Measurement Matrix Design for Compressive Sensing Based MIMO Radar (1102.5079v1)

Abstract: In colocated multiple-input multiple-output (MIMO) radar using compressive sensing (CS), a receive node compresses its received signal via a linear transformation, referred to as measurement matrix. The samples are subsequently forwarded to a fusion center, where an L1-optimization problem is formulated and solved for target information. CS-based MIMO radar exploits the target sparsity in the angle-Doppler-range space and thus achieves the high localization performance of traditional MIMO radar but with many fewer measurements. The measurement matrix is vital for CS recovery performance. This paper considers the design of measurement matrices that achieve an optimality criterion that depends on the coherence of the sensing matrix (CSM) and/or signal-to-interference ratio (SIR). The first approach minimizes a performance penalty that is a linear combination of CSM and the inverse SIR. The second one imposes a structure on the measurement matrix and determines the parameters involved so that the SIR is enhanced. Depending on the transmit waveforms, the second approach can significantly improve SIR, while maintaining CSM comparable to that of the Gaussian random measurement matrix (GRMM). Simulations indicate that the proposed measurement matrices can improve detection accuracy as compared to a GRMM.

• The paper introduces two design strategies—hybrid and SIR-focused—that enhance measurement matrix performance by balancing coherence and SIR.
• It employs convex optimization and waveform adaptation to improve CS recovery quality and mitigate interference in radar systems.
• Simulations confirm that the proposed matrices significantly boost target detection accuracy while reducing computational complexity for real-time applications.

Measurement Matrix Design for Compressive Sensing Based MIMO Radar

The paper presents a framework for designing measurement matrices to improve compressive sensing (CS) recovery performance in colocated MIMO radar systems. The authors propose two distinct strategies aimed at enhancing measurement optimality through the manipulation of coherence and signal-to-interference ratio (SIR).

In CS-based MIMO radar, a receive node employs a linear transformation known as the measurement matrix to compress received signals. Target information is retrieved at a fusion center by solving an $\ell_1$-optimization problem. The exploitation of target sparsity in the angle-Doppler-range space by CS allows for fewer measurements while retaining high localization performance. Undoubtedly, the measurement matrix plays a crucial role in CS recovery success.

The primary objective in designing measurement matrices is to optimize both the coherence of the sensing matrix (CSM) and the SIR. The paper introduces two novel approaches:

1. Hybrid Approach:
   • The first approach involves minimizing a linear combination of the coherence metric and the inverse SIR, attempting to achieve a balanced improvement in both criteria. This entails solving a high-complexity convex optimization problem.
   • A suboptimal method with lower computational complexity is also proposed. It structures the measurement matrix so that SIR is enhanced without requiring significant coherence compromise.
2. SIR-Focus Approach:
   • The second design focuses specifically on maximizing the SIR. It constructs the measurement matrix according to transmit signal waveforms and potential discretized target return delays. Depending on the transmitted waveforms, this strategy can markedly enhance the SIR, unlike the Gaussian random measurement matrix which does not adapt to these parameters.

The theoretical claims made in the paper have been supported through simulations. These simulations exhibit that the newly designed measurement matrices can significantly heighten target detection accuracy compared to a Gaussian random measurement matrix (GRMM). Particularly, when dealing with strong interference, these custom-designed matrices prove especially beneficial.

A key advancement demonstrated is the ability of the proposed measurement matrices in reducing the necessary computational load, overcoming a typical shortcoming found in CS-based radar systems concerning runtime inefficiencies. This enables real-time adaptability, which is pivotal for practical applications in dynamic radar scenarios.

Implications and Future Directions

The implications of this research are manifold. Practically speaking, the proposed designs could be implemented in radar systems where high-resolution target localization is essential under conditions of constrained resources. Theoretically, this work enriches the CS and radar literature by addressing measurement matrix design - a previously less explored dimension in MIMO radar.

For future developments, investigation into hybrid models that dynamically adapt matrix design based on environmental feedback could prove valuable. Additionally, application of these theoretical developments to extended models of radar employing mobility or higher frequency operations could yield useful enhancement to military and civilian radar systems alike.

Research bridging the gap between theoretical matrix design and practical implementation constraints would further solidify this work's foundation, potentially leading to standardized approaches for measurement matrix optimization in CS-related technologies. As the landscape of AI and radar evolves, such explorations hold promise in unlocking efficiency gains across a spectrum of applications, from autonomous navigation to remote sensing.