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.