Transmit Antenna Placement Based on Graph Theory for MIMO Radar Detection

Optimal antenna placement for target detection using multiple-input multiple-output (MIMO) radar system with widely separated antennas is studied in this paper. Considering the problem of placing a limited number of transmit antennas in a given space to maximize the detection performance, an optimization problem is formulated with the output signal-to-noise ratio (SNR) indicator as the performance metric. The initial problem is a nonlinear integer programming problem, and with the increase of the number of antennas, the computational complexity using traditional methods can be huge. In this paper, we discretize the feasible space into several grid points and employ graph theory to handle the problem. The antennas and grid points can be viewed as vertices in a bipartite graph, so that the antenna placement problem can be viewed as seeking for a proper matching between two vertex sets. We transform the problem into a stable matching (SM) problem and a maximum weighted matching (MWM) problem respectively, and propose Gale-Shapley (GS)-based and Kuhn-Munkres (KM)-based algorithms to deal with them with polynomial complexity. Numerical examples are provided to evaluate the effectiveness of the proposed methods.