Excess MSE analysis of the concurrent constant modulus algorithm and soft decision-directed scheme for blind equalisation

The concurrent constant modulus algorithm (CMA) and soft decision-directed (SDD) scheme (CCMA+SDD) blind equalisation achieves a considerable improvement in equalisation performance over the CMA for high-order quadrature amplitude modulation (QAM) channels. Because of its concurrent adaptive filter structure and the complexity in analysing the estimation error signal, the actual steady-state performance has largely been left uninvestigated. By introducing an equivalent blind equalisation algorithm, the steady-state excess mean square error (EMSE) of the CCMA+SDD algorithm in a noise-free environment is studied. Based on the energy preservation approach, two first-order approximation closed-form solutions for the EMSE are derived for real-valued and complex-valued cases, respectively. The experimental simulation results for 16- and 64-QAMs show that the proposed steady-state theoretical EMSE results are reasonably accurate.