Theoretical performance analysis assisted by machine learning for spatial permutation modulation (SPM) in slow-fading channels

Based on spatial modulation (SM), spatial permu- tation modulation (SPM) has been recently proposed to enhance the performance of the multiple-input multiple-output (MIMO) system. SPM maps data bits to both the QAM symbol and permutation array. At successive time instants, different transmit antennas are activated according to the mapped permutation array to transmit the QAM symbol. In this work, the error rate of SPM in slow-fading channels is analyzed. The performance is first analyzed with the closed-form expression for the special case, and then is generalized to arbitrary cases by using the approximation of Gamma random variables. The machine learning algorithm is adopted to simplify the generalization and estimate the diversity. Through the analyses, we discover that by simply adding transmit antennas, the performance of SPM in slow-fading channels can be greatly enhanced due to the reduction of the time dependency. Numerical simulations demonstrate the accuracy of our analyses and show that by adding one transmit antenna, the time dependency can almost be removed, leading to around 3 dB SNR gain for the BER performance.