Sparse loudspeaker array design for wideband frequency-invariant beamforming with multiple targets

Beamforming technology using loudspeaker arrays is widely used in sound applications, but current sparse array design methods focus on optimizing a single beam for a single target direction, limiting their applicability to multi-channel sound systems. This paper presents a design method for sparse loudspeaker line arrays to generate wideband frequency-invariant beams in multiple target directions. A model based on tapped delay lines is developed and a two-stage design approach is proposed. In the first stage, a compressive sensing framework combined with an extended fast iterative shrinkage-thresholding algorithm is employed to determine the optimal locations of active drivers. In the second stage, the excitations of the active drivers are calculated using the least squares method. Numerical simulations show a 32.3% reduction in the number of drivers compared to that of traditional uniform linear loudspeaker arrays while maintaining frequency-invariant properties. The proposed algorithm exhibits considerable computational efficiency, rendering it highly suitable for addressing large-scale optimization problems and substantially reducing the design time. This design method is applicable to sound projection scenarios and can be extended to other multi-channel beamforming systems to achieve reliable beam performance and reduce system costs.