LAUSR

Waveform adaptation grants cognitive radar (CR) the ability to adapt to its environment, which requires an effective framework to synthesize waveforms sharing a desired ambiguity function (AF). In this letter, we propose a novel method for shaping the slow-time AF in order to adaptively suppress the interference power. The problem is formulated as minimizing the average value of the slow-time AF over some range Doppler bins spanned by the interference, which can be identified exploiting a plurality of knowledge sources. From a technical point of view, this is tantamount to optimizing a complex quartic-order polynomial with a constant modulus (CM) constraint on each optimization variable. To solve this problem, we proposed a quartic Riemannian trust region algorithm. This algorithm first transforms the optimization into an unconstrained one in a complex circle Riemannian manifold, then devises a new Riemannian trust region optimization algorithm that invokes Riemannian gradient and Hessian matrix to obtain an iterative solution with super-linear convergence rate and ability to escape potential saddle points. Simulation results demonstrated that our proposed algorithm outperformed state-of-the art approaches for AF shaping while being computationally less expensive.