[Paper Review] MIMO radar waveform design with practical constraints: A low-complexity approach

Chenglin Ren, Fan liu+4 more|arXiv (Cornell University)|May 10, 2018

Radar Systems and Signal Processing8 references3 citations

TL;DR

This paper proposes an Accelerated Gradient Projection (AGP) algorithm for MIMO radar waveform design under constant modulus and similarity constraints, transforming the non-convex problem into a sequence of convex QCQP subproblems. The AGP achieves SINR and beampattern performance comparable to interior-point methods (IPM) while reducing computational complexity from 𝒪(N_T^{3.5}N^{3.5}) to 𝒪(N_T^2N^2), enabling faster convergence with lower runtime.

ABSTRACT

In this letter, we consider the multiple-input multiple-output (MIMO) radar waveform design in the presence of signal-dependent clutters and additive white Gaussian noise. By imposing the constant modulus constraint (CMC) and waveform similarity constraint (SC), the signal-to-interference-plus-noise (SINR) maximization problem is non-convex and NP-hard in general, which can be transformed into a sequence of convex quadratically constrained quadratic programming (QCQP) subproblems. Aiming at solving each subproblem efficiently, we propose a low-complexity method termed Accelerated Gradient Projection (AGP). In contrast to the conventional IPM based method, our proposed algorithm achieves the same performance in terms of the receive SINR and the beampattern, while notably reduces computational complexity.

Motivation & Objective

• Address the challenge of non-convex, NP-hard MIMO radar waveform design under practical constraints like constant modulus and waveform similarity.
• Develop a low-complexity alternative to interior-point methods (IPM) that maintain high performance in SINR and beampattern directivity.
• Enable efficient optimization of transmit waveforms and receive filters under signal-dependent clutter and additive white Gaussian noise.
• Achieve a balance between SINR maximization, waveform similarity to a reference, and constant envelope constraints in a computationally tractable framework.

Proposed method

• Relax the non-convex waveform design problem into a sequence of convex quadratically constrained quadratic programming (QCQP) subproblems using an iterative scheme.
• Propose a novel Accelerated Gradient Projection (AGP) algorithm that combines FISTA-based gradient descent with a customized projection onto the feasible set defined by CMC and SC.
• Perform complex-valued optimization directly without converting to real-valued representations, reducing computational overhead.
• Use a tailored projection step that enforces both constant modulus and similarity constraints simultaneously at each iteration.
• Integrate an adaptive step size and momentum update rule inspired by FISTA to accelerate convergence.
• Apply a final normalization to ensure the final waveform satisfies the constant modulus constraint via phase-only adjustment.

Experimental results

Research questions

• RQ1 Can a low-complexity algorithm achieve SINR and beampattern performance comparable to IPM-based methods in MIMO radar waveform design with practical constraints?
• RQ2 How does the proposed AGP algorithm compare to IPM in terms of computational complexity and convergence speed under CMC and SC constraints?
• RQ3 To what extent does the waveform similarity constraint affect the beampattern directivity and SINR performance in the presence of signal-dependent clutter?
• RQ4 Does the proposed method maintain performance gains as the number of transmit antennas increases, especially in high-dimensional waveform spaces?

Key findings

• The AGP algorithm achieves SINR performance within 0.25 dB of the IPM method across all tested scenarios, including varying similarity constraints (ε = 0.4 and ε = 1.2).
• For ε = 1.2, the AGP outperforms IPM in side lobe suppression, demonstrating superior beampattern shaping under looser similarity constraints.
• The AGP reduces computational complexity from 𝒪(N_T^{3.5}N^{3.5}) (IPM) to 𝒪(N_T^2N^2) per iteration, significantly lowering runtime.
• With increasing transmit antennas (N_T), the AGP maintains a notable SINR advantage over IPM, especially at higher N_T.
• CPU time measurements show the AGP is substantially faster than IPM, with average execution time growing much more slowly as N_T increases.
• The algorithm converges in 𝒪(log(1/ζ)) iterations, matching the iteration count of IPM but with far fewer operations per iteration.