Joint antenna selection and waveform design for coexistence of MIMO radar and communications

As the problem of spectral congestion is becoming severe, the coexistence between two primary spectrum users, radar and communications, has spurred extensive research interest. To reduce the mutual interferences between the two functions, MIMO radar waveform design needs to consider the compatibility in both spectral and spatial domains, where the former is achieved by null forming in the frequency domain and the latter is achieved by shaped beampattern synthesis. Additionally, high power efficiency and low system overhead are two desirable characteristics for MIMO radar system design. To this end, we first introduce a new realistic waveform constraint, peak-to-valley-power-ratio (PVPR) constraint per antenna to improve the power efficiency. Then, combined with PVPR constraint, we propose a switchable individual antenna power control scheme to jointly optimize waveforms and antenna locations. We adopt a max–min beampattern matching criterion and impose the ℓ_{2 , 1}-norm penalty on the waveform matrix to promote the sparsity of the array. To solve the resultant non-smooth and non-convex problem, we develop a modified alternating directions method of multipliers, where a surrogate subproblem over primal variables is solved instead of the original problem, and its local convergence is analyzed. Finally, numerical experiments demonstrate the effectiveness and superiority of the proposed method over counterparts, especially obtaining the lowest sidelobe level and deeper spectral nulls using much fewer antennas.