Geometrical characterizations of constant modulus receivers

Convergence properties of the constant modulus (CM) and the Shalvi-Weinstein (SW) algorithms in the presence of noise remain largely unknown. A new geometrical approach to the analysis of constant modulus and Shalvi-Weinstein receivers is proposed by considering a special constrained optimization involving norms of the combined channel-receiver response. This approach provides a unified framework within which various blind and (nonblind) Wiener receivers can all be analyzed by circumscribing an ellipsoid by norm balls of different types, A necessary and sufficient condition for the equivalence among constant modulus. Shalvi-Weinstein, zero forcing, and Wiener receivers are obtained. Answers to open questions with regard to CM and SW receivers, including their locations and their relationship with Wiener receivers, are provided for the special orthogonal channel and the general two-dimensional (2-D) channel-receiver impulse response. It is also shown that in two dimensions, each CM or SW receiver is associated with one and only one Wiener receiver.