An improved least squares blind channel identification algorithm for linearly and affinely precoded communication systems

Certain linear and affine precoders introduce enough algebraic redundancy to enable the receiver to identify a. single-input single-output finite-impulse response channel without making any statistical assumptions on the source sequence. However, quite surprisingly, the traditional steepest descent least squares algorithm for estimating the channel often fails to converge, even in the absence of noise. This article explains why this is the case and derives a novel steepest descent algorithm on complex projective space that is guaranteed to converge. The complex projective space formulation also provides a standard framework for understanding different performance measures proposed in the literature.