Sparse complex FxLMS for active noise cancellation over spatial regions

In this paper, we investigate active noise control over large 2D spatial regions when the noise source is sparsely distributed. The l1 relaxation technique originated from compressive sensing is adopted and based on that we develop the algorithm for two cases: multipoint noise cancellation and wave domain noise cancellation. This results in two new variants (i) zero-attracting multi-point complex FxLMS and (ii) zero-attracting wave domain complex FxLMS. Both approaches use a feedback control system, where a microphone array is distributed over the boundary of the control region to measure the residual noise signals and a loudspeaker array is placed outside the microphone array to generate the anti-noise signals. Simulation results demonstrate the performance and advantages of the proposed methods in terms of convergence rate and spatial noise reduction levels.