Convergence analysis of the least squares constant modulus algorithm in interference cancellation applications

The convergence behavior of the least squares constant modulus (CM) algorithm in an adaptive beamforming application is examined. It is assumed that the desired signal and the interference are uncorrelated. The improvement in output signal-to-interference ratio (SIR) with each iteration of the algorithm is predicted for several different signal environments. Deterministic results are presented for an environment containing two complete sinusoids. Probabilistic results are presented for a CM desired signal with a CM interferer and with a Gaussian interferer. The asymptotic improvement in output SIR as the output SIR becomes high is also derived. The results of Monte Carlo simulations using sinusoidal, frequency modulation, and quadrature phase-shift keying signals are included to support the derivations.