Domains of attraction of Shalvi-Weinstein receivers

Domains of attraction (DoA) of Shalvi-Weinstein (1990) receivers are analyzed. It is shown that there is a one-to-one correspondence between DoA in the receiver parameter space and those in the global (or combined channel-receiver) parameter space. For general noiseless channels, DoA of SW receivers in the global response space are the minimum distance decision regions on a unit sphere. In the presence of noise and for the class of orthogonal channels, DoA of SW receivers for independent and identically distributed (i.i.d.) input signals are the minimum distance decision regions on an ellipsoid determined by the channel coefficients and the noise variance. The DoA in the receiver parameter space are also characterized for the general nonuniformly distributed sources. The size of the DoA is shown to be affected by the signal power, the signal constellation, the noise level, and the channel condition. It is also demonstrated that although the optima of the Shalvi-Weinstein algorithm and those of the constant modulus algorithm are one-to-one correspondent, their DoA are different in general.