Efficient Algorithms for Synthesizing Probing Waveforms with Desired Spectral Shapes

We consider the design of constant-modulus probing waveforms to improve the spectral compatibility of radar systems with the congested radio frequency environments. We seek to synthesize radar probing waveforms with desired spectral shapes. We use a weighted least-squares fitting approach to formulate the spectral shaping problem. We introduce two algorithms to tackle the optimization problem we encounter. Both algorithms are devised based on cyclic approaches and have guaranteed convergence of the objective values. Moreover, the proposed algorithms can be implemented via fast Fourier transforms and, hence, are computationally efficient. Furthermore, we extend the proposed algorithms to deal with peak-to-average-power ratio and similarity constraints, which are desirable in some radar applications. Finally, we provide several numerical examples to demonstrate the effectiveness of the proposed algorithms.