Joint Pulse-Amplitude and Transmission-Instant Optimization in Non-Uniform PRF Radar for Moving Target Detection

Conventional uniform Pulse Repetition Frequency (PRF) radars face an inherent tradeoff between maximum unambiguous range and maximum unambiguous velocity, which fundamentally limits the detection of distant moving targets. Non-uniform PRF radar mitigates this tradeoff by breaking sampling periodicity, thereby extending the unambiguous detection region, alleviating velocity ambiguities, and improving Low-Probability-of-Intercept (LPI) performance. In this paper, pulse transmission instants are introduced as an additional design variable, jointly optimized with the waveform to enhance target detection in cluttered environments. The resultant design is formulated as a Signal-to-Interference-plus-Noise Ratio (SINR) maximization problem under practical constraints on waveform dynamics and interpulse transmission intervals. The proposed joinT pulSe-amplitUde aNd trAnsMission-instant optImization (TSUNAMI) algorithm employs an alternating optimization scheme. It is shown that waveform phase does not affect the maximum achievable SINR, enabling a globally optimal solution for the waveform subproblem, whereas the transmission-instant subproblem is solved via a sequence of Quadratic Programming (QP) steps. Simulation results demonstrate that joint optimization of waveform amplitude and transmission instants provides substantial SINR gains and enables favorable tradeoffs between range and velocity ambiguities for long-range, high-speed targets.