives and complements the first adaptation control signal to provide the second adaptation control signal.
In accordance with another embodiment of the presently claimed invention, an adaptive feedback coefficient signal generator for use in an adaptive signal equalizer with an adaptive filter responsive to a plurality of adaptive filter coefficient signals related to an error signal, with fractionally-spaced feedback and in which an equalization feedback signal adaptively equalizes an incoming data signal to form a pre-slicer data signal that is sliced to provide a post-slicer data signal includes first and second control signal generator circuitry. The first control signal generator circuitry receives and processes a plurality of input signals and first and second adaptation control signals and in response thereto provides a plurality of adaptive feedback coefficient signals. The plurality of input signals includes: a first data signal corresponding to a post-slicer data signal and having a data symbol period associated therewith; a second data signal corresponding to the first data signal and delayed by a fraction of the data symbol period; and an error signal corresponding to a difference between the post-slicer data signal and a pre-slicer data signal. The second control signal generator circuitry, coupled to the first control signal generator circuitry, receives and processes a plurality of adaptive filter coefficient signals and in response thereto provides the first and second adaptation control signals.
In accordance with another embodiment of the presently claimed invention, a method for generating adaptive feedback coefficient signals for adaptive signal equalization using an adaptive filter responsive to a plurality of adaptive filter coefficient signals related to an error signal, fractionally-spaced feedback and an equalization feedback signal to generate an adaptively equalized data signal as a pre-slicer data signal that is sliced to provide a post-slicer data signal includes:
receiving and multiplying a plurality of multiplicand signals to generate a plurality of product signals, wherein

    
    
        the plurality of multiplicand signals includes
        
            a first data signal corresponding to a post-slicer data signal and having a data symbol period associated therewith,
            a second data signal corresponding to the first data signal and delayed by a fraction of the data symbol period,
            an error signal corresponding to a difference between the post-slicer data signal and a pre-slicer data signal,
            a first adaptation control signal having a first value bounded by lower and upper values, and
            a second adaptation control signal having a second value related to a difference between a normalized value and the first value, and
        
        
        the plurality of product signals includes
        
            a first product signal corresponding to a product of the first data signal, the error signal and the first adaptation control signal, and
            a second product signal corresponding to a product of the second data signal, the error signal and the second adaptation control signal;
        
        
    
    


combining the plurality of product signals to generate a first combined signal;
integrating the first combined signal to generate a third adaptation control signal;
multiplying the first, second and third adaptation control signals to generate a plurality of adaptive coefficient signals;
receiving a plurality of weighted coefficient signals and in response thereto receiving and weighting a plurality of adaptive filter coefficient signals to generate the first adaptation control signal; and
complementing the first adaptation control signal to generate the second adaptation control signal.
In accordance with another embodiment of the presently claimed invention, a method for generating adaptive feedback coefficient signals for adaptive signal equalization using an adaptive filter responsive to a plurality of adaptive filter coefficient signals related to an error signal, fractionally-spaced feedback and an equalization feedback signal to generate an adaptively equalized data signal as a pre-slicer data signal that is sliced to provide a post-slicer data signal includes:
receiving and processing a plurality of input signals and first and second adaptation control signals to generate a plurality of adaptive feedback coefficient signals, wherein the plurality of input signals includes

    
    
        a first data signal corresponding to a post-slicer data signal and having a data symbol period associated therewith,
        a second data signal corresponding to the first data signal and delayed by a fraction of the data symbol period, and
        an error signal corresponding to a difference between the post-slicer data signal and a pre-slicer data signal; and
    
    


receiving and processing a plurality of adaptive filter coefficient signals to generate the first and second adaptation control signals.



BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a block diagram of decision feedback equalization (DFE) circuitry in which an adaptive coefficient signal generator in accordance with the presently claimed invention can advantageously provide for improved data signal equalization.
FIG. 2 is a block diagram of the feedback portion of a DFE circuit in which an adaptive coefficient signal generator in accordance with the presently claimed invention is used to provide the adaptive coefficient signals.
FIG. 3 is a block diagram of one embodiment of an adaptive coefficient signal generator in accordance with the presently claimed invention.
FIG. 4 is a block diagram of an exemplary implementation of the adaptive coefficient signal generator of FIG. 3.
FIG. 5 is a block diagram of another embodiment of an adaptive coefficient signal generator in accordance with the presently claimed invention.
FIG. 6 is a block diagram of an exemplary implementation of the adaptive coefficient signal generator of FIG. 5.
FIG. 7 is a block diagram of an alternative implementation of the adaptive coefficient signal generator of FIG. 4.
FIG. 8 is a block diagram of an alternative implementation of the adaptive coefficient signal generator of FIG. 6.
FIG. 9 is a block diagram depicting signal adaptation using correlated taps in accordance with another embodiment of the presently claimed invention.
FIG. 10 is a block diagram of another embodiment of an adaptive coefficient signal generator in accordance with the presently claimed invention.
FIG. 11 is a block diagram of feedforward equalization (FFE) circuitry with which the adaptive coefficient signal generator of FIG. 10 can share adaptive filter coefficient signals.
FIG. 12 is a block diagram of an exemplary implementation of an adaptive filter coefficient signal generator for providing adaptive filter coefficient signals for the adaptive coefficient signal generator of FIG. 10.
FIG. 13 is a block diagram of an exemplary implementation of a portion of the adaptive coefficient signal generator of FIG. 10.
FIG. 14 is a block diagram of an alternative implementation of a portion of the adaptive coefficient signal generator of FIG. 10.
FIG. 15 is a block diagram of an exemplary implementation of the adaptive coefficient signal generator of FIG. 10.
FIGS. 16A and 16B illustrate expected performance improvement with use of an analog continuous-time feedforward filter in conjunction with “fat tap” adaptation in accordance with the presently claimed invention.



DETAILED DESCRIPTION OF THE INVENTION
The following detailed description is of example embodiments of the presently claimed invention with references to the accompanying drawings. Such description is intended to be illustrative and not limiting with respect to the scope of the present invention. Such embodiments are described in sufficient detail to enable one of ordinary skill in the art to practice the subject invention, and it will be understood that other embodiments may be practiced with some variations without departing from the spirit or scope of the subject invention.
Throughout the present disclosure, absent a clear indication to the contrary from the context, it will be understood that individual circuit elements as described may be singular or plural in number. For example, the terms “circuit” and “circuitry” may include either a single component or a plurality of components, which are either active and/or passive and are connected or otherwise coupled together to provide the described function. Additionally, the term “signal” may refer to one or more currents, one or more voltages, or a data signal. Within the drawings, like or related elements will have like or related alpha, numeric or alphanumeric designators. Further, while the present invention has been discussed in the context of implementations using discrete electronic circuitry (preferably in the form of one or more integrated circuit chips), the functions of any part of such circuitry may alternatively be implemented using one or more appropriately programmed processors, depending upon the signal frequencies or data rates to be processed.
The subject matter discussed herein, including the presently claimed invention, is compatible and suitable for use with the subject matter disclosed in the following copending, commonly assigned patent applications (the disclosures of which are incorporated herein by reference): U.S. patent application Ser. No. 10/117,293, filed Apr. 5, 2002, and entitled “Compensation Circuit For Reducing Intersymbol Interference Products Caused By Signal Transmission Via Dispersive Media”; U.S. patent application Ser. No. 10/179,689, filed Jun. 24, 2002, and entitled “Crosstalk Compensation Engine For Reducing Signal Crosstalk Effects Within A Data Signal”; U.S. patent application Ser. No. 10/244,500, filed Sep. 16, 2002, and entitled “Compensation Method For Reducing Intersymbol Interference Products Caused By Signal Transmission Via Dispersive Media”; U.S. patent application Ser. No. 10/290,674, filed Nov. 8, 2002, and entitled “Compensation Circuit And Method For Reducing Intersymbol Interference Products Caused By Signal Transmission Via Dispersive Media”; U.S. patent application Ser. No. 10/290,993, filed Nov. 8, 2002, and entitled “Adaptive Signal Equalizer With Adaptive Error Timing And Precursor/Postcursor Configuration Control”; U.S. patent application Ser. No. 10/321,893, filed Dec. 17, 2002 and entitled “Adaptive Signal Latency Control For Communications Systems Signals”; U.S. patent application Ser. No. 10/321,876, filed Dec. 17, 2002 and entitled “Adaptive Signal Equalizer With Adaptive Error Timing And Precursor/Postcursor Configuration Control”; and U.S. patent application Ser. No. 10/179,996, filed Jun. 24, 2002, and entitled “Programmable Decoding of Codes of Varying Error-Correction Capability”.
In accordance with the presently claimed invention, a group of two or more adjacent fractionally-spaced feedback taps are viewed to be correlated and corresponding to essentially the same symbol so that this group of fractionally-spaced taps essentially emulates a symbol-spaced feedback tap. Such a group of fractionally-spaced taps that emulates a symbol-spaced feedback tap is referred herein as a “fat tap.” Thus, successive fat taps emulate different symbol-spaced feedback taps. The adaptation of the taps within the fat tap should have some kind of adaptive timing interpolation between them so that the effective timing of the fat tap corresponds to the corresponding symbol timing. Further, both taps in the fat tap need to adapt together using LMSE adaptation, for instance, since their inputs are correlated.
The emphasized case will be that in which successive fat taps consist of disjoint taps and, thus, represent independent symbols (e.g., referred to as Independent Fat Tap Adaptation (IFTA)). Also emphasized will be the case with the constraint of only two taps within the fat tap.
Let the feedback tap spacing be denoted by τ which is sufficiently less than the symbol period. It is assumed that the feedback symbol waveform is approximately piece-wise linear within the span of time interval τ. Thus, if the feedback signal is denoted as s(t), the parametric equation of the line passing through s(t) and s(t−τ) may be denoted via:

r·s(t)+(1−r)·s(t−τ)

for the parameter r (in general, −∞<r<∞). With the piecewise linear assumption of s(t), we have:

s(t−τr)≈r·s(t)+(1−r)·s(t−τ)

for a suitable choice of the delay τr. Note that with the piecewise linear approximation:

τr≈(1−r)·τ

With a linear approximation of the feedback signal waveform, we represent the two tap coefficients of the fat tap as c·r and c·(1−r) where the quantity r is the timing interpolation parameter which ideally should achieve effective symbol spaced timing for the fat tap, and the quantity c is used for LMSE adaptation for estimating the past ISI that needs to be cancelled. Thus, with these two parameters, the fat tap tries to emulate the corresponding symbol-spaced feedback tap with LMS tap coefficient c. The correlation ratio between the two adapting taps of the fat tap is then




  
    r
    
      1
      -
      r
    
  
  .




It is then required to adapt the parameters c and r for the fat tap.

For the continuous-time case, the LMSE adaptation of the parameters c and r can then be shown to be:



  
    
      
        c
        ⁡
        
          (
          t
          )
        
      
      =
      
        
          μ
          c
        
        ·
        
          
            ∫
            0
            t
          
          ⁢
          
            
              
                e
                ⁡
                
                  (
                  v
                  )
                
              
              ·
              
                [
                
                  
                    r
                    ·
                    
                      s
                      ⁡
                      
                        (
                        v
                        )
                      
                    
                  
                  +
                  
                    
                      (
                      
                        1
                        -
                        r
                      
                      )
                    
                    ·
                    
                      s
                      ⁡
                      
                        (
                        
                          v
                          -
                          τ
                        
                        )
                      
                    
                  
                
                ]
              
            
            ⁢
            
              
            
            ⁢
            
              d
              v
            
          
        
      
    
    ;
  




  
    
      r
      ⁡
      
        (
        t
        )
      
    
    =
    
      
        μ
        r
      
      ·
      
        
          ∫
          0
          t
        
        ⁢
        
          
            
              c
              ⁡
              
                (
                v
                )
              
            
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                    (
                    v
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                -
                
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                    (
                    
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                      -
                      τ
                    
                    )
                  
                
              
              ]
            
          
          ⁢
          
            
          
          ⁢
          
            d
            v
          
        
      
    
  



If, as may be typical, sign(c)=−1, and since





  
    
      
        s
        ⁡
        
          (
          v
          )
        
      
      -
      
        s
        ⁡
        
          (
          
            v
            -
            τ
          
          )
        
      
    
    ≈
    
      k
      ⁢
      
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      ⁢
      
        s
        ⁡
        
          (
          
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            -
            
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  ,




for a constant k, the update equation for r(t) may also be simplified to:





  
    r
    ⁡
    
      (
      t
      )
    
  
  =
  
    
      -
      
        μ
        r
        1
      
    
    ·
    
      
        ∫
        0
        t
      
      ⁢
      
        
          
            e
            ⁡
            
              (
              v
              )
            
          
          ·
          
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              v
            
          
        
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          ⁡
          
            (
            
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              -
              
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                r
              
            
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            d
            v
          
          .
        
      
    
  




Note that





  
    d
    
      d
      t
    
  
  ⁢
  
    s
    ⁡
    
      (
      
        t
        -
        
          τ
          r
        
      
      )
    
  




may easily be implemented by passing the output of the fat tap through a C-R differentiator block, which is a high-pass filter.

For the discrete-time case, the LMSE adaptation of the parameters c and r can then be shown to be:

c(k+1)=c(k)+μc·e(k)·[r(k)·s(t)+(1−r(k))·s(t−τ)]

r(k+1)=r(k)+μr·c(k)·e(k)·[s(t)−s(t−τ)]

The update equation for r can also be simplified to (if its known that sign(c) =−1):

r(k+1)=r(k)−μr·e(k)·[s(t)−s(t−τ)]

The next step is determining which pair of two (or more) taps belong to the same fat tap. The specific two adjacent taps which form a fat tap corresponding to a specific past symbol may vary depending on the group delay variations of different analog or digital components within the feedback path such as the slicer, delay elements, summer, mixer, etc. One approach is to hypothesize that different (disjoint) pairs of taps correspond to different fat taps corresponding to different past symbols. Then, depending on the values of the feedback tap coefficients after convergence, specifically the timing interpolation parameter which should ideally be within the range (0,1) and/or the hypothesis which corresponds to the minimum mean squared error, the winning hypothesis may be selected as part of the start-up procedures of the circuit. (As noted above, ideally 0<r<1, although in general, −∞<r<∞. However, it should be understood that maximum advantages of timing interpolation as provided by the presently claimed invention are realized when 0<r<1 (e.g., where the complement 1−r of r when r=0.2 is 1−r=1−0.2=0.8). When r lies outside of the range (0,1), i.e., −∞<r<0 or 1<r<∞ (e.g., where the complement 1−r of r when r=1.2 is 1−r=1−1.2=−0.2), extrapolation takes place instead of interpolation and performance degradation may result.
Referring to FIG. 1, a decision feedback equalizer (DFE) 100 typically includes a feed forward filter 102 and a feedback filter 104. The feedback filter 104 processes the decisions dk from the output of the final signal slicer 106. The coefficients, or gains, F*i can be adjusted to cancel ISI on the current symbol based upon past detected symbols. The feed forward filter 102 has N1+N2+1 taps while the feedback filter 104 has N3 taps, and the output {circumflex over (d)}k 109 of the final signal summer 108 can be expressed as follows:




  
    
      d
      ^
    
    k
  
  =
  
    
      
        ∑
        
          n
          =
          
            -
            
              N
              1
            
          
        
        
          N
          2
        
      
      ⁢
      
        
          c
          n
          *
        
        ⁢
        
          y
          
            k
            -
            n
          
        
      
    
    +
    
      
        ∑
        
          i
          =
          1
        
        
          N
          3
        
      
      ⁢
      
        
          F
          i
        
        ⁢
        
          d
          
            k
            -
            i
          
        
      
    
  




where

    
    
        c*n=tap gains for feed forward filter 102
        yn=input signals to feed forward filter 102
        F*i=tap gains for feedback filter 104
        di(i<k)=previous decision made upon detected signal dk 
    
    


Accordingly, once the output dk is provided by the output summer 108 of the feed forward filter 102, the final output dk is decided. Then, the final output dk and the previous decisions dk−1, dk−2, . . . are fed back through the feedback filter 104, thereby providing the solution for the next decision {circumflex over (d)}k+1 at the output 109 of the final signal summer 108 in the feed forward filter 102 in accordance with the foregoing equation.
More specifically, with respect to the feedback filter section 104, the output signal 107 is successively delayed through a sequence of time delay elements 110a, . . . 110n (e.g., with each successive time delay element 110 imparting a time delay equal to one symbol). Each of the successively time-delayed signals 111a, . . . 111n are processed in their respective adaptive gain stages 112a, . . . 112n to provide corresponding adaptive feedback signals 113a, . . . 113n which are summed together in a signal summing circuit 114 to produce the equalization feedback signal 115.
The adaptive gain stages 112a, . . . 112n process their respective time-delayed signals 111a, . . . 111n based upon an error signal 117 representing the error, if any, between the post-slicer data signal 107 and the pre-slicer data signal 109. This error signal 117 is typically generated by subtracting the pre-slicer data signal 109 from the post-slicer data signal 107 in a signal summing circuit 116.
Referring to FIG. 2, a feedback filter 104a for use in a DFE in a continuous time signal application includes the time delay elements 110 as well as the adaptive gain stages 112. In accordance with the presently claimed invention, each of the time delay elements 110 is a fractional delay element and, therefore, imparts to its data signal a time delay of a fraction of the data symbol, and each of the adaptive gain stages 112 is a multiplier that multiplies its respective time-delayed input signal 111 by one of two adaptive coefficient signals 205b, 205c (discussed in more detail below). Additionally, a fat tap adaptation (FTA) stage 200 is included. As discussed in more detail below, this FTA stage 200 provides the adaptive coefficient signals 205b, 205c. In accordance with one embodiment, this FTA stage 200 provides these adaptive coefficient signals 205b, 205c in accordance with the error signal 117 and the corresponding time-delayed signal 111a, 111b processed by the related adaptive gain stages 112aa, 112ba. In accordance with another embodiment, the FTA stage 200 also uses the equalization feedback signal 115.
It should be understood that, in conformance with the discussion herein, additional pairs of adaptive gain stages 112 can also have corresponding FTA stages 200; however, only one such FTA stage 200 is shown in FIG. 2 for purposes of simplified illustration.
By using the adaptive coefficient signals 205b, 205c provided by the FTA stage 200, adaptive gain stages 112aa and 112ba operate as correlated taps since adaptive coefficient signals 205b and 205c are correlated (discussed in more detail below). On the other hand, those among the remaining adaptive gain stages 112ca, . . . , 112na−1, 112na that do not use a corresponding FTA stage 200 are independent taps to the extent that their respective adaptive coefficient signals Cca, . . . , Cna−1, Can are independent, i.e., uncorrelated.
Referring to FIG. 3, one example 200a of the FTA stage 200 (FIG. 2) includes multiplier circuits 202a, 202b and control signal generator circuitry implemented as a coefficient signal generator 204a and a timing interpolation parameter signal generator 206a, all interconnected substantially as shown. The adjacent time-delayed feedback signals 111a, 111b are multiplied in their respective multiplier circuits 202a, 202b with the error signal 117. The resulting product signals 203a, 203b are processed by the control signal generator circuits 204a, 206a. As discussed in more detail below, the first control signal generator circuit 204a provides an adaptation control signal 205a to the second control signal generator circuit 206a which, in return, provides two other adaptation control signals 207a, 207b to the first control signal generator 204a. As a result of processing these input signals 203a, 203b, 207a, 207b, the first control signal generator circuit 204a provides the adaptive coefficient signals c(t)r(t) 205b, c(t)(1−r(t)) 205c, where signal element c(t) is the weighting factor and signal element r(t) is the factor indicative of the degree of correlation between the adjacent time-delayed feedback signals 111a, 111b. 
Referring to FIG. 4, one example 200aa of the FTA circuit 200a of FIG. 3 implements the control signal generators 204a, 206a substantially as shown. In the first control signal generator 204aa, the initial product signals 203a, 203b are further multiplied in further multiplier circuits 212aa, 212ba with the adaptation control signals 207aa, 207ba from the other control signal generator 206aa. An additional constant signal 211 can also be multiplied as part of the product operations, or can be implemented as a constant scaling factor within the multiplier circuits 212aa, 212ba. 
The resulting product signal 213aa, 213ba are summed in a signal summing circuit 214. The resulting sum signal 215 is integrated in an integration circuit 216 (e.g., a low pass filter) to produce the first adaptation control signal 205aa. This adaptation control signal 205aa, in addition to being provided to the other control signal generator 206a, is multiplied within further multiplication circuits 218a, 218b with the other adaptation control signals 207aa, 207ba provided by the other control signal generator 206aa. The product signals resulting from these multiplication operations are the adaptive coefficient signals 205ba, 205ca. 
In the second control signal generator 206aa, the initial product signals 203a, 203b are differentially summed in a signal summing circuit 222, where the second product signal 203b is subtracted from the first product signal 203a. The resulting difference signal 223 is multiplied in a multiplier circuit 224a with the adaptation control signal 205aa provided by the first control signal generator 204aa. As with the input multiplier circuits 212aa, 212ba of the first control signal generator 204aa, an additional constant signal 221 can also be used in this multiplication operation, or, alternatively, be implemented as a constant scaling factor within the multiplication circuit 224a operation.
The resulting product signal 225 is integrated by another signal integration circuit 226 (e.g., a low pass filter) to produce one of the adaptation control signals 207aa used by the first control signal generator 204aa. 
This adaptation control signal 207aa is further processed by a signal complement circuit 228 in which the input signal 207aa is subtracted from a reference signal having a normalized value, with the resulting difference signal 207ba serving as the other adaptation control signal used by the first control signal generator 204aa. For example, if the value of the incoming signal 207aa were considered to have a normalized signal value range bounded by the values of zero and unity, the signal complement circuit 228 subtracts the incoming signal 207aa from the value of unity to produce the output signal 207ba. 
Referring to FIG. 5, another embodiment 200b of the FTA circuitry 200 (FIG. 2) uses alternative implementations 204b, 206b of the control signal generators to process the incoming data signals 111a, 111b, the error signal 117 and the equalization feedback signal 115.
Referring to FIG. 6, one implementation 200ab of the FTA circuit 200b of FIG. 5 can be implemented substantially as shown. In the first control signal generator 204ba, the time-delayed data signals 111a, 111b and error signal 117 are multiplied in the multiplier circuits 212ab, 212bb (with the multiplication, or scaling, constant 211 included as part of the operation as discussed above) along with the adaptation control signals 207ab, 207bb from the other control signal generator 206ba. The resulting product signals 213ab, 213bb are summed in the summing circuit 214. The resulting sum signal 215 is integrated in the signal integration circuit 216 (e.g., a low pass filter) to produce an adaptation control signal 205ab (which, in this implementation, is used internally and is not provided to the other control signal generator 206ba). This signal 205ab is multiplied in output multiplier circuits 218a, 218b with the adaptation control signals 207ab, 207bb provided by the other control signal generator 206ba to produce the adaptive coefficient signals 205bb, 205cb. 
In the second control signal generator 206ba, the equalization feedback signal 115 is differentiated in a signal differentiation circuit 232 (e.g., a high pass filter). The resulting differentiated signal 233 is multiplied in a multiplier circuit 224b with the error signal 117 (with the multiplication, or scaling, constant 221 included as part of the operation as discussed above). The resulting product signal 207ab forms one of the adaptation control signals provided to the first control signal generator 204ba. This signal 207ab is also complemented by the signal complement circuit 228 (as discussed above) to produce the other adaptation control signal 207bb provided to the first control signal generator 204ba. 
Referring to FIG. 7, an adaptive coefficient signal generator in accordance with another embodiment 300 of the presently claimed invention includes error mixer stages 302, 304, a complement integrating mixer stage 306, an integrating mixer stage 308 and a complement coefficient mixer stage 312, all interconnected substantially as shown. The time-delayed data signals 111a, 111b are received and processed by the error mixer stages 302, 304. Each error mixer stage 302, 304 multiplies these signals 111a, 111b with the error signal 117 in signal multipliers 352, 354. The resulting product signals 353, 355 are summed in a signal combiner 356 and the sum signal 357 is integrated by a signal integration circuit 358 (e.g., a low pass filter).
The signals 303, 305 produced by these mixer stages 302, 304 are further processed by the complement integrating mixer stage 306 and integrating mixer stage 308. The complement integrating mixer 306 multiplies signals 303 and 305 in signal multipliers 360, 362 with the signal 309 produced by the integrating mixer stage 308. The resulting product signals 361, 363 are summed in a signal combiner 364. The sum signal 365 is integrated by a signal integration circuit 366 (e.g., a low pass filter).
The integrating mixer stage 308 multiplies signal 303 and signal 305 (which is inverted by a signal inversion circuit 310) in signal multipliers 370, 372 with the signal 307 produced by the complement integrating mixer stage 306. The resulting product signals 371, 373 are summed in a signal combiner 374. The sum signal 375 is integrated by a signal integration circuit 376 (e.g., a low pass filter).
The signals 307, 309 produced by the complement integrating mixer stage 306 and integrating mixer stage 308 are multiplied in the signal multipliers 380, 382 of the complement coefficient mixer stage 312 with the signal 309 produced by the integrating mixer stage 308. The resulting product signals 381, 383 are integrated in respective signal integration circuits 384, 386 (e.g., low pass filters), thereby producing the adaptive coefficient signals 205bc, 205cc. 
Referring to FIG. 8, an adaptive coefficient signal generator in accordance with another embodiment 240 of the presently claimed invention shares some similarities with the implementation shown in FIG. 6. The data signals 111a, 111b are multiplied in multiplier circuits 212ac, 212bc (with a multiplication, or scaling, constant 211 as desired). The resulting product signals 213ac, 213bc are summed in a signal combiner 214a and the sum signal 215a is buffered by a gain stage 214b. The resulting buffered signal 215b is multiplied in a signal multiplier 118 with an integrated signal 245 (discussed in more detail below) to produce the equalization feedback signal 115a, and is also processed by two signal delay stages 246, 248 (discussed in more detail below).
The buffered signal 215b is processed by the first signal delay stage 246, which compensates for signal delays introduced by the signal slicer 106 (FIG. 1), the feedback signal multiplication circuit 118 and the feedback signal summing circuitry 108 (FIG. 1) while subtracting out a delay corresponding to that introduced by the signal inversion circuitry 250 and signal differentiation circuit 232a. The delayed signal 247 is inverted in a signal inversion circuit 250. The inverted signal 251 is differentiated in a signal differentiation circuit 232a (e.g., a high pass filter).
The differentiated signal 233a is multiplied in a signal multiplier 224c with the error signal 117 (along with a multiplication, or scaling, constant 221 as desired). The resulting product signal 225c is integrated in a signal integration circuit 226a (e.g., a low pass filter) to produce the adaptation control signal 227a for signal multiplier 212bc. This signal 227a is also complemented by a signal complement circuit 228a (as discussed above) to produce the other adaptation control signal 229a for signal multiplier 212ac. 
The second signal delay stage 248 compensates for signal delays introduced by the signal slicer 106 (FIG. 1), the feedback multiplier 118 and feedback signal summer 108 (FIG. 1). The resulting delayed signal 249 is multiplied in a signal multiplier 242 with the error signal 117. The resulting product signal 243 is integrated in a signal integration circuit 244 (e.g., a low pass filter). The integrated signal 245 is multiplied with the buffered signal 215b in the feedback signal multiplier 118 to produce the equalization feedback signal 115a. 
Referring to FIG. 9, the adaptive coefficient signals as discussed above can be used in an adaptive signal equalizer with fractionally-spaced feedback in a number of ways. As discussed above, the time-delayed data signals 111a, 111b are multiplied in signal multipliers 112aa, 112ba with the adaptive coefficient signals 205b, 205c, with the resulting product signals 113aa, 113ba combined in a signal combiner 114a to produce a signal 115a which may or may not be the final equalization feedback signal (discussed in more detail below). For example, in scenario A, the first adaptation control signal 205b corresponds to a product of a weighting factor c(t) and the correlation factor r(t), while the second adaptation control signal 205c corresponds to a product of the weighting factor c(t) and the complement [1−r(t)] of the correlation factor r(t). The sum signal 115a can be used directly as the final equalization feedback signal or can be further scaled (e.g., multiplied by a value of unity) in the output multiplier 114b to produce the final equalization feedback signal 115b. 
In scenario B, the first adaptation control signal 205b corresponds to a product of a partial weighting factor c1(t) and the correlation factor r(t), while the second adaptation control signal 205c corresponds to a product of the partial weighting factor c1(t) and the complement [1−(t)] of the correlation factor r(t). The sum signal 115a is multiplied in the multiplier 114b by a final weighting factor c2(t) to produce the final equalization feedback signal 115b. 
In scenario C, the first adaptation control signal 205b corresponds to the correlation factor r(t), while the second adaptation control signal 205c corresponds to the complement [1−r(t)] of the correlation factor r(t). The sum signal 115a is multiplied in the output multiplier 114b by the weighting factor c(t) to produce the final equalization feedback signal 115b. 
A number of enhancements or modifications may be used to improve the performance over the IFTA with two taps within the fat tap.
Fixed Ratio Fat Tap with Hypothesis Testing
In this modification, adaptation of r may not occur in a continuous-time basis. One tap in the fat tap may be set to be at c with LMS adaptation (discrete-time or continuous-time), while the coefficient of the other tap within the fat tap is related to the first tap coefficient as a multiple by a correlation parameter (of the form




  
    1
    -
    r
  
  r




as described above). A discrete set of such hypotheses corresponding to different values of the correlation parameter





  
    1
    -
    r
  
  r




may be assumed. Each hypothesis is tested and the different taps, which may be LMS-adaptable, are adapted and, after convergence, the steady-state mean square error and/or the adapted filter coefficients may be used to decide on the right hypothesis (the right hypothesis may be selected to be the one with minimum MSE and/or acceptable patterns within the tap coefficients).

Multi-Tap Fat Tap with Linear Interpolation
Multiple taps (more than two) and/or a variable number of taps may be used within a fat tap. A simple but effective approach here is to do multiple stages of linear interpolation, each stage consisting of a linear interpolation between some two points obtained from the earlier stage to give one new point which may be used in the next stage. The multi-tap fat tap will then have more than two parameters to adapt.
As an example, consider three feedback taps within a fat tap with input signals s(t), s(t−τ), s(t−2·τ). Then, s(t−τr1)=r1·s(t)+(1−r1)·s(t−τ) may first be formed as a linear interpolation of s(t),s(t−τ), and then s(t−τr2)=r2·s(t−τr1)+(1−r2)·s(t−2·τ) is expected to be the symbol-spaced feedback signal. The feedback tap coefficients for the fat tap with input signals s(t), s(t−τ), s(t−2·τ) are then c·r1·r2, c·(1−r1)·r2, c·(1−r2). The adaptation updates of the 3 parameters r1, r2, c in the continuous-time domain are as follows:



  
    
      c
      ⁡
      
        (
        t
        )
      
    
    =
    
      
        μ
        c
      
      ·
      
        
          ∫
          0
          t
        
        ⁢
        
          
            
              e
              ⁡
              
                (
                v
                )
              
            
            ·
            
              [
              
                
                  
                    r
                    1
                  
                  ·
                  
                    r
                    2
                  
                  ·
                  
                    s
                    ⁡
                    
                      (
                      v
                      )
                    
                  
                
                +
                
                  
                    (
                    
                      1
                      -
                      
                        r
                        1
                      
                    
                    )
                  
                  ·
                  
                    r
                    2
                  
                  ·
                  
                    s
                    ⁡
                    
                      (
                      
                        v
                        -
                        τ
                      
                      )
                    
                  
                
                +
                
                  
                    (
                    
                      1
                      -
                      
                        r
                        2
                      
                    
                    )
                  
                  ·
                  
                    s
                    ⁡
                    
                      (
                      
                        v
                        -
                        
                          2
                          ·
                          τ
                        
                      
                      )
                    
                  
                
              
              ]
            
          
          ⁢
          
            
          
          ⁢
          
            d
            v
          
        
      
    
  




  
    
      
        r
        1
      
      ⁡
      
        (
        t
        )
      
    
    =
    
      
        μ
        r
      
      ·
      
        
          ∫
          0
          t
        
        ⁢
        
          
            
              c
              ⁡
              
                (
                v
                )
              
            
            ·
            
              
                r
                2
              
              ⁡
              
                (
                v
                )
              
            
            ·
            
              e
              ⁡
              
                (
                v
                )
              
            
            ·
            
              [
              
                
                  s
                  ⁡
                  
                    (
                    v
                    )
                  
                
                -
                
                  s
                  ⁡
                  
                    (
                    
                      v
                      -
                      τ
                    
                    )
                  
                
              
              ]
            
          
          ⁢
          
            
          
          ⁢
          
            d
            v
          
        
      
    
  




  
    
      
        r
        2
      
      ⁡
      
        (
        t
        )
      
    
    =
    
      
        μ
        r
      
      ·
      
        
          ∫
          0
          t
        
        ⁢
        
          
            
              c
              ⁡
              
                (
                v
                )
              
            
            ·
            
              e
              ⁡
              
                (
                v
                )
              
            
            ·
            
              [
              
                
                  
                    r
                    1
                  
                  ·
                  
                    s
                    ⁡
                    
                      (
                      v
                      )
                    
                  
                
                +
                
                  
                    (
                    
                      1
                      -
                      
                        r
                        1
                      
                    
                    )
                  
                  ·
                  
                    s
                    ⁡
                    
                      (
                      
                        v
                        -
                        τ
                      
                      )
                    
                  
                
                -
                
                  s
                  ⁡
                  
                    (
                    
                      v
                      -
                      
                        2
                        ·
                        τ
                      
                    
                    )
                  
                
              
              ]
            
          
          ⁢
          
            
          
          ⁢
          
            d
            v
          
        
      
    
  



Knowing a priori the signs of c, r2 above equations may be simplified. With an intermediate output of the fat tap defined as

ƒi(t)=c·r1·r2s(t)+c·(1−r1)·r2s(t−τ),

and the final output as

ƒ(t)=ƒi(t)+c·(1−r2)·s(t−2·τ),

then the following simplified update equations result:




  
    
      
        r
        1
      
      ⁡
      
        (
        t
        )
      
    
    =
    
      
        μ
        r
      
      ·
      
        
          ∫
          0
          t
        
        ⁢
        
          
            
              e
              ⁡
              
                (
                v
                )
              
            
            ·
            
              
                d
                
                  
                    f
                    i
                  
                  ⁡
                  
                    (
                    v
                    )
                  
                
              
              
                d
                v
              
            
          
          ⁢
          
            
          
          ⁢
          
            d
            v
          
        
      
    
  




  
    
      
        r
        2
      
      ⁡
      
        (
        t
        )
      
    
    =
    
      
        μ
        r
      
      ·
      
        
          ∫
          0
          t
        
        ⁢
        
          
            
              e
              ⁡
              
                (
                v
                )
              
            
            ·
            
              
                d
                
                  f
                  ⁡
                  
                    (
                    v
                    )
                  
                
              
              
                d
                v
              
            
          
          ⁢
          
            
          
          ⁢
          
            d
            v
          
        
      
    
  



Note that





  
    
      d
      
        
          f
          i
        
        ⁡
        
          (
          v
          )
        
      
    
    
      d
      v
    
  
  ,
  
    
      d
      
        f
        ⁡
        
          (
          v
          )
        
      
    
    
      d
      v
    
  




may easily be implemented by passing the outputs of the fat tap ƒi(t), ƒ(t) through the C-R differentiator block, which is a high-pass filter.

Multi-Tap Fat Tap with Superlinear Interpolation
More general interpolation can also be employed, especially when more than two taps are included within the fat tap, such as quadratic interpolation. For example, with three feedback taps within a fat tap and with input signals s(t), s(t−τ), s(t−2·τ), the corresponding tap coefficients may be given as c·ƒ0(r), c·ƒ1(r), c·ƒ2(r) for some appropriately selected functions ƒ0(·), ƒ1(·), ƒ2(·), which in general may also be functions of more than one parameter. The adaptation updates are then given as:



  
    
      c
      ⁡
      
        (
        t
        )
      
    
    =
    
      
        μ
        c
      
      ·
      
        
          ∫
          0
          t
        
        ⁢
        
          
            
              e
              ⁡
              
                (
                v
                )
              
            
            ·
            
              [
              
                
                  
                    f
                    0
                  
                  ⁡
                  
                    (
                    r
                    )
                  
                
                ⁣
                
                  
                    ·
                    
                      s
                      ⁡
                      
                        (
                        v
                        )
                      
                    
                  
                  +
                  
                    
                      
                        f
                        1
                      
                      ⁡
                      
                        (
                        r
                        )
                      
                    
                    ·
                    
                      s
                      ⁡
                      
                        (
                        
                          v
                          -
                          τ
                        
                        )
                      
                    
                  
                  +
                  
                    
                      
                        f
                        2
                      
                      ⁡
                      
                        (
                        r
                        )
                      
                    
                    ·
                    
                      s
                      ⁡
                      
                        (
                        
                          v
                          -
                          
                            2
                            ·
                            τ
                          
                        
                        )
                      
                    
                  
                
              
              ]
            
          
          ⁢
          
            
          
          ⁢
          
            d
            v
          
        
      
    
  




  
    
      
        d
        
          d
          t
        
      
      ⁢
      
        r
        ⁡
        
          (
          t
          )
        
      
    
    =
    
      
        c
        ⁡
        
          (
          t
          )
        
      
      ·
      
        e
        ⁡
        
          (
          t
          )
        
      
      ·
      
        [
        
          
            
              
                f
                0
                ′
              
              ⁡
              
                (
                r
                )
              
            
            ·
            
              s
              ⁡
              
                (
                t
                )
              
            
          
          +
          
            
              
                f
                1
                ′
              
              ⁡
              
                (
                r
                )
              
            
            ·
            
              s
              ⁡
              
                (
                
                  t
                  -
                  τ
                
                )
              
            
          
          +
          
            
              
                f
                2
                ′
              
              ⁡
              
                (
                r
                )
              
            
            ·
            
              s
              ⁡
              
                (
                
                  t
                  -
                  
                    2
                    ·
                    τ
                  
                
                )
              
            
          
        
        ]
      
    
  



which may be approximated by the following explicit update equation for r(t):





  
    r
    ⁡
    
      (
      t
      )
    
  
  =
  
    
      μ
      r
    
    ·
    
      
        ∫
        0
        t
      
      ⁢
      
        
          
            c
            ⁡
            
              (
              v
              )
            
          
          ·
          
            e
            ⁡
            
              (
              v
              )
            
          
          ·
          
            [
            
              
                
                  
                    f
                    0
                    ′
                  
                  ⁡
                  
                    (
                    r
                    )
                  
                
                ·
                
                  s
                  ⁡
                  
                    (
                    v
                    )
                  
                
              
              +
              
                
                  
                    f
                    1
                    ′
                  
                  ⁡
                  
                    (
                    r
                    )
                  
                
                ·
                
                  s
                  ⁡
                  
                    (
                    
                      v
                      -
                      τ
                    
                    )
                  
                
              
              +
              
                
                  
                    f
                    2
                    ′
                  
                  ⁡
                  
                    (
                    r
                    )
                  
                
                ·
                
                  s
                  ⁡
                  
                    (
                    
                      v
                      -
                      
                        2
                        ·
                        τ
                      
                    
                    )
                  
                
              
            
            ]
          
        
        ⁢
        
          
        
        ⁢
        
          d
          v
        
      
    
  




Fat Tap with Gain Offset
To compensate for a residual but unknown gain offset between the taps in a fat tap or to control the linearity range, a fat tap with gain offset may be used. For example, consider two feedback taps within a fat tap with input signals s(t),s(t−τ). The tap coefficients for these two taps are then respectively c·r, c·a·(1−r). The adaptation updates for the three parameters (c,a,r ) are then given as:



  
    
      c
      ⁡
      
        (
        t
        )
      
    
    =
    
      
        μ
        c
      
      ·
      
        
          ∫
          0
          t
        
        ⁢
        
          
            
              e
              ⁡
              
                (
                v
                )
              
            
            ·
            
              [
              
                
                  r
                  ·
                  
                    s
                    ⁡
                    
                      (
                      v
                      )
                    
                  
                
                +
                
                  a
                  ·
                  
                    (
                    
                      1
                      -
                      r
                    
                    )
                  
                  ·
                  
                    s
                    ⁡
                    
                      (
                      
                        v
                        -
                        τ
                      
                      )
                    
                  
                
              
              ]
            
          
          ⁢
          
            
          
          ⁢
          
            d
            v
          
        
      
    
  




  
    
      r
      ⁡
      
        (
        t
        )
      
    
    =
    
      
        μ
        r
      
      ·
      
        
          ∫
          0
          t
        
        ⁢
        
          
            
              c
              ⁡
              
                (
                v
                )
              
            
            ·
            
              e
              ⁡
              
                (
                v
                )
              
            
            ·
            
              [
              
                
                  s
                  ⁡
                  
                    (
                    v
                    )
                  
                
                -
                
                  a
                  ·
                  
                    s
                    ⁡
                    
                      (
                      
                        v
                        -
                        τ
                      
                      )
                    
                  
                
              
              ]
            
          
          ⁢
          
            
          
          ⁢
          
            d
            v
          
        
      
    
  




  
    
      a
      ⁡
      
        (
        t
        )
      
    
    =
    
      
        μ
        c
      
      ·
      
        
          ∫
          0
          t
        
        ⁢
        
          
            
              c
              ⁡
              
                (
                v
                )
              
            
            ·
            e
          
          ⁢
          
            
              (
              v
              )
            
            ·
            
              (
              
                1
                -
                r
              
              )
            
            ·
            
              s
              ⁡
              
                (
                
                  v
                  -
                  τ
                
                )
              
            
          
          ⁢
          
            d
            v
          
        
      
    
  



Correlated Fat Tap Adaptation (CFTA)
Multiple fat taps may share one or more taps such that each tap could correspond to more than one symbol (e.g., two symbols). It would then be expected that a set of fat taps together emulate multiple symbol-spaced feedback taps. For example, consider three feedback taps with input signals s(t), s(t−τ), s(t−2·τ) such that these together could correspond to two symbol-spaced feedback taps. The first fat tap which corresponds to the first past symbol consists of the feedback taps with inputs s(t), s(t−τ), and the second fat tap corresponds to the second past symbol and consists of the feedback taps with inputs s(t−τ), s(t−2·τ); thus, the fat taps have an overlapping feedback tap. The feedback tap coefficients may then be expressed as c1·r1, c1·(1−r1)+c2·r2,c2·(1−r2). The update equations for c1,c2,r1,r2 are similarly expressed as follows:



  
    
      
        c
        1
      
      ⁡
      
        (
        t
        )
      
    
    =
    
      
        μ
        c
      
      ·
      
        
          ∫
          0
          t
        
        ⁢
        
          
            
              e
              ⁡
              
                (
                v
                )
              
            
            ·
            
              [
              
                
                  
                    r
                    1
                  
                  ·
                  
                    s
                    ⁡
                    
                      (
                      v
                      )
                    
                  
                
                +
                
                  
                    (
                    
                      1
                      -
                      
                        r
                        1
                      
                    
                    )
                  
                  ·
                  
                    s
                    ⁡
                    
                      (
                      
                        v
                        -
                        τ
                      
                      )
                    
                  
                
              
              ]
            
          
          ⁢
          
            
          
          ⁢
          
            d
            v
          
        
      
    
  




  
    
      
        r
        1
      
      ⁡
      
        (
        t
        )
      
    
    =
    
      
        μ
        r
      
      ·
      
        
          ∫
          0
          t
        
        ⁢
        
          
            
              
                c
                1
              
              ⁡
              
                (
                v
                )
              
            
            ·
            
              e
              ⁡
              
                (
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Quasi-LMSE-Based Adaptation Schemes for Fat Tap Interpolating Mixer
Other adaptation techniques for controlling the timing control ratio parameter in the interpolating mixer within the Fat Tap may also be used. One such technique may include the use of tap coefficients on the feedforward/feedback equalizers which adapt based on LMSE, in a manner that this approximates LMSE-based adaptation for the timing control ratio parameter. Thus, if the feedforward tap coefficients within the Fat Tap are of the form {ci}i=0L, two alternative manners of adapting the timing control ratio are provided below:




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for appropriately selected adaptation parameter: μ and real number weights {wi}i=0L or {wi,j}i,j=0i,j=L.

Referring to FIG. 10, another embodiment 200c of the FTA circuitry 200 (FIG. 2) uses alternative implementations 204b, 206c of the control signal generators to process the incoming time-delayed data signals 111a, 111b, the error signal 117 and adaptive filter coefficient signals 15 (discussed in more detail below) from the feedforward filter 102a of the equalizer 100 (FIG. 1).
Referring to FIG. 11, the feedforward filter 102a processes the incoming data signal 101 to produce the equalized signal 109 using a series of signal delay elements 32a, 32b, . . . , 32n, multiplier circuits 34a, 34b, . . . , 34n and output summing circuit 108a in accordance with well-known techniques. Each of the successively delayed versions 33a, 33b, . . . , 33n of the data signal, as well as the incoming data signal 101, is multiplied in one of the multiplication circuits 34a, 34b, . . . , 34n with its respective adaptive filter coefficient signal 15a, 15b, . . . , 15n (along with a multiplication, or scaling, constant, as desired). The resulting product signals 35a, 35b, . . . , 35n are summed in the signal summing circuit 108a, with the resulting sum signal forming the equalized signal 109.
Referring to FIG. 12, an adaptive coefficients generator 14 processes the incoming data signal 101 and the error signal 117 using series of signal delay elements 42a, 42b, . . . , 42n, signal multipliers 44a, 44b, . . . , 44n and signal integrators (e.g., low pass filters) 46a, 46b, . . . , 46n in accordance with well known techniques. The incoming signal 101 is successively delayed by the signal delay elements 42a, 42b, . . . , 42n to produce successively delayed versions 43a, 43b, . . . , 43n of the incoming signal 101. Each of these signals 101, 43a, 43b, . . . , 43n is multiplied in its respective signal multiplier 44a, 44b, . . . , 44n with the error signal 117 (along with a multiplication, or scaling, constant, as desired). The resulting product signals 45a, 45b, . . . , 45n are individually integrated in the signal integration circuits 46a, 46b, . . . , 46n to produce the individual adaptive filter coefficient signals 15a, 15b, . . . , 15n.
Referring to FIG. 13, one embodiment 206ca of this alternative second control signal generator in accordance with the presently claimed invention includes a set of signal weighting circuits (e.g., multipliers) 156a, 156b, . . . , 156n, a signal combining (e.g., summing) circuit 158 and a signal integration circuit (e.g., low pass filter) 160, interconnected substantially as shown. Each of the adaptive filter coefficient signals 15a, 15b, . . . , 15n is weighted (e.g., multiplied) in a respective multiplier 156a, 156b . . . , 156n with a corresponding weighted, or scaled, signal 155a, 155b, . . . , 155n (as well as a multiplication, or scaling, factor μ 161, as desired). The resulting product signals 157a, 157b, . . . 157n are combined (e.g., summed) in the signal combiner 158. The combined signal 159 is integrated (e.g., low pass filtered) by the signal integrator 160 to produce the adaptation control signal 207ac r(t). This signal 207ac is also complemented by signal complement circuitry 228 (as discussed above) to produce the other adaptation control signal 207bc[1−r(t)] provided to the first control signal generator 204b. 
Referring to FIG. 14, another embodiment 206cb of the second control signal generator 206c in accordance with the presently claimed invention includes an alternative implementation 164 of weighting circuitry for weighting the adaptive filter coefficient signals 15 with corresponding weighted, or scaled, signals 155 (as well as a multiplication, or scaling, factor μ 161, as desired). Such weighting circuitry 164 can be implemented in accordance with well-known techniques using multiple signal weighting circuits (e.g., multipliers) and signal combining (e.g., summing) circuits to perform the prescribed weighting of the respective adaptive filter coefficient signals 15 with the corresponding weighted, or scaled, signals 155 over the appropriate ranges of i and j. As before, the resultant signal 165 is integrated (e.g., low pass filtered) by a signal integrator 160 to produce the adaptation control signal 207ad r(t). This signal 207ad is also complemented by signal complement circuitry 228 (as discussed above) to produce the other adaptation control signal 207bd[1−r(t)] provided to the first control signal generator 204b. 
Alternatively, it should be understood that this technique can also be implemented using adaptive coefficient signals from an adaptive feedback filter 104 (FIG. 1).
Referring to FIG. 15, one implementation 200ac of the FTA circuit 200c of FIG. 10 can be implemented substantially as shown. Using the adaptation control signals 207a, 207b from the second control signal generator 206c (e.g., FIG. 13 or 14), the first control signal generator 204ba operates as discussed above in connection with FIG. 6.
Yet another technique for adapting the timing control ratio parameter may be using the “eye monitor” test.
Referring to FIGS. 16A and 16B, expected performance improvement with use of an analog continuous-time feedforward filter in conjunction with “fat tap” adaptation in accordance with the presently claimed invention is as illustrated. FIG. 16A illustrates the “eye” diagram for the incoming data signal 101 (FIG. 11) prior to equalization, while FIG. 16B illustrates the “eye” diagram for the output signal 107 of the slicer 106 following equalization in accordance with the presently claimed invention. As shown, the uncompensated waveform of FIG. 16A has “eyes” Ea which are substantially closed, thereby producing a high BER corresponding to an eye-opening penalty approaching infinity. In contrast thereto, the compensated waveform of FIG. 16B has “eyes” Eb which are substantially open, thereby producing a low BER corresponding to an eye-opening penalty of approximately three decibels.
Based upon the foregoing discussion, it should be recognized that each of the exemplary embodiments of the presently claimed invention as depicted and discussed herein offer similar advantages without any one of such embodiments necessarily being preferred over the others. As will be readily appreciated by one of ordinary skill in the art, the particular topology of each embodiment may cause one particular embodiment to be deemed more advantageous for the specific host system or network in which such embodiment is to be implemented (e.g., due to circuit design rules or layout constraints).
Various other modifications and alternations in the structure and method of operation of this invention will be apparent to those skilled in the art without departing from the scope and the spirit of the invention. Although the invention has been described in connection with specific preferred embodiments, it should be understood that the invention as claimed should not be unduly limited to such specific embodiments. It is intended that the following claims define the scope of the present invention and that structures and methods within the scope of these claims and their equivalents be covered thereby.

## Claims

1. An apparatus including fractionally-spaced signal taps for use in an adaptive signal equalizer in which an equalization feedback signal adaptively equalizes a data signal to form a pre-slicer data signal that is sliced to provide a post-slicer data signal, comprising:
a first signal terminal that conveys a first data signal corresponding to said post-slicer data signal and having a data symbol period associated therewith;
a second signal terminal that conveys a second data signal corresponding to said first data signal and delayed by a fraction of said data symbol period;
fractional delay circuitry, coupled between said first and second signal terminals, that receives and delays said first data signal to provide said second data signal;
control circuitry, coupled to said first and second signal terminals, that receives said first and second data signals, and an error signal indicative of a difference between said pre-slicer and post-slicer data signals, and in response thereto provides first and second weighting signals, wherein said first weighting signal corresponds to a correlation factor which is indicative of a degree of correlation between said first and second data signals, and said second weighting signal corresponds to a complement of said correlation factor;
signal weighting circuitry, coupled to said first and second signal terminals and said control circuitry, that receives said first and second weighting signals and in response thereto receives and weights said first and second data signals to provide first and second weighted signals; and
signal combining circuitry, coupled to said signal weighting circuitry, that receives and combines said first and second weighted signals to provide an equalization feedback signal.

2. The apparatus of claim 1, wherein said signal weighting circuitry comprises:
a first weighting circuit, coupled to said first signal terminal, that receives said first weighting signal and in response thereto receives and weights said first data signal to provide said first weighted signal; and
a second weighting circuit, coupled to said second signal terminal, that receives said second weighting signal and in response thereto receives and weights said second data signal to provide said second weighted signal.

3. The apparatus of claim 1, wherein said signal weighting circuitry comprises signal multiplication circuitry that:
multiplies said first data signal and said first weighting signal to provide said first weighted signal; and
multiplies said second data signal and said second weighting signal to provide said second weighted signal.

4. The apparatus of claim 1, wherein said signal combining circuitry comprises signal summing circuitry that sums said first and second weighted signals to provide said equalization feedback signal.

5. An apparatus including fractionally-spaced signal taps for use in an adaptive signal equalizer in which an equalization feedback signal adaptively equalizes a data signal to form a pre-slicer data signal that is sliced to provide a post-slicer data signal, comprising:
a first signal terminal that conveys a first data signal corresponding to said post-slicer data signal and having a data symbol period associated therewith;
a second signal terminal that conveys a second data signal corresponding to said first data signal and delayed by a fraction of said data symbol period;
fractional delay circuitry, coupled between said first and second signal terminals, that receives and delays said first data signal to provide said second data signal;
control circuitry, coupled to said first and second signal terminals, that receives said first and second data signals, and an error signal indictive of a difference between said pre-slicer and post-slicer data signals, and in response thereto provides first and second weighting signals, wherein said first weighting signal corresponds to a correlation factor which is indicative of a degree of correlation between said first and second data signals, and said second weighting signal corresponds to a complement of said correlation factor;
first signal weighting circuitry, coupled to said first and second signal terminals and said control circuitry, that receives said first and second weighting signals and in response thereto receives and weights said first and second data signals to provide first and second weighted signals;
signal combining circuitry, coupled to said first signal weighting circuitry, that receives and combines said first and second weighted signals to provide a combined signal; and
second signal weighting circuitry, coupled to said signal combining circuitry, that receives a third weighting signal and in response thereto receives and weights said combined signal to provide an equalization feedback signal.

6. The apparatus of claim 5, wherein said first signal weighting circuitry comprises:
a first weighting circuit, coupled to said first signal terminal, that receives said first weighting signal and in response thereto receives and weights said first data signal to provide said first weighted signal; and
a second weighting circuit, coupled to said second signal terminal, that receives said second weighting signal and in response thereto receives and weights said second data signal to provide said second weighted signal.

7. The apparatus of claim 5, wherein said first signal weighting circuitry comprises first signal multiplication circuitry that multiplies said first and second data signals and said first and second weighting signals to provide said first and second weighted signals, respectively.

8. The apparatus of claim 7, wherein said second signal weighting circuitry comprises second signal multiplication circuitry that multiplies said combined signal and said third weighting signal to provide said equalization feedback signal.

9. The apparatus of claim 5, wherein said signal combining circuitry comprises signal summing circuitry that sums said first and second weighted signals to provide said combined signal.

10. An apparatus including fractionally-spaced signal taps for use in an adaptive signal equalizer in which an equalization feedback signal adaptively equalizes a data signal to form a pre-slicer data signal that is sliced to provide a post-slicer data signal, comprising:
fractional delay means for receiving and delaying a first data signal to generate a second data signal, wherein said first data signal corresponds to said post-slicer data signal and has a data symbol period associated therewith, and said second data signal corresponds to said first data signal delayed by a fraction of said data symbol period;
control means for receiving said first and second data signals, and an error signal indicative of a difference between said pre-slicer and post-slicer data signals, and in response thereto generating first and second weighting signals, wherein said first weighting signal corresponds to a correlation factor which is indictive of a degree of correlation between said first and second data signals, and said second weighting signal corresponds to a complement of said correlation factor;
signal weighting means for receiving said first and second weighting signals and in response thereto weighting said first and second data signals to generate first and second weighted signals; and
signal combiner means for combining said first and second weighted signals to generate an equalization feedback signal.

11. An apparatus including fractionally-spaced signal taps for use in an adaptive signal equalizer in which an equalization feedback signal adaptively equalizes a data signal to form a pre-slicer data signal that is sliced to provide a post-slicer data signal, comprising;
fractional delay means for receiving and delaying a first data signal to generate a second data signal, wherein said first data signal corresponds to said post-slicer data signal and has a data symbol period associated therewith, and said second data signal corresponds to said first data signal delayed by a fraction of said data symbol period;
control means for receiving said first and second data signals, and an error signal indicative of a difference between said pre-slicer and post-slicer data signals, and in response thereto generating first and second weighting signals, wherein said first weighting signals corresponds to a correlation factor which is indicative of a degree of correlation between said first and second data signals, and said second weighting signal corresponds to a complement of said correlation factor;
first signal weighting means for receiving said first and second weighting signals and in response thereto weighting said first and second data signals to generate first and second weighted signals;
signal combiner means for combining said first and second weighted signals to generate a combined signal; and
second signal weighting means for receiving a third weighting signal and in response thereto weighting said combined signal to generate an equalization feedback signal.

12. A method for providing fractionally-spaced signal taps for use in an adaptive signal equalizer in which an equalization feedback signal adaptively equalizes a data signal to form a pre-slicer data signal that is sliced to provide a post-slicer data signal, comprising:
receiving a first data signal corresponding to a post-slicer data signal and having a data symbol period associated therewith;
delaying said first data signal to generate a second data signal corresponding to said first data signal and delayed by a fraction of said data symbol period;
generating first and second weighting signals in response to said first and second data signals, and an error signal indictive of a difference between said pre-slicer and post-slicer data signals, wherein said first weighting signal corresponds to a correlation factor which is indictive of a degree of correlation between said first and second data signals, and said second weighting signal corresponds to a complement of said correlation factor;
weighting said first and second data signals in response to said first and second weighting signals to generate first and second weighted signals; and
combining said first and second weighted signals to generate an equalization feedback signal.

13. The method of claim 12, wherein said receiving first and second weighting signals and in response thereto weighting said first and second data signals to generate first and second weighted signals comprises:
receiving said first weighting signal and in response thereto weighting said first data signal to generate said first weighted signal; and
receiving said second weighting signal and in response thereto weighting said second data signal to generate said second weighted signal.

14. The method of claim 12, wherein said receiving first and second weighting signals and in response thereto weighting said first and second data signals to generate first and second weighted signals comprises multiplying said first and second data signals and said first and second weighting signals to generate said first and second weighted signals, respectively.

15. The method of claim 12, wherein said combining said first and second weighted signals to generate an equalization feedback signal comprises summing said first and second weighted signals.

16. A method for providing fractionally-spaced signal taps for use in an adaptive signal equalizer in which an equalization feedback signal adaptively equalizes a data signal to form a pre-slicer data signal that is sliced to provide a post-slicer data signal, comprising:
receiving a first data signal corresponding to a post-slicer data signal and having a data symbol period associated therewith;
delaying said first data signal to generate a second data signal corresponding to said first data signal and delayed by a fraction of said data symbol period;
generating first and second weighting signals in response to said first and second data signals, and an error signal indicative of a difference between said pre-slicer and post-slicer data signals, wherein said first weighting signal corresponds to a correlation factor which is indicative of a degree of correlation between said first and second data signals, and said second weighting signal corresponds to a complement of said correlation factor;
weighting said first and second data signals in response to said first and second weighting signals to generate first and second weighted signals;
combining said first and second weighted signals to generate a combined signal; and
receiving a third weighting signal and in response thereto weighting said combined signal to generate an equalization feedback signal.

17. The method of claim 16, wherein said receiving first and second weighting signals and in response thereto weighting said first and second data signals to generate first and second weighted signals comprises:
receiving said first weighting signal and in response thereto weighting said first data signal to generate said first weighted signal; and
receiving said second weighting signal and in response thereto weighting said second data signal to generate said second weighted signal.

18. The method of claim 16, wherein said receiving first and second weighting signals and in response thereto weighting said first and second data signals to generate first and second weighted signals comprises:
multiplying said first data signal and said first weighting signal to generate said first weighted signal; and
multiplying said second data signal and said second weighting signal to generate said second weighted signal.

19. The method of claim 18, wherein said receiving a third weighting signal and in response thereto weighting said combined signal to generate an equalization feedback signal comprises multiplying said combined signal and said third weighting signal to generate said equalization feedback signal.

20. The method of claim 16, wherein said combining said first and second weighted signals to generate a combined signal comprises summing said first and second weighted signals to generate said combined signal.