# US 4,394,768 A · Adaptive system in a digital data receiver providing compensation for amplitude and phase distortions introduced by a data transmission channel

> Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt

- Number: US 4,394,768 A
- Document ID: US4394768A
- Status: Granted
- Kind: A
- Application number: 06/263,453
- Filed: 1981-05-14
- Granted: 1983-07-19
- Earliest claimed: 1980-05-14
- Assignees: U.S. Philips Corporation
- Inventors: Hikmet Sari
- Web page: https://patentgrep.com/patent/US4394768A

## CPC

- H04L 25/03038: {with a non-recursive structure (H04L25/03031 takes precedence)}
- H04L: TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION (arrangements common to telegraphic and telephonic communication H04M)

## Abstract

An adaptive system in a digital data receiver providing compensation for amplitude and phase distortions introduced by the data transmission channel having, at the output of the transmission channel which supplies a signal vector X.sub.k, a transversal filter having N weighting coefficients, followed by a decision circuit and further a summing circuit and a multiplying circuit. To determine the N coefficients iteratively the system comprises a circuit for determining an estimated matrix A.sub.k of the autocorrelation matrix A of the signal vectors X.sub.k, a circuit for approximating A.sub.k by a circulant matrix R.sub.k, a circuit for calculating the diagonal matrix G.sub.k whose diagonal elements are the eigenvalues of R.sub.k, a number of calculating circuits and a circuit for up-dating the vector C.sub.k which represents the N weighting coefficients of the filter at the instant t.sub.o +kT.

## Claims

### Claim 1

In a digital data receiver, an adaptive system providing compensation for amplitude and phase distortions introduced by a data transmission channel and comprising an adaptive equalizing circuit receiving a signal vector X.sub.k from the data transmission channel output and producing an output signal y.sub.k, a decision circuit receiving this output signal y.sub.k and producing an estimation s.sub.k-d of each one of the digital data s.sub.k-d applied to the data transmission channel input, a summing circuit receiving said output signal y.sub.k and said estimation s.sub.k-d for producing a difference signal e.sub.k =y.sub.k -s.sub.k-d, and a multiplying circuit for multiplying said difference signal e.sub.k by an iteration step .alpha..sub.k, characterized in that the adaptive equalizing circuit is a non-recursive transversal filter having N adjustable weighting coefficients and the adaptive systems comprises for the determination of these coefficients by consecutive iterations:
a first circuit for determining, in a matrix A.sub.k which is an estimation of the square signal autocorrelation matrix A=E(X.sub.k .multidot.X.sub.k.sbsb.TR.sup. TR) at an instant t.sub.o +kT, where E is the expectation operator, X.sub.k is the transpose of X.sub.K, t.sub.o is a constant, k is an integer and T is the duration of a data symbol period, the (N/2+1) first elements a.sub.i.sbsb.(k) of the first row if N is even, or the (N+1)/2 first elements a.sub.i of the first row if N is odd, said estimation being based on the relation:
a.sub.i.sup.(k) =.beta.a.sub.i.sup.(k-1) +x.sub.k .multidot.x.sub.k-i
where i is an integer with 0.ltoreq.i.ltoreq.N-1 and .beta. is a constant with 0<.beta.<1,
a second circuit connected to said first circuit for forming a vector ##EQU20## in which r.sub.i.sup.(k) =a.sub.i.sup.(k) for every i not exceeding N/2 if N is even, or not exceeding (N-1)/2 if N is odd, and ##EQU21## for every i exceeding said limits, a third circuit connected to said second circuit for forming a vector ##EQU22## whose components are the eigenvalues of a circulant matrix having the transpose of the said vector U.sup.(k) as a first row, with the aid of the relation: ##EQU23## where P is the unitary matrix of the order N defined by:
P=.vertline.P.sub.f,g .vertline.
(f.g=0, 1, 2, . . . , N-2, N-1)
and ##EQU24## a fourth circuit connected to the data transmission channel output and the multiplying circuit output for forming a vector Q.sup.(k) with the aid of the relation:
Q.sup.(k) =.alpha..sub.k e.sub.k .multidot.P.sup.cc .multidot.X.sub.k
where P.sup.cc is the complex conjugate of said unitary matrix P,
a fifth circuit connected to said fourth and third circuits for dividing said vector Q.sup.(k) by said vector .LAMBDA..sup.(k) on a term-by-term basis so that the resulting vector ##EQU25## has components f.sub.i.sup.(k)=q.sub.i.sup.(k) /.lambda..sub.i.sup.(k) for every i not exceeding N-1,
a sixth circuit connected to said fifth circuit for multiplying said vector F.sup.(k) by said unitary matrix for producing a vector H.sup.(k) =P.multidot.F.sup.(k),
a seventh circuit connected to said sixth circuit and said transversal filter for up-dating the vector C.sub.k of the N weighting coefficients of said transversal filter at the instant t.sub.o +kT so as to produce a coefficient vector C.sub.k+1 at the instant t.sub.o +(k+1)T in accordance with the relation:
C.sub.k+1 =C.sub.k -H.sup.(k)

### Claim 2 (depends on 1)

An adaptive system as claimed in claim 1, characterized in that the system further comprises:
an eighth circuit connected to the data transmission channel output for multiplying said signal vector X.sub.k by said unitary matrix P, the resulting signal vector Z.sub.k =P.multidot.X.sub.k being applied to said transversal filter input,
a ninth circuit interconnecting said sixth and seventh circuits for multiplying said vector H.sup.(k) at the output of said sixth circuit by said matrix P.sup.cc and applying the resulting vector P.sup.cc .multidot.H.sup.(k) to said seventh circuit, said seventh circuit being arranged for up-dating the vector D.sub.k =P.sup.cc .multidot.C.sub.k representing the N weighting coefficients of said transversal filter at the instant t.sub.o +kT when this filter receives said signal vector Z.sub.k, so as to produce a coefficient vector D.sub.k+1 =P.sup.cc .multidot.C.sub.k+1 at the instant t.sub.o +(k+1)T in accordance with the relation:
D.sub.k+1 =D.sub.k -P.sup.cc .multidot.H.sup.(k)