Self-Orthogonalizing Adaptive Equalization in the Discrete Frequency Domain

A self-orthogonalizing discrete adaptive equalizer for synchronous data transmission is presented, based on the overlapsave filtering technique. Self-orthogonalization in the discrete frequency domain is adaptively performed by premultiplying by a diagonal matrix the MSE gradient estimates before projecting by means of Rosen´s gradient projection method. The diagonal of the matrix is the inverse of the power spectrum of the received sequence taken at equally spaced frequencies, and estimates are obtained by using Bartlett´s procedure of periodograms averaging for spectrum estimation. Projection is accomplished by means of an off-line derived projection matrix. Confidence of gradient estimates is improved by means of a block correlated estimation technique using available DFT´s of blocks of data. This equalizer is compared to time-domain self-orthogonalizing algorithms as regards speed of convergence and ease of implementation. During the short startup phase, convergence is competitive with that of Godard´s algorithm, which is the fastest algorithm known, and in the decision-directed mode, fast convolution performed by blocks results in a considerable reduction of the number of multiplications with respect to the time domain algorithms. A computationally simpler, unconstrained startup algorithm is also examined, obtained by removing the projection while retaining gradient block estimates in the DFD.