JPS622724A - Waveform equalizer - Google Patents

Abstract

PURPOSE:To decide a filter coefficient with high accuracy and high stability with the small arithmetic quantity and short processing time, by selecting the filter coefficient correcting direction vector as a vector conjugate with a co- decentralized matrix of the filter input series and deciding the optimum coefficient vector in a repetitive arithmetic operation. CONSTITUTION:A filter part is formed by connecting the unit delay devices 1 in series by N stages. The outputs of these devices 1 are amplified by a multiplier 2 with use of coefficients hO-hN and then totalized by an adder 4. These filter coefficients hO-hN are decided according to the input signal of each multiplier 2 after the error between the filter output signal yn and the equalization target signal dn is evaluated by a control part 3. Then the correcting direction of the coefficient vector is set in the same direction as the vector conjugate with a co-decentralized matrix of the filter input series. Then the arithmetic operations are repeated by the part 3 to obtain the optimum coefficient vector of the adder 2 with a limited repeating frequency.

Description

DETAILED DESCRIPTION OF THE INVENTION [Technical Field] The present invention relates to a waveform equalization device, and particularly to a waveform equalization device that performs waveform equalization using an adaptive transversal filter in the field of digital transmission.

[Prior art] In the field of digital transmission or recording/playback technology, signal deterioration due to data errors may occur depending on the quality of the transmission line and the characteristics of the recording/playback device, so waveform equalization is performed in the middle or at the end of the transmission line. It has become essential.

FIG. 1 shows the configuration of a digital recording and reproducing system.

In FIG. 1, reference numeral a indicates an information sequence to be recorded, which is usually a 0orl binary symbol sequence. Block 11 is a
It is a transmission filter that converts information into an appropriate waveform.
The output X is recorded on a recording medium such as a magnetic disk indicated by block 12. At the time of reproduction, the signal y is passed through the amplifier shown in block 13 by the readout system, and its output W is used to restore the original sequence a. However, the output W includes the dynamic characteristics of blocks 11, 12, and 13;
There is a high possibility that the waveform is distorted due to the influence of noise, and as a result, the original sequence ak may not be correctly restored. To compensate for this phenomenon, the equalizer 14 is used to equalize the waveform distortion, and the equalized waveform 2 is used to correctly restore the original data series aK.

Conventionally, as the equalizer 14, an adaptive FIR filter is often used, which connects unit delay elements in multiple stages, amplifies each tap output with an appropriate gain, and adds the amplified outputs to obtain an equalized output. The gain of each tap, that is, the filter coefficient, is determined in the automatic vase based on a predetermined computer algorithm.

However, in conventional filter coefficient determination, the coefficients are determined by approximating the optimal solution using the steepest descent method, which is a type of iterative method, but from the viewpoint of algorithm convergence, it is not always possible to There is no guarantee, and even if it converges, it may require a considerable amount of calculation.

[Purpose] The present invention has been made in view of the above problems, and provides a waveform equalization device that can obtain stable convergence with a small amount of calculation and processing time, and can obtain desired equalization characteristics at high speed. is intended to provide.

[Structure of the Invention] In order to achieve the above object, the present invention provides a waveform equalization device using an adaptive transversal filter as an equalization filter, in which a quadratic form of a filter coefficient vector of the transversal filter is used as an evaluation function. an arithmetic control means for calculating the optimum coefficient vector using a sequential method, and in the iterative calculation using the sequential method, the optimum coefficient vector is determined by selecting a filter coefficient correction direction vector to be a vector conjugate to the covariance matrix of the filter input series. The configuration was adopted.

[Example] The present invention will be described in detail below based on an example shown in one drawing.

FIG. 2 shows a block diagram of a waveform equalizer according to the invention. The filter section has N stages of unit delay units 1 connected in series, and each tap output is converted into a coefficient ha by a multiplier 2.
-hs and summed by an adder 4. In FIG. 2, xn is the input signal to be equalized that has been distorted in the transmission system, yn is the output signal when Xn is input to the filter, and dn is the equalization target signal prepared in advance. Each filter coefficient ha
-hN is a control unit 3 composed of a microcomputer or the like, and outputs a filter output signal y. and equalized target signal d. is determined based on the input signal of each multiplier 2.

y as an evaluation criterion. , and dh When the root mean square of the error e^ of E [en 2] =J is adopted, the optimal filter coefficient vector thopt to minimize J is given by the following equation.

hopt*Rxx(e E[X-dnl ”...
(1) However, Rxx! E[X-X'l, X-(xn, x
n-', m, xn-sf (T indicates transposition) The symbols are defined as follows.

h meeting [ho *Ht + ”'+HN]” e
-14-h Now, since Iel12 (ff・H means norm) is used as an evaluation model, -Ge12-ete・e
-(14-h)T(d-th>-a a 12-c-x
-h-1-t=a+h1-r-x-h-(2) That is
J can be shown as a quadratic form with respect to h.

J-f(h)-h'X'-r-h-d'・rhh-h
￥d+II d 112 ・−−−−−・−(3)(3
), h to make J t & I is CI) f) h
Matches opt.

At that time, J reaches its extreme value at h=hapt, so the following condition is satisfied. That is, Lt/ahlhghaptm2M"-X-hopt-
2'-d*0-= = (4) Therefore, hopt is hopt-A(-bcA-X”Lb4T-d)TeJ!
+6. = (4) 'It is shown below that this hopt can be obtained by a linear combination of vague conjugate vectors without directly calculating A''4.

From equation (3), J=f(h)=h'-A-h-b'rh-
hT-b+ n d ff 2-1h"・A ・h-2
1・h+1Id12・・・・・・・・・・・・・・・
・・・・・・・・・(5)1) J/v fr+(Ih)
-2A 4+-2To = ・・・・・・” (8)
Now the conjugate vector C1 of matrix A (i=0, 1...,)
is defined as follows.

h that minimizes J in equation (5) is determined successively as an initial value hO.

First, TomihO+αo Co Go-go...
...(8゛), go meeting v J/ v h ly -Th
o-2 (Afo-b) Here, C0 is determined so that the CO force direction evaluation model J is minimized.

J=f(ht)J(h□+ao Cotof(ha
)+Q o・co' fh(ho) + 士−a
o"-Co' ・fhh(Tho)・Co---
------- (13) Using Taylor expansion approximation for J as in the above equation, differentiate this (8) with respect to C0 and set it to 0.

Therefore, hl is determined. Also GL meeting v, J/25. h
Assuming lh=ht, CI is determined by the following formula.

C1a-gl +Bo・Co・・・・・・・・・・・・
(11) Here, since Ci satisfies the relational expression (7), C1 can be found from equations (11) and (12).

Next, set h2-hl ten α1・C (refer to 10X and set J2@τJ/vhlh-h2 as C2-82+
By repeating the above operation based on equation (12) with βBIC1, the following procedure is expressed.

1i) lhi÷1-hi+αi・C1 1ii), gift -fh(hi+t)ima)βi
mc i"・A・, gin /Ci'・A-CIma)
(::i+1=-g itt÷βi・CiThis procedure is stored in the memory as a program for the control unit 3,
By repeating the operation, the coefficient g h of the adder 2 is
o +Thl...hrv can be done.

Now, the vector Ci that reveals the properties of the coefficient vector h~+1 obtained by repeating steps i) to V) (N+ 1) times is conjugate with respect to the matrix ^, that is, it is linearly independent, so it is an (N+ 1)-dimensional space. The pect and ru V can be expressed by the inflectional combination of Ci.

lhm+1 wing b++++ a m・Cm=h□+Σa
It becomes i・ci.

That is, from hm to h1+t, it moves in the direction of Cm.

At this time, Cm'[71J/'? hlh-hm+1
] = O, a m (7) The value is Cm' [A-ho -bl Cm, A(. ------- (14) In (N+1) steps, hII41 becomes.

That is, A-V=A ・ha-1b Therefore, V-h□ -h
N+ = t [h□ −A4・Furnace・・・・・・・・・
(18) Therefore, hN+1 -A(, b Since this hN+l is equivalent to hopt in equation (4)', it is clear that the evaluation criterion J can be minimized.

Therefore, by setting the correction direction of the coefficient vector in the same direction as the vector conjugate to the covariance matrix of the input signal sequence, and repeating the steps i) to m) above in the control unit 3, the adder 2 can be optimized within a finite number of iterations. The coefficient vector can be found, and the equal-other sin can be constructed.

[Effect] As is clear from the above description, according to the present invention, in a waveform equalization device that uses an adaptive transversal filter as an equalization filter, the quadratic form of the filter coefficient vector of the transversal filter is evaluated. An arithmetic control means is provided to obtain an optimal coefficient vector using a sequential method as a function, and the optimal coefficient vector is obtained by selecting a filter coefficient correction direction vector to be a vector conjugate to a covariance matrix of a filter input series in the iterative calculation using the sequential method. Since the filter coefficients are determined reliably and stably with a small amount of calculation and processing time, it is possible to provide a highly reliable waveform equalization device that can obtain desired filter characteristics. can.

[Brief explanation of the drawing]

FIG. 1 is a block diagram showing the configuration of a digital recording/reproducing system, and FIG. 2 is a block diagram showing the configuration of a waveform equalization device according to the present invention. 1... Unit delay unit 2... Multiplier 3... Control section 4... Adder Figure 1 Figure 2

Claims (1)

[Claims] In a waveform equalization device using an adaptive transversal filter as an equalization filter, an arithmetic control means is provided for calculating an optimal coefficient vector by a sequential method using a quadratic form of a filter coefficient vector of the transversal filter as an evaluation function, A waveform equalization device characterized in that an optimal coefficient vector is determined by selecting a filter coefficient correction direction vector to be a vector conjugate to a covariance matrix of a filter input sequence in an iterative calculation using a method.