Parameters estimation using a random linear array and compressed sensing

Abstract

Existing sensor array signal processing techniques always use linear arrays sampled at Nyquist rate which demands the inter-element spacing is less than or equal to half of the system wavelength. Only in this way can algorithms such as MUSIC, Capon's beamformer estimate the direction-of-arrival (DOA) of the sources unambiguously. However, in some practical use, it seems difficult to satisfy the spatial sampling theorem. Compressed Sensing (CS) is a novel theory which enables perfect recovery of signals and data from what appear highly sub-Nyquist-rate samples on the condition that the signals or data are sparse or compressible in some domain. This implies that for spatially sparse signals, we can design a linear array with sparse property that will enable us to implement DOA estimates or even reconstruct the original signals accurately. In this paper, we proposed a parameters estimation method based on arrays with sub-Nyquist spatio-temporal sampling. We first sample the signals randomly in spatial domain, which means extracting a finite number of elements from a conventional uniform linear array. Then the signal in each channel is sampled by a random demodulator. By performing CS reconstruction algorithms, not only the DOAs can be estimated, but the original sources' waveforms will be recovered accurately.