Fixed-window constant modulus algorithms: adaptive implementations

Adaptive implementations of two previously proposed block-iterative algorithms; referred to as fixed-window constant modulus algorithms (FWCMA), are developed. Their transient behavior, in relation to the delay at which the user sequence is recovered, is discussed and compared with other existing variations of CMA. The adaptive FWCMA-2 appears to be particularly promising, attaining convergence with little data. It retains the merits of its batch counterpart, namely, fast convergence, robustness to ill-conditioning, no required step-size tuning, and relatively low complexity. The built-in control over the converged delay translates into more reliable and predictable transient behavior. Equalizer calculation can be initiated from any initialization, and at any time instant, to attain convergence instantaneously without storing any received data. Thus, different initializations can be used to easily obtain multiple equalizers recovering the signal at different delays or recovering distinct users under a near-far simulation.