The detection performances of MIMO radar can be improved by waveform diversity technology. The waveform diversity gain depends on the correlation side-lobe level of the orthogonal waveform set. Generally, peak side-lobe level (PSL) and integrated side-lobe level (ISL) are two most important performance metrics of the correlation side-lobe level. Few existing orthogonal waveform set design algorithms can minimize PSL and ISL simultaneously. To tackle this problem, this paper first proposes a correlation side-lobe performance metric in the form of p -norm, denoted by p -ISL. Then, in order to minimize the p -ISL, this paper develops a p -MM algorithm based on Majorization-Minimization (MM) framework, which transforms the complex p -order polynomial minimization problem into a series of low-order simple optimization problems. Numerical results show that the p -MM algorithm can effectively suppress the correlation side-lobe level and strike a good balance between the PSL and ISL metrics. Compared with the best PSL optimization algorithm based on primal dual method, the p -MM obtains about the same PSL and lower ISL values. Compared with Multi-CAN, MM-Corr, ISL-New and the other state-of-the-art ISL minimization algorithms, the p -MM obtains slightly higher ISL and much lower PSL. Briefly, the p -MM is able to obtain almost the best PSL and relatively low ISL values.

Aiming at maximizing waveform diversity gain when designing a phase-coded multiple-input multiple-output (MIMO) radar waveform set, it is desirable that all waveforms are orthogonal to each other. Hence, the lowest possible peak cross-correlation ratio (PCCR) is expected. Meanwhile, low peak auto-correlation side-lobe ratio (PASR) is needed for good detection performance. However, it is difficult to obtain a closed form solution to the waveform set from the expected values of the PASR and PCCR. In this paper, the waveform set design problem is modeled as a multi-objective, NP-hard constrained optimization problem. Unlike conventional approaches that design the waveform set through optimizing a weighted sum objective function, the proposed optimization model evaluates the performance of multi-objective functions based on Pareto level and obtains a set of Pareto non-dominated solutions. That means that the MIMO radar system can trade off each objective function for different requirements. To solve this problem, this paper presents a multi-objective quantum genetic algorithm (MoQGA) based on the framework of quantum genetic algorithm. A new population update strategy for the MoQGA is designed based on the proposed model. Compared to the state-of-the-art methods, like BiST and Multi-CAN, the PASR and PCCR metrics of the waveform set are 0.95–3.91 dB lower with the parameters of the numerical simulation. The MoQGA is able to minimize PASR and PCCR of the MIMO radar waveform set simultaneously.

Digital radio frequency memory (DRFM) has emerged as an advanced technique to achieve a range of jamming signals, due to its capability to intercept waveforms within a short time. multiple-input multiple-output (MIMO) radars can transmit agile orthogonal waveform sets for different pulses to combat DRFM-based jamming, where any two groups of waveform sets are also orthogonal. In this article, a group orthogonal waveform optimal design model is formulated in order to combat DRFM-based jamming by flexibly designing waveforms for MIMO radars. Aiming at balancing the intra- and intergroup orthogonal performances, the objective function is defined as the weighted sum of the intra- and intergroup orthogonal performance metrics. To solve the formulated model, in this article, a group orthogonal waveform design algorithm is proposed. Based on a primal-dual-type method and proper relaxations, the proposed algorithm transforms the original problem into a series of simple subproblems. Numerical results demonstrate that the obtained group orthogonal waveforms have the ability to flexibly suppress DRFM-based deceptive jamming, which is not achievable using p-majorization–minimization (p-MM) and primal-dual, two of the most advanced orthogonal waveform design algorithms.

The OFDM chirp signal is suitable for MIMO radar applications due to its large time-bandwidth product, constant time-domain, and almost constant frequency-domain modulus. Particularly, by introducing the time-frequency structure of the non-linear frequency modulation (NLFM) signal into the design of an OFDM chirp waveform, a new OFDM-NLFM waveform with low peak auto-correlation sidelobe ratio (PASR) and peak cross-correlation ratio (PCCR) is obtained. IN-OFDM is the OFDM-NLFM waveform set currently with the lowest PASR and PCCR. Here we construct the optimization model of the OFDM-NLFM waveform set with the objective function being the maximum of the PASR and PCCR. Further, this paper proposes an OFDM-NLFM waveform set design algorithm inspired by alternating optimization. We implement the proposed algorithm by the alternate execution of two sub-algorithms. First, we keep both the sub-chirp sequence code matrix and sub-chirp rate plus and minus (PM) code matrix unchanged and use the particle swarm optimization (PSO) algorithm to obtain the optimal parameters of the NLFM signal’s time-frequency structure (NLFM parameters). Next, we keep current optimal NLFM parameters unchanged, and optimize the sub-chirp sequence code matrix and sub-chirp rate PM code matrix using the block coordinate descent (BCD) algorithm. The above two sub-algorithms are alternately executed until the objective function converges to the optimal solution. The results show that the PASR and PCCR of the obtained OFDM-NLFM waveform set are about 5 dB lower than that of the IN-OFDM.

Digital-Radio-Frequency-Memory (DRFM) has emerged as an advanced technique to achieve diverse jamming signals, due to its capability of intercepting waveforms within a short time. Multiple-Input Multiple-Output (MIMO) radars can transmit agile orthogonal waveform sets for different pulses to combat the DRFM-based jamming, where any two groups of waveform sets are also orthogonal. In order to design multiple groups of orthogonal waveform sets at the same time, this article formulates a group orthogonal waveforms optimal design model, whose objec-tive function is the weighted sum of the intra- and inter-group orthogonal performances metrics. To solve this optimization problem, this article proposes a group orthogonal waveforms design algorithm. Based on a primal-dual type method and proper relaxations, the proposed algorithm transforms the original problem into a series of simple sub-problems. Numerical results demonstrate that the proposed algorithm has the ability to balance the intra- and inter-group orthogonal performances by adjusting the weighting factors, which is not available using other state-of-the-art orthogonal waveform design algorithms.