Waveform Design using Second Order Cone Programming in Radar Systems

Transmit waveform design is one of the most important problems in active sensing and communication systems. This problem, due to the complexity and nonconvexity, has been always the main topic of many papers for the decades. However, still an optimal solution which guarantees a global minimum for this multi-variable optimization problem is not found. In this paper, we propose an attracting methodology to design transmit waveform of active sensing and communication systems with good auto-correlation properties. To this end, we tackle the non-convexoptimization problem of Integrated Sidelobe Level (ISL) minimization with the unimodular constraint. Using the epigraph and Second Order Cone Programming (SOCP) approach, theinhand nonconvex optimization will resort to a Semi-Definite Programming (SDP). Then, we use Majorization-Minimization to deal with constraints and convert the obtained problem to aconvex optimization problem. Finally, the obtained optimization problem is tackled using CVX toolbox. To obtain the code vectors from the extracted optimal code matrix, we use rank-one-decomposition. The simulation and results indicate the powerfulness of the proposed algorithm in designing radar transmit sequences with unimodular constraint. We show the proposed algorithm can design long length sequences with a very small ISL values. The proposed framework further can be investigated for the future optimization problems, like Peak Sidelobe Level (PSL) minimization.