Constant Modulus Waveform Design for Slow-Time Ambiguity Function

This work addresses the synthesis of constant-modulus (CM) radar waveforms whose range-Doppler behavior approximates a prescribed profile in the presence of multiple interference sources. Since the interference power at the matched-filter output amounts to an average of the slow-time ambiguity function (STAF) of the transmitted code evaluated at the interference range-Doppler bins, the design task is essentially one of shaping the STAF. The resulting formulation is high-dimensional and non-convex because of the CM requirement, which hampers conventional optimization tools in Euclidean space. To circumvent this difficulty, we recast the design as an unconstrained problem on a Riemannian manifold and tackle it directly with a trust-region scheme defined on that manifold. The Riemannian gradient and Hessian of the quartic cost are derived in closed form, the trust-region subproblem is solved by a truncated conjugate gradient procedure, and the computational complexity of each iteration is analyzed. Then an enhanced solver called Adaptive regularization with cubics (ARC) is developed, improving the performance based on the step-acceptance mechanism. Numerical results under two interference scenarios show that, compared with the existing method, the proposed approach produces deeper nulls at the interference locations while requiring less computation time.