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.

Many blind adaptive beamforming algorithms require the selection of one or more non-zero initial weight vectors. Proper selection of the initial weight vectors can speed algorithm convergence and help ensure convergence to the desired solutions. Three alternative initialization approaches are compared here, all of which depend only on second order statistics of the observed data. These methods are based on Gram-Schmidt orthogonalization, eigendecomposition, and QR decomposition of the observed data covariance matrix. We show through computer simulation that the eigendecomposition approach yields the best performance.

The existing self coherence restoral (SCORE) beamforming techniques have been shown to be capable of blindly extracting a desired signal in the presence of unknown noise and interference by exploiting the cyclostationarity of the signal of interest. The versions of SCORE which offer the best convergence properties require computation of the observed data cyclic correlation matrix. This can be a large computational burden, particularly if the number of antennas in the array is large. This paper introduces a method which requires only a column-wise subset of the cyclic correlation matrix. It is shown that in many cases the new method performs as well as existing SCORE methods yet requires many fewer computations.