Effect of Varying Source Kurtosis on the Multimodulus Algorithm

This paper presents a theoretical analysis of the effect of constellation shaping in the transmitter on multimodulus (MMA) blind equalization in the receiver. Constellation shaping reduces average signal energy by a non-uniform distribution of constellation point utilization. Optimal transmit efficiency is achieved by a Gaussian distribution but many blind equalization algorithms require a non-Gaussian source. We demonstrate, using complex constellations, MMA convergence failure as a Gaussian source kurtosis is approached. Our generalized cost function analysis of the related constant modulus algorithm (CMA) for complex constellations identifies the mechanism of the MMA convergence failure. We introduce a new design procedure for determining the kurtosis-specific MMA moduli and present simulation results that illustrate MMA convergence properties for varying source kurtosis.