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

TL;DR

This work addresses FH-MIMO radar resolution limits by introducing movable antennas (MAs) to reshape the MIMO channel. It develops a detailed ambiguity-function framework, derives a closed-form angular main-lobe bound $B_{min}$ and an optimal two-group MA distribution $oldsymbol{d}^*$, and provides lower bounds for the Doppler and delay domains via $oldsymbol{ eq}^*(v)$ and $oldsymbol{ eq}^d( au)$. To balance main-lobe and side-lobe performance across angular, Doppler, and delay domains, the authors formulate a non-convex optimization in the MA positions and propose a low-complexity Rosen’s gradient projection method (RGPM) that is competitive with GA but far more efficient. Numerical results corroborate the theoretical insights, showing that MA configurations yield narrower angular main lobes and reduced side lobes, while enabling task-adaptive sensing; the Doppler and delay gains are more limited, illustrating domain-specific trade-offs. Overall, the paper offers design principles and a practical optimization algorithm to enhance FH-MIMO radar sensing with movable antennas, with potential impact on high-resolution radar imaging and ISAC/DFRC systems.

Abstract

In this paper, we propose a movable antenna (MA)-enabled frequency-hopping (FH) multiple-input multiple-output (MIMO) radar system and investigate its sensing resolution. 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 in the angular domain is characterized. We discover that this minimum width is related to the antenna size, the antenna number, and the target angle. Meanwhile, we present lower bounds of the ambiguity function in the Doppler and delay domains, and show that the impact of the antenna size on the radar performance in these two domains is very different from that in the angular domain. Moreover, the performance enhancement brought by MAs exhibits a certain trade-off between the main lobe width and the side lobe peak levels. 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, and show that its performance is very close to the baseline. Simulation results are presented to validate the theoretical analysis on the properties of the ambiguity function, and demonstrate that MAs can reduce the main lobe width and suppress the side lobe levels of the ambiguity function, thereby enhancing radar performance.

Figures (13)

• Figure 1: Proposed MA-enabled FH-MIMO radar system.
• Figure 2: Illustration of $a_m$ distribution for $m=0,1,\cdots,M_t-1$.
• Figure 3: Illustration of the optimal MAs’ positions for minimum main lobe width.
• Figure 4: Ambiguity function in the angular domain.
• Figure 5: Minimum main lobe width versus antenna size $L$, antenna number $M_t$, and target direction angle $\theta$.

Theorems & Definitions (3)

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