Digital beamforming employing subband techniques

Abstract

In this thesis, we propose some different methods to reduce the computational complexity of a broadband beamformer based on the generalised sidelobe canceller (GSC) structure.

A GSC is an alternative implementation of the linearly constrained minimum variance beamformer and relys on well-known adaptive filtering algorithms to perform unconstrained adaptive optimisation. Due to the low computational complexity of subband adaptive filtering techniques, we embed the subband adaptive algorithms into the adaptive part of the GSC and propose a new subband adaptive GSC structure. In addition to its lower computational complexity than those previously suggested subband beamforming structures, it achieves a faster convergence rate than the traditional fullband adaptive GSC due to its pre-whitening effect.

By studying the input-output relationship of the blocking matrix of a GSC, we also propose a specific construction of the blocking matrix, in which the impulse responses hosted by its column vectors constitute those of a series of bandpass filters. These filters select signals with specific directions of arrival and frequencies and result in bandlimited spectra of its outputs. This spatially/temporally subband-selective blocking matrix can be applied to the subband adaptive GSC or the transform-domain GSC to reduce their computational complexities due to the discarding of some of the subbands or frequency bin outputs prior to the following adaptation. Since an overlap and finite transition band between the bandpass filters in the blocking matrix have to be permitted, a better design quality can be attained by reducing the output dimension of the blocking matrix, which yields a partially adaptive beamformer with further reduction of the computational complexity. Because of its combined spatial/temporal decorrelation effect, a faster convergence speed is also achieved, as demonstrated in the corresponding simulations.

Moreover, based on one of the traditional blocking matrices, we propose a spatially/temporally subband-selective transformation matrix, which can be regarded as another implementation of the subband-selective blocking matrix, because it has the same effect as the subband-selective blocking matrix, when combined with the traditional blocking matrix. The advantage of this method is that it simplifies the design of the subband-selective blocking matrix into a general filter design problem and can be implemented efficiently by cosine modulation.

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