Sparse reconstruction for direction-of-arrival estimation using multi-frequency co-prime arrays

In this paper, multi-frequency co-prime arrays are employed to perform direction-of-arrival (DOA) estimation with enhanced degrees of freedom (DOFs). Operation at multiple frequencies creates additional virtual elements in the difference co-array of the co-prime array corresponding to the reference frequency. Sparse reconstruction is then used to fully exploit the enhanced DOFs offered by the multi-frequency co-array, thereby increasing the number of resolvable sources. For the case where the sources have proportional spectra, the received signal vectors at the different frequencies are combined to form an equivalent single measurement vector model corresponding to the multi-frequency co-array. When the sources have nonproportional spectra, a group sparsity-based reconstruction approach is used to determine the direction of signal arrivals. Performance evaluation of the proposed multi-frequency approach is performed using numerical simulations for both cases of proportional and nonproportional source spectra.