Generalized spatial representation for digital modulation and its potential application

Abstract

Constellation mapping has provided a great convenience to measure the performance of digital signal modulation in Euclid space. However, traditional in-phase and quadrature (IQ) plane is difficult to express the frequency modulation scheme such as minimum shift keying (MSK) and the time domain modulation such as cyclic code shift keying (CCSK). How to represent the digital signal modulation visually through constellation mapping is an attractive problem. To address this issue, in this paper, the combined frequency and phase modulation are utilized to define a new kind of constellation mapping, where the phase and frequency are quantized to the same elements. The uniform geometric construction for combined phase and frequency modulation is redefined in the 3D cylindrical coordinate system based on frequency (f), in-phase component (I) and quadrature component (Q). In the new coordinates, the quadrature frequency-phase shift keying (QFPSK) is produced by the QPSK with dimensional rotation matrix and denoted by the reduced dual quaternion. Furthermore, the spatial extension from QFPSK to chirp cyclic shift keying (Chirp CSK) is analyzed with bandwidth efficiency and energy efficiency. At last, the QFPSK is combined with the 2D OFDM, yielding the image OFDM system. Experimental results verify the effectiveness of QFPSK in the proposed system with the time-varying wireless channel and frequency selective fading channel respectively.

创新点

信号的维度空间由频率和时间的乘积组成, 决定了数字信号调制的边界。针对每个给定的维度点, 通过二维星座图能够直观的表征出传统的数字信号调制如MPSK及MQAM的空间结构, 并借助于欧氏距离的定义量化了信号调制的误码率。然而传统的星座图表征无法衡量维度点之间调制的量化表征, 如频域MFSK调制,时域的CCSK调制等, 本文基于此, 初步提出了频域与传统IQ平面结合的广义空间表征及基于双缩四元数的数学表征, 并借助于广义欧式距离给出了MSK等固有信号空间的三维量化关系。最后借助于三维空间表征, 我们将OFDM调制映射为不同类型的拓扑图, 构建新型的空间结构关系。