Joint Design Methods of Unimodular Sequences and Receiving Filters With Good Correlation Properties and Doppler Tolerance

Sequence set design with good correlation properties and Doppler tolerance has been a classic and important problem in many multichannel systems, including but not limited to the multiple-input multiple-output (MIMO) and simultaneous polarimetric radar systems. In this article, we first consider the problem of jointly designing Doppler resilient unimodular sequences and receiving filters to minimize the metric weighted integrated sidelobe level (WISL), which can be used to construct sequence sets with 'thumbtack' co-channel and zero cross-channel ambiguity functions (AFs). To control the signal-to-noise ratio (SNR) loss caused by the mismatched filter, a peak constraint function is added to the objective function based on the penalty function method. An algorithm based on the alternatively iterative scheme and general majorization-minimization (MM) method is developed to tackle the constrained joint design problem. Moreover, the proposed algorithm is then extended to optimize the ${l_{p}}$ -norm of sidelobes of AFs, which gives a way to optimize the weighted peak sidelobe level (WPSL) metric. Due to the use of the fast Fourier transform (FFT) algorithm and a general acceleration scheme, the proposed algorithm can be realized efficiently. A number of simulations are provided to demonstrate the excellent performance of the proposed sequence set synthesis algorithms. Besides, an application of using the designed Doppler resilient sequence set on the simultaneous polarimetric radar to detect multiple moving targets in a strong clutter scene is given via simulation, which further verifies the practicability of the proposed algorithm.