Calculation the infinite norm ball of constant modulus receivers by D-K iterations

Abstract

In practical approach, a Constant Modulus (CM) receiver is usually obtained from the stochastic gradient algorithm. leading to ABsrucr-CMA. Suppose that we have a sequence of obs&ations fromthe linear Inode] 111 this paper, we propose a inethod to calculate the infinite of the Constant norm ball for the geometrical characterization Modulus Alrorithm (CMA) and Shavi and Weinstein's blind ~[ k ] = Hs[k] + w[k].(3) I . ,. estimation of linear receivers. The Constant Modulus Algorithm uses the second-and fourth-order moments of a pre-whitened chip-rate received signal. The approach provides a framework within which various blind and nonblind Wiener receivers can be finding an ellipsoid by infinite nonn balls of different types. A necessaiy and sufficient condition for the equivalence among constant modulus, Shalvi-Weistein, zero-forcing, and Wiener receivers is obtained. Including their locations and their relationship with Wiener receivers are provided for the special orthogonal channel and general two-dimensional (2-D) channel-receiver impulse response. It is also shown that the calculation of infinite norm ball via D-K iteration [I71 in 2-D, each CM or SW receiver can be obtained from associated with one and only one Wiener receiver for QAM system. Some design examples are simulated to verify our results. 1.