An N-dimensional Amplitude Modulation Based On Permutation Group Codes And Its Error Probability Analysis

Ultra-Reliable Low-Latency Communications(URLLC)is one of the three major application scenarios of 5G wireless communications.Facing the stringent quality of service requirements of the URLLC,the communication field has realized that new coding,modulation and access technologies are needed to match it.This paper focuses on the research of new n-dimensional high-order amplitude modulation schemes,with the ultra-reliable and low-latency requirements as the constraint.Different from the traditional amplitude modulation technology,the modulation technology proposed in this paper uses the permutation group code defined in the positive integer domain as a mathematical tool to encode the n-dimensional amplitude signal to form a time-amplitude dual-domain modulation signal model,and its high-order permutation array constellation.The design goal is to find low-complexity mapping encoding,decoding and signal detection algorithms.The main research work and content of this paper are as follows:First,five permutation array constellations of multi-dimensional high-order time-amplitude modulation signals,which is characterized in that the average transmit power decreases sequentially,are designed based on the positive integer domain permutation group code.And establish a multi-dimensional modulation signal model for the vector signal points of the constellation.On this basis,a simplified demodulation algorithm with linear time complexity is proposed.In addition,in order to improve the spectrum efficiency,the maximum and minimum index modulation signal model is designed based on the permutation group code.Secondly,the analysis of the error probability of multi-dimensional time-amplitude modulation signals on Gaussian and Rayleigh fading channels is carried out.and the theoretical word error rate and bit error rate expressions of the simplified demodulator on the additive Gaussian white noise channel are derived,as well as the upper bound expression of the pairwise error probability and the union bound expression of the bit error rate of the minimal square Euclidean distance demodulator on the Rayleigh fading channel.Finally,simulation experiments of the proposed novel time-amplitude modulation signal are carried out on the Gaussian white noise channel and the Rayleigh fading channel.And the simulation error probability curve and the theoretical error probability curve are compared and analyzed.At 10^-5 bit error rate,the experiment shows that the best bit error rate performance of multi-dimensional time amplitude modulation on Gaussian channel is 6.4d B,which is 3.2d B better than BPSK.And the theoretical error probability curve basically coincides with the simulation error probability curve.