Adaptive noise cancellation of Doppler shifted noise signals: A linear framework

In this paper we investigate the performance of single channel adaptive noise cancellation techniques for situations where the noise signal received by the two microphones cannot be related by a fixed weight canceller's (linear) digital filter due to Doppler shift on the two signals. A mathematical signal model is produced, which shows that the adaptive filter is in fact required to identify a time-varying system which incorporates Doppler shift, and potential rapid variations in signal power as the Doppler producing source passes the filter microphones. We present theory, simulated performance and real world performance for both the least mean square (LMS) and normalised LMS (NLMS) when operating in a Doppler noise environment.