Performance issues in recursive least-squares adaptive GSC for speech enhancement

One fundamental non-stationary scenario involves a time-varying system in which the cross-correlation between the input signal and the desired response is time-varying. This case occurs in speech enhancement applications, where the optimal solution is time-varying due to the speech signal non-stationarity. Adaptive filtering performance analysis of time-varying systems is crucial to further understand the tracking behavior and to dasiaoptimallypsila design the update schemes. In this work, we investigate the tracking performance of the adaptive GSC applied for speech denoising. First, we interpret the noise cancellation in terms of non-stationary system identification. Then, we formulate the RLS adaptation as a filtering operation on the (time-varying) optimal filter and the instantaneous gradient noise (induced by the measurement noise). Under some structural assumptions, we derive an expression for the Excess Mean Squared Error (EMSE). Monte-Carlo simulations show that the proposed expression allows for a good prediction of the EMSE, and outperforms the state-of-the-art approximations.