Ambiguity Function Analysis of Frequency-Hopping MIMO Radar with Movable Antennas

In this paper, we propose a movable antenna (MA)-enabled frequency-hopping (FH) multiple-input multiple-output (MIMO) radar system and analyze the properties of its radar ambiguity function. Specifically, we derive the expression of the ambiguity function and analyze the relationship between its main lobe width and the transmit antenna positions. In particular, the optimal antenna distribution to achieve the minimum main lobe width is revealed and we discover that this minimum width is related to the ratio of antenna dimension to wavelength, the number of antennas, and the target angle. However, to achieve this minimum width, there is inevitable performance loss in the side lobes. Therefore, we propose to balance between minimizing the side lobe levels and narrowing the main lobe of the ambiguity function by optimizing the antenna positions. To achieve this goal, we propose a low-complexity algorithm based on the Rosen’s gradient projection method (RGPM), and we show that its performance is very close to that of the genetic algorithm (GA). Simulation results are presented to validate the theoretical analysis on the properties of the ambiguity function, and demonstrate the advantages of MAs in improving the radar performance.