Robust wideband waveform design with constant modulus and discrete phase constraints for distributed precision jamming

Abstract

Distributed precision jamming (DPJ) is a novel blanket jamming concept in electronic warfare, which delivers the jamming resource to the opponent equipment precisely and ensures that friendly devices are not affected. Robust jamming performance and low hardware burden on the jammers are crucial for practical DPJ implementation. To achieve these goals, we study the robust design of wideband constant modulus (CM) discrete phase waveform for DPJ, where the worst-case combined power spectrum (CPS) of both the opponent and friendly devices is considered in the objective function, and the CM discrete phase constraints are used to design the wideband waveform. Specifically, the resultant mathematical model is a large-scale minimax multi-objective optimization problem (MOP) with CM and discrete phase constraints. To tackle the challenging MOP, we transform it into a single-objective minimization problem using the Lp-norm and Pareto framework. For the approximation problem, we propose the Riemannian conjugate gradient for CM discrete phase constraints (RCG-CMDPC) algorithm with low computational complexity, which leverages the complex circle manifold and a projection method to satisfy the CM discrete phase constraints within the RCG framework. Numerical examples demonstrate the superior robust DPJ effectiveness and computational efficiency compared to other competing algorithms.

1. Introduction

For most electronic devices, the quality of service (QoS) highly depends on the signal-to-interference-plus-noise ratio (SINR) in practice (Wang et al., 2018; Gao et al., 2020; Geng et al., 2023). Therefore, blanket jamming is usually used in electronic warfare to degrade the QoS of these devices (Pärlin et al., 2021; Kelsey, 2023; Wu et al., 2023). Conventional blanket jamming is typically implemented by a single jammer, where a high power is required for jamming effectiveness but results in low utilization efficiency (Tai et al., 2016). Meanwhile, the beamforming technique is also usually used to enhance the transmit gain by directing the jamming energy toward two-dimensional (2D) directions. However, due to the insufficient dimensionality in the spatial domain, it may cause unexpected injuries to adjacent friendly devices in the three-dimensional (3D) area of interest (Li and Stoica, 2008; Blunt and Mokole, 2016). To overcome these problems, a novel blanket jamming concept, namely, distributed precision jamming (DPJ), was proposed by the US Defense Advanced Research Project Agency (https://www.fbo.gov/spg/ODA/DARPA/CMO/DARPA-BAA-09-65/listing.html). This method requires that the opponent equipment is jammed precisely in the 3D spatial domain, and the adjacent friendly devices are not affected by the jammers. Compared to the transmit beamforming technique, in this technique, a group of distributed aerial platforms is adopted to improve the coherent synthesis efficiency. More importantly, DPJ exhibits excellent jamming energy performance within the desired 3D area rather than along specific 2D directions (Song D et al., 2016).

The existing research on DPJ falls into two distinct categories from the perspective of the transmitted signal model. One category adopts the narrowband signal model and regards the combined energy control performance as the main design metric. Chen et al. (2020) proposed an efficient method to design the single snapshot constant modulus (CM) transmit signals, and the grating lobes in the area of interest are mitigated to some extent. Yang ZP et al. (2022) jointly optimized the CM signals and the location of distributed platforms to improve the spatial energy control performance. Zhang KD et al. (2022b) proposed a method to endow the narrowband waveform with jamming characteristics by fitting the combined waveform with white noise, and Yang ZP et al. (2023) further improved the algorithm’s performance in terms of both jamming and computational efficiency. Other research works, including those by Yang ZP et al. (2021), Xu et al. (2022), and Zhang KD et al. (2022a), designed the narrowband transmitted waveform to improve the DPJ performance based on previous works, and interested readers may refer to them.

The other category uses the wideband transmitted waveform for the jamming tasks, where the combined power spectrum (CPS) is considered as the design metric.