A novel wavelet-based generalized sidelobe canceller

This paper presents a novel narrow-band adaptive beamformer with the generalized sidelobe canceller (GSC) as the underlying structure. The new beamformer employs a wavelet-based approach for the design of the blocking matrix of the GSC, which is now constituted by a set of regular M-band wavelet filters. Such a construction of the blocking matrix can not only block the desired signals from the lower path as required provided the wavelet filters have sufficiently high regularity, but it also encompasses the widely used one with ones and minus ones along the diagonals as a special case. In addition, it possesses two advantageous features. First, the eigenvalue spreads of the covariance matrices of the blocking matrix outputs, as demonstrated in various scenarios, are decreased as compared with those of previous approaches. Since the popular least-mean squares (LMS) algorithm has been notorious for its slow convergence rate, the reduction of the eigenvalue spreads can, in general, accelerate the convergence speed of the succeeding LMS algorithm. Second, the new beamformer belongs to a specific type of partially adaptive beamformers, wherein only a portion of the available degree of freedom is utilized in the adaptive processing. As such, the overall computational complexity is substantially reduced when compared to previous works. The issues of choosing the parameters involved for superior performance are also addressed. Simulation results are furnished as well to justify this new approach.