Patent GB-1535850-A (GB)
Title: Apparatus for determining the initial values of the coefficients of a coupled transversal equalizer
IPC: H03H17/00
Filed: 1976-11-18
Abstract: 1535850 Preset transversal equalizers INTERNATIONAL BUSINESS MACHINES CORP 18 Nov 1976 [30 Dec 1975] 48196/76 Heading H4R The initial settings of the multiplier coefficients of a complex transversal equalizer for a double sideband quadrature carrier modulation data transmission system are determined by transmitting over the system a pseudo-random sequence of complex numbers, the sequence being of a type which has a periodic autocorrelation function only the first coefficient of which is not zero, and in which the amplitude of all the complex numbers is constant. Such sequences are termed CAZAC sequences. Examples of sequences which can be employed are maximum length binary pseudo random sequences in which the terms are - 1 or + 1 and in which a constant where L is the sequence length, is added to each term, or a sequence whose elements are determined by the quadratic and non-quadratic residues of prime numbers of the 4K - 1 form, of length L=4K-1, again with the constant added to each term. In preferred embodiments the first auto correlation coefficient is made to have the value L by dividing each term of the series by a suitable constant. A further family of CAZAC sequences can be of length L = K<SP>2</SP> with each term u i  = W<SP>#γ</SP> where #,γ = 0,1,..., (K - 1), i = K#+γ = 0, 1,...,(K-1), and W = a primitive K<SP>th</SP> root of unity, e.g. =<SP>2j#</SP>/ k . The sequence is obtained by using the elements in the successive rows of the matrix (W<SP>#γ</SP>). A further family of CAZAC sequences is formed by the sequences (u i ) of length L = m<SP>2K+1</SP> where where (a n ) is a CAZAC sequence of length m n=0, 1,...,(m - 1) #=0, 1,...,(M - 1); M = m<SP>K+1</SP> γ=0, 1,...(N-); N = m<SP>K</SP> i = M#+ γ and W is a primitive M<SP>th</SP> root of unity. A further sequence u i  of length L = 4m can be obtained from two CAZAC sequences of a i  and b, of length m where u 2K  = a K  (modulo m), u 2K+1  = b K  (modulo m) W<SP>K</SP> for K=0, 1, ..., 2(m - 1) where W=a primitive root of unity. A further sequence of length L = mÎn can be obtained from two CAZAC sequences of a i  and b, of length m and n respectively where u i  = a i (mod m)  Î b i (mod   n)  where i = 1, 2, ..., m Î n. The optimum settings of the transversal equalizer coefficients are determined from the received sequence in accordance with the relation where C opt is the column vector whose 1 terms are the equalizer coefficients, #is the autocorrelation matrix of the transmission channel impulse response, R is the inverted column vector whose terms are the transmission channel impulse response samples, where inverted means the first term of vector R is the last sample of the impulse response etc. Values of the samples r n  of the complex impulse response of the transmission channel are obtained by the apparatus of Fig. 3 (not shown) from the relations and where p g  and q g  are the real and imaginary parts of the impulse response samples at time g, X i  and Y i  are the real and imaginary parts of the received sequence, V i  and W i  are the real and imaginary parts of the transmitted sequence. The autocorrelation matrix of the channel impulse response is determined by the apparatus of Fig. 4 (not shown) which operates according to the relation where and Rather than invert the matrix #for the solution of the relation C opt = #<SP>-1</SP>R the equation is solved by an iterative adjustment method using the relation which is performed by the apparatus of Fig. 5 (not shown) which, since the equalizer is complex, operates on the relations