The main focus of this paper is an active sensing application that involves selecting transmit and receive sensors to optimize the Cramér-Rao bound (CRB) on target parameters. Although the CRB is non-convex in the transmit and receive selection, we demonstrate that it is convex in the virtual array weight vector, which describes the multiplicity of the virtual array elements. Based on this finding, we propose a novel algorithm that optimizes the virtual array weight vector first and then finds a matching transceiver array. This greatly enhances the efficiency of the transmit and receive sensor selection problem.

Spatial cues allow a listener to determine the direction sound is coming from. In addition, recognising spatially separated sound sources facilitate the listener to focus on specific sound sources. Because of this, preservation of spatial cues in multi-microphone hearing assistive devices is important to the listening experience and safety of the user.
A number of linearly-constrained-minimum-variance-based methods exist for this purpose. Most of these are limited in the number of interfering sources for which they can preserve the spatial cues. In this thesis, a method of selecting the most important interfering point sources using convex optimisation is proposed.
The method is presented based on two different convex relaxations, which are compared, using simulation experiments, to existing, exhaustive search and randomised methods in terms of noise suppression and localisation errors.
Both methods are shown to improve the performance of the joint binaural linearly constrained minimum variance beamformer, an existing method for simultaneous noise reduction and spatial cue preservation, by giving it more degrees of freedom for noise reduction and allowing it to handle a larger number of (virtual) sources present in the scene.