JPH01149618A - Decision feedback type equalization system - Google Patents

Abstract

PURPOSE:To guarantee the adaptive operation of an adaptive filter by finding residual inter-code interference by performing subtraction on difference signals and updating the coefficient of the filter by using the interference after fetching data corresponding to the symbolic waveform of the difference signals and already preserved in a memory by using the decided results of the difference signals. CONSTITUTION:The false inter-code interference produced by an adaptive filter 5 is supplied to a subtracter 2. At the subtracter 2 difference signals which are produced by subtracting the false inter-code interference from received signals which are the input signals of an input terminal 1 are obtained and supplied to a deciding device 3 and delaying element 8. At another subtracter 13 the received signals are offset by performing subtraction on the output signal of the delaying element 8 and signals selected from memory groups 101, 102,..., 10m by means of a selector 11 and only residual inter-code interference is supplied to the filter 5. Results decided by the discriminator 3 are supplied to the filter 5 and, at the same time, appear at an output terminal 7. Therefore, when the adaptive filter is controlled by performing coefficient updating by using the output signal of the subtractor 13, the adaptive operation of the filter is guaranteed.

Description

DETAILED DESCRIPTION OF THE INVENTION [Field of Industrial Application] The present invention relates to a decision feedback equalization method, and more particularly to a decision feedback equalization method used to eliminate intersymbol interference that occurs during waveform transmission.

[Conventional technology]

A decision feedback type is known as a well-known technique for eliminating intersymbol interference that occurs during waveform transmission (IEEE TRANSACTIONS ON COMMUNICATIONS).
COMMUNICATIONS) Volume 32, No. 3, 198
4, pp. 258-266).

A decision feedback equalizer uses an adaptive filter with tap coefficients that are long enough to be affected by intersymbol interference to generate pseudo intersymbol interference corresponding to the received data sequence, thereby changing the waveform of the transmission path. It operates to suppress intersymbol interference received during transmission. At this time, each coefficient of the adaptive filter is successively modified by correlating the residual intersymbol interference with the determination result of the received signal.

When modifying coefficients in a decision feedback equalizer, if the residual intersymbol interference contained in the difference signal obtained by subtracting the pseudo intersymbol interference from the received signal containing intersymbol interference cannot be detected correctly, the adaptive operation will fail. The problem arises that it becomes impossible. For example, when a binary code such as a bi-phase code is used as a transmission path code, due to the □ nature of the binary code, there is no section where the received signal level is zero, and only intersymbol interference can be extracted independently. is no longer possible, and the above-mentioned problem occurs. Next, a conventional technique for solving this problem will be described.

FIG. 5 is a block diagram showing a conventional example of a decision feedback type vase. Here, the circuit shown in FIG. 5 is connected to the transmitting side via a transmission path. For simplicity, the explanation will be based on the assumption that baseband transmission is used.

In FIG. 5, a received signal containing intersymbol interference is supplied from a transmission path to an input terminal 1, and is input to a subtracter 2.

The subtracter 2 generates a difference signal obtained by subtracting the pseudo intersymbol interference from the received signal supplied to the input terminal 1 (=received signal including residual intersymbol interference, where [residual intersymbol interference] = [intersymbol interference] - [ Pseudo intersymbol interference]) is obtained, and the determiner 3. It is supplied to a subtracter 6. The result determined by the determiner 3 becomes a binary data series, which is supplied to the output terminal 4, the AGC 7, and the adaptive filter 5. Adaptive filter 5
The output of is supplied to subtractor 2. The closed loop circuit consisting of the subtracter 6 and the AGC 7 operates to accurately extract only the residual intersymbol interference in the difference signal input to the subtracter 6.

This is achieved by the AGC 7 multiplying the signal supplied from the determiner 3 by a certain constant to generate a received signal that does not contain residual intersymbol interference. The received signal generated by the AGC 7 is subtracted from the difference signal, which is the output of the subtracter 2, in a subtracter 6. The output of the subtracter 6 is supplied to the adaptive filter 5 and used for updating coefficients. Subtractor 21
Judgment device 3. A closed loop circuit consisting of an adaptive filter 5 operates to remove intersymbol interference in the received signal applied to the input terminal 1. This is achieved by the adaptive filter 5 generating pseudo intersymbol interference.

Therefore, the adaptive filter 5 will be explained in detail. FIG. 6 is a detailed block diagram of the adaptive filter 5 of FIG. Input signals 106 and 107 in FIG. 6 correspond to the binary data series that is the output signal of the determiner 3 and the output signal of the subtractor 6 in FIG. 5, respectively. Further, the output signal 108 in FIG. 6 corresponds to the output signal of the adaptive filter 5 in FIG. Input signal 106 is input to delay element 1001. Multiplier 101o.

101s, . . . , l0IR-1 and coefficient generators 1°2o, 1021, --, 102R-1.

Delay elements 1001, 1002 providing a delay of T seconds.

......, 100 N/R-1 are connected in this order, and each can be realized by a flip-flop.

Here, N and R are positive integers, and R is a divisor of N. Further, the data period of the input signal 106 is T seconds. Delay element 1oO+ (i=1.2.・”-.

N/R-1)<7)-outputs are each multiplier 101J.

101J+1. ......, 101 J+R-1 and coefficient generator 102J, 102J+1, -...
, 102J+R-1. However, j=ixR
It is. Multiplier 1゜1o, l O11,=, 1
01x-s-R (k=o.

1, ..., R-1), respectively, the coefficient generator 1
゜2o, 102t, -..., 102)
After the input data of each coefficient, which is the output of l-N-R, is multiplied, all of the multiplication results are input to an adder 103x and added. R adders 103o, 103+, -
The output of the switch 104 becomes the input contact of the switch 104. The switch 104 is a multi-contact switch with a period of T seconds, and has R adders 103o and 103+.

. . . , the output of 103R-1 is selected and outputted in this order every T/R seconds to form the output signal 108. Output signal 108 is pseudo intersymbol interference generated every T/R seconds. R is called an interpolation constant (interpolation factor), and in order to eliminate intersymbol interference within a required signal band, R is usually an integer of 2 or more. On the other hand, switch 104
The switch 105, which operates in synchronization with the switch 104, has a human output opposite to that of the switch 104. That is, the switch 105 functions to sequentially distribute the input signal 1.7 to R contacts every T/R seconds. Each contact output of the switch 105 is supplied to a coefficient generator present in a signal path input to the contact corresponding to the switch 104 operating synchronously.

Next, the coefficient generation circuit will be explained in detail.

FIG. 7 shows the coefficient generator 102+(1=0°1, ・
. . . , N-1). The input signal 200 in FIG. 7 is the input signal 10 in FIG.
6 or delay elements 100r, 1002.

......, corresponds to an output signal of 100 N/R-1.

Furthermore, the input signal 201 in FIG. 7 corresponds to the contact output of the switch 105 in FIG. Furthermore, output signal 203 in FIG. 7 corresponds to the output of coefficient generator 1021 in FIG. In FIG. 7, the input signal 200
and 201 are supplied to a multiplier 204, and the multiplication result becomes one input of an adder 205. The output of the adder 205 is fed back through a delay element 206 of T seconds, and the coefficients are updated every T seconds by updating the correlation value of the input signals 200 and 201 supplied to the multiplier 204 by one sample. This is realized by adding it to the coefficient value of . Output signal 20
3 is the coefficient.

[Problem that the invention seeks to solve]

As described above, the pseudo intersymbol interference generated by the adaptive filter 5 of FIG. 5, which has been explained with reference to FIGS. 6 and 7, becomes one input of the subtracter 2.

The subtracter 2 generates a difference signal obtained by subtracting the pseudo intersymbol interference from the received signal supplied from the input terminal 1 (=received signal including residual intersymbol interference, where [residual intersymbol interference] = [intersymbol interference] - [pseudo intersymbol interference]) is obtained, and the determiner 3.
It is supplied to a subtracter 6. On the other hand, the closed loop circuit consisting of the AGC 7 and the subtracter 6 operates to accurately extract only the residual intersymbol interference in the difference signal supplied to the subtracter 6. A
The output signal of the determiner 3 supplied to the GC 7 is multiplied by 1 and input to the subtracter 6. Here, γ is a positive number. AGC7
The signal supplied to the subtracter 6 is subtracted from the difference signal supplied to the subtracter 6, and is fed back to the AGC 7 as a control signal. The AGC 7 uses the signal fed back from the subtracter 6 to correct γ so that the output of the subtracter 6 is equal to the residual intersymbol interference. That is, the AGC 7 pseudo-generates a signal other than the residual intersymbol interference included in the difference signal.

The output of the subtracter 6 is sent to the adaptive filter 5 as an error.
and used for coefficient update. Here, in order for the adaptive filter 5 to perform an adaptive operation, the residual intersymbol interference must be correctly supplied to the adaptive filter 5. However, since the difference signal that is the output signal of subtractor 2 also contains signals other than residual intersymbol interference,
If it is assumed that the output signal of the subtracter 2 is directly supplied to the adaptive filter 5, the residual intersymbol interference cannot be accurately obtained. Therefore, the adaptive ability of the adaptive filter 5 will be lost. Therefore, conventionally, as shown in FIG. 5, a subtracter 6. A method has been used in which the adaptive operation of the adaptive filter 5 is guaranteed by adding the AGC 7 and subtracting signals other than pseudo residual intersymbol interference from the difference signal that is the output signal of the subtracter 2. In this method, the AGC 7 generates a received signal that does not include intersymbol interference using a binary data sequence that is the determination result of the received signal, and the subtracter 6 subtracts it from the difference signal. The residual intersymbol interference component will be obtained, and the adaptive operation of the adaptive filter 5 will be guaranteed. However, in the conventional control method, AGC
7 is required, and in order to obtain a sufficient degree of intersymbol interference suppression, complex control is required to maintain the received signal, which does not include intersymbol interference, supplied from the AGC7 to the subtracter 6 at a desired level. The disadvantage is that the hardware scale becomes large. Further, when the amplitudes of the positive and negative pulses differ due to the nonlinearity of the received signal, it is necessary to perform separate control corresponding to the positive and negative pulses in 80C7.

An object of the present invention is to provide a decision feedback equalization method that is simple and requires small hardware.

[Means for solving problems]

The present invention provides a decision feedback equalization method that removes intersymbol interference that occurs during waveform transmission by using pseudo intersymbol interference generated by an adaptive filter. After subtracting the inter-interference interference to obtain a difference signal, the determination result of the difference signal is used to retrieve the data already stored in the memory corresponding to the symbol waveform of the difference signal, and then subtracted from the difference signal. The present invention is characterized in that residual inter-symbol interference is determined, the difference signal is stored in a memory corresponding to the symbol waveform, and the coefficients of the adaptive filter are updated using the residual inter-symbol interference.

[Effect]

Unlike the conventional method of multiplying the determiner output by a constant to generate a received signal that does not include residual intersymbol interference and subtracting it from the difference signal, the present invention focuses on the characteristics of the eye pattern of the received signal and generates a received signal that does not contain residual intersymbol interference. The structure was designed to accurately extract interference between the two. That is, according to the characteristics of the eye pattern of the received signal of the transmission line code including the binary code system, the current sample value and J
The minimum probability that the sample values T seconds ago (J is a positive integer) have almost the same value takes a certain positive value that is not zero. Therefore, while the difference signal (=received signal containing residual intersymbol interference) is stored in the memory corresponding to the symbol waveform to which each sample value belongs, it is retrieved when sample values of the same polarity and equal absolute value are received. By subtracting it from the current sample value, the difference is negligible when there is no intersymbol interference, and otherwise becomes the residual intersymbol interference itself. Therefore, since the residual intersymbol interference can be detected accurately, if the difference is used as an error signal, the adaptive operation of the adaptive filter is guaranteed.

〔Example〕

Next, the present invention will be explained in detail with reference to the drawings. FIG. 1 is a block diagram showing one embodiment of the present invention. In the figure, functional blocks given the same reference numbers as in FIG. 5 have the same functions as in FIG. 5. The difference between FIG. 1 and FIG. 5 is that a delay element (M,
T>8. Switch 9. Memory groups 101, 102,...
..., 10□9 selector 11. This part consists of the subtracter 13, and the other configurations are exactly the same as in FIG.

Before explaining this circuit, the overall configuration will be briefly described. A received signal input to input terminal 1 is supplied to subtracter 2 . The difference signal obtained by subtracting the pseudo intersymbol interference generated by the adaptive filter 5 in the subtracter 2 (=received signal containing residual intersymbol interference) is supplied to the determiner 3 and the delay element 8. The output of the determiner 3 is supplied to an output terminal 4, a switch 9, a selector 11, and an adaptive filter 5. Adaptive filter 5
゜Subtractor 2. Delay element 8. Switch 9. Memory group 10S
, 102. ......, 10. , selector 11. A closed loop circuit consisting of the subtracter 13 realizes the adaptive operation of the adaptive filter 5, and the switch 9 and the selector 11 are connected to the memory groups 101, 102, . . .
10. The signal supplied to the subtracter 13 is controlled by selecting the signal to be supplied to the subtracter 13 and the signal to be extracted. The configuration of the adaptive filter 5 may be the same as the circuit configuration shown in FIGS. 6 and 7, similar to that explained in FIG. 5.

Next, the relationship between the output of the selector 11 and the residual intersymbol interference in the difference signal that is the output of the subtracter 2 will be explained in detail, but before that, the transmission line codes will be described.

FIG. 2 is a diagram showing a typical example of a binary code for explaining a transmission line code, and (a) of the same figure shows a biphase code (
b) shows the pulse waveform of an MSK (minimum shift keying) code.

As shown in Figure 2(a), in the biphase code, °0
A pulse waveform with inverted polarity is assigned to the data of '' and '1'. The polarity of both pulses is reversed at the center of the 1-bit width T seconds, and the polarity is balanced within 1 bit. On the other hand, as shown in FIG. 2(b), four types of pulse waveforms are prepared in the MSK code. That is, for data “O′° and “1”, “0° mode and °
“1゛.

Prepare two types of pulse waveforms for each mode. “0°.

mode and 1” mode represent positive and negative waveform polarities, respectively. These two types of mode transitions are shown in Figure 2 (
This is indicated by the arrow b), and the current mode is determined by the mode one symbol before. This MSK code has a property that the polarity always inverts at the boundary of the transmitted symbol waveform.

In addition, in the MSK code, the positive and negative values are balanced within one symbol for °1'°, but the positive and negative values are not balanced for 0°'. However, as shown in Fig. 2(b) As is clear from the direction of the arrow indicating the mode transition, "0" in the continuous data series.

If there is an even number of , the positive and negative values are balanced and the DC component can be almost ignored. The transmission path code shown in FIG. 2 is transmitted through the transmission path and is input to the input terminal 1 of FIG. 1 after receiving intersymbol interference.

Figures 3 and 4 show an example of a received signal eye pattern and an example of a received signal waveform pattern, respectively, corresponding to the transmission line code in Figure 2. Figures 3 (a) and (b) correspond to Figure 2. These are the eye patterns of the biphase code and the MSK code, respectively. As shown in the figure, the received signal eye pattern has high frequency components removed and becomes rounded. Originally, a received signal eye pattern includes intersymbol interference components, but for the sake of simplicity, the eye pattern shown is ideal and does not include intersymbol interference.

Now, the received signal eye of the MSK code shown in Fig. 3(b) is
Pay attention to patterns. According to the characteristics of the received signal eye pattern, the probability that the sample value JT seconds (J is a positive integer) before the current sample value has the same polarity and almost the same absolute value is a non-zero positive value. Take. Therefore, the received signal can be canceled by storing sample values every T seconds in memory and subtracting them from the sample values when a waveform of the same polarity is received. FIG. 4(b) shows how the received signal is canceled in the case of J=2, and the three waveforms are, from the right, the symbol waveforms of the present, T seconds ago, and 2T seconds ago. In the example shown in FIG. 4(b), the current waveform and the symbol waveform 2T seconds ago have the same polarity. Therefore, regarding the sample value, it is easy to see that the current sample value and the sample value 2T seconds ago have the same polarity and the same absolute value.

Therefore, by retrieving the sample value 2T seconds ago from the memory corresponding to the symbol waveform to which the sample value belongs and subtracting it from the current sample value, the received signal components are canceled and the output becomes zero. It is clear that this is also true for cases other than J=2. Now, considering a non-ideal case, the received signal includes residual intersymbol interference components. Considering the residual intersymbol interference component, the current residual intersymbol interference value and the residual intersymbol interference value JT seconds ago are uncorrelated, so the residual intersymbol interference value JT seconds ago is random noise. It can be considered. The amplitude distribution of the residual intersymbol interference value J] seconds ago is symmetrical in sign and negative, and the probability that the amplitude d becomes 1d1 x δ (however, O x δ) is not zero but takes a certain positive value. Therefore, it can be seen that the probability that the output signal of the subtractor 13 contains accurate residual intersymbol interference takes a certain positive value that is not zero. Furthermore, the magnitude of the residual intersymbol interference at -a is sufficiently small with respect to the received signal. Therefore, the waveform shown in FIG. 4(b) can be regarded as the received signal waveform even if it is not ideal.

Next, the memory groups 10□, 102°... in FIG.
..., 10. The operation of the switch 9 and selector 11 that control input/output signals will be explained. The switch 9 connects memories for storing sample values corresponding to symbol waveforms to which the received sample values belong to memory groups 101, 102, . . .
..., 10. The eye pattern of the 0M5K code selected from 48! is shown in FIG. Since similar waveforms are superimposed, m = 4, and for example, memory 10
□, 102, 103.104 are “00” i
+ 01 n, "10", and "11" can be considered to correspond to symbol waveforms. Here, 0
1'° represents a symbol waveform defined by a data signal "0" and a mode signal "1'°. Switch 9 is judger 3
Using the data signal and mode signal supplied from , these combinations are "00", "01", and ° "10".

The circuit is switched so that the signals supplied from the delay element 8 when the signal is "11" are stored in the memories 101, 102.10.3.104, respectively. In addition, in FIG. 1, the determiner 3 and the switch 9. The path connecting the selector 11 and the adaptive filter 5 is shown as one line, but when MSK codes are adopted, two paths are shown corresponding to the data signal and the mode signal. The determiner 3 cannot determine the received symbol waveform until this symbol waveform is received after f&, and the data signal and mode signal are not determined, so the signal supplied to the switch 9 is delayed by the delay element 8. Delay T seconds. That is, M=1 in the MSK code. At the same time, the difference signal supplied to the subtracter 13 is also delayed by the delay element 8 for T seconds.

In the embodiment shown in FIG. 1, assuming that the interpolation constant explained using FIG. 6 is R=4, there are sample values at four types of phases per one symbol waveform. Therefore, the memory io,,1o□.

10s and 104 each consist of four sub-memories, each sub-memory corresponding to one symbol waveform in one sample phase. Conversely, since there is only one memory that corresponds to one symbol waveform in one sample phase, the sample values corresponding to the same symbol value form in the same sample phase are always updated, and the latest values are stored in the memory. This also applies to the case where R≠4.

The selector 11 selects a memory group 101, 10 from which data is extracted corresponding to the symbol waveform to which the received sample value belongs.
2,...,10. , to choose from.

In the case of MSK code, the data signal and mode signal supplied from the determiner 3 are used to determine whether these are "00" or "01".
', "10" and "'11", the circuit is switched so that the data stored in the memories 101, 102, 103, and 104 are selected and supplied to the subtracter 13, respectively. In this way, the selector 11 selects the data from the memory corresponding to the symbol waveform of the same polarity as the symbol waveform determined by the determiner 3, so the received signal is canceled by the subtracter 13, and the residual intersymbol interference is accurately eliminated. can be taken out. In order to avoid subtracting the current sample value itself, the selector 11 is configured to take out the value from the memory and then write the value supplied through the switch 9 into the memory.

The pseudo intersymbol interference generated by the adaptive filters shown in FIG.

Subtractor 2 generates a difference signal obtained by subtracting pseudo intersymbol interference from the received signal that is the input signal of input terminal 1 (=received signal including residual intersymbol interference, residual intersymbol interference = intersymbol interference - pseudo intersymbol interference) is obtained, and the determiner 3. The signal is supplied to the delay element 8. In the subtracter i3, the output signal of the delay element 8 and the memory group 101.10□.

. . . The signal selected by the selector 11 is subtracted from 10° to cancel out the received signal, and only the residual intersymbol interference is supplied to the adaptive filter 5. The result determined by the 0 determiner 3 is supplied to the adaptive filter 5 and appears at the output terminal 7 at the same time. Adaptive filter 5 uses the output signal of subtracter 13 to update coefficients.

Note that when the MSK code is adopted as explained above, the configuration of the adaptive filter 5 is changed due to two reasons: the pulse waveforms for "0" and "1" are different, and each has a 0 mode and a 1 mode. is slightly different from the case in Figure 6. That is, it is necessary to prepare two types of tap coefficients corresponding to the different pulse waveforms of "0" and "1" and update them separately, and it is also necessary to distinguish the coefficients by the mode signal received from the judger 3. It is necessary to do so.

Up to now, the present invention has been described in detail using the MSK code as an example, but for example, a biphase code shown in FIG. 2(a) can be used as the transmission line code. What differs between biphase codes and MSK codes is the received signal eye pattern.

FIG. 4(a) shows an example of a continuous symbol waveform of a biphase code. The five consecutive waveforms are, in order from the right, symbol waveforms T seconds after the present, the present, T seconds before, 2T seconds before, and BTT seconds before. In the case of a bi-phase code, the symbol waveform of interest is different depending on the symbol waveforms before and after the current symbol waveform, so the memory groups 101, 102, . . .
..., select 10. Figure 4(a) is 101
It is easy to see that the current sample value and the sample value 2T seconds ago are similar and have the same absolute value.

Therefore, a sample value every T/R seconds is stored in a memory corresponding to the symbol waveform to which this sample value belongs and the sample phase, while corresponding to a symbol waveform with the same polarity and the same absolute value as the symbol waveform to which the current sample value belongs. By adding the value in memory to the current sample value,
In the case of a phase code as well, the received signal components are canceled and the output becomes zero.

However, in the case of the pi-phase code, the input signals to the switch and selector 11 are only data signals. Since it is impossible to know in advance the symbol waveform T seconds from now, the coefficients are updated after waiting until the symbol waveform T seconds from now is determined. Therefore, in the case of a pi-phase code, M=2 and the delay element 8 must provide a delay of 2T seconds.

Considering the transmission line codes other than these codes in the same way, the memory groups 101, 102, . . .

It is clear that the residual intersymbol interference can be accurately extracted by assigning 10.fi and using it to update the coefficients of the adaptive filter 5 after canceling the received signal.

〔Effect of the invention〕

As described in detail above, according to the present invention, a difference signal having the same polarity and almost equal absolute value as the current value is selected from past values stored in the memory and subtracted from the current value. As a result, the residual intersymbol interference component included in the received signal can be accurately extracted.

Therefore, by using said difference to update the coefficients and control the adaptive filter, adaptive operation is guaranteed. In addition, since sample values with the same polarity and the same absolute value are subtracted from the current sample value, the same effect can be expected without special operations even when the amplitudes of positive and negative pulses differ due to nonlinearity of the received signal. . Furthermore, according to the present invention, the above-mentioned adaptive operation can be guaranteed by combining delay elements, switches, memory groups, selectors, and subtracters, so that the decision feedback is simple and small in hardware scale without requiring complicated control. This has the effect of providing a type equalization method.

[Brief explanation of the drawing]

FIG. 1 is a block diagram showing one embodiment of the present invention, and FIG. 2 (
FIG. 3(a) is a diagram showing a typical example of a binary code for explaining a transmission line code. (b) shows the received signal eye corresponding to the transmission line code in Figure 2.
Figures 4(a) and 4(b) are diagrams showing examples of received signal waveform patterns corresponding to transmission line codes. Figure 5 is a block diagram showing a conventional example of a decision feedback type flower vase. The figure is a detailed block diagram of the adaptive filter 5 in FIG.
FIG. 7 is a detailed block diagram of the coefficient generation circuit shown in FIG. 6. 1... Input terminal, 2... Subtractor, 3... Determiner,
4... Output terminal, 5... Adaptive filter,
8...Delay element (M, T), 9...Switch, 1
0...Memory, 11...Selector, 13...Subtractor. 2nd I! r lO// / /#$ 3rd, 1 1 ←T-@I +(b) $7WJ

Claims (1)

[Claims] In a decision feedback equalization method that uses pseudo intersymbol interference generated by an adaptive filter to remove intersymbol interference that occurs during waveform transmission, the pseudo intersymbol interference is subtracted from the received signal that contains the intersymbol interference. After obtaining the difference signal, the data already stored in the memory corresponding to the symbol waveform of the difference signal is retrieved using the determination result of the difference signal, and then subtracted from the difference signal to eliminate residual intersymbol interference. The decision feedback equalization method is characterized in that the difference signal is calculated, the difference signal is stored in a memory corresponding to the symbol waveform, and the coefficients of the adaptive filter are updated using the residual intersymbol interference.