Time-Averaged ACLMS Algorithm for Improper Cyclostationary Inputs: Performance Analysis and Application to Interference-Limited Systems

In interference-limited communications systems, the use of improper signaling has been demonstrated to improve throughput and fairness, as compared to proper signaling. Considering that signals in such scenarios exhibit both impropriety and cyclostationarity, this paper rigorously studies the optimal adaptive filtering of jointly improper cyclostationary signals. Upon rearranging the cyclic frequencies in the conjugate-linear branch of the FREquency SHift (FRESH) filter, we first propose a widely linear estimation model equivalent to the optimal FRESH filtering. This new structure admits the same form as the widely linear estimator derived with stationary signals, facilitating direct utilization of the augmented complex statistics of the jointly improper cyclostationary input and signal of interest. By minimizing the time-averaged mean-squared error, an adaptive algorithm is obtained for the proposed estimation model, referred to as the time-averaged augmented complex least-mean-squares (TA-ACLMS). We establish a full second-order statistical framework to comprehensively assess the error and the weight error vector of the TA-ACLMS at both transient and steady-state stages, and derive the stability bound on the step-size. The performance of the proposed TA-ACLMS is evaluated through a system identification setting and channel estimation in an interference-limited narrowband power line communication system. Simulation results support the analysis.