This paper focuses on the combined radar and communications problem and conducts a thorough analytical investigation on the effect of phase and frequency change on the communication and sensing functionality. First, we consider the classical stepped frequency radar waveform and modulate data using M-ary phase shift keying (MPSK). Two important analytical tools in radar waveform design, namely the ambiguity function (AF) and the Fisher information matrix (FIM) are derived, based on which, we make the important conclusion that MPSK modulation has a negligible effect on radar local accuracy. Next, we extend the analysis to incorporate frequency permutations and propose a new signalling scheme in which the mapping between incoming data and waveforms is performed based on an efficient combinatorial transform called the Lehmer code. We also provide an efficient communications receiver based on the Hungarian algorithm. From the communications perspective, we consider the optimal maximum likelihood (ML) detector and derive the union bound and nearest neighbour approximation on the block error probability. From the radar sensing perspective, we discuss the broader structure of the waveform based on the AF derivation and quantify the radar local accuracy based on the FIM. Extensive numerical examples are provided to illustrate the accuracy of our results.
翻译:本文侧重于雷达和通信的综合问题,对阶段和频率变化对通信和遥感功能的影响进行透彻的分析调查。首先,我们考虑使用M-ary 级转换键(MPSK)的经典中继频率雷达波形和调制数据。在雷达波形设计中,有两个重要的分析工具,即模棱两可功能(AF)和渔业信息矩阵(FIM),我们据此得出重要结论,即MPSK调制对当地雷达精确度的影响微不足道。接着,我们扩大分析范围,纳入频率调整,并提出一个新的信号方案,根据称为Lehmer码的高效组合式转换对收到的数据和波形进行绘图。我们还根据匈牙利算法提供高效的通信接收器。从通信角度,我们考虑最大可能性(ML)探测器,并根据块误差概率得出连接和近邻的联盟。从雷达遥感角度,我们讨论波形的较广结构,根据AF的衍生结果,并量化基于FIM的当地雷达准确性。提供了广泛的数字示例,以说明我们的结果的准确性。