JPH0831820B2 - Decision feedback equalizer - Google Patents

Description

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a decision feedback equalizer, and more particularly to a decision feedback equalizer that removes waveform distortion caused by strong multipath fading propagation.

(Summary) The present invention provides a conventional decision feedback equalizer only for intersymbol interference due to the trailing edge (Postcursor) of the impulse response.
Although the equalization was performed by decision feedback, the leading edge of the impulse response (Pr
We also provide a control algorithm to perform equalization by decision feedback for ecursor), adaptive equalization for multipath fading, and equalizer configuration that can obtain equalization capability than before.

(Prior Art) Conventionally, an adaptive equalizer has been used for the purpose of removing waveform distortion generated in a multipath fading line or the like. The adaptive equalizer is classified into a linear equalizer (LE) shown in FIG. 4 and a non-linear equalizer shown in FIG. Both of them are configured by a transversal filter, and the tap coefficient is controlled so that the mean square of the error signal ε between the input and output of the determiner or the m mean of the absolute value is minimized.

A linear equalizer is mainly used in terrestrial digital microwave communication. However, in a linear equalizer, as a means for removing intersymbol interference, a received signal containing intersymbol interference and noise distributed on each tap is multiplied by a tap coefficient to perform linear synthesis, so that strong malpass distortion is not achieved. , The residual intersymbol interference after equalization becomes large. In particular, the linear equalizer cannot sufficiently equalize against severe selective fading in which the delay spread of the multipath with respect to the transmission symbol length spreads as the transmission speed increases or the propagation section becomes longer.

As shown in FIG. 5, the non-linear equalizer is a decision feedback equalizer (DFE) composed of a front equalizer (FE) linear to the input and a non-linear back equalizer (BE). . The center tap is usually set to the last tap of the FE, and the intersymbol interference due to the leading edge (Precursor) of the impulse response is FE.
Then, the intersymbol interference due to the trailing edge (Postcursor) is eliminated by BE. Since the decision signal output from the decision device does not include intersymbol interference or noise, the BE equalization capability by decision feedback is larger than that of the linear equalizer, and intersymbol interference due to the impulse response Postcursor, that is, the delay of the main wave Multipath distortion is completely eliminated within the BE tap range. Therefore, DFE is superior to FE when fading is caused by delayed multipath (minimum phase shift fading). On the other hand, P
Intersymbol interference due to recursor, that is, LE is not equal to progressive multipath distortion BE, but is equalized by LE and equal FE. Therefore, DFE is LE with respect to fading due to progressive multipath (non-minimum phase transition fading). It only shows the same equalization ability. Therefore, in terrestrial digital microwave communication where strong progressive multipath state may occur, LE which is easy to implement is mainly used and DFE is rarely used.

As a method for improving the equalization ability of the DFE with respect to progressive multipath, there is an MF / DFE reception method using an adaptive matched filter (MF) in the preceding stage of the DFE as shown in FIG. This is the "adaptive reception method in a multipath transmission line" (CS78-2
It was proposed as 03). Here by MF
By optimizing reception by maximizing the SN ratio and equalizing distortion by the DFE, DFE for the progressive multipath of strength
The ability to improve the equalization ability of MF and various effects of MF are described in detail.

In FIG. 7, 81 is the impulse response of the line before MF input, and 82 is the impulse response after MF output. Since MF makes the impulse response symmetrical, it is strong at t <0 of waveform 81.
The Precursor component is focused on the main response, as shown at 82, and some power is also distributed to the Postcursor component with t> 0. That is, since a part of the progressive distortion is converted into the delayed distortion, the burden on the FE is reduced, and conversely, the increased Postcursor is equalized by the BE of the decision feedback, so the advanced multipath of the DFE is reduced. The equalization ability for is improved. For such progressive multipath, MF / DFE
Can exhibit better equalization ability than DFE alone. However, the MF / DFE is designed to maximize the SN ratio by MF diversity reception for multipath fading lines where the SN ratio is restricted, such as in non-line-of-sight communications where this method has already been put to practical use. Priority is given to one, and it is not always optimal for a line where the SN ratio is relatively high and waveform distortion is a problem. MF / DFE is far superior to DFE alone for progressive multipath distortion, but deteriorates more than DFE for delayed multipath distortion. This is because of the waveform distortion newly generated by the MF, and in the case of multilevel QAM transmission, this distortion cannot be ignored as the multilevel level increases. The waveform distortion caused by MF is that the impulse response after MF converges to the main response at t = 0 as shown in Fig. 7 by convolution of MF and the delayed and dispersed impulse response, but the level is low. This is because the response spreads, and it is not realistic because the number of DFE taps needs to be increased considerably to equalize this.

(Problems to be Solved by the Invention) In the conventional equalization method described above, there is a problem that the equalization capability is insufficient in realizing high-speed transmission by multilevel QAM under a strong multipath fading condition. is there. In order to solve this problem, the present invention is to provide an equalizer configuration and a control algorithm for adaptive equalization that can obtain equalization capability higher than that of the conventional method.

(Means for Solving Problems) In the present invention, in a forward equalizer (FE) including a transversal filter having a symbol length of T, the center tap c ₀ position is moved to the front stage side from the FE final stage side by N taps. And a means for linearly equalizing the input signal,
In a backward equalizer (BE) composed of a transversal filter having a symbol length of T, a means for performing non-linear equalization on an input signal and a difference between the decision unit input and output are obtained.
LMS from means for obtaining an error signal epsilon _1, the signal on each tap of the first error signal epsilon ₁ and FE and BE between determinator input and output of
The normal tap correction means for obtaining the tap count by the algorithm, and the received signal and the decision device on each c ₀ , c ₊₁ ...... c _{+ i} ...... c _{+ N} tap from the FE center tap to the FE final stage side The main response h ₀ of the impulse response of the line and the leading edge (Precursor) h _-1 ...... h
_-i ...... h _-N monitoring means and each c ₊₁ , c ₊₂ , ...... c _{+ i} ...... c _{+ N} tap after the FE center tap c ₀ , and each BE tap from the first stage. At d ₁ , d ₂ , …… d _i …… d _N taps,
The difference between the output of the c _{+ i} tap multiplier of FE and the output of the d _i tap multiplier of BE is calculated, and the difference between the difference and the output of the decision device is defined as error signal ε.
_{i + 1} means and Precurs of monitored impulse response
In accordance with the increase of orh _-i with respect to the main response h ₀ , tap correction by the LMS algorithm for the c _{+ i} tap after the i-tap from the center tap c _{0 is} corrected from the first error signal ε ₁ to the error signal ε _{i + 1.} The tap correction controlled by the error signal ε _{i + 1} is switched to the _first error signal ε ₁ in accordance with the decrease of the main response of Precursorh _-i , and the tap coefficient is set to 1 It is characterized in that it is provided with means for performing a multiplication by a small coefficient _one by _one and returning to a normal LMS algorithm using the first error signal ε ₁ when Precursorh _-i becomes steady or zero.

(Example) Next, the present invention will be described with reference to the drawings. First
The figure is a block diagram of an embodiment of the present invention. In FIG. 1, 1 is an N-tap forward equalizer (FE), 1a is N-1 delay elements having a delay time of a transmission symbol length T, and 1b is N.
Number of multipliers, 1c is a combiner, 2 is an M-tap backward equalizer (BE), 2a is M delay elements having a delay time of a transmission symbol length T, 2b is M multipliers, and 2c is A synthesizer 3, a determiner, 4,5, 6 and 7 subtractors, 8 two correlators, 9 tap coefficient control circuits I and 10 tap coefficient control circuits II.

Here, the transmission symbol sequence is an (n = −∞ ... + ∞), FE
The discrete values of the impulse response of the transmission system until input to
_Let h _n be the discrete value r _n of the received signal Indicated by. In Fig. 1, r _n is input to FE and delay element 1a
R ₋₁ , u ₀ , u ₊₁ , ... u _N-2 on each tap
_n-1 , r _n , ... r _{n + N-2} are distributed in this order, and the tap coefficients c ₊₁ , c ₀ , c _-1 ...... c _{-n + 2} are obtained at each tap by the multiplier 1b. After being multiplied and combined by the combiner 1c, it is output from the FE. The decision device 3 which is a non-linear element receives the signal y _n obtained by subtracting the FE output and the BE output by the subtractor 4, and y _n
The judgment signal (identification signal) _n for is output. on the other hand,
Determination signal _n is input to the BE, through the delay elements 2a, respectively decision signal _n-1 ...... _nM tap coefficients on each tap
It is multiplied by d ₁ ... d _M by the multiplier 2b, synthesized by the synthesizer 2c, and then fed back to the reducer 4 as the BE output. Therefore, y _{n of the} discriminator input is expressed by the following equation.

The subtractor 5 also takes the difference between the input and output of the determiner 3 and outputs a first error signal ε ₁ = y _{n −n} (3). In order for the DFE to act as an equalizer, the root mean square value of the error signal ε1 of the discriminator ξ ₁ = E [ε ₁ ² ] (E indicates an expected value) as in the linear equalizer (Wiener filter) ( The tap coefficients of FE and BE need to be set so that 4) is minimized. Therefore, the tap coefficient is The ideal value of the tap coefficient can be obtained by solving the following normal equation.

Here, ^* indicates a complex conjugate, and the tap coefficient is shown as a vector of the next tap coefficient.

Further, (N + M) × (N +) including the small matrix A on the left side of the equation (5).
M) matrix is the correlation matrix for the entire DFE, and Has become. The above A is composed of the correlation coefficient a _ij , and its element is represented by the following equation by the impulse response.

On the other hand, in FIG. 1, the tap coefficient control circuit I9 has the FE tap signals u ₀ ... u _N-2 and the BE tap signal _n-1 excluding the C ₊₁ tap.
...... Normal LMS with _nM and error signal ε ₁ as inputs
(Least mean square) algorithm, that is, c _i ^{n + 1} = c _i ⁿ −με ₁ ⁿ u _-i ^{n *} (i = −N + 2 ...- 1,0)
(7) The FE tap coefficients c ₀ ... c _{-N + 2} and d ₁ ... d _M are sequentially calculated for each symbol. Here, by setting the tap correction coefficients μ and v within the convergence range, the tap coefficient can be obtained without solving the normal equation (5). By the way, the operation up to the above and the components other than 6, 7, 8, and 10 of FIG. 1 are the same as those of the normal DFE, but in the embodiment of FIG. 1, the center tap c ₀ is only one tap from the FE final stage. It is shifting. This is an embodiment in which the DFE of the present invention is applied to terrestrial digital microwave communication, and multipath propagation in normal terrestrial digital microwave communication is mainly due to leading or lagging multipath with respect to the main wave. It is known to be approximated by a two-wave model in which waves exist, and the delay time difference between the main wave and the multipath wave hardly exceeds the symbol length T. For such a multipath fading line, simply shift the center tap c ₀ of the FE from the conventional FE final tap position to the FE input side by one tap,
It is derived from the normal equation that the equalization ability over the conventional DFE is exhibited for progressive multipath distortion. This will be described with reference to FIG.

In FIG. 2, 20 is a transmission symbol string, 21 is an impulse response of a multipath line shown in a two-wave model, 22 is an embodiment of the DFE of the present invention, and 22a is a shift register.
FE taps, 22b multipliers, 22c combiner, 22d BE taps shown in shift register, 22e multipliers, 22f combiner, 22g, 22h, 22i, 22j subtractor, 22k judge It is a vessel.
In FIG. 2, the impulse response 21 is the leading edge (Precurso) of the impulse response at t = -T due to the progressive multipath.
r) h _-1 indicates an extremely severe multipath line in which the main response h ₀ exists at approximately the same level and in antiphase. If this is expressed in the frequency domain, an extremely deep wedge-shaped drop (dip) occurs in the carrier frequency level of the modulated wave signal band. The transmission symbol string 20 (... a _-1 a ₀ a ₊₁ ...) is convolved with the impulse response 21 and input to the DFE 22. When the digital of the discriminator 22k is ₀ , the received signal on the center tap c _{0 of the} FE is r ₀ = h ₀ a ₀ + h _-1 a ₊₁ . In this, h ₀ a ₀ is the desired signal due to the main response h _0. Component, h _-1 a ₊₁ is Precursorh
_-1 is the intersymbol interference. Second for each tap other than c ₀
The received signals are distributed as shown in the figure.

In the case of a normal DFE, after the signal distributed on each tap of the FE is multiplied by the tap coefficient in a state where there is no C ₊₁ tap in the second DFE 22 (center tap c ₀ is the FE final stage). Since the combiner 22c performs linear combination so as to remove intersymbol interference, BE does not operate. For example, in FIG.
c ₀ tap output is _{c 0 (h 0 a 0 +} h -1 a +1). Here, the intersymbol interference component is c ₀ h ₋₁ a _{+1. In} order to eliminate the interference due to this a ₊₁ the h of the main response component distributed on the c ₋₁ tap that is one tap before c _{0. 0} a ₊₁ is multiplied by c _{-1 of} the main response component h ₀ a ₊₁ distributed on the c _-1 tap, and the combiner 22c outputs c ₀
Interference due to a ₊₁ is eliminated by combining the tap and c ₋₁ outputs. However, since c _-1 is multiplied and combined by the combiner 22c, interference due to a ₊₂ occurs. An additional c _-2 tap is needed to remove this. c _{-2 on} tap
The interference component due to a ₊₃ is included, and further c _-3 taps are required to remove this, and if this operation is repeated, an infinite number of taps is required. When the intersymbol interference due to such a powerful Precursor is removed with a finite number of taps, the conventional DFE cannot equalize the linear equalizer (LE) as well.

By the way, in the DFE according to the present invention, the center tap is 1
By tap-shifting, c _{+ 1} taps can be prepared, and received signals of r ₋₁ = h ₀ a ₋₁ + h ₋₁ a ₀ are distributed on this tap. In Fig. 2, the main response and Prec
When ursor is h ₀ = 1.0h _-1 = -0.99, 22 output DFE
Solving the normal equation (5) with respect to c ₀ , c _-1 , c _-2
And d ₂ is substantially zero, and the has a c ₊₁ = -1.01d ₁ = -1.01. Here, by c ₀ of the center tap is not impossible in normal equalizer to become zero, the desired signal component, that h ₀ a ₀ present on the center tap is led to the decision unit as a main signal, ₀ In order to be judged, it is necessary that c ₀ is not zero but has a necessary and sufficient size. However, in the solution of the above normal equation, instead of c ₀ becoming zero,
Since c ₊₁ is -1.01, the FE output is c ₊₁ r _-1 = c ₊₁ (h ₀ a _-1 + h _-1 a ₀ ) =-1.01 · (1.0a _-1 -0.99a ₀₎ = - a 1.01a _-1 + a _0. On the other hand, BE output is d _{1 -1} next, _-1 if the determination signal is not erroneously be approximated as a _-1, FE output and BE
Taking the difference from the output, the inter-symbol interference due to a _-1 is completely eliminated, and only a ₀ is input to the determiner and the correct determination is made. That is, for a strong Precursor, it is set by shifting the center tap, not the desired signal component h ₀ a ₀ due to the main response on the center tap.
₊₁ tap is used as the main signal, a ₀ of the interference component h _-1 a ₀ as the main signal, and the decision unit decides to convert forward forward / reverse multipath distortion into delayed delay distortion equivalently. Strong equalization by feedback can be performed, and even for progressive multipath distortion of strength that could not be equalized by the conventional method,
A very high equalization capability can be realized. Also, comparing with the MF / DFE method, which is strong against progressive multipath distortion in the conventional method, this method does not use a matched filter (MF), so there is no waveform distortion due to MF and the number of taps is relatively small. so,
Equalization ability exceeding MF / DFE is obtained. In addition, with respect to delay multipath distortion, in FIG. 2, the tap coefficient becomes a dominant level so that the center tap c ₀ becomes the main signal route, and the same operation as that of the conventional DFE is performed. Equalization capability is obtained.

By the way, the center tap has been shifted up to this point.
Regarding DFE, it was stated that a higher equalization ability can be obtained from the solution of the normal equation, but when applied equalization, the normal LM
It will be explained below that the tap coefficient does not converge only with the S algorithm.

In FIG. 2, FE is basically a linear equalizer, and when BE does not operate, the C ₊₁ tap tries to eliminate intersymbol interference due to a ₋₁ that precedes a ₀ by one symbol. Also BE
If s works, the d ₁ tap attempts to cancel the intersymbol interference due to a ₋₁ . That is, c ₊₁ and d ₁ have the same object to be equalized, and when viewed from the center tap c ₀ ,
It can be said that c ₊₁ and d ₁ correspond in time. It is shown below that in the DFE with the center tap shifted, the eigenvalue of the correlation matrix for the taps of the FE thus temporally corresponding (overlapping) may approach zero. From the normal equation of (5), d = HT ^* c (9) Φc = H ₀ (10) where Φ is an N × N correlation matrix for only N tap FE, and Φ = A−HHT ^* (11) Diagonal element a _ii of matrix A (i = -N + 2, ...
… 1) is the autocorrelation coefficient, And the same value regardless of i, and its magnitude is the main response h ₀ of the impulse response and the response in the vicinity of it.
It depends on high-level components such as h _-2 , h _-1 , h ₁ , h ₂ ....

Equation (11) is as follows for the DFE configuration shown in FIG. 2, for example.

Here, c + 1 of FE corresponding to d ₁ tap of BE temporally
The autocorrelation function for taps is ₁₁ , which is Therefore, if the main response h ₀ component is not included and Precursorh ₋₁ of impulse response 21 in FIG. 2 is large, ₁₁ has a value, but h ₋₁ is zero, that is, progressive multipath. ₁₁ is closer to zero when there is no distortion, or when h ₁ has a value in a delayed multipath state. By the way, for the correlation matrix Φ, there exists an eigenvector Q and an eigenvalue matrix Λ, and ΦQ = ΛQ (13) where To be satisfied. The eigenvalue matrix Λ is obtained by the Jacobi method or the like in which the correlation matrix Φ is subjected to orthogonal transformation and the components other than the diagonal components are set to 0. However, when the autocorrelation function is zero, the eigenvalue for it is also zero. As shown above, as ₁₁ approaches zero, the eigenvalue Λ ₁ for it, ie for the c ₊₁ tap, also approaches zero. This decrease is not seen in normal DFE, when the center tap is shifted,
BE Only occurs for FE taps that overlap.

By the way, when the eigenvalue becomes smaller, the tap coefficient corresponding to it becomes extremely poor in convergence, and when it becomes zero, it no longer converges.

If the solution of the normal equation for FE in Eq. (10), that is, the ideal tap coefficient vector is c ^opt , and the difference from the tap coefficient vector c by adaptive control is introduced as a coefficient error vector V = cc ^opt (14), Eq. (4) The evaluation function ξ _{1 of} is transformed as follows.

ξ ₁ = ξ _min ＋ (cc ^optT ) Φ (cc ^opt ) ＝ ξ _min ＋ V ^T ΦV ＝ ξ _min ＋ ▽ _T Λ ▽ (15) where ξ _min is the minimum value of ξ ₁ and ▽ is V according to the eigenvector Q. It is a unitary conversion and is shown as ▽ = Q ^T V. That is, the evaluation function ξ ₁ is a quadratic form of ∇ where the second-order differential coefficient is twice the eigenvalue Λ, and the eigenvalue is ξ ₁
Determines the shape of the quadric surface of. By the solution of the normal equation, i
As long as there is an ideal value c _i ^opt for the th tap c _i ,
ξ ₁ represents the change of the quadratic curve that minimizes ▽ ₁ = 0 in the coefficient error ▽ _i- axis direction. However, as the eigenvalue Λ _{i in} Λ decreases, the curve gradually flattens, and when Λ _i becomes zero, ξ ₁ becomes a straight line in the ▽ _i axis direction. When tap correction is performed by the LMS algorithm in this state, the tap no longer converges and the tap maintains the initial value.

The tap coefficient change when the impulse response of the two-wave model changes as shown in FIG. 3 for the DFE of FIG. 2 will be described.

In FIG. 3, 31 is a distortion-free state in which only the main response h ₀ exists, and the tap coefficient obtained from the normal equation is 31 as shown in FIG. Since 31 does not need to be equalized, 34 has only the FE center tap c ₀ . In FIG. 32, the _value of Precursorh _{−1 at} t = −T is slightly increased with respect to 31 in FIG. 32, and the tap coefficient for it is as shown in 35. When Precursor is small compared to the main response, the solution of the normal equation shows that the distortion is equalized by FE, similar to a normal DFE, and c ₊₁ and d ₁ overlapping each other are It is zero. In Fig. 3, 33 is the state where the Precursor is further increased, and the solution of the normal equation in this case is 36
It is shown that the main signal route is not c ₀ but c ₊₁ and the distortion due to Precursor is equalized by d ₁ of BE which is the decision feedback. Next, when the progressive multipath is in the increasing direction, that is, for the impulse response change of 31 → 32 → 33, the initial value of the tap coefficient is set to 34, and all the DFE taps are corrected by the LMS algorithm. The change in tap coefficient obtained by this is 37 → 38 → 39. From 31 to 32, the eigenvalue λ ₁ for the c ₊₁ tap is very small, and the c ₊₁ of 38 holds the initial value 0 of 37. Therefore, the distortion due to h _-1 is linearly equalized by the c _-1 tap. However, when h ₋₁ is further increased and a strong progressive multipath state such as 33 is obtained, λ ₁ has a value, but eigenvalues λ ₀ and λ for c ₀ and c ₋₁ .
_{Since -1} is much larger, c ₀ and c _-1 converge faster, and as shown in 39, the c ₀ tap is the signal component due to the main response.
Keep h _{0 0} as the main signal, and c _{-1 as} h _-1 increases
Taps grow further. Further, by equalization with c _-1 , ₀
Interference from the signal ₊₂ two more symbols later occurs, and c- ₂ attempts to equalize it. In this way, when the progressive multipath increases from the undistorted state, when the DFE with the shifted center tap is operated by the normal LMS algorithm, the same operation as that of the normal DFE is performed. It does not converge to the ideal solution of the normal equation shown in 36. Next, 33 → 32 → 31
Change, that is, when progressive multipath is in the decreasing direction, when the initial value of the tap coefficient is set to an ideal solution of 36 and the DFE is operated by the LMS algorithm, the tap coefficient change is 42
→ 41 → 40.

When Precursorh _-1 decreases as 32 .lambda.1 is reduced, the tap modification c ₊₁ can not follow the fluctuation of the impulse response, c ₊₁ 41 is substantially retain the value at 42. On the other hand, c ₊₁
A c _-1 tap with a larger eigenvalue follows 35 ideal solutions, trying to equalize the distortion due to h _-1 . Here, c ₀ is relatively smaller than 35, but this is because c ₊₁ taps remain large, and the c ₊₁ tap causes the signal in the response component h _{−1 0} due to h _{−1. This is because 0} is added to the main signal route from the center tap c ₀ , and c ₀ does not require a level as shown at 35. On the other hand, since c ₊₁ has a value, the resulting distortion is removed by the overlapping d ₁ . If further becomes 32 from the non-strain state of 31, h _-1 for distortion not by c _-1 it becomes zero, since the c ₊₁ signal components h _{-1 0} supplied from the tap is zero, c ₀ Reaches the same regular level as 34. But c ₊₁ and d ₁ still hold 41 states.

The above is the case of the variation of the progressive multipath, but the variation of the delayed multipath is sufficiently converged by the normal LMS algorithm. In this case, since the BE operates while the tap coefficient on the FE end side of the center tap remains zero, it can be said that this is completely equalization to the normal DFE.

Next, the equalizer configuration and control algorithm for solving this convergence problem are described.

The impulse response change 32 → 33 shown in FIG. 3 does not converge like the ideal solution in FIG. 36 because the center tap serves as the main signal route and the impulse response main response h ₀ a ₀ Since a ₀ of DF continues to be determined by the determiner, DF
If you modify all taps E in LMS algorithm, once cause such instantaneous interruption, a main signal route transitions to c ₊₁ taps, not as a ₀ for h _-1 a ₀ by Precursor is determined As long as it does not move to the ideal solution of 36. By the way, c ₊₁ and d ₁ which overlap each other are not independent, but d ₁ is dependent on c ₊₁ . In particular, the eigenvalue of the c ₊₁ tap is smaller than that of the other taps, so even if the c ₊₁ tap coefficient is deviated from the ideal value, the evaluation function ξ ₁ is not significantly affected. This is because the d ₁ tap subordinately equalizes the distortion caused by the shift of c ₊₁ . This is confirmed by the fact that the residual strain slightly remains in the state of 40 in FIG. 3, but the strain by c ₊₁ is equalized by d ₁ . Thus, depending on the proceeds of the multipath component is large, the a ₀ on c ₊₁ tap main signal from a ₀ on the center tap c _0, To be determined by gradually migration, It is necessary to introduce an algorithm that grows the c _{+ 1} tap instead of the usual LMS algorithm. Nor should it significantly disturb the control form of the DFE. Here, focusing on the fact that the eigenvalue of c ₊₁ is small and that the c ₊₁ tap coefficient of the ideal solution becomes large in response to the increase of h ₋₁ , tap correction of c ₊₁ tap Ordinary LMS using the error signal ε ₁ of
Instead of the algorithm, the second error signal ε ₂ is introduced so that the c ₊₁ tap grows smaller in accordance with the increase of h ₋₁ , and the correction is performed by the LMS algorithm using ε ₂ . As shown in FIG. 1, the subtractor 6 subtracts the d ₁ tap output from the c ₊₁ tap output, and the subtractor 7 subtracts the subtractor 6 output from the determiner 3 output to obtain the second error. With the signal ε ₂ , the tap coefficient control circuit II of 10 uses the received signal u ₋₁ on the C ₊₁ tap input to the ε ₂ and 10 tap coefficient control circuit II 10 to calculate the c ₊₁ tap by the following equation. Sequential correction is performed for each symbol.

Where μ is a correction coefficient.

As shown in FIG. 2, the output of the c ₊₁ tap multiplier c ₊₁ (h ₀
The error signal ε ₂ is obtained by subtracting the d ₁ tap output d _{1 -1} from a _-1 + h _-1 a ₀ ) by the subtractor 22g, and then subtracting the difference from the determiner output by the subtractor 22h. when the determination signal is _{correct, ε 2 = C +1 (h} 0 a -1 + h -1 a 0) -d 1 -1 - 0 = (c +1 h 0 -d 1) a -1 + (c +1 It is shown as h ₋₁ −1) a ₀ (17), and when c ₊₁ is zero, d ₁ is also zero, so ε _{2 in} the above equation has a value of −a ₀ . On the other hand, u ₋₁ = h ₀ a ₋₁ + h ₋₁ a ₀ , and averaging the second term on the right-hand side of Eq. (16) gives the correlation between the error signal and the input signal, and E [ε ₂ u _-1 ^* ] =-H- ₁ . Therefore, even if the initial value of c ₊₁ is zero, c ₊₁ begins to grow as h _-1 increases while the symbols are sequentially corrected in Eq. (16). When c ₊₁ begins to have a value, c
Interference about a _-1 from the ₊₁ tap occurs, d _{1 of} BE equalizes it, and the first term in the second row of equation (17) approaches zero. c
_If the value of ₊₁ is not sufficient, the second term in the second line of equation (17) is c
_{The +1} tap has a value as an error signal for becoming the main signal route, and while controlling the c ₊₁ tap in equation (16), the c ₊₁ tap becomes the main signal route, depending on Grows up.

Since Eq. (16) does not use the error signal of the discriminator, it cannot be called a normal LMS algorithm, but the root mean square value of ε ₂ ξ ₂ = E [ε ₂ ² ] (18) should be minimized. Correct the c ₊₁ tap coefficient. (18)
The expression can be expressed as follows.

Therefore, c ₊₁ that minimizes ξ ₂ is ∂ξ ₂ / ∂c ₊₁ = 0, And shows that c ₊₁ grows as h _-1 increases. Incidentally, the epsilon ₂ inserted here, when performing correction of c ₊₁ tap coefficient, defined by ε ₁ (4) evaluation function xi] ₁ of Formula is according to the value of c ₊₁ taps, c _{+ 1}
Under the condition that the taps are modified by the algorithm of Eq. (16), all taps except c _{+ 1} taps are set so that the evaluation function ξ ₁ for the error signal ε ₁ of the discriminator is minimized.
It is controlled by the LMS algorithm. So in this case Next, (5) The normal equation is deleted section on c ₊₁ taps, the DFE shown in FIG. 2 (FE4 tap BE2 taps), when they are modified tap the c ₊₁ taps by epsilon _2, c Normal equation for taps except ₊₁ is 5 × 5
It has the correlation matrix of and is as follows from the equations (20) and (5).

here, Further, in FIG. 2, 21 impulse responses are, for example, h ₀ =
When 1.0, h ₋₁ = −0.99, equation (21) becomes as follows.

Furthermore, when the eigenvalues of the correlation matrix on the left side of Equation (22) are obtained, λ _-2 = 2.39λ _-1 = 1.98λ ₀ = 1.98λ ₁ = 0.50 λ ₂ = 1.00, neither of which is zero. . Therefore,
Each tap in Eq. (22) is the matrix solution of Eq. (22) by the LMS algorithm using ε _1. Converge to. On the other hand, since c ₊₁ is given by (20), by substituting d ₁ = -1.0 (23), and c ₊₁ = -1.0. This result is ∂ξ ₁ / ∂c ₊₁ = 0 in DFE of Fig. 2.
Is almost equal to the solution of the normal equation of the equation (5) including. That introduces a second error signal epsilon _2, the tap modification of c ₊₁ epsilon ₂
Even if is used, the error signal ε ₁ of the discriminator has a minimum solution without being disturbed by ε ₂ , and it can be approximated to the solution of the normal equation (5) focusing only on ε ₁ . By the way, what has been explained above is the introduction of the ideal solution of equation (5) and ε ₂ (20)
And the solution from equation (21) is almost the same,
It is only an approximate solution when Precursorh _-1 is increasing, and it does not necessarily mean that they are exactly the same. In such a case, once the algorithm of (16) using ε ₂ converges to the approximate solution given by Eqs. (20) and (21), the modification of c ₊₁ tap is given by Eq. (7). Similarly, by switching to the LMS algorithm using ε ₁ ,
It is possible to converge to the ideal solution of equation (5). This is h
Since _-1 is a relatively large with respect to h _0, eigenvalues for c ₊₁ taps in the case of modifying the c ₊₁ tap epsilon ₁ is smaller than other tap has a value rather than zero Because
Once the state is close to the ideal solution at ε ₂ , the c ₊₁ coefficient grows sufficiently and the main signal route shifts to the c ₊₁ tap, so even if it switches to ε ₁ , it will converge to the ideal solution. Is. However, switching the adaptive algorithm in this way gives discontinuity to the adaptive operation, but generally the tap correction coefficient is sufficiently small and the fluctuation speed of multipath fading is sufficiently slow compared to the transmission speed. By
Almost continuity is maintained in the adaptive motion. By the way, even if h ₋₁ is in the increasing direction, if h ₋₁ is smaller than a certain value as compared to h ₀ , the solution of the normal equation of (5) is a normal signal route in which the main signal root is held at c ₀ . It is close to the tap coefficient of DFE. In such a case, tap correction with ε ₂ is not necessary. Therefore, at the time of switching the adaptive algorithm for c ₊₁ , ε ₂ is used when h ₋₁ increases and exceeds a certain value, and then switches to ε ₁ when it becomes stationary.

Next, when h ₋₁ is decreasing, if the tap correction by ε _{2 in} Eq. (20) is used, the main signal route continues to be held at c ₊₁ taps and converges to the ideal solution for Eq. (5). do not do.
In this case, use ε ₁ to correct the c ₊₁ tap, and add c ₊₁
In order to reduce the tap coefficient and gradually return the main signal route to the center tap c ₀ , the following tap correction algorithm is introduced.

In Eq. (24), (1-μ) is added to the usual LMS algorithm that uses ε ₁ for tap correction of c ₊₁ . In the tap coefficient change of → 41 → 40, c ₊₁ does not maintain a constant value, but gradually decreases. In this case, the value of c ₊₁ does not necessarily match the ideal solution of equation (5), but since the distortion due to the deviation from the ideal solution of c ₊₁ is removed by d ₁ of BE, the Does not affect the equalization operation of path distortion. If h _-1 is decreasing and a steady state is reached on the way, use formula (24) to calculate (1-μ)
As in the case where h _-1 becomes steady in the increasing direction without multiplying,
Tap correction is performed by the usual LMS algorithm using ε _{1 in} equation (7). In the above switching of the correction algorithm for c ₊₁ taps, ε ₂ is a means for obtaining the approximate solution by shifting the main signal route to c ₊₁ taps, and as shown in equation (24), (1-μ) Multiplying is mainly used as a means to return the main signal route to the center tap c ₀ , and when either h ₋₁ increases or decreases, eventually h ₋₁ becomes steady. By tap correction by ε ₁ of
It is converged to the ideal solution of the normal equation of (5). In addition, since the fading speed is sufficiently slower than the transmission speed, even if h _-1 fluctuates in a long cycle, it can be considered to be steady in a short cycle. , It is possible to converge the DFE with the center tap shifted with respect to the progressive multipath fluctuation. On the other hand, in the case where h ₋₁ becomes zero and delay multipath occurs, the modification of c ₊₁ tap is ε ₁ as described above.
Since the LMS algorithm according to (3) sufficiently converges, such switching of tap correction algorithms is not required.

As described above, in the DFE of the present invention, it is necessary to monitor the fluctuation of Precursorh ₋₁ with respect to the main response h ₀ of the impulse response for the tap correction algorithm switching control. As shown, the DFE output decision signal _n and the received signals u ₀ and u ₋₁ on C ₀ and c _{+1 of the} FE are input to the two correlators 8 and the absolute value of the correlation value output by the correlator 8 is input. Utilize the values W ₀ and W ₊₁ . C as shown in FIG.
The received signal on the ₀ , c ₊₁ taps is u ₀ = h ₀ a ₀ + h _-1 a ₊₁ u _-1 = h ₀ a _-1 + h _-1 a ₀ , so the correlation with the discriminator output ₀ Then, W ₀ = | h ₀ | W ₊₁ = | h _-1 |, and the main response h _{0 of} impulse response and Prec at t = -T
ursorh _-1 is obtained and the variation of h _-1 with respect to h ₀ can be monitored. Therefore, the tap coefficient control circuit II10 outputs the output of the correlator 8.
W ₀ , W ₊₁ , the error signal ε _{1 of the} decision unit, the error signal ε ₂ of the output of the subtractor 7 and the received signal u ₋₁ on the FEc ₊₁ tap are input, and the absolute value of the correlation value for each symbol is input. From the values W ₀ ⁿ and W ₊₁ ⁿ , switch the tap correction algorithm as follows,
The c ₊₁ tap coefficient is sequentially calculated for each symbol.

In above and γ, Precursor h _-1 is smaller than the main response h _0, and in the region where the distortion due to h _-1 is equalized by FE like the normal DFE, the main signal route shifts to the c ₊₁ tap. This is a control threshold value for preventing it.

With the above operation, the tap coefficient can be converged for both the progressive multipath distortion and the progressive multipath distortion, and equalization by decision feedback is applied to the progressive multipath distortion as in the case of the delay. It is possible to strongly equalize the fading (non-minimum phase shift fading) due to the progressive multipath, which is a weak point of the conventional DFE.

(Effects of the Invention) As described above, the present invention shifts the center tap of a decision feedback equalizer (DFE), monitors the impulse response of the line, and switches and controls the tap correction algorithm accordingly. As a result, even with respect to fading (advanced non-minimum phase transition fading) due to progressive multipath, which was the conventional DFE linear equalization, strong adaptive equalization by decision feedback can be performed, and with a relatively small number of taps, Since the equalization capability that exceeds the conventional equalization method cannot be obtained, it is possible to further increase the transmission speed and lengthen the line section in multilevel QAM transmission over severe multipath fading lines. is there.

[Brief description of drawings]

FIG. 1 is a block diagram showing an embodiment of the present invention, and FIG.
FIG. 3 is a diagram for explaining the operation for the embodiment shown in FIG. 3, FIG. 3 is a diagram for explaining adaptive equalization in the embodiment shown in FIG. 1, and FIG. 4 is a block diagram of a conventional linear equalizer, and FIG. Is a block diagram of a conventional decision feedback equalizer, FIG. 6 is a block diagram of a conventional MF / DFE receiver, and FIG. 7 is a diagram for explaining the effect of a matched filter (MF). In the figure, 1 ... Forward equalizer (FE), 1a ... Delay element, 1b ... Multiplier, 1c ... Combiner, 2 ... Back equalizer (BE), 2a ... Multiplier, 2b ...... Multiplier, 2c …… Combiner,
3 ... Judge, 4,5,6,7 ... Subtractor, 8 ... Correlator, 9
...... Tap coefficient control circuit I, 10 ...... Tap coefficient control circuit
II.

Claims (1)

[Claims] 1. A front equalizer (FE) composed of a transversal filter with a symbol length of T intervals shifts a center tap c ₀ position from the final stage of the front equalizer to the front stage side by N taps to input the input signal. On the other hand, means for performing linear equalization, means for performing non-linear equalization on an input signal in a backward equalizer (BE) composed of transversal filters with symbol length T intervals, and between the decision unit input and output. means for obtaining a first error signal epsilon ₁ takes the difference, the first LMS algorithm and a signal on each tap of the error signal epsilon ₁ and the front equalizer and rear equalizer between determinator input , The normal tap correction means for obtaining the tap coefficient, and the received signal on the c ₀ , c ₊₁ … c _{+ i} … c _{+ N} taps from the FE center tap to the FE final stage side and the decision signal of the decision device output By making a correlation with Response main response h ₀ and leading edge
h _-1 ... h _-i ... h _-N monitoring means and FE center tap c ₀
At each c _{+ 1} , c ₊₂ , ... c _{+ i} ... c _{+ N} tap in the subsequent stage and each d ₁ , d ₂ , ... d _i ... d _N tap in the order from the BE tap first stage, the FE
means for taking the difference between the output of the c _{+ i} tap multiplier and the output of the BE d _i tap multiplier, and taking the difference between the difference and the decision device output as the error signal ε _{i + 1,} and before the monitored impulse response. The center taps c ₀ to i corresponding to the increase of the edge h _−i with respect to the main response h ₀ .
The tap correction by the LMS algorithm for the c _{+ i} tap after the tap is performed from the first error signal ε ₁ to the error signal ε _{i + 1.}
And the tap correction controlled by the error signal ε _{i + 1} is switched to the _first error signal ε ₁ in accordance with the decrease of the leading edge h _-i with respect to the main response, and the tap coefficient is changed to Sequential multiplication with a coefficient smaller than 1 and leading edge h _-i
A decision feedback equalizer characterized by including means for returning to a normal LMS algorithm using the first error signal ε ₁ when is constant or zero.