Movable Antenna Enhanced Beampattern Synthesis for Spectrum Constrained MIMO Radar

Designing Constant Mode (CM) waveforms to synthesize spectrum-compatible beampatterns is crucial for Multiple-Input Multiple-Output (MIMO) radar systems. Unlike traditional Fixed Position Antenna (FPA) arrays, we propose a Movable Antenna (MA) enhanced MIMO radar that improves sensing performance by introducing new degrees of freedom (DoFs). This flexibility allows for the adjustment of each antenna’s position based on sensing requirements and optimizing the allocation of sensing power. Specifically, we co-design the transmit waveform and Antenna Position Vector (APV) to minimize the Mean Squared Error (MSE) of beampattern synthesis while adhering to constraints on MA array position, spectrum compatibility, and CM. This leads to a non-convex Quadratic-Constrained Quartic-Programming (QCQP) problem with two highly coupled variables. To solve this problem, we propose an Exact-Penalized-Product-Manifold (EPPM) method. First, we construct a Product Positivity Complex-Circle Manifold (PPC${}^{2}$M) space based on the constraint features of MA array position and CM, projecting both the APV and transmit waveform onto this space. Then, we employ a smoothing technique to transform the spectrum compatibility constraint into an exact penalty function, converting the problem into an unconstrained one on the PPC$^{2}$M space. Finally, we derive a Parallel Conjugate Gradient (PCG) method to optimize the APV and transmit waveform in parallel. Simulation results show that compared with the existing FPA-based method, the proposed method reduces the beampattern sidelobe by 2.3 dB and the beampatterns matching MSE by about 4 dB.