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

We propose a method to calculate the infinite norm ball for the geometrical characterization of the constant modulus algorithm (CMA) and O. Shalvi and E. Weinstein's blind estimation of linear receivers (IEEE Trans. Inform. Theory, vol.36, no.2, p.312-20, 1990). 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 non-blind Wiener receivers can find an ellipsoid by infinite norm balls of different types. A necessary and sufficient condition for equivalence among constant modulus, Shalvi-Weinstein, zero-forcing, and Wiener receivers is obtained. Their locations and their relationship with Wiener receivers are provided for the special orthogonal channel and general two-dimensional (2D) channel-receiver impulse response. It is also shown from the calculation of the infinite norm ball via D-K iterations in 2D, that each CM or SW receiver can be obtained associated with one and only one Wiener receiver for a QAM system. Some design examples are simulated to verify our results.