接收空间调制信道容量计算及其鲁棒性设计
On the Channel Capacity of Receive Spatial Modulation and Its Robust Design

针对接收空间调制(RSM)系统中信道输入为有限码集导致香农容量公式不适用于RSM信道容量计算的问题,通过分析信道输入输出之间的互信息,推导了发射机拥有完美信道信息情况下的RSM系统的信道容量表达式,并进一步给出发射机的信道信息存在误差时具有鲁棒性的RSM预编码矩阵设计(RRSM)方法。该方法将二进制数据流映射成某根期望接收天线空间序号和传统调制符号,把它们作为RSM系统的信道输入,经发射预编码后得到信道输出;然后采用迫零算法使得信号功率在选定的期望接收天线处聚集而在其他接收天线处迫零,用所选定的期望接收天线的空间序号来传输额外信息比特;最后考虑RSM发射机的信道状态信息有误差,根据最小均方误差准则建立目标函数,求解得到RSM最优的鲁棒预编码矩阵。数值仿真实验表明:当发射机的信道状态信息误差的方差为0.3时,RRSM方法相比原始的RSM方法可使最优检测在误码率为10－4时获得1 dB性能增益,次优检测在误码率为10－2时获得2 dB增益。
The capacity of receive spatial modulation (RSM) is developed to solve the problem that Shannon capacity cannot evaluate the performance of RSM with finite？？alphabet inputs by analyzing the mutual information between the channel inputs and outputs, and a robust RSM with imperfect channel state information (CSI) is proposed to improve the bit error rate performance. The channel inputs of RSM are discrete spatial modulation symbols formed by combinations of a conventional modulation symbol and the spatial index of the expected receive antenna, both of which are carrying binary source information. Then, zero forcing pre？？coding is used by the transmitter with perfect CSI to focus the signal power on that selected receive antenna while the signal powers on other receive antennas are forced to zero. The spatial index of the selected receive antenna can be easily detected and decoded for extra information bits. When there exists imperfect CSI at the transmitter, an object function based on the minimum mean square error principle is constructed to find the optimal robust RSM pre？？coding matrix. Results from numerical simulation and comparisons with the original RSM show that the proposed robust RSM achieves 1 dB performance gain for the optimal RSM detection at BER of 10－4 and 2 dB gain for the suboptimal RSM detection at BER of 10－2 when the variance of the transmitter’s CSI error is 0.3