Constrained CMA-based multiuser detection under unknown multipath

In this paper, a constant modulus algorithm (CMA) based multiuser detector is proposed under linear constraints. Different from previous work, we explicitly consider the multipath effect. Therefore multiple constraints are incorporated into the optimization problem to mitigate multipath distortions. The algorithm will work well if constraint parameters are properly pre-selected. However, the detector's performance highly depends on the constraints. Thus we jointly update the detector and the constraint vector by minimizing the Godard's cost function with respect to both the detector and the constraint vector. It is shown that under certain conditions in the absence of noise, the algorithm guarantees global convergence. Numerical examples are presented to demonstrate the results.