Cognitive Radar-Based Sequence Design via SINR Maximization

The ambiguity function plays an important role in radar systems. In fact, many radar design problems can be interpreted from the perspective of persuing desired ambiguity functions to adapt to various application scenes. In this paper, we consider designing a radar sequence, subject to a peak-to-average power ratio (PAR) constraint, to maximize the signal-to-interference plus noise ratio, which can also be interpreted as designing a sequence with a desired ambiguity function. From an optimization point of view, this is equivalent to optimizing a complex quartic function with the PAR constraint. An efficient algorithm based on the general majorization-minimization (MM) method is developed to solve this problem with guaranteed convergence to a stationary point under some mild conditions. In addition, the unit-modulus constraint, as a special case, is considered and another algorithm is proposed, which is the combination of the general MM and the coordinate descent method. Numerical experiments show that the proposed algorithms can shape a desired ambiguity function based on the prior information, and the performance is much better compared with the existing methods.