Recursive least squares algorithm for blind deconvolution of channels with cyclostationary inputs

The authors propose a new discrete time blind deconvolution technique for linear channels driven by cyclostationary inputs. This problem arises in digital communications, seismic signal processing, and many other applications. In particular, homomorphic approaches are applied to the cyclic autocorrelation of the fractionally-spaced sampled output of the channel. First, the method identifies the differential cepstrum parameters of the complex channel by means of a recursive least squares (RLS) algorithm. The RLS algorithm is based on the special characteristics of a cyclic autocorrelation matrix and an appropriate matrix inversion lemma. Once the differential cepstrum parameters are recovered, then the impulse response of the channel/equalizer is obtained by simple recursive formulas. Only partial information is required, i.e., the cyclic period and the distribution of the input data. It is shown that the method can directly identify the characteristics of either the channel or its inverse, provided that an unknown channel satisfies a special condition. The method is evaluated by means of computer simulations and is found to perform efficiently