Patent Publication Number: US-7218672-B2

Title: Apparatus and method for constraining the value of feedback filter tap coefficients in a decision feedback equalizer

Description:
TECHNICAL FIELD OF THE INVENTION 
     The present invention is directed, in general, to decision feedback equalizers in digital communication devices and, more specifically, to an apparatus and method for constraining the valve of feedback filter tap coefficients in a decision feedback equalizer to reduce error propagation. 
     BACKGROUND OF THE INVENTION 
     The Digital High Definition Television (HDTV) Grand Alliance (Grand Alliance) is a group of television manufacturing and research organization in the television industry. After years of cooperative effort the Grand Alliance developed and proposed a standard for digital HDTV systems. The Grand Alliance standard has been adopted (with a few changes) by the Federal Communication Commission (FCC) as an official broadcasting standard for HDTV. The standard is known as the Advanced Television Systems Committee Digital Television Standard (the “ATSC Standard”). 
     The ATSC Standard for HDTV transmission over terrestrial broadcast channels uses a signal that consists of a sequence of twelve (12) independent time-multiplexed trellis-coded data streams modulated as an eight (8) level vestigial sideband (VSB) symbol stream with a rate of 10.76 MHz. This signal is converted to a six (6) MHz frequency band that corresponds to a standard VHF or UHF terrestrial television channel, over which the signal is then broadcast. 
     The ATSC Standard calls for two (2) bit data symbols of the HDTV signal to be trellis encoded in accordance with an eight (8) level (i.e., a three (3) bit) one dimensional constellation. One bit of each data symbol is pre-coded, and the other is subjected to a ½ encoding rate that produces two coded bits in accordance with a four (4) state trellis code. For purposes of interleaving, twelve (12) identical encoders and pre-coders operate successively on every twelve successive data symbols. Symbols 0, 12, 24, 36, . . . are encoded as one series. Symbols 1, 13, 25, 37, . . . as a second series. Symbols 2, 14, 26, 38, . . . as a third series. And so on for a total of twelve (12) series. Therefore, the ATSC Standard requires twelve (12) trellis decoders in the HDTV receiver for the twelve (12) series of time division interleaved data symbols in the signal. Each trellis decoder in the HDTV receiver decodes every twelfth (12th) data symbol in the stream of coded data symbols. 
     In an ATSC Standard receiver trellis decoders are used to retrieve the original digital data that was trellis encoded just before being converted to 8-VSB symbols, modulated and broadcast. The use of trellis coding provides an improvement in the signal to noise ratio of the received signal, and the time multiplexing of twelve (12) independent streams reduces the possibility of co-channel interference from an analog NTSC broadcast signal residing on the same frequency. The abbreviation NTSC stands for National Television Standards Committee. 
     Each of the trellis decoders for the four (4) state trellis code operates in accordance with the well-known Viterbi decoding algorithm. Each of the decoders comprises a branch metric generator unit, an add-compare-select unit, and a path-memory unit. See, for example, “Trellis-coded Modulation With Redundant Signal Set, Part I, Introduction; Part II, State of the Art,” by G. Ungerboeck, IEEE Communications Magazine, Vol. 25, pp. 5–21, February 1987. 
     In addition to being corrupted by noise, the transmitted signal is also subject to deterministic channel distortions and distortions caused by multipath interference. Consequently, an adaptive channel equalizer is generally used in front of the trellis decoders to compensate for these effects. The goal is to create a symbol stream that resembles, as much as possible, the symbol stream that was created by the twelve (12) trellis encoders at the transmitter. 
     One commonly used equalizer architecture makes use of a second equalizer known as a decision feedback equalizer (DFE). In this architecture, a conventional, or forward equalizer (FE) is supplemented by a DFE. The input to the DFE is an estimate of the original transmitted value of the current output symbol of the complete equalizer (FE and DFE). The output of the decision feedback equalizer (DFE) is subsequently added to the output of the forward equalizer (FE) to generate the output symbol. In a typical implementation, this estimate of the output symbol is obtained by simply “slicing” the equalizer output. The term “slicing” refers to the process of taking the allowed symbol value (of the eight (8) levels specified by the 8-VSB ATSC Standard) that is nearest to that of the actual output. Using the “sliced” symbols in a decision feedback equalizer (DFE) gives a near optimum error rate performance with low complexity. This approach, however, can suffer from error propagation caused by slicing errors. Because the typical symbol error rate after the equalizer for the HDTV signal can be up to twenty percent (20%), this can be a serious problem if the number of DFE filter taps is large. 
     After the equalizer, the HDTV signal is decoded in a trellis decoder that uses the Viterbi algorithm to decode the symbol stream based on the ½ rate trellis coding performed in the transmitter. As previously mentioned, the ATSC Standard specifies that twelve (12) trellis encoders and decoders are used in parallel in a time multiplexed fashion. Trellis decoding is then followed by byte de-interleaving and Reed Solomon decoding to further correct transmission errors in the signal. 
     A decision feedback equalizer (DFE) generally comprises a forward linear filter and a feedback filter inside a feedback loop. The feedback loop comprises a decision device (e.g., a slicer) and an error calculation unit. When errors are made by the decision device, the errors circulate in the feedback loop causing performance loss. The circulation of errors in the feedback loop is referred to as error propagation. 
     When the magnitude of the feedback filter taps is large, the effect of the error propagation often increases. This is because the error is multiplied by a large constant, thereby causing a greater error propagation. The resulting error continues to circulate in the feedback loop of the DFE, sometimes endlessly. 
     The filter tap coefficients of the DFE may be updated by using various prior art algorithms that exist for computing filter tap coefficients for adaptive equalizers. One commonly used method uses the well known least mean square (LMS) algorithm. The LMS algorithm is a successive approximation technique that uses the current coefficient and data tap values as well as the calculated error to compute the new coefficient value. The LMS algorithm repeats the procedure until each filter tap coefficient converges to the desired optimum value. 
     In a typical LMS algorithm the coefficient vector ƒ n   k+1  for the forward linear filter of a DFE is determined using the following formula: 
               f   n     k   +   1       =       f   n   k     +     μ   ⁢           ⁢     e   k     ⁢     r     k   -   n                 
where
 
             f   n   k         
is a forward filter tap coefficient at time k, μ is an adaptation speed constant, e k  is an error term, and r k−n  is a value of the forward filter tap data in the forward filter at time k. The error term e k  is the error calculated from the output of the DFE. The error term e k  can be calculated in a decision directed fashion using a known training sequence embedded in the data stream. Alternatively, the error term e k  can be calculated in a blind fashion using a Constant Modulus Algorithm (CMA) or a Decision Directed (DD) algorithm.
 
     Similarly, the coefficient vector 
             g   n     k   +   1           
for the feedback filter of a DFE is determined using the following formula:
 
               g   n     k   +   1       =       g   n   k     +     μ   ⁢           ⁢     e   k     ⁢     a     k   -   n                 
where
 
             g   n   k         
is a feedback filter tap coefficient at time k, μ is an adaptation speed constant, e k  is an error term, and a k−n  is a value of the feedback filter tap data in the feedback filter at time k.
 
     In a typical LMS algorithm the coefficients 
             f   n   k         
and
 
             g   n   k         
are unconstrained. That is, the coefficients
 
             f   n   k         
and
 
             g   n   k         
can assume any value to reduce multipath interference effects in the DFE. For severe post-echoes and pre-echoes the value of the feedback filter tap coefficients
 
             g   n   k         
can grow to such an extent that they reduce the performance of the DFE through error propagation.
 
     There is therefore a need in the art for an apparatus and method that is capable of constraining the value of feedback filter tap coefficients 
             g   n   k         
in a decision feedback equalizer in order to reduce error propagation.
 
     SUMMARY OF THE INVENTION 
     To address the deficiencies of the prior art mentioned above, the apparatus and method of the present invention reduce error propagation in a decision feedback equalizer by constraining the values of feedback filter tap coefficients in a feedback filter of the decision feedback equalizer. 
     The present invention constrains the values of the feedback filter tap coefficients by calculating updated coefficient values using a constraint cost function and a related constraint function. A coefficient adaptation unit within each filter tap cell of the feedback filter calculates the updated coefficient values. 
     It is an object of the present invention to prevent error propagation in a decision feedback equalizer. 
     It is another object of the present invention to prevent error from circulating within a feedback loop of a decision feedback equalizer. 
     It is still another object of the present invention to provide an apparatus and method for calculating values of feedback filter tap coefficients in a feedback filter of a decision feedback equalizer by applying a constraint condition to the values of the feedback filter tap coefficients. 
     It is also an object of the present invention to provide an apparatus and method for calculating values of feedback filter tap coefficients in a feedback filter of a decision feedback equalizer by applying a constraint condition to the values of the feedback filter tap coefficients where the constraint condition limits the total energy of the feedback filter tap coefficients. 
     It is another object of the present invention to provide an apparatus and method for calculating values of feedback filter tap coefficients in a feedback filter of a decision feedback equalizer by applying a constraint condition to the values of the feedback filter tap coefficients where the constraint condition limits the magnitude of each feedback filter tap coefficient to a threshold constant. 
     The foregoing has outlined rather broadly the features and technical advantages of the present invention so that those skilled in the art may better understand the detailed description of the invention that follows. Additional features and advantages of the invention will be described hereinafter that form the subject of the claims of the invention. Those skilled in the art should appreciate that they may readily use the conception and the specific embodiment disclosed as a basis for modifying or designing other structures for carrying out the same purposes of the present invention. Those skilled in the art should also realize that such equivalent constructions do not depart from the spirit and scope of the invention in its broadest form. 
     Before undertaking the Detailed Description of the Invention, it may be advantageous to set forth definitions of certain words and phrases used throughout this patent document: the terms “include” and “comprise” and derivatives thereof, mean inclusion without limitation; the term “or,” is inclusive, meaning and/or; the phrases “associated with” and “associated therewith,” as well as derivatives thereof, may mean to include, be included within, interconnect with, contain, be contained within, connect to or with, couple to or with, be communicable with, cooperate with, interleave, juxtapose, be proximate to, be bound to or with, have, have a property of, or the like; and the term “controller,” “processor,” or “apparatus” means any device, system or part thereof that controls at least one operation, such a device may be implemented in hardware, firmware or software, or some combination of at least two of the same. It should be noted that the functionality associated with any particular controller may be centralized or distributed, whether locally or remotely. In particular, a controller may comprise one or more data processors, and associated input/output devices and memory, that execute one or more application programs and/or an operating system program. Definitions for certain words and phrases are provided throughout this patent document. Those of ordinary skill in the art should understand that in many, if not most instances, such definitions apply to prior uses, as well as future uses, of such defined words and phrases. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       For a more complete understanding of the present invention, and the advantages thereof, reference is now made to the following descriptions taken in conjunction with the accompanying drawings, wherein like numbers designate like objects, and in which: 
         FIG. 1  illustrates a block diagram of an exemplary prior art high definition television (HDTV) transmitter; 
         FIG. 2  illustrates a block diagram of an exemplary prior art high definition television (HDTV) receiver; 
         FIG. 3  illustrates a block diagram of a prior art adaptive channel equalizer comprising a forward equalizer (FE) filter and a decision feedback equalizer (DFE) filter; 
         FIG. 4  illustrates a block diagram showing a prior art decision feedback equalizer (DFE) comprising a forward filter, a feedback filter, a decision device, and an error calculation unit; 
         FIG. 5  illustrates a block diagram of an adaptive finite impulse response (FIR) filter for use in feedback filter of a decision feedback equalizer utilizing the principles of the present invention; 
         FIG. 6  illustrates a flowchart showing the steps of a method of one advantageous embodiment of the present invention; and 
         FIG. 7  illustrates a graph showing a symbol error rate curve for a conventional dynamic channel and showing a symbol error rate curve for a dynamic channel in which the values of the feedback filter tap coefficients of a decision feedback equalizer have been constrained in accordance with the principles of the present invention. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       FIGS. 1 through 7 , discussed below, and the various embodiments used to describe the principles of the present invention in this patent document are by way of illustration only and should not be construed in any way to limit the scope of the invention. The present invention for constraining the value of feedback filter tap coefficients in a decision feedback equalizer in order to reduce error propagation may be used in any system that employs a decision feedback equalizer. 
     In the description of the exemplary embodiment that follows, the present invention is integrated into, or is used in connection with, a decision feedback equalizer within a digital television receiver. The present invention is not limited to use in a digital television system. Those skilled in the art will recognize that the exemplary embodiment of the present invention may easily be modified for use in any type of digital receiver system that uses a decision feedback equalizer including, without limitation, digital television systems, set top boxes, digital storage devices, digital radio systems, and any type of digital system that utilizes a decision feedback equalizer. The term “digital receiver system” is used to refer to these types of equipment. 
       FIG. 1  illustrates a block diagram of an exemplary prior art high definition television (HDTV) transmitter  100 . MPEG compatible data packets are encoded for forward error correction (FEC) by a Reed Solomon (RS) encoder  110 . The data packets in successive segments of each data field are then interleaved by data interleaver  120 , and the interleaved data packets are then further interleaved and encoded by trellis encoder unit  130 . Trellis encoder unit  130  produces a stream of data symbols representing three (3) bits for each symbol. One of the three bits is pre-coded and the other two bits are produced by a four (4) state trellis encoding. 
     Trellis encoder unit  130  comprises twelve (12) parallel trellis encoder and pre-coder units to provide twelve interleaved coded data sequences. The encoded three (3) bits of each trellis encoder and pre-coder unit are combined with field and segment synchronization bit sequences in multiplexer  140 . A pilot signal is inserted by pilot insertion unit  150 . The data stream is then subjected to vestigial sideband (VSB) suppressed carrier eight (8) level modulation by VSB modulator  160 . The data stream is then finally up-converted to a radio frequency by radio frequency (RF) by converter  170 . 
       FIG. 2  illustrates a block diagram of an exemplary prior art high definition television (HDTV) receiver  200 . The received RF signal is down-converted to an intermediate frequency (IF) by tuner  210 . The signal is then filtered and converted to digital form by IF filter and detector  220 . The detected signal is then in the form of a stream of data symbols that each signify a level in an eight (8) level constellation. The signal is then filtered by NTSC rejection filter  230  and subjected to equalization and phase tracking by equalizer and phase tracker unit  240 . The recovered encoded data symbols are then subjected to trellis decoding by trellis decoder unit  250 . The decoded data symbols are then further de-interleaved by data de-interleaver  260 . The data symbols are then subjected to Reed-Solomon decoding by Reed Solomon decoder  270 . This recovers the MPEG compatible data packets transmitted by transmitter  100 . 
     A schematic representation of computer diskette  280  is also shown in  FIG. 2 . In an alternate advantageous embodiment of the present invention, computer diskette  280  may be inserted into a computer disk drive (not shown) in television receiver  200 . The computer disk drive is capable of receiving information that relates to the values of feedback filter tap coefficients in a decision feedback equalizer within television receiver  200  and is capable of writing the information to computer diskette  280 . In another alternate advantageous embodiment of the present invention, computer diskette  280  contains computer executable method steps for implementing the method of the present invention. Computer diskette  280  may be considered as a representation of any type of medium that is capable of storing and sending computerized data and instructions. 
       FIG. 3  illustrates a block diagram of a prior art adaptive channel equalizer  300  for use in equalizer and phase tracker unit  240 . Prior art adaptive channel equalizer unit  300  comprises a forward equalizer (FE) filter  310  and a decision feedback equalizer (DFE) filter  320 . The output from forward equalizer (FE) filter  310  is added to the output from decision feedback equalizer (DFE) filter  320  in adder unit  330  to form the output of adaptive channel equalizer unit  300 . 
     Forward equalizer (FE) filter  310  accepts the uncompensated channel symbol data as its input. In contrast, decision feedback equalizer (DFE) filter  320  requires for its input an “estimate” of the symbol that was transmitted over the channel before the symbol was corrupted by noise. 
     As is well known, DFE filter  320  can receive an estimate of the output symbol by simply “slicing” the equalizer output. The term “slicing” refers to the process of taking the allowed symbol value (of the eight (8) levels specified by the 8-VSB ATSC Standard) that is nearest to that of the actual output. In the embodiment shown in  FIG. 3 , level slicer  340  provides the “sliced” symbols to DFE filter  320  through multiplexer  350 . This method of providing estimates of the output symbols to DFE filter  320  can suffer from error propagation caused by slicing errors. 
     As is also well known, DFE filter  320  can be adapted either in a “trained mode” or in a “blind” mode. In the “trained mode” DFE filter  320  receives a “training sequence” of known symbols (through multiplexer  350 ) at a certain known time. DFE filter  320  compares the known training sequence with the “equalizer error for trained adaptation.” The equalizer error for trained adaptation is obtained by subtracting the equalizer output from the known training sequence. The subtraction process occurs in subtract unit  360 . DFE filter  320  then adjusts its operation to cause the equalizer output to match the known training sequence. 
     Alternatively, DFE filter  320  can operate in a “blind mode.” In the “blind mode” DFE filter  320  receives an “equalizer error for blind adaptation” from blind error unit  370 . Blind error unit  370  compares the equalizer output with an expected statistical distribution of the data to generate the equalizer error blind adaptation. DFE filter  320  then adjusts its operation to cause the equalizer output to match the expected statistical distribution of the data. 
       FIG. 4  illustrates a block diagram showing a prior art decision feedback equalizer (DFE)  320 . DFE  320  comprises forward filter  410 , feedback filter  420 , adder unit  430 , decision device  440 , and error calculation unit  450 . An input signal to DFE  320  is received in forward filter  410 . The output from forward filter  410  is added to the output from feedback filter  420  in adder unit  430  to form the output of DFE  320 . The output of DFE  320  is fed to decision device  440  and to error calculation unit  450 . The output of decision device  440  is fed to feedback filter  420 . The output of error calculation unit  450  is fed to forward filter  410  and to feedback filter  420 . Information from decision device  440  and error calculation unit  450  is used to reduce errors in feedback filter  420 . 
       FIG. 5  illustrates an adaptive finite impulse response (FIR) filter  500  of the present invention for use in forward filter  410  and for use in feedback filter  420  of decision feedback equalizer  320 . The coefficients of FIR filter  500  are computed to compensate  155  as much as possible for channel distortions. The length of FIR filter  500  corresponds to the maximum impairment delay that FIR filter  500  is designed to correct for. 
     FIR filter  500  comprises a number of filter tap cells  510  (also referred to as “filter taps”). Each filter tap  510  comprises a data storage register  520 , a coefficient storage register  530 , and multiplier  540 . The output of multiplier  540  is input to an adder unit  550 . Adder unit  550  sums all of the weighted tap values to generate a filter output. Filter tap  510  also comprises a coefficient adaptation unit  560  that computes the updated filter coefficients. The coefficient adaptation unit  560  has the following inputs: (1) the current coefficient value, (2) the data tap value, and (3) a measure of the equalizer error (i.e., the difference between the expected signal value and the actual output signal value). The calculation of filter coefficients in accordance with the principles of the present invention occurs in coefficient adaptation unit  560 . The coefficient adaptation unit  560  operates only when the adaptation process is being performed. 
     As previously mentioned, a commonly used prior art method of computing the filter coefficients uses the well-known least mean square (LMS) algorithm. The LMS algorithm is a successive approximation technique that uses the current coefficient and data tap values as well as the calculated error to compute a new coefficient value. The LMS algorithm repeats the procedure until each filter tap coefficient converges to the desired optimum value. 
     The LMS algorithm determines the coefficient vector 
             f   n     k   +   1           
for the forward linear filter of a DFE as follows:
 
                       f   n     k   +   1       =       f   n   k     +     μ   ⁢           ⁢     e   k     ⁢     r     k   -   n             ⁢                   (   1   )               
where
 
             f   n   k         
is a forward filter tap coefficient at time k, μ is an adaptation speed constant, e k  is an error term, and r k−n  is a value of the forward filter tap data in the forward filter at time k. The error term e k  is the error calculated from the output of the DFE. The LMS algorithm determines the coefficient vector
 
             g   n     k   +   1           
for the feedback filter of the DFE as follows:
 
                       g   n     k   +   1       =       g   n   k     +     μ   ⁢           ⁢     e   k     ⁢     a     k   -   n             ⁢                   (   2   )               
where
 
             g   n   k         
is a feedback filter tap coefficient at time k, μ is an adaptation speed constant, e k  is an error term, and a k−n  is a value of the feedback filter tap data in the feedback filter at time k.
 
     Equations (1) and (2) leave the coefficients 
             f   n   k         
and
 
             g   n   k         
unconstrained. That is, the coefficients
 
             f   n   k         
and
 
             g   n   k         
can assume any value to reduce multipath interference effects in the DFE. For severe post-echoes and pre-echoes the value of the feedback filter tap coefficients
 
             g   n   k         
can grow to such an extent that they reduce the performance of the DFE through error propagation.
 
     The present invention provides and an apparatus and method for constraining the values of the feedback filter tap coefficients 
               g   n   k     .         
In the method of the present invention the following equations are used:
 
                     f   n     k   +   1       =       f   n   k     +     μ   ⁢           ⁢     e   k     ⁢     r     k   -   n                   (   3   )                 g   n     k   +   1       =       g   n   k     +     μ   ⁢           ⁢     e   k     ⁢     a     k   -   n         -     λ   ⁢           ⁢       ∂   J       ∂     g   n                     (   4   )               
where the symbols in Equations (3) and (4) have the same meaning as in Equations (1) and (2) and where the term J is a constraint cost function and where the term λ is a small positive constant factor that is usually less than one.
 
     The constraint function M(g n ) is a function of g n . To properly constrain the values of g n  the value of the constraint function M(g n ) must be less than or equal to zero.
 
 M ( g   n )≦0   (5)
 
If the value of the constraint function M(g n ) becomes larger than zero, then the value of the term
 
               -   λ     ⁢           ⁢       ∂   J       ∂     g   n               
in Equation (4) must be adjusted. The constraint cost function J can defined as:
   J=[M ( g   n )] 2  if  M ( g   n )&gt;0  (6)   J= 0 if  M ( g   n )≦0  (7) 
     For a given constraint cost function J, the gradient of the constraint cost function J with respect to the feedback filter tap coefficients 
             g   n   k         
can be evaluated. The result
 
               ∂   J       ∂     g   n             
is used in Equation (4) to update the feedback filter tap coefficients of feedback filter  420 .
 
     In order to demonstrate the benefit of using the method of the present invention, consider a constraint that limits the total energy of the taps. This constraint can be described as: 
                     M   ⁡     (     g   n     )       =         ∑     n   =   0       N   -   1       ⁢            g   n          2       -   D             (   8   )               
where D is a threshold constant (i.e., the total energy of the feedback taps). This constraint means that the total energy of the feedback taps should not exceed a value equal to D.
 
     The value of J for the M(g n ) of Equation (8) is: 
                   J   =           [         ∑     n   =   0       N   -   1       ⁢            g   n          2       -   D     ]     2     ⁢           ⁢   if   ⁢           ⁢     M   ⁡     (     g   n     )         &gt;   0             (   9   )                 J= 0 if  M ( g   n )≦0  (10) 
     The gradient of the constraint cost function J that is related to the constraint function of Equation (8) is then described as: 
     
       
         
           
             
               
                 
                   
                     
                       ∂ 
                       J 
                     
                     
                       ∂ 
                       
                         g 
                         n 
                       
                     
                   
                   = 
                   
                     
                       4 
                       ⁢ 
                       
                         M 
                         ⁡ 
                         
                           ( 
                           
                             g 
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                           ) 
                         
                       
                       ⁢ 
                       
                         g 
                         n 
                       
                       ⁢ 
                       
                           
                       
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                       ⁢ 
                       
                         M 
                         ⁡ 
                         
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                     &gt; 
                     0 
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       ∂ 
                       J 
                     
                     
                       ∂ 
                       
                         g 
                         n 
                       
                     
                   
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                         M 
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                     0 
                   
                 
               
               
                 
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                   12 
                   ) 
                 
               
             
           
         
       
     
     As a second example, consider a constraint that limits the magnitude of each tap to the value D. Specifically,
 
 M ( g   n )=| g   n   |−D   (13)
 
The value of J for the M(g n ) of Equation (13) is:
 
 J=[|g   n   |−D]   2  if  M ( g   n )&gt;0  (14)
 
 J= 0 if  M ( g   n )≦0  (15)
 
The gradient of the constraint cost function J that is related to the constraint function of Equation (13) is then described as:
 
     
       
         
           
             
               
                 
                   
                     
                       ∂ 
                       J 
                     
                     
                       ∂ 
                       
                         g 
                         n 
                       
                     
                   
                   = 
                   
                     
                       2 
                       ⁢ 
                       
                         M 
                         ⁡ 
                         
                           ( 
                           
                             g 
                             n 
                           
                           ) 
                         
                       
                       ⁢ 
                       
                         sign 
                         ⁡ 
                         
                           ( 
                           
                             g 
                             n 
                           
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                       ⁢ 
                       
                           
                       
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                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         M 
                         ⁡ 
                         
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                           ) 
                         
                       
                     
                     &gt; 
                     0 
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       ∂ 
                       J 
                     
                     
                       ∂ 
                       
                         g 
                         n 
                       
                     
                   
                   = 
                   
                     
                       0 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       if 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         M 
                         ⁡ 
                         
                           ( 
                           
                             g 
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                           ) 
                         
                       
                     
                     ≤ 
                     0 
                   
                 
               
               
                 
                   ( 
                   17 
                   ) 
                 
               
             
           
         
       
     
     The closest approximation to the constraint of Equation (13) may be made by clipping each tap to a value of D. This provides a simple implementation for the constraint of Equation (13). 
     It is understood that the method of the present invention may also be used to constrain the values of 
               f   n   k     .         
That is, the values of
 
             f   n   k         
may be obtained from the equation:
 
                     f   n     k   +   1       =       f   n   k     +     μ   ⁢           ⁢     e   k     ⁢     r     k   -   n         -     λ   ⁢           ⁢       ∂   J       ∂     f   n                     (   18   )               
where
 
             f   n   k         
is a forward filter tap coefficient at time k, μ is an adaptation speed constant, e k  is an error term, and r k−n  is a value of the forward filter tap data in the forward filter at time k, J is a constraint cost function, and λ is a small positive constant that is usually less than one.
 
     In an alternate advantageous embodiment of the present invention, the values of both 
             f   n   k         
and
 
             g   n   k         
may be constrained simultaneously.
 
       FIG. 6  illustrates a flowchart showing the steps of a method of one advantageous embodiment of the present invention. The steps are collectively referred to with reference numeral  600 . 
     First a constraint M(g n ) is selected (step  610 ). Then the value of the constraint cost function J is calculated using the selected value of the constraint M(g n ) (step  620 ). Next the value of the gradient of the constraint cost function J with respect to the feedback filter tap coefficients 
             g   n   k         
is calculated (step  630 ).
 
     Then coefficient adaptation unit  560  within feedback filter  420  uses Equation (4) to update a feedback filter tap coefficient 
             g   n   k         
(step  640 ). That is, the next feedback filter tap coefficient
 
             g   n     k   +   1           
is calculated using:
 
     
       
         
           
             
               
                 
                   
                     g 
                     n 
                     
                       k 
                       + 
                       1 
                     
                   
                   = 
                   
                     
                       g 
                       n 
                       k 
                     
                     + 
                     
                       μ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         e 
                         k 
                       
                       ⁢ 
                       
                         a 
                         
                           k 
                           - 
                           n 
                         
                       
                     
                     - 
                     
                       λ 
                       ⁢ 
                       
                         
                           ∂ 
                           J 
                         
                         
                           ∂ 
                           
                             g 
                             n 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     Then coefficient adaptation unit  560  within forward filter  410  uses Equation (3) to update a forward filter tap coefficient 
                   f   n   k               f   n     k   +   1                 
(step  650 ). That is, the next forward filter tap coefficient is calculated using:
 
     
       
         
           
             
               
                 
                   
                     f 
                     n 
                     
                       k 
                       + 
                       1 
                     
                   
                   = 
                   
                     
                       f 
                       n 
                       k 
                     
                     + 
                     
                       μ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         e 
                         k 
                       
                       ⁢ 
                       
                         r 
                         
                           k 
                           - 
                           n 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
     In this description step  640  has been described as preceding step  650  for purposes of clarity. In practice step  640  and step  650  may be performed simultaneously. Forward filter  410  and feedback filter  420  then perform their respective filtering operations (step  660 ). The time index k is then incremented (step  670 ). Control then returns to step  640  and the method continues to update the filter tap coefficients. 
     As previously described the presence of the term 
               -   λ     ⁢           ⁢       ∂   J       ∂     g   n               
in Equation (4) constrains the values of the feedback filter tap coefficients
 
               g   n   k     .         
The constraint provided by the present invention limits the size of the error that circulates in the feedback loop. Error propagation is commensurately limited.
 
       FIG. 7  illustrates a graph showing a symbol error rate (SER) curve for a conventional dynamic channel plotted against 8-VSB segments.  FIG. 7  also shows a symbol error rate (SER) curve for a dynamic channel plotted against 8-VSB segments in which the values of the feedback filter tap coefficients of a decision feedback equalizer have been constrained in accordance with the principles of the present invention. 
     The graph shown in  FIG. 7  represents results from a simulation of a dynamic channel using an 8-PAM (8-VSB) signal with a channel that has a post echo of negative two decibels (−2 dB) at four microseconds (4 μs) and a twenty five decibel (25 dB) signal to noise ratio (SNR). The decision feedback equalizer contained a forward filter having one hundred twenty eight (128) taps and a feedback filter having one hundred twenty eight (128) taps. The post echo was subject to a doppler frequency of one hundred Hertz (100 Hz). The intended application for the simulation was the Advanced Television Systems Committee Digital Television Standard. 
     The data plotted in  FIG. 7  shows that a decision feedback equalizer using the constrained feedback filter tap coefficients of the present invention correctly tracks a dynamic channel. The data plotted in  FIG. 7  also show that a conventional decision feedback equalizer using unconstrained feedback filter tap coefficients is not able to correctly track a dynamic channel. The decision device used in the simulation was a trellis decoder. 
     It is understood that the present invention may be used in a variety of different decision feedback equalizer circuits. In the exemplary decision feedback equalizer circuit  320  illustrated in  FIG. 4 , the method of the present invention may be used to calculate the feedback filter tap coefficients g n   k  that are provided to feedback filter  420 . It is understood that the equalizer circuit illustrated in  FIG. 4  is shown as an example. The method of the present invention is not limited to use only in the equalizer circuit shown in  FIG. 4 . 
     While the present invention has been described in detail with respect to certain embodiments thereof, those skilled in the art should understand that they can make various changes, substitutions modifications, alterations, and adaptations in the present invention without departing from the concept and scope of the invention in its broadest form.