The design of the finite impulse response (FIR) notch filter with controlled null width is expressed as a derivatively contrained quadratic optimization problem. The problem is transformed into an unconstrained one by choosing a null matrix orthogonal to the derivative constraint matrix. In this paper, subband decomposition using wavelet filters is employed to construct the null matrix. Taking advantage of the vanishing moment property of the wavelet filters, the proposed method can adjust the null width of the notch filter for eliminating the intractable iterference by controlling the regularity of the wavelet filters. Simulation results show that the new method can offer comparable performance as those of the existing full-rank-based ones and thus provides a promising alternative to the existing works.

This paper presents a wavelet-based approach for the design of the finite impulse response (FIR) notch filter with controlled null width. The M-band P-regular wavelet filters are employed to constitute the null space of the derivative constraint matrix. Taking advantage of the vanishing moment property of the wavelet filters, the proposed method controls the null width of the notch filter by adjusting the regularity of the employed wavelet filters. Besides, the selection of large number of bands of the wavelet filters can effectively reduce the minimum mean square error and thus improve the performance of the notch filter. Computer simulations show that, in addition to possessing lower computational complexity, the proposed reduced-rank method has similar frequency response compared to those of the full-rank-based techniques.

In this paper, we examine the effect of random steering errors on the signal-to-interference-plus-noise-ratio (SINR) at the output of the recently addressed wavelet-based generalized sidelobe canceller (GSC). This new beamformer employs a set of P-regular M-band wavelet bases for the design of the blocking matrix of the GSC. We first carry out a general expression of the output SINR of the GSC with multiple interferers present. With this expression, we then examine the analysis of wavelet-based GSC by expressing the SINR in terms of parameters such as the regularity of wavelet filters, the number of bands of wavelet filters, the length of adaptive weights, and the input signal-to-noise ratio (SNR). Some simulation results verify the analytically predicted performance.

In this paper, we present a new approach for the design of partially adaptive broadband beamformers with the generalized sidelobe canceller (GSC) as an underlying structure. The approach designs the blocking matrix involved by utilizing a set of P-regular, M-band wavelet filters, whose vanishing moment property is shown to meet the requirement of a blocking matrix in the GSC structure. Furthermore, basing on the subband decomposition property of these wavelet filters, we introduce a new dynamic subband selection scheme succeeding the blocking matrix. The scheme only retains the principal subband components of the blocking matrix outputs based on a prescribed statistical hypothesis test and thus further reduces the dimension of weights in adaptive processing. As such, the overall computational complexity, which is mainly dictated by the dimension of adaptive weights, is substantially reduced. The furnished simulations show that this new approach offers comparable performance as the existing fully adaptive beamformers but with reduced computations.