Cross-ambiguity Function Shaping Through Fractional Quadratic Programming

Abstract

Due to the mismatch between transmit waveforms and receive filters, Cross-Ambiguity Function (CAF) shaping plays an important role in the design of cognitive radar waveforms and allows more freedom for waveform optimization problem than conventional ambiguity function shaping. A CAF shaping method is proposed for designing phase-shift keying transmit waveforms and receive filters jointly to maximize the output Signal-to-Interference-plus-Noise Ratio (SINR), thereby solving the problem of weaking-moving target detection under strong clutter conditions. The optimization problem is first modeled as a quadratic fractional programming problem under the Constant Modulus (CM) constraint of the transmit waveform. The conjugated gradient method is utilized to solve the minimization problem of the Stiefel manifold space through the introduction of auxiliary variables; furthermore the nonconvex optimization problem is converted into a unimodular quadratic programming problem. An algorithm based on alternately iterative maximization and power method-like iteration is proposed to solve the quadratic optimization problem. Since transmit waveforms are limited by hardware and achieving CM is difficult, the nearest vector method is employed under the constraint of a low peak-to-average power ratio. Finally, the experiments with simulated and real measured data under different parameters reveal that the transmit waveforms and receive filters designed using the proposed method exhibit better SINR performance and faster convergence speed compared with other existing algorithms.

Keywords

• cognitive radar
• waveform design
• cross-ambiguity function (caf)
• signal-to-interference-plus-noise ratio (sinr) maximization
• constant modulus constraints
• low peak-to-average power ratio (par) constraints