Jointly optimal design for MIMO radar frequency-hopping waveforms using game theory

Using a colocated multiple input/multiple output (MIMO) radar system, we consider the problem of joint design of amplitudes and frequency-hopping codes for frequency-hopping waveforms. The joint design method yields better combined code and amplitude matrices that result in improved performance over that of separate designs. We propose a game theory framework for the joint design. First, we present the MIMO radar signal model and the sparse representation. Then the problem formulation is constructed based on sparse recovery and the ambiguity function of the MIMO radar system for frequency-hopping waveforms. For amplitude design, we propose two strategies: amplitude design with separate constraints and amplitude design by fusing all transmitters. We formulate a novel game model and propose two joint design algorithms, one applying a noncooperative scheme and the other applying a cooperative scheme. Owing to the extremely large size of the feasible set of the discrete code, we propose to use these algorithms to obtain the ∈-approximate equilibrium. We demonstrate the improvement of the resulting codes and amplitudes through numerical examples.