Convergence analysis of a twin-reference complex least-mean-squares algorithm

In many noise control applications, the noise is dominated by low frequencies and generated by several independent periodic sources. In such situations the tonal noise may be suppressed by using a narrowband multiple-reference feedforward controller. The performance characteristics of the control system, e.g., the convergence behavior and noise reduction are directly related to the controller adaptation rate as well as the frequency separation of the tonal components in the noise, i.e., the beat frequency. This paper treats the convergence performance of a complex least-mean-squares (LMS) algorithm using two reference signals. An analysis of its convergence behavior is presented as well as the results from computer simulations validating the convergence behavior. The convergence of the filter weights and the decrease rate of the squared error (the learning curve) for noise control applications are also discussed.