Quantized augmented complex least-mean square algorithm: Derivation and performance analysis

• We firstly derive the quantized version of the QACLMS algorithm.
• Starting with an energy conservation relation we derive closed-form expression for mean-square performance curve in terms of EMSE.
• We show that the steady-state curve is not monotonically increasing functions of the step size.
• We find the optimum value of the step-size learning parameter. We also derive the mean stability condition in terms of the step size parameter.
• Simulation results illustrate the theoretical findings.

Augmented adaptive filters provide superior performance over their conventional counterparts when dealing with noncircular complex signals. However, the performance of such filters may change considerably when they are implemented in finite-precision arithmetic due to round-off errors. In this paper, we study the performance of recently introduced augmented complex least mean-square (ACLMS) algorithm when it is implemented in finite-precision arithmetic. To this aim, we first derive a model for the finite-precision ACLMS updating equations. Then, using the established energy conservation argument, we derive a closed-form expression, in terms of the excess mean-square error (EMSE) metric which explains how the quantized ACLMS (QACLMS) algorithm performs in the steady-state. We further derive the required conditions for mean stability of the QACLMS algorithm. The derived expression, supported by simulations, reveals that unlike the infinite-precision case, the EMSE curve for QACLMS is not monotonically increasing function of the step-size parameter. We use this observation to optimize the step-size learning parameter. Simulation results illustrate the theoretical findings.