Tracking analysis of augmented complex least mean square algorithm. (English) Zbl 1348.93286
Summary: The Augmented Complex Least Mean-Square (ACLMS) algorithm is a suitable algorithm for the processing of both second-order circular (proper) and noncircular (improper) signals. In this paper, we provide tracking analysis of the ACLMS algorithm in the non-stationary environments. Using the established energy conservation argument, we derive a variance relation that contains moments that represent the effects of non-stationary environment. We evaluate these moments and derive closed-form expressions for the Excess Mean-Square Error (EMSE) and Mean-Square Error (MSE). The derived expressions, supported by simulations, reveal that unlike the stationary case, the steady-state EMSE, and MSE curves are not monotonically increasing functions of the step-size parameter. We also use this observation to optimize the step-size learning parameter. Simulation results illustrate the theoretical findings and match well with theory.
MSC:
| 93E24 | Least squares and related methods for stochastic control systems |
| 93E11 | Filtering in stochastic control theory |
| 93E10 | Estimation and detection in stochastic control theory |
| 94A08 | Image processing (compression, reconstruction, etc.) in information and communication theory |
| 93C05 | Linear systems in control theory |
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