Two non-convex optimization approaches for joint transmit waveform and receive filter design

Abstract

This study presents two innovative approaches for jointly optimizing the radar transmit waveform and receive filter to improve the signal-to-interference-plus-noise ratio (SINR) for extended targets under signal-dependent interference. We operate under the assumption of incomplete information about the target impulse response (TIR), which is confined within a predefined uncertainty set. To ensure robustness against this uncertainty, we frame the problem as a max–min (worst-case) optimization. Additionally, we impose a constant modulus constraint (because it has the lowest possible peak-to-average power ratio (PAPR)) on the transmit waveform to guarantee our system operates close to saturation. To solve this, both approaches use a sequential optimization procedure, alternating between the transmit waveform and receive filter subproblems. The first approach employs the ADMM, decomposing each subproblem into a semi-definite programming (SDP) problem and a least squares problem with a fixed rank constraint, solvable via SVD. The second approach tackles the problem over two Riemannian manifolds: the sphere manifold for the receive filter and the product of complex circles for the transmit signal. By applying manifold optimization, the constrained problem is transformed into an unconstrained one within a restricted search space. The max–min problem is reformulated as a minimization problem, yielding a closed-form expression involving log-sum-exp. This is solved using the Riemannian conjugate gradient descent (RCG) algorithm, which builds on Euclidean conjugate gradient descent and utilizes the manifold’s properties, such as the Riemannian metric and retraction. Our numerical results demonstrate the robustness and effectiveness of these methods across various uncertainty sets and target types.