Sensing Matrix Optimization for Random Stepped-Frequency Signal Based on Two-Dimensional Ambiguity Function

Compressive sensing technique has been widely applied to achieve range-Doppler reconstruction of high frequency radar by utilizing sparse random stepped-frequency (SRSF) signal, which can suppress the complex electromagnetic interference and greatly reduce the coherent processing interval. An important way to improve the performance of sparse signal reconstruction is to optimize the sensing matrix (SM). However, the existing research on the SM optimization needs to design a measurement matrix with superior performance, which needs a large amount of computation and does not consider the influence of the waveform parameters design. In order to improve the superior reconstruction performance, a novel SM optimization approach for SRSF signal is proposed by using two-dimensional ambiguity function (TDAF) in this paper. Firstly, based on the two-dimensional sparse reconstruction model of the SRSFs, the internal relationship between the waveform parameters and the SM was derived. Secondly, the SM optimization problem was directly transformed into the waveform design of SRSFs. Furthermore, on the basis of analyzing the relationship between the mutual coherence matrix of SM and the TDAF matrix of SRSFs, the purpose of optimizing the SM can be achieved by designing the TDAF of the SRSFs. Based on this analysis, a sparse waveform optimization method with joint constraints of maximum and mean sidelobes of the TDAF by using the genetic algorithm was derived. Compared with the traditional SM optimization method, our method not only avoids generating a new measurement matrix, but also further reduces the complexity of the waveform optimization. Simulation experiments verified the effectiveness of the proposed method.