Abstract:
A communication device including circuitry configured to receive a signal transmitted to the communication device via a communication channel. A receiver is configured to generate a filter coefficient to be used for filtering the received signal, generate a gain coefficient, wherein the gain coefficient corresponds to a condition of the communication channel, adjust the filter coefficient using the gain coefficient, and filter the received signal using the filter coefficient, as adjusted using the gain coefficient, to remove intersymbol interference from the received signal.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     The present disclosure is a continuation of U.S. patent application Ser. No. 11/656,729 (now U.S. Pat. No. 8,767,813), filed on Jan. 23, 2007, which is a continuation of U.S. patent application Ser. No. 09/572,155 (now U.S. Pat. No. 7,167,516), filed on May 17, 2000. The entire disclosures of the applications referenced above are incorporated herein by reference. 
    
    
     FIELD 
     This invention is generally related to receivers in a communication system. More particularly, this invention is related to removal of precursor intersymbol interference from encoded signals received on a communication channel. 
     DESCRIPTION OF THE RELATED ART 
     In digital communication systems such as the popular Fast Ethernet, digital data is formatted to a pulsed multilevel voltage signal to be transferred through a communication channel such as common telephone wire, fiberoptic cable or open atmosphere. It is well known in the art that as the pulsed multilevel voltage signal transits the communication channel, the communication channel acts as a low pass filter and that the pulsed multilevel voltage signal becomes a continuous time signal. The low pass filter spreads or smears the shape of the input pulsed multilevel voltage signal to form the continuous time signal. 
     The operation can be described mathematically by the convolution of the function of the pulsed multilevel voltage signal x(t−τ) by a continuous time channel response h(t). That is 
     
       
         
           
             
               
                 
                   
                     
                       
                         
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     where:
         r(t) is the received continuous time signal,   h(t) is the channel response   x (t) is the pulsed multilevel voltage signal.
 
The second half of the formula is a result of the fact that convolution is a commutative process.
       

     The pulsed multilevel voltage signal is expressed as the function
 
 x ( t )=0 for  t≠T  
 
 x ( t )= X   k δ( t−kT ) for  t=kT  
 
     where:
         T is the period of a symbol of the encoded digital data,   k is a counting variable representing integral periods of the symbols,   X K  is the voltage level of the pulsed multiple level voltage signal a the time kT.
 
As is known in the art, the significant values in the integration occur where τ=KT. Therefore, the integration of Eq.1 can be rewritten as:
       

                     r   ⁡     (   t   )       =       ∑     -   ∞     ∞     ⁢           ⁢       x   k     ⁢     h   ⁡     (     t   -   kT     )                   EQ   .           ⁢   2               
EQ. 2, as written, still represents a continuous time system rather than the discrete time system employed in most digital communication systems. In pulse amplitude modulated systems, such as Ethernet, the sampling rate of the discrete time system is at the symbol transmit rate
 
             (     1   T     )         
and therefore can be written as:
 
                     r   ⁡     (     n   ⁢           ⁢   t     )       =       ∑     -   ∞     ∞     ⁢           ⁢       x   k     ⁢     h   ⁡     (     nT   -   kT     )                   EQ   .           ⁢   3               
This can be rewritten as:
 
     
       
         
           
             
               
                 
                   
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                   4 
                 
               
             
           
         
       
     
     Since the sampling clock of a receiver generally is not perfectly aligned with the clock of the transmitter of the communication system, the sampling phase offset will be non-zero. To account for the arbitrary phase offset, EQ. 4 is rewritten to add an offset time to the time index. EQ. 4 is now written as: 
                     r   ⁡     (     nT   +     t   0       )       =       ∑     -   ∞     N     ⁢           ⁢       x   k     ⁢     h   ⁡     (       t   0     +   nT   -   kT     )                   EQ   .           ⁢   5               
The first term of EQ. 5 is the component of the received signal of the nth symbol. The remaining terms in the summation are intersymbol interference (ISI) terms, previous symbols (postcursor intersymbol interference) and subsequent symbols (precursor intersymbol interference).
 
     Refer now to  FIG. 1   a  to discuss a typical communication system. The digital data is scrambled, encoded and formed into a symbol that forms the pulsed multilevel voltage signal a i    5 . The pulsed multilevel voltage signal a i    5  is transferred to the communication channel  10 . The communication channel  10 , as described above, has the impulse response h(t) and acts as a low pass filter to distort the pulsed multilevel voltage signal a i    5 . The communication channel  10  includes the driver circuitry, receiver circuitry and the connecting transmission medium.  FIG. 1   b  is a plot of the magnitude of the received pulsed multilevel voltage signal a irec    12  versus frequency. As is shown, the frequency content of the received pulsed multilevel voltage signal a irec    12  contains the frequencies of the previous and subsequent symbols of the received pulsed multilevel voltage signal a irec    12 . To demonstrate the frequencies EQ. 5 is reorganized with the magnitude of the pulsed multilevel voltage signal a i    5  included as follows:
 
 a   irec   =a   i +1 f− 1+ a   0 −1 f+ 1+ . . . .  EQ. 6
 
     The output of communication channel  10  is the input to an analog-to-digital converter (ADC)  15 . The analog-to-digital converter  15  samples the received signal from the communication channel to create the sampled digitized version h k    25  of the received signal. The sampled digitized version h k    25  of the received signal contains the precursor and postcursor intersymbol interference described above. Removal of the precursor intersymbol interference is accomplished by the feed forward filter  30 . The decision feedback filter  70  accomplishes the removal of the postcursor intersymbol interference (a i −1f+1+ . . . of EQ. 6). 
     The feed forward filter  30  consists of multiple delay elements  35   a ,  35   b ,  35   c  and  35   d  that are serially connected output to input. The input of the first delay element is connected to the analog-to-digital converter  15  to receive the sampled digitized received signal h k    25 . Each delay element  35   a ,  35   b ,  35   c  and  35   d  delays the sampled digitized received signal h k  by the amount of time of the period of the sampling clock of the analog-to-digital converter  15 . The outputs of the analog-to-digital converter  15  and the delay elements  35   a ,  35   b ,  35   c  and  35   d  respectively are connected to the multiplier circuits  40   a ,  40   b ,  40   c ,  40   d  and  40   e . Each delayed version of the sampled digitized received signals is multiplied by one of the filter coefficients w x ,  45   a ,  45   b ,  45   c ,  45   d  and  45   e . The output of each of the multiplier circuits  40   a ,  40   b ,  40   c ,  40   d  and  40   e  are connected to the combining circuits  50   a ,  50   b ,  50   c  and  50   d . The combining circuits  50   a ,  50   b ,  50   c  and  50   d  additively combine the resulting products from the multiplier circuits  40   a ,  40   b ,  40   c ,  40   d  and  40   e  to form the sampled digitized signal f k    5  having the precursor intersymbol interference removed. 
     The filter coefficients w x ,  45   a ,  45   b ,  45   c ,  45   d  and  45   e  normally are chosen as a function of an error signal e k  determined as the difference of the estimated value â i    95  of pulsed multilevel voltage signal a i    5  and the sampled digitized signal g i    62  having the total intersymbol interference removed. That is: e k =(g i −â k ). 
     The sampled and digitized signal f k    5  having the precursor intersymbol interference removed and the output of feedback filter  70 , which is the calculated postcursor intersymbol interference, are subtractively combined in the combining circuit  60 . The output of the combining circuit  60  is the input to the decision circuit  65 . The decision circuit  65  determines the received estimate a i    95  of the pulsed multilevel voltage signal a i . The received estimate a i    95  is the input of the feedback filter  70 . The feedback filter  70  has multiple delay elements  75   a ,  75   b , and  75   c  that are serially connected to delay the received estimate â i    95  by a time equal to the period of the sampling clock of the analog-to-digital converter  15 . The outputs of the delay elements  75   a ,  75   b , and  75   c  are the inputs to the multiplier circuits  80   a ,  80   b , and  80   c . The multiplier circuits multiply the delayed received estimates â i  by the filter coefficients f x    80   a ,  80   b , and  80   c . The products of the multiplier circuits  75   a ,  75   b , and  75   c  are additively combined in the combining circuit  90  to form the estimate of the postcursor intersymbol interference to be removed from the received, sampled and digitized pulsed multilevel voltage signal f k    5 . 
     The filter coefficients f x    85   a ,  85   b , and  85   c  are adaptively chosen by tracking the error signal e k  that is determined as the difference of the estimated value â i    95  of pulsed multilevel voltage signal a i    5  and the sampled digitized signal g i    62 , which is the output of the combining circuit  60 . 
     In EQ. 5, it is apparent that the sampling phase offset contributes to the magnitude of the precursor and postcursor intersymbol interference. The better aligned the sampling clock and the transmit clock, the less intersymbol interference in the sampled digitized version of the received signal h k    25 . The timing phase adjustment signal φ samp    20  is used to adjust the sampling position within the period of the pulsed multilevel voltage signal a i . A clock extraction circuit and a phase-locked loop generally establish the timing of the sampling clock of the ADC. Thus, the sampling phase, the filter coefficients w x    40   a ,  40   b ,  40   c ,  40   d , and  40   e , and the filter coefficients f x    85   a ,  85   b , and  85   c  are interdependent in fully adaptive systems. It is desirable to uncouple the sampling phase and the filer coefficients w x    40   a ,  40   b ,  40   c ,  40   d  and  40   e  to find the best combinations of values and to improve stability. 
     In magnetic recording media, the nonlinear effects in the write process appear in the readback waveform as shifts in the peak positions and changes in the amplitude. The pulse shift causes a nonlinear intersymbol interference (ISI) on the readback signal. “Adaptive Nonlinear Decision Feedback Equalization With Channel Estimation And Timing Recovery In Digital Magnetic Recording Systems” (Lin et al.), IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, Volume: 42 3, IEEE, pp. 196-206 describes a Volterra-DFE, in which a Volterra filter is used in the feedback section of decision feedback structure to equalize the nonlinear ISI. 
     U.S. Pat. No. 5,159,291 (Ghoshal) discloses a digitally controlled timing recovery loop with low intrinsic jitter and high jitter tolerance. The timing recovery loop has a triple loop structure for improved jitter tolerance and bandwidth control. 
     U.S. Pat. No. 5,430,661 (Fisher, et al.) teaches an adaptive decision feedback equalizer. The adaptive decision feedback equalizer operates in either a set-up/test mode or a run mode. The read signals input from a storage media are sampled, amplified and digitally processed to decode store information bits with the result that storage density may be increased and error rate decreased. 
     U.S. Pat. No. 5,822,143 (Cloke, et al.) describes a partial-response maximum-likelihood (PRML) sequence detector with decision feedback equalization (DFE) for a disk drive read channel. A DFE circuit generates a sequence of equalized samples and includes a feed forward filter that removes precursor ISI from the sequence of sample signal to produce a sequence of feed-forward equalized samples, detection logic that translates the sequence of equalized samples into a sequence of detected symbols and a feedback filter that filters the sequence of detected symbols to produce a sequence of equalization feedback values to offset postcursor ISI remaining in the sequence of feed-forward equalized samples. 
     SUMMARY 
     An object of this invention is providing an apparatus to determine a sampling phase of a sampling clock of an analog-to-digital converter in a receiver of a communication system. 
     Another object of this invention is to adjust the sampling clock of an analog-to-digital converter in a receiver of a communication system based on the determined sampling phase of the sampling clock to remove a first intersymbol interference from a signal received by the receiver. 
     Further, another object of this invention is to provide an open loop filter to remove any remaining intersymbol interference from the received signal. 
     And still further, another object of this invention is to provide a receiver within a communication system where the adaptive equalization necessary to eliminate precursor and postcursor intersymbol interference is decoupled and independent. 
     To accomplish these and other objects a circuit for canceling precursor intersymbol interference from a signal within a communication receiver has an adaptive timing loop circuit, which adjusts a timing phase of a sampling clock of an analog-to-digital converter within the communication receiver. The adjustment of the timing phase of the sampling clock removes a first precursor intersymbol interference from the signal. The circuit additionally has an open loop finite impulse response filter, which is connected to the output of the analog-to-digital converter. A coefficient of the open loop finite impulse response filter is determined by a gain mapping of a condition measurement of the communication receiver to cancel all precursor intersymbol interference beyond the first precursor intersymbol interference. 
     The adaptive timing loop circuit includes a first delay element connected within the communication receiver to acquire an error signal and to delay the error signal by one sampling period of the sampling clock. The error signal is a difference between an estimate of the transmitted data and an equalized version of received data indicative of an amount of the first precursor intersymbol interference. The adaptive timing loop additionally includes a first multiplier circuit connected within the communication receiver to receive the estimate of the transmitted data and to the first delay element to multiply a magnitude of the estimate of the transmitted data by a magnitude of the error signal to produce a first product. A second multiplier circuit is connected to receive a loop gain control constant and to the first multiplier to receive the first product. The second multiplier multiplies the loop gain control constant by the first product to form a second product. A combining circuit is connected to the second multiplier circuit and to an output of the adaptive timing loop circuit to subtractively combine the second product with a current timing phase adjustment signal to form a next timing phase adjustment signal. A second delay element delays the next timing phase adjustment signal to adjust the timing phase of a next sampling clock pulse. 
     The timing phase adjustment can be expressed by the formula:
 
φ sampn+1 =φ sampn −μ f ( â   i   e   i−1 )
 
     where:
         φ sampn+1  is the timing phase adjustment signal for the next sample h n+1    25  from the analog-to-digital converter  15 ,   φ sampn  is the timing phase adjustment signal for the current sample h n    25  from the analog-to-digital converter  15 ,   μ f  is the control constant,   e i−1  is the error signal for the previous sample.       

     The open loop finite impulse response filter includes a feed forward filter connected to the analog-to-digital converter to receive a sampled digital form of a received signal. The feed forward filter has a third delay element connected to the analog-to-digital converter to delay the sampled digital form of the received signal by one sampling period, a third multiplier circuit connected to the analog-to-digital converter to multiply the sampled digital form of the received signal by a filter coefficient to form a third product, and a third combining circuit to combine the delayed sampled digital form of the received signal with the third product to form a preliminary equalized signal. The open loop finite impulse response filter additionally has a fourth multiplier circuit connected to the feed forward filter to multiply the preliminary equalized signal by a constant gain factor to produce a signal having the intersymbol interference removed. A gain setting circuit is connected to the fourth multiplier circuit to generate the constant gain factor as a function of receiver condition, and a gain mapping circuit is connected to the third multiplier circuit and the gain setting circuit to provide the filter coefficient as a function of the constant gain factor. 
     The open loop finite impulse response filter generates its output signal according to the formula:
 
 f   k   =A   v ( h   k +( h   k+1 )* w   −1 )
 
     where:
         f k  is the digitized and sampled pulsed multilevel voltage signal.   A v  is the gain constant of the gain block  140 .   h k  is the present sampled and digitized received pulsed multilevel voltage signal.   h k+1  is the next sampled and digitized received pulsed multilevel voltage signal.   w −1  is the filter coefficient mapped from the gain constant   A v  of the gain block  140 .       

     The gain setting circuit establishes the gain constant factor according to the formula:
 
 G   k   =G   k−1 −μ FF   e   f   f   k  
 
     where:
         G k  is the current value of the gain constant factor at the output of the gain setting circuit.   G k−1  is the previous value of the constant factor at the output of the gain setting circuit.   μ FF  is a small positive constant.   f k  is digitized and sampled pulsed multilevel voltage signal.   e i  is the error signal indicating the condition of the communication channel and is a difference between an estimate of the transmitted data and an equalized version of received data indicative of an amount of the first precursor intersymbol interference.       

     To execute to the above formula the gain setting circuit has a fifth multiplier circuit to multiply the error signal, the preliminary equalized signal, and a gain constant to produce a fourth product. The gain constant must be sufficiently small to insure stability of the gain setting circuit and sufficiently large so as to track variations in the condition measurement. The gain setting circuit further has a fourth delay element to delay a present constant gain factor by a sampling time of the sampling clock. A fourth combining circuit subtractively combines a previous constant gain factor with the fourth product to generate a present constant gain factor. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1   a  is a schematic diagram of a communication channel and receiver of the prior art. 
         FIG. 1   b  is a plot of the gain versus frequency of the communication channel of the prior art as shown in  FIG. 1   a.    
         FIG. 2  is an eye diagram of the pulsed multilevel voltage signal having transited the communication channel and at the input of the receiver compared to the positioning of the sampling clock. 
         FIG. 3  is a block diagram of a communication channel and receiver of this invention. 
         FIG. 4   a  is a schematic diagram of one embodiment of an open loop feed forward equalizer of this invention. 
         FIG. 4   b  is a schematic diagram of a second embodiment of an open loop feed forward equalizer of this invention. 
         FIG. 5  is a schematic diagram of an adaptive timing loop of this invention. 
         FIGS. 6   a - 6   c  are flowcharts outlining the method for canceling precursor intersymbol interference from an encoded signal. 
     
    
    
     DESCRIPTION 
     Refer now to  FIG. 2  for a discussion of the impact of the sampling timing phase on the accuracy of the received estimate â 1  of the pulsed multilevel voltage signal a i . The plot of  FIG. 2  is of the pulsed multilevel voltage signal a irec    12  after having transited the communication channel  10  and at the input of the analog-to-digital converter  15 . It is apparent that the low pass filter characteristics of the communication channel have “smeared” the transitions between samples of pulsed multilevel voltage signal a irec    12 . If the sampling clock CLK samp  is placed incorrectly in the period, the effects of the adjacent signals impact the accuracy of the received signal. The timing phase adjustment signal φ samp  must adjust the timing clock CLK samp  to insure a minimum of intersymbol interference. 
     Refer now to  FIG. 3  to discuss the structure of the apparatus that is to remove the precursor intersymbol interference from the received pulsed multilevel voltage signal a irec    12 . As described above, the digital data is encoded and formatted to form the pulsed multilevel voltage signal a 1    5 . The pulsed multilevel voltage signal a i    5  is transferred to the communication channel  10 . The received pulsed multilevel voltage signal a irec    12  is the input to the analog-to-digital converter  15 . 
     The phase sampling adjustment signal φ samp    20  signals the adjustment necessary for the timing phase of the sampling clock of analog-to-digital converter  15  versus the clock of the transmitter (not shown). The output of the analog-to-digital converter  15 , which is the sampled and digitized received pulsed multilevel voltage signal h k    25 , is the input to the feed forward filter  130 . The feed forward filter  130  is an open loop finite impulse response filter in which its filter coefficients are derived from a gain-to-coefficient map  145  connected to the feed forward filter  130 . 
     The gain block  140  is an input of the gain-to-coefficient mapping circuit  145 . The gain of the gain block  140  provides an indication of the condition of the communication channel  10 . 
     The gain of the gain block  140  establishes an adaptive gain loop. The adaptive gain loop that is a function of the error signal e i    155  and the digitized and sampled pulsed multilevel voltage signal f k    55 . The combining circuit  160  generates the error signal e i    155 . The combining circuit subtractively combines the digitized sampled pulsed multilevel voltage signal g i    62  having the precursor and postcursor intersymbol interference removed with the estimated pulsed multilevel voltage signal â i  to form the error signal e i . The output G k    142  of the gain block  140  is an indication of the condition of the communication channel  10 . The output G k    142  of the gain block  140  is determined by the formula:
 
 G   k   =G   k−1 −μ FF   e   i   f   k   EQ. 7
 
     where:
         G k  is the current value of the gain constant at the output of the gain block  140 .   G k−1  is the previous value of the gain constant at the output of the gain block  140 .   μ FF  is a small positive constant.   f k    55  is digitized and sampled pulsed multilevel voltage signal.   e i  is the error signal indicating the condition of the communication channel  10 .       

     The small positive constant μ FF    420  is small enough to make the gain loop stable, but large enough to track slowly varying changes in the gain of the communication channel. 
     The gain-to-coefficient mapping block  145  has an initial value of gain constant for the gain block  140  and an initial value of filter coefficients for the feed forward filter  130 . If the initial values of the gain constant G k    142  of the gain block  140  and the coefficients for the feed forward filter  130  are not sufficient to cancel the intersymbol interference then the adaptive gain loop will increment the gain constant G k    142  by some reasonable but arbitrary value. The filter coefficients of the feed forward filter  130  are found according to the formula:
 
 w   xnew   =w   xold   +k *INC gain   EQ. 8
 
     where:
         w xnew  is the new value of the filter coefficient of the feed forward filter  130 .   w xold  is the present value of the filter coefficient of the feed forward filter  130 .   INC gain  is the incremental change of the gain constant made by the adaptive gain loop to incorrect removal of the intersymbol interference.   k is a constant chosen by experience and testing or channel characterization. For example, the value of k is chosen to be 1/64 for 100BASE-T Ethernet systems using Cat-5 unshielded twisted pair cabling.       

     The output of the feed forward filter  130  is the input to the multiplier circuit  135 . The second input of the multiplier circuit is the gain constant that is the output of the gain block  140 . The multiplier circuit  135  has an output that is the product of the output of the feed forward filter  130  and the gain constant to form the digitized and sampled pulsed multilevel voltage signal f k    55  having the precursor intersymbol interference removed. The digitized and sampled pulsed multilevel voltage signal f k    55  is determined by the formula:
 
 f   k   =A   v ( h   k +( h   k+1 )* w− 1)  EQ. 9
 
     where:
         f k  is the digitized and sampled pulsed multilevel voltage signal.   A v  is the gain constant of the gain block  140 .   h k  is the present sampled and digitized received pulsed multilevel voltage signal.   h k+1  is the next sampled and digitized received pulsed multilevel voltage signal.   w −1  is the filter coefficient mapped from the gain constant   A v  of the gain block  140 .       

     The removal of a first precursor intersymbol interference is accomplished with appropriate selection of the timing phase of EQ. 5. This is controlled by the timing phase adjustment signal φ samp    20 . 
     The ADC, as is known in the art, is sampled at a critical edge of a sampling clock generated by a voltage-controlled oscillator (considered integral to the analog-to-digital converter  10  for this example). The timing phase adjustment signal φ samp    20  is an input to the voltage controlled oscillator to adjust the placement of the critical edge of the sampling clock to appropriately set the timing phase to eliminate the first precursor intersymbol interference. 
     The output of the adaptive timing loop circuit  150  is the timing phase adjustment signal φ samp    20 . The inputs to the adaptive timing loop circuit  150  are the estimate of the pulsed multilevel voltage signal â i    95 , the error signal e i    155  and the control constant μ t    165 . 
     The control constant μ k    165  is a small constant chosen to meet the requirements of a specific application. The control constant μ t    165  should be small enough such that it can keep the timing loop stable and the gradient of the actual noise generated by the adaptive loop small. However, it should be large enough such that the timing loop can keep track of the slow timing variance of the communication channel  10 . 
     The adaptive timing loop executes the formula:
 
φ sampn+1 =φ sampn −μ f ( â   i   e   i−1 )
 
     where:
         φ sampon+1  is the timing phase adjustment signal for the next sample h n+1    25  from the analog-to-digital converter  15 ,   ® sampn  is the timing phase adjustment signal for the current sample h n    25  from the analog-to-digital converter  15 ,   μ t  is the control constant.   e i−1  is the error signal for the previous sample.       

     From EQ 6, it can be seen that the components of the feed forward filter  130  with the gain-to-coefficient mapping block  145 , and the gain block  140 , as described above, eliminate the post cursor intersymbol interference components (a i−1 f +1 + . . . ). EQ. 6 can thus be reduced to the equation:
 
 y   i   =a   i+1   f   −1   +a   i   f   0  
 
     The error signal e i    155  is then only the precursor intersymbol interference component a i+1 f − 1. If that frequency component is successfully nulled by appropriate selection of the timing sampling phase φ samp    20 , then the precursor intersymbol interference is removed. To extract the timing information, the sign of the frequency component f −1  indicates whether the timing sampling phase φ samp  is before or after the zero crossing point −ZC of  FIG. 1   b . To determine the sign of the frequency component f −1 , the error signal is multiplied by the estimate of the pulsed multilevel voltage signal â i    95 . The sign of this multiplication is only the sign of the frequency component f −1 . That is since
 
 e   i   =â   i+1   f   −1  then
 
 â   i+1   e   i =( â   +1 ) 2   f   −1 .
 
     As can be seen from the above equation, this provides an adaptive adjustment to the timing phase adjustment signal to minimize the precursor interference. 
     The adaptive timing loop adjusts the timing phase such that it is at the zero decibel (dB) crossing of the frequency response of the communication channel  10 . This is the position where the precursor noise is approaching a zero level. The error signal e i−1  is essentially the precursor intersymbol interference, once the post cursor intersymbol interference has been removed. Therefore the multiplication of the error signal by the estimated value of the estimated pulsed multilevel voltage signal â i  gives an estimate of the sign of the value of the frequency component f i−1  of the precursor interference. This allows the timing of the information to be extracted to indicate the offset of the timing phase (the sign frequency component f i−1  of the precursor interference) determines the correction required in the timing phase adjustment signal φ sampn  of the sampling clock. 
     The digitized and sampled pulsed multilevel voltage signal f x  is the input to the combining circuit  60 . The second input of the combining circuit  60 , as described in  FIG. 1 , is the output of the feedback filter  70 . The combining circuit  60  subtractively combines the output of the digitized and sampled pulsed multilevel voltage signal f k  having the precursor intersymbol interference removed with the output of the feedback filter  70  to generate the digitized and sampled pulsed multilevel voltage signal g i    62  having all intersymbol interference removed. 
     The output g i    62  of the combining circuit  60  is the input of the decision circuit  65 . The decision circuit  65  generates the estimated pulsed multilevel voltage signal â i    95 . The estimated pulsed multilevel voltage signal â i    95  is transferred to an external circuit for decoding and error correction to recreate the transmitted digital data. 
     The estimated pulsed multilevel voltage signal â i    95  is the input to the feedback filter  70 . The feedback filter  70 , as describes in  FIG. 1 , generates a representative form of the postcursor intersymbol interference that is to be subtracted from the digitized and sampled pulsed multilevel voltage signal f k . 
     Refer now to  FIGS. 4   a  and  4   b  to discuss the structure of the open loop feed forward filter  130  of  FIG. 3 .  FIG. 4   a  shows the open loop feed forward filter  130  having one tap to remove any of the precursor intersymbol interference from the digitized and sampled pulsed multilevel voltage signal h k    25 . The feed forward filter  130  consists of a first delay element  200  that delays the digitized and sampled pulsed multilevel voltage signal h k    25  by the time period equal to the period of the feed forward filter of the analog-to-digital converter  15 . 
     The digitized and sampled pulsed multilevel voltage signal h k    25  is the first input to the multiplier circuit  205 . The second input to the multiplier circuit  205  is the filter coefficient w- 1    147 . The output of the multiplier circuit  205  is the product of the digitized and sampled pulsed multilevel voltage signal h k    25  and the filter coefficient w- 1    147 . 
     The output of the delay element  200  and the output of the multiplier circuit  205  are the inputs of the combining circuit  210 . The output of the combining circuit  210  is the additive combination of the delayed version of the digitized and sampled pulsed multilevel voltage signal H k−1  and the product of the digitized and sampled pulsed multilevel voltage signal h k    25  and the filter coefficient w- 1    147 . The output of the combining circuit  210  is the output of the feed forward filter  130  and is connected, as described above, to the multiplier circuit  135 . The output of the combining circuit  210  is multiplied by the gain constant G k    142  in the multiplier circuit  135  to generate the digitized and sampled pulsed multilevel voltage signal f k    55  that has the precursor intersymbol interference removed. 
     The gain block  140  has two multiplier circuits  400  and  405  that multiply the error signal e i    155 , the feed forward constant μ FF    420 , and the digitized and sampled pulsed multilevel voltage signal f k    55  to produce the indication of the condition of the communication channel  10 . 
     The delay element  415  is connected to the output of the gain block  140  and delays the present value of the gain constant G k    142  by one sampling of the received signal a irec . The delayed version of the gain constant G k−1    143  is subtractively combined in the combining block  410  to form the gain constant G k    142  for the next sampling of the received signal a irec . 
     An alternative embodiment, as shown in  FIG. 4   b , illustrates a feed forward filter  230  having multiple taps or filter coefficients. In this case, the first tap of the feed forward filter  230  is the open loop feed forward filter  130  of  FIG. 3 , as described in  FIG. 4   a  and incorporates the multiplier circuit  135  of  FIG. 3 . The remaining taps  270  of the feed forward filter  230  are adaptive loops as shown in  FIG. 1 . The output f 1    237  of the multiplier circuit  235  is the digitized and sampled pulsed multilevel voltage signal having most precursor symbols of the precursor intersymbol interference removed. Any residual precursor symbols of the precursor intersymbol interference is removed by the remaining taps  270  of the feed forward filter  230 . 
     The remaining taps  270  of the feed forward filter  230  consist of multiple delay elements  250   a ,  250   b , and  250   c  that are serially connected output to input. The input of the first delay element is connected to the output f i    237  of the multiplier circuit  235 . 
     Each delay element  250   a ,  250   b , and  250   c  delays the output f i    237  of the multiplier circuit  235  by the amount of time of the period of the sampling clock of the analog-to-digital converter  15 . The outputs of the delay elements  250   a ,  250   b , and  250   c  respectively are connected to the multiplier circuit  255   a ,  255   b , and  255   c . Each delayed version of the output f i    237  of the multiplier circuit  235  is multiplied by one of the filter coefficients w x    260   a ,  260   b , and  260   c.    
     The output of each of the multiplier circuits  255   a ,  255   b , and  255   c  are connected to the combining circuits  265   a ,  265   b , and  265   c . The combining circuits  265   a ,  265   b , and  265   c  additively combine the resulting products from the multiplier circuits  255   a ,  255   b , and  255   c  with the output f 1    237  of the multiplier circuit  235  to form the sampled digitized signal f k    55  having the precursor intersymbol interference. 
     The filter coefficients normally are chosen as a function of an error signal determined as the difference of the estimate value â i    95  of the pulsed multilevel voltage signal a i    5  and the sampled digitized signal f k    55  having the precursor intersymbol interference removed. 
     Refer now to  FIG. 5 . to discuss the structure of the adaptive timing loop  150  of  FIG. 3 . As described above, the error signal e i    155 , the estimate â i    95  of the pulsed multilevel voltage signal a i , and the control constant μ t  are the inputs to the adaptive timing loop circuit  150 . The adaptive timing loop circuit  150  has a delay element  300  that receives the error signal e i    155 . The delay element  300  delays the error signal by the time equal to the period of the sampling clock of the analog-to-digital converter  15 . The delayed error signal e i−1    302  and the estimated pulsed multilevel voltage signal â i    95  are the inputs to the multiplier circuit  305 . The output of the multiplier circuit  305  is the product of the delayed error signal e i−1    302  and the estimated pulsed multilevel voltage signal â i    95 . The inputs of the multiplier circuit  310  is the gain constant μ t    165  and the output of the multiplier circuit  305 . The output of the multiplier circuit  310  is the product of the gain constant m and the output of the multiplier circuit  305 . 
     The inputs of the combining circuit  315  are the output of the multiplier circuit  310  and the current value of the timing phase adjustment signal φ samp    20 . The combining circuit  315  subtractively combines the current value timing phase adjustment signal φ samp    20  and the output of the multiplier circuit  310  to form the next value of the timing phase adjustment signal φ sampn+1    317 . The delay element  320  delays the next value of the timing phase adjustment signal φ sampn+1    317  to adjust the timing phase of the next sampling clock sufficiently to remove the first precursor intersymbol interference from the received pulsed multilevel voltage signal a irec    12 . 
     It is well-known in the art that, while the above describes individual circuitry to implement an apparatus that removes the precursor intersymbol interference from the received pulsed multilevel voltage signal, the apparatus may be implemented as a program code for execution on a computational processor. The program code maybe obtained from media such as storage nodes of an internal or external network or stored on a storage media such as read only memory (ROM) or a magnetic disk. Further, the apparatus that will remove the precursor intersymbol interference may be implemented as analog filters using continuous time processing. 
     In summary, the method for removing precursor intersymbol interference from a sampled, received, and digitized multilevel voltage signal, as shown in  FIGS. 6   a - 6   c , begins by adjusting a timing phase  400  of the sampling clock to remove a first precursor symbol interference from the precursor intersymbol interferences. After the timing phase is adjusted the method continues by filtering  450  any remaining precursor symbols of the precursor intersymbol interference with an open loop finite impulse response filter having a filter coefficient that is a function of a fixed gain parameter that is indicative of a condition of the communication channel. 
     The adjusting the timing phase  400  of the sampling clock begins by delaying  405  an error signal by one sampling period of the sampling clock. The error signal is a difference between an estimate of data transmitted on the communication channel and an equalized version of the received and sampled encoded signal and is indicative of an amount of the first precursor symbol interference. The adjusting of the timing phase  400  continues by multiplying  410  the estimate of the transmitted data by the error signal to form a first product. The first product is then further multiplied  415  by a loop gain control constant to form a second product. The second product is then subtractively combined  420  with a current timing phase adjustment to form a next timing phase adjustment. The next timing phase adjustment is then delayed  425  to align with a next sampling clock. The generating a next sample phase adjustment according to the formula of EQ. 8. 
     The filtering  450  any remaining precursor symbol interference is accomplished by first delaying  455  by one period of the sampling clock the encoded signal that is received and sampled and then multiplying  475  the encoded signal that is received and sampled by a filter coefficient to form a fourth product. The fourth product is then additively combined  480  with a previous sample of the encoded signal to form a preliminary equalized signal. The preliminary equalized signal is then multiplied  485  by a constant gain factor to produce a signal having the precursor intersymbol interference removed. The constant gain factor is set  460 ,  465  as a function of the channel condition as indicated by the error signal e i  and the filter coefficient is a mapping  470  of the constant gain factor. This filtering of any remaining precursor symbol interference is accomplished such that the encoded signal that is received and sampled with the phase adjusted sampling clock is modified according to the formula of EQ. 9 
     While this invention has been particularly shown and described with reference to the preferred embodiments thereof, it will be understood by those skilled in the art that various changes in form and details may be made without departing from the spirit and scope of the invention.