3-D MUSIC Spectrum Reconstruction for Joint Azimuth-Elevation-Frequency Band Estimation

This paper introduces a three-dimensional (3-D) multiple signal classification (MUSIC) spectrum reconstruction that can be used to jointly estimate the frequency band, the azimuth, and the elevation angles of the sources from digital samples produced by time- and spatial-domain (SD) compression. An SD compression is applied on the output of the underlying uniform rectangular array of N = NxNy antenna elements based on the solution for the length-(Nx - 1) and length-(Ny - 1) minimal sparse ruler leading to a sparse rectangular array having M < N elements. Then, a sub-Nyquist rate sampling is applied on the received analogue signals to relieve the burden on the analogue-to-digital converter. In order to estimate the three signal parameters, the three-step least-square method is applied to reconstruct the 3-D correlation tensor followed by the application of MUSIC on the resulting correlation tensor. By only using 25 sensors and low signal-to-noise ratio (SNR), i.e. 0 dB, the proposed approach can simultaneously and accurately locate the azimuth and elevation angles, and the frequency band of 28 far-field sources. Note that the number of sources is greater than the number of sensors.