Frequency-Hopping Code Design for Target Detection via Optimization Theory

We present a signaling scheme for information embedding into the illumination of radar using frequency-hopping pulses. A frequency-hopping-based joint radar-communication system enables implementing a primary radar operation and a secondary communication function simultaneously. Then, we consider the problems of radar codes optimization under a peak-to-average-power ratio and an energy constraint. These radar codes design problems can be converted into non-convex quadratic programs with a finite or an infinite number of quadratic constraints. All problems are proved to be NP-hard optimization problems. Therefore, we develop optimization approaches, resorting to semi-definite programming relaxation technique along with to the idea of trigonometric polynomials, offering expected approximate solutions with a polynomial time calculation burden. We assess the capability of the proposed schemes, considering both the detection probability and the robustness in correspondence of Doppler shifts offered by the Neyman–Pearson detector. Simulation results show an improvement in detection performance as the average signal-to-noise ratio value increases, while still maintaining low symbol error rates between the proposed system nodes.