KR100273446B1 - Decision feedback equalizer for receiver - Google Patents

Abstract

The present invention focuses on the fact that a determiner that makes a decision on an equalizer output value suppresses noise, and generates a training signal and an equalizer output in generating an error signal reflected in a tap coefficient update expression by an LMS algorithm. That is, to improve the use of only the difference value of the judging input and to reflect the difference between the training signal and the judging output, ultimately to minimize the tap coefficient flow due to additive noise. A positive feedback filter for removing ghosts; A negative feedback filter that removes the post-ghost from the output signal of the determiner; An adder for adding tap outputs output from the positive feedback filter and the negative feedback filter; A determiner for determining an equalizer output output from the adder; Two subtractors for obtaining a difference between a training signal and the output of the determiner, and a difference between the training signal and the equalizer output; An error detector which receives the difference value output from each subtractor and generates an error signal in which noise is suppressed; And a mixed error signal generator configured to generate a mixed error signal by receiving a difference value between the training signal, the equalizer output, and an error suppressed noise, and supply the mixed error signal to the positive feedback filter and the negative feedback filter.

Description

Judgment feedback equalizer of the receiver

The present invention relates to a technique for suppressing irregular flow of filter tap coefficients of a decision feedback equalizer in a wireless communication system. In particular, the performance of the equalizer in the training mode of the decision feedback equalizer is sensitive to additive noise. The present invention relates to a decision feedback equalizer of a receiver capable of preventing the filter tap coefficient from flowing irregularly and thereby preventing the square error mean from increasing.

In a wireless communication system, a multi-path channel situation is a big obstacle for a receiver, and in a communication channel, a symbol value is expressed when a limited band-width is used. Dispersion of the analog signal along the time axis unintentionally interferes with adjacent symbols. This interference is called inter-symbol interference (ISI).

Recently, many techniques for solving ISI in multi-channel situation have been studied [1] and [2]. Among them, the decision feedback equalizer (DFE) proved to be the best in poor channel conditions.

In the decision feedback equalizer, the interference caused by post-ghost is eliminated by using a value already determined based on a symbol to be determined. That is, in order to remove the interference caused by the symbol when the determined symbol values are correct, the symbol value is multiplied by an appropriate weight and subtracted from the current symbol value.

In general, the channel state is not known in advance, and when the tap coefficient of the equalizer is set, the coefficient is adaptively set according to the channel. This is called adaptive equalization. In the conventional DFE, coefficient adaptation training is performed using the trained training sequence a _k as a reference signal, and the execution period is called a training mode.

At the end of the training mode, a symbol containing information is transmitted. In this case, the value determined by the decision device instead of the true symbol value a _k is determined. Switch to decision-directed (DD) mode using.

Since the training signal is periodically transmitted between the information signals, the training mode and the determination mode are alternately performed.

Algorithm for updating the filter coefficient of the equalizer is the most widely applied algorithm is LMS (Least Mean-squared Error Argorithm) algorithm. This LMS algorithm is an approximation of the steepest descent method, which modifies the coefficient in the negative direction of the instan-laneous error gradient.

Here, the error refers to the difference between the transmission symbol a _k and the equalizer output y _k . Vector equalizer coefficient at kth symbol instant Vector equalizer input signal In this case, the k + 1th tap coefficient update expression based on the LMS algorithm is expressed as the following expression.

In Equation 1, μ is called an adaptation constant or step size, and as shown in Equation 1, it can be seen that the tap coefficient is repeatedly updated in a symbol period.

Noise in the equalization process is a decisive factor for degrading the performance of the equalizer, and solving the noise problem is very important for accurate counting in high speed communication.

1 is a block diagram of a decision feedback equalizer according to the prior art, and as shown therein, a transmission symbol input through a channel 1. a _k An adder 2 that adds noise n (t) to it; A forward feedback filter (3) comprising a finite impulse response (FIR) filter, and receiving pre-ghost from the data sampled at a predetermined period of the output signal of the adder 1; The equalizer output by subtracting the output component of the negative feedback filter 6 to be described later from the output component of the positive feedback filter (3) A subtractor 4 for generating a; Equalizer output from the subtractor 4 A determiner 5 for making a judgment on the object; A determination value composed of an IIR filter and negative feedback from the determiner 5 It is composed of a negative feedback filter (6) for removing the post-ghost to the target, the operation thereof will be described with reference to FIG.

Transmission symbol a _k Is contaminated by thermal noise (AWGN) generated at the front of the transceiver as it passes through channel (1). Here, the positive feedback filter 3 is configured as a finite impulse response (FIR) filter to remove pre-ghosts.

In digital communication, the information signal has an analog form. This is because an analog pulse is applied after mapping a binary bit to be transmitted to a contracted alphabet. This is called pulse-shaping. For example, the signal representation in PAM (Pulse Amplitude Modulation) is as follows.

An analog pulse p (t) is applied to the _ak symbol so that the signal superimposed at intervals of the symbol period T is s (t). If the signal to which noise n (t) is added is called x (t), the data sampled at the T interval can be represented by {x _k }. This is the input signal of the positive feedback filter 3.

Assuming a transmission symbol has 2m levels, the symbol value is { -2m + 1, ⃛, -1,1, ⃛, 2m-1 } Is determined by the value in.

Digital communication channels modeled in the form of FIR filters h ₀ 〉 0 Cursor and ghost cursor (called tail), H _N = [h ₁ , h ₂ , ⃛, h _N ] ^T It is expressed as Here, "T" denotes a transpose matrix, and h ₀ denotes a weight of a symbol value at sampling timing. h _1, ⃛, h _N Represents the weight of the ghost. h ₀ is often left at 1. Ghost eliminates adjacent symbol interference and causes errors when determining symbol values. Noise (often additive white noise, AWGN) also serves to contaminate the received signal.

Equalizer input Is input to the positive feedback filter 3, for example, the positive feedback filter of the tap coefficient N _f N _f -1 Delays, delayed Coefficient to (d _0, ⃛, d _{1-N f} ) N _f multipliers for multiplying and delayed to determine the coefficients And an error signal ( e _k ) Times the adaptive constant (μ) μe _k N _f multipliers for multiplying and N _f accumulators for accumulating their outputs.

The output of each tap multiplied by the coefficient is input to adder 4, the output of which is the equalizer output. to be. The output of the positive feedback filter 3 and the output of the negative feedback filter 6 are provided as inputs of the adder 4.

Equalizer output Is determined by the determiner 5 The value is input to the negative feedback filter 6, for example, the negative feedback filter having the number of taps N _b includes N _b delayers and delayed signals. Coefficient to (d _1, ⃛, d _Nb ) N _b multipliers for multiplying and delayed to determine the coefficients as in the positive feedback filter Wow μe _k N _b multipliers for multiplying and N _b accumulators for accumulating the multiplied output.

The output of each tap multiplied by the coefficient is input to the adder 4. Judgment And training signal sequence Is input to the switch 7. The training signal is input periodically, which is a signal that is correctly recognized by the receiver because it has contracted symbol values. Transmission symbol of Equation 1 a _k The training signal can be seen to be received without being contaminated by AWGN and ghost.

DFE refers to a structure including both training mode and judgment mode. It's training signal train It is possible to intentionally enter the judgment mode even when the time comes.

Equalizer output And the output of the switch 7 is input to the subtractor 8 from which the difference component ( e _r ) Is outputted, and the difference component ( e _r ) Is multiplied by the adaptation constant (μ), and the result eμ _k Is input to the positive feedback filter 3 and the negative feedback filter 6 to perform the equation (1) of the algorithm of the LMS.

Vector tap coefficients of the positive feedback filter 3 and the negative feedback filter 6 d ₀ , d ₁ , ⃛, d _{N b} ] Assuming that the positive feedback filter 3 is designed by a zero forcing criterion [6], the input of the determiner 5 is given by the following equation.

Here, the lengths of the negative feedback filter 6 and the positive feedback filter 3 are the same. N _b H 'is the equalized channel, which is the convolution of the channel and the positive feedback filter (3), n _k Is the sampled additive white noise n (t). Assuming that the training signal is fed back to the negative feedback filter 6, Equation 3 is briefly expressed as follows.

here, = _I = h _i ′ -d _i to be. The k + 1th equation updated by the LMS algorithm is as follows.

here, In training mode instead Is used. In the LMS algorithm for DFE, the output error equation is generally given by

here, to be.

As shown in Equation 5, the estimated value of the gradient vector in the coefficient adjustment algorithm repeatedly performed every symbol period There is noise in the camera. This noise causes random fluctuation in coefficient adaptation, e _k The variance of is expressed as

here, σ _n ² = e [N _K ² ] Is the variance of noise, and (Eq. 6) Is the energy of the m-level PAM signal.

The noise inflow in estimating the slope vector increases the mean square error (MSE) at the output of the equalizer, and the increase of the error is called an "excess MSE" [9]. Excess MSE is the power of additive noise σ _n ² It is found to be proportional to.

However, in the conventional decision feedback equalizer, only the difference between the training sequence and the equalizer output (determiner input) is generated when generating an error signal reflected in the tap coefficient update equation by the LMS algorithm. Since it is used, the tap coefficient flow due to additive noise is increased, and as a result, there is a defect that the mean of the square error is increased.

Accordingly, the technical problem to be achieved by the present invention is that the determination signal for the equalizer output value is to suppress the noise to generate the error signal reflected in the tap coefficient update formula by the LMS algorithm. In addition, the present invention provides a decision feedback equalizer of a receiver that generates an error signal by reflecting a difference between a training signal and a determiner output value as well as a difference value of an equalizer output.

1 is a block diagram of a decision feedback equalizer according to the prior art.

2 is a detailed block diagram of FIG.

3 is an exemplary block diagram of a decision feedback equalizer of a communication device according to the present invention;

4 is a detailed block diagram showing a first embodiment of the error detector in FIG.

FIG. 5 is a detailed block diagram illustrating a second embodiment of the error detector in FIG. 3; FIG.

6 is an explanatory diagram of error variance comparison according to the present invention;

7 is a graph showing the mean square error after equalization coefficient convergence.

8 is a symbol decision error probability comparison graph.

* Description of the symbols for the main parts of the drawings *

101: positive feedback filter 102: negative feedback filter

103: adder 104: judge

105,106: subtractor 107: error detector

108: mixed error signal generator 109: error detector

3 is a block diagram of an exemplary embodiment of a decision feedback equalizer of a receiver for achieving an object of the present invention. As shown in FIG. A positive feedback filter 101 for reducing tap coefficient flow by reflecting a difference value, a difference value between a training signal and a determiner output; A negative feedback filter (102) for reducing the tap coefficient flow by removing the post-ghost for the output of the determiner, reflecting the difference between the training signal and the equalizer output, and the difference between the training signal and the determiner output; An adder (103) for adding the respective tap outputs output from the positive feedback filter (101) and the negative feedback filter (102); A determiner (104) for determining an equalizer output output from the adder (103); A subtractor 105 for obtaining a difference value between a training signal and the output of the determiner; A subtractor (106) for obtaining a difference value between the training signal and the equalizer output; An error detector 107 which receives the difference values respectively output from the subtractors 105 and 106 and generates an error signal in which noise is suppressed; The mixed error signal is supplied to the positive feedback filter 101 and the negative feedback filter 102 by generating a new type of mixed error signal by receiving a difference value between the training signal and the equalizer output and an error suppressed noise signal. It will be described in detail with reference to Figures 4 to 8 attached to the operation of the present invention configured as described above, configured as a generator 108 as follows.

The positive feedback filter 101 is a FIR filter that removes pre-ghosts, and the negative feedback filter 102 is a filter that removes post-ghosts as an IIR filter. The gist of the present invention relates to the contents applied in the training mode of the DFE, and the basic operation is the same as that of the existing DFE. However, the error signal detection method of the LMS algorithm, which is a tap coefficient update algorithm, is different.

Equalizer input Is input to the positive feedback filter 101, from which the output of each tap multiplied by a coefficient is generated.

For example, N _f If personal, enter that Is sequentially delayed through the N _f-1 delay units 101D,... N _f Delayed through two multipliers 101E and 101A x _k Coefficients to d ₀ , ⃛, d _{1-N f} Multiply by) to generate the output of that tap. At this time, to determine the count value, N _f Delays using two multipliers 101B and 101F Mixed error signal ( e _k ^NSA ) And the adaptive constant (μ) N _f Through the two accumulators 101C and 101G, the multiplied output is accumulated.

The output of each tap multiplied by the coefficient is input to an adder 103, the output of which is equal to the output of the equalizer { }to be. Another input string of the adder 103 is the output of the negative feedback filter 102, which is connected as follows.

The equalizer output { } Is determined via the determiner 104. The output of each tap is multiplied by a coefficient from the input feedback to the negative feedback filter 102.

For example, if the number of taps is N _b , the judgment value N _b is one retarder (102A, 102E, ...) and then sequentially delayed through N _b multipliers (102B, 102F) via a respective decision value delayed Coefficients to d ₁ , ⃛, d _Nb Multiply by) to generate the output of that tap. At this time, to determine the count value, N _b Delayed Values Using Two Multipliers 102C and 102G on μe _k ^NSA Multiply by N _b The two accumulators 102D and 102H accumulate the multiplied output.

Equalizer output Training signals known from the receiver and receiver Is input to the subtractor 106, the output of which is a DFE error signal. e _k ^DFE Becomes this e _k ^DFE Is input to multiplier 108A and multiplied by the distribution weight 1-α, the output of which is input to adder 108C.

On the other hand, the determination value Training signal Is input to the subtractor 105 with the difference value Is input to the error detector 107 suppressed by noise. To another input of this noise suppressed error detector 107 e _k ^DFE And its output is e _k ^NS to be. e _k ^NS Is input to multiplier 108B and multiplied by the distribution weight α, the output of which is provided to the other input of adder 108C.

The output of the adder 108C e _k ^NSA Is multiplied by the adaptive constant μ in the multiplier 108D, and its output is supplied to one input of each of the multipliers 101B, 101F, 102C, 102G of the positive feedback filter 101 and the negative feedback filter 102, and remind , Is multiplied by.

As a result, when generating an error signal, the mixed error signal is reflected by reflecting not only the difference between the training signal and the equalizer output, but also the difference between the training signal and the determiner 104 output value. μe _k ^NSA Will be raised.

In order to prove the effect of the present invention, first, it is shown that the determiner 104 exhibits a noise suppression effect, and when it is reflected by an existing DFE error signal alone and when it is reflected in an algorithm together with an error signal suppressed by noise. By revealing that the coefficient flow due to additive noise is reduced, the performance of the equalizer is ultimately improved.

First, the difference between the training signal and the determination signal The variance of is given by the following equation.

Where pr (·) represents the probability and E [·] represents the expected value operation. In the constellation of the received data, it is assumed that noise is added to a symbol value so that it does not change more than one level in a situation of changing to another symbol value. In fact, this assumption is very valid when the Signal to Noise Ratio (SNR) is good. Under this assumption, Equation 7 is simplified as follows.

Where m is the number of symbols in the PAM and R _k is R _k = to be. In the above Equation 8, the value of 4 is the square of the distance between symbols. In the common sense h ₀ = 1 Assume that This assumption is also valid considering most receivers with automatic gain control (AGC).

If the coefficient of the negative feedback filter 102 converged to the equalized channel h ', the above expression (8) is expressed as follows.

Here, the Q function is used. The Q function is defined as follows.

Here, since the Q function is a case where the variance is normalized to 1, n _k The variance of was divided. From the above equation (9) for all the SNR Of the above formula (6) It can be seen that less.

6 actually shows the two variances according to SNR. As a result, it was proved that the determiner 104 had a noise suppression effect. This effect is more pronounced when the number of symbols increases by 2 m. If the SNR is 0 dB, then the variance of the signal Is equal to the variance of the noise,

And,

If m is increased Increases to infinity, Converges to 4. The noise suppression effect is demonstrated even in the situation where the negative feedback filter 102 does not converge.

This noise suppression effect at the determiner 104 provides a way to minimize the sensitivity of the equalizer coefficients to noise. e _k ^DFE In order to use the new error signal suppressed with noise, first, Is introduced into the tap coefficient update equation for the LMS algorithm as a nonlinear gradient. The resulting error equation is obtained by multiplying the distribution weights by two errors, as shown in the following equation.

Where the coding function sgn (⋅) Gives a value of ± 1. e _k ^DFE The sign of Multiplied by e _k ^DFE Wow To maintain the orthogonality of the liver, the effect appears to reduce the resulting coefficient flow. Experimentally sgn (e _k ^DFE ) It has been verified to work even if

now, e _k ^NSA Dispersion of e _k ^DFE It is smaller than the variance of. First, the orthogonality ensures the following equation.

Next, the variance of the new error equation defined in Equation 11 is obtained using Equation 12 as follows.

This shows that the LMS algorithm using the new error equation becomes an equalizer coefficient update equation that is resistant to noise. In the above, NSA means Noise Suppressed Adaptation. Noise suppressor equalizer adapts as follows By defining the error suppression can be performed more effectively.

In other words, if a decision error occurs In this case, the influence of the determination error on the tap coefficient update is contributed by the weight β, and the influence correctly determined in the past remains.

In the above formula (11) For convenience e _k ^NS Expressed as, it is shown in Figure 3, 4, 5.

4 and 5 e _k ^NS It shows the equivalent structure of the error detector to find.

That is, in Figure 4, the training signal And judgment value The difference of is input to the multiplier 201 and multiplied by the distribution weight β, and then the result is input to the adder 202 and added to the output of the multiplier 204. The output of the adder 202 is input to the multiplier 204 via the delayer 203 and multiplied by the distribution weight (1-β), the output of which is applied to the adder 202. Meanwhile, DFE error e _k ^DFE Is applied to the code detector 205 and converted into a signal error of ± 1, and then multiplied by the output of the adder 202 in the multiplier 206. The multiplied signal is an error suppressed by noise. e _k ^NS Becomes

In addition, FIG. 5 has the same transmission characteristics as in FIG. 4. However, unlike FIG. 4, the multiplier 304 multiplying the distribution weight β is positioned immediately in front of the multiplier 306.

Meanwhile, the reference list cited in the above detailed description is as follows.

[1] J.G. Proakis, Digital Communications, New York: McGraw-Hill, 1983.

[2] S.U.H Qureshi, Adaptive Equalization, "Proc, IEEE, Vol. 73, no 9,

PP. 1349-1389, sep 1985.

[3] J. Salz "Optimal mean-square decision feedback Equalization," Bell Syst.

Tech. J. "Vol 52, pp. 1431, Oct 1973.

[4] R.A. Kennedy, B.D.O Anderson and R.R. Bitmead, "Tight bounds on

the crror Probabilities of decision feedback equaizers, "IEEE Trans,

commun Vol. C.D.M-35, no 10, PP. 1022-1028, Oct. 1987.

[5] D.L. Duttweiler, J.E. Mazo, and D.G. Messerschmit, "An Upper Bound

on the error Probability in decision feedback equalizater, "IEEE Trans,

Inform. Theory, Vol. IT-20, PP. 490-497, July 1974.

[6] E.A. Lee and D.G Messershmit, Digital Communications, Boston, MA:

Kluwer 1988.

[7] S.G.Wilson, Digital Modulation and coding, New Jersey, Prentice Hall,

1996

[8] R.W. Lucky, "Automatic Equalization for Digital Communication," Bell

Syst. Tech. J, Vol 44, pp. 547-588 April 1965.

[9] B. Widrow, "Adaptive filters I; Fundamentals," stanford Electronics

Laboratory, Stanford University, Stanford, Calif Tech, Report No

6764-6766, Dec 1966.

As described in detail above, the present invention focuses on the fact that a determiner that makes a decision on an equalizer output value suppresses noise, and generates a training signal when generating an error signal reflected in a tap coefficient update expression by an LMS algorithm. By generating an error signal by reflecting the difference between the training signal and the judge output value as well as the difference value of the equalizer output, the performance of the equalizer is sensitive to the additive noise, so that the filter tap coefficient is randomly suppressed. As a result, an increase in the mean of the squared error is prevented.

Claims (5)

A positive feedback filter which receives the equalizer input signal and generates each tap signal reflecting the error signal to remove all ghosts; A negative feedback filter which receives the output signal of the determiner and generates each tap signal reflecting the error signal to remove the post-ghost; An adder for adding tap outputs output from the positive feedback filter and the negative feedback filter; A determiner for determining an equalizer output output from the adder; A first subtractor for obtaining a difference value between a training signal and the determiner output; A second subtractor for obtaining a difference value between the training signal and the equalizer output; And an error detection unit configured to generate an error signal in which noise is suppressed by receiving respective difference values output from the first subtractor and the second subtractor, respectively. The display apparatus of claim 1, wherein the error detector comprises: an error detector configured to receive an error value output from the first subtractor and the second subtractor, respectively, and detect an error signal having a suppressed noise; The output signal of the second subtractor, the error signal of the type suppressed the noise output from the error detector ( e _k ^NS The mixed error signal of the form of noise suppressed by calculating the adaptive constant (μ), the distribution weight values (α) and (1-α) e _k ^NSA ) And a mixed error signal generator for supplying the positive feedback filter and the negative feedback filter to the positive feedback filter and the negative feedback filter. The method of claim 2, wherein the error detector is a training signal And judgment value A multiplier 201 for multiplying the difference of? By the distribution weight? An adder (202) for adding the output of the multiplier (204) to be described later with the multiplication result of the multiplier; A delay unit (203) for delaying the output of the adder (202) by a predetermined time; A multiplier (204) for multiplying the output of the delay (203) by the distribution weight (1-β); DFE error e _k ^DFE A code detector 205 for converting the signal into a signal error of ± 1; Error in the form of suppressed noise by multiplying the output of multiplier 206 by the output of adder 202 e _k ^NS The decision feedback equalizer of the receiver, characterized in that consisting of a multiplier (206) for generating a. 4. The decision feedback equalizer of the receiver according to claim 3, wherein the multiplier (201) is connected between the adder (202) and the multiplier (203). The method of claim 2, wherein the mixed error signal generator is a difference value between the training signal output from the subtractor and the equalizer output ( e _k ^DFE A multiplier 108A multiplying the distribution weight value (1-α) by Error suppressed by noise output from the error detector 107 e _k ^NS A multiplier 108B multiplying the distribution weight α by the multiplication factor; An adder (108C) for adding the outputs of the respective multipliers (108A) and (108B); Error output from the adder 108C e _k ^NSA Multiply the adaptive constant (μ) by the mixed error signal ( μe _k ^NSA The decision feedback equalizer of the receiver, characterized by comprising a multiplier (108D) for generating a).