Spectrally Compatible MIMO Radar Beampattern Design under Constant Modulus Constraints

In this article, we propose a new algorithm that designs a transmit beampattern for multiple-input multiple-output (MIMO) radar considering coexistence with other wireless systems. This design process is conducted by minimizing the deviation of the generated beampattern (which in turn is a function of the transmit waveform) against an idealized one while enforcing the waveform elements to be constant modulus and in the presence of spectral restrictions. This leads to a hard nonconvex optimization problem primarily due to the presence of the constant modulus constraint (CMC). In this article, we exploit the geometrical structure of CMC, i.e., we redefine this constraint as an intersection of two sets (one convex and other nonconvex). This new perspective allows us to solve the nonconvex design problem via a tractable method called iterative beampattern with spectral design (IBS). In particular, the proposed IBS algorithm develops and solves a sequence of convex problems such that constant modulus is achieved at convergence. Crucially, we show that at convergence the obtained solution satisfies the Karush-Kuhn-Tucker conditions of the aforementioned nonconvex problem. Finally, we evaluate the proposed algorithm over challenging simulated scenarios, and show that it outperforms the state-of-the-art competing methods.