Joint Design of Integrated Sensing And Communication Waveforms and Receiving Filters
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摘要: 通感一体化波形的多普勒容忍性和低旁瓣电平对于通感一体化场景中的目标探测和信息传输至关重要，但其设计面临着诸多挑战。为此，该文提出一种基于多普勒容忍的通感一体化波形与接收滤波器联合设计方法。以最小化加权积分旁瓣电平和处理增益损失为优化指标，同时考虑发射波形的恒模约束、发射波形与通信波形之间的相位差约束以及失配滤波器的能量约束，提出了基于迭代扭曲近似算法的框架来解决波形优化设计问题。仿真结果表明，该文提出的一体化波形在小处理增益损失的情况下，在感兴趣时延区间宽度上实现了很低的旁瓣电平和误符号率，可有效提升雷达感知性能和通信质量。Abstract:
Objective With the continuous increase in wireless communication traffic and the growing scarcity of spectrum resources, the overlapping frequency bands of communication and radar systems have led to mutual interference. Therefore, Integrated Sensing And Communication (ISAC) has emerged as a critical area of research. A key technology in this field is the design of ISAC waveforms, which is of significant research interest. The Doppler resilience and low sidelobe levels of ISAC waveforms are essential for effective target detection and information transmission in ISAC scenarios. However, designing waveforms that optimize both radar and communication performance presents substantial challenges. To address these challenges, a method for the joint design of ISAC waveforms and receiving filters is proposed. An ISAC model based on mismatched filtering is proposed, and an optimization problem is formulated. The Iterative Twisted appROXimation (ITROX) algorithm is presented to solve this nonconvex problem with guaranteed convergence. This approach enables the design of unimodular ISAC waveforms with Doppler resilience, achieving enhanced performance in both communication and radar functions. Methods To design ISAC waveforms that optimize radar and communication performance, the concept of mismatched filtering is introduced to formulate an optimization problem. The requirements for Doppler-resilient ISAC waveforms are first analyzed, followed by the proposal of a waveform model based on mismatched filtering. An optimization problem is then formulated, with the objective of minimizing the Weighted Integrated Sidelobe Level (WISL) and the Loss-in-Processing Gain (LPG). Constraints include the unimodular property of the transmitted waveform, the phase difference between the transmitted ISAC waveform and the communication data-modulated waveform, and the energy of the receiving filter. To solve this nonconvex optimization problem, the task is transformed into identifying a suitable Mismatched Filtering Sequences Pair (MFSP) under multiple constraints. An ISAC waveform design algorithm based on an improved ITROX framework is proposed to simplify the optimization process. The core concept of the ITROX algorithm is to iteratively search for the optimal projection of the matrix set, with the goal of maximizing the main lobe and minimizing the sidelobes within the region of interest. This approach minimizes WISL and LPG, satisfying the objective function requirements. Additionally, the combination of the three constraints ensures that the waveform meets both communication and radar sensing requirements. The SQUAREd Iterative Method (SQUAREM) is employed to improve the algorithm's convergence speed. The balance between WISL and LPG is controlled by adjusting the coefficients. Results and Discussions The ITROX-based ISAC waveform design method proposed in this paper effectively solves the formulated optimization problem, resulting in unimodular ISAC waveforms with Doppler resilience. Compared to existing ISAC waveform methods, the proposed ISAC waveform demonstrates a lower sidelobe level and Symbol Error Rate (SER) within the region of interest, with only a minor sacrifice in LPG. This leads to significant improvements in both radar sensing and communication performance. Simulation results validate the effectiveness of the proposed ISAC waveforms. These results show that the proposed method exhibits excellent convergence, with WISL rapidly converging to a stable value as iterations increase ( Fig. 1 ). When the LPG coefficient is set to 0.9, a low sidelobe level and SER are achieved, despite a processing gain loss of 0.91 dB (Fig. 2 ,Fig. 3 ). For the same phase difference threshold, the proposed ISAC waveform exhibits a lower SER than existing methods, indicating superior communication performance (Fig. 4 ). When comparing the ISAC waveform designed by this method to existing methods with the same time-delay interval width, the proposed waveform demonstrates a lower sidelobe level, with sidelobes nearly zero, approaching ideal correlation performance (Fig. 5 ,Fig. 6 ). This leads to significant improvements in target detection by the ISAC system. Furthermore, the proposed ISAC waveform exhibits excellent Doppler resilience, maintaining low sidelobe levels within the given Doppler interval (Fig. 6 ), which contributes to improved target detection performance.Conclusions This paper proposes a method for the joint design of ISAC waveforms and receiving filters based on Doppler resilience. By integrating the concept of mismatched filtering with the ISAC model, an optimization problem is formulated to minimize WISL and LPG without compromising communication quality. Additionally, an improved ITROX algorithm is proposed to effectively solve the formulated nonconvex optimization problem. The results demonstrate that the proposed scheme maintains near-ideal correlation performance within the region of interest under specified Doppler intervals, with only a minor sacrifice in LPG, and enables communication with a low SER. Compared to existing ISAC waveform methods, the proposed ISAC waveform exhibits a lower sidelobe level and SER, showing superior radar sensing and communication performance. Furthermore, low sidelobe levels can be achieved in one or more regions of interest to meet different requirements by appropriately adjusting the weighting coefficient. Future work could explore more efficient optimization algorithms to design ISAC waveforms with enhanced Doppler resilience. -
1 基于改进ITROX算法的ISAC波形设计
输入：$ \delta $, $ \varepsilon $, $ {\omega _\tau } $, $ {{{\boldsymbol{e}}}_n} $, $ {\boldsymbol a}_n^{(0)} = {{{\boldsymbol{e}}}_n} $, $ {{A}^{(0)}} = ({\boldsymbol a}_n^{(0)}){({\boldsymbol b}_n^{(0)})^{\mathrm{H}}} $，其中
$ {\boldsymbol b}_n^{(0)} $为初始化随机相位序列for $ t = 0, 1, 2, \cdots $执行 寻找$ {{{\boldsymbol{B}}}^{(t)}} \in {\boldsymbol{\varGamma}} $(根据定理1) 对$ {{{\boldsymbol{B}}}^{(t)}} $进行奇异值分解，计算$ {\bar {\boldsymbol{a}}}_n^{(t + 1)} $和$ {\boldsymbol b}_n^{(t + 1)} $ (根据式(23)和
式(24))计算$ {\boldsymbol a}_n^{(t + 1)} = \varPi ({\bar {\boldsymbol{a}}}_n^{(t + 1)}) $ (根据式(25)) 寻找$ {{{\boldsymbol{A}}}^{(t + 1)}} = ({\boldsymbol a}_n^{(t + 1)}){({\boldsymbol b}_n^{(t + 1)})^{\mathrm{H}}} \in {\boldsymbol{\varLambda}} $ (根据定理2) end for(当收敛时) 输出：$ {\boldsymbol a}_n^{(t + 1)} $, $ {\boldsymbol b}_n^{(t + 1)} $ 
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