It is possible to demodulate the embedded communication symbols from the transmitted base waveform by using the relationship between the transmitted base signal and the synthesized signal in the spatial domain of a circulating code array. The spatial-frequency modulation coefficient (SFMC) is firstly analyzed to determine the frequency band used for the communication user in a certain direction. Perturbation phase modulation (PM) term is attached to the certain time duration of a linear frequency modulation (LFM) signal to embed communication symbols. The perturbation PM term is designed to be a weighted sum of multiple orthogonal sub-PM terms and the communication symbols are carried out by the coefficients of different sub-PM terms. An adjustable weighted coefficient is applied to control the degree of the perturbation PM term to make a balance between radar performance and communication bit error rate (BER) performance. The designed dual-function radar-communications (DFRC) system has the following properties: 1) Multidimensional waveform design issue for a DFRC system based on multiple input multiple output (MIMO) is converted into a transmitted base waveform design issue; 2) the communication receiver can be located in any direction; 3) the effect of embedded communication symbols on radar performance can be effectively controlled while with a satisfactory BER performance.

中文翻译：

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双功能雷达通信系统的循环码阵列

在循环码阵列的空间域中，可以利用传输的基本信号和合成信号之间的关系从传输的基本波形中解调嵌入的通信符号。首先分析空间频率调制系数（SFMC）以确定通信用户在某个方向上使用的频带。扰动相位调制 (PM) 项附加到线性频率调制 (LFM) 信号的特定持续时间以嵌入通信符号。扰动PM项设计为多个正交子PM项的加权和，通信符号由不同子PM项的系数进行。应用可调加权系数来控制扰动 PM 项的程度，以在雷达性能和通信误码率 (BER) 性能之间取得平衡。设计的双功能雷达通信（DFRC）系统具有以下特性：1）基于多输入多输出（MIMO）的DFRC系统的多维波形设计问题转化为发射基波设计问题；2) 通讯接收器可以位于任何方向；3) 可以有效控制嵌入通信符号对雷达性能的影响，同时具有令人满意的误码率性能。1) 将基于多输入多输出 (MIMO) 的 DFRC 系统的多维波形设计问题转换为发射基本波形设计问题；2) 通讯接收器可以位于任何方向；3) 可以有效控制嵌入通信符号对雷达性能的影响，同时具有令人满意的误码率性能。1) 将基于多输入多输出 (MIMO) 的 DFRC 系统的多维波形设计问题转换为发射基本波形设计问题；2) 通讯接收器可以位于任何方向；3) 可以有效控制嵌入通信符号对雷达性能的影响，同时具有令人满意的误码率性能。