Adaptive system in a digital data receiver providing compensation for amplitude and phase distortions introduced by a data transmission channel

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)