Permutation Design for Ultra-Low Latency Communication and Spatial Permutation Modulation (SPM)

Recently, spatial permutation modulation (SPM) and path-permutation code (PPC) are proposed for the baseband multiple-input multiple-output (MIMO) system and the virtual MIMO system on the network/session layer for ultra-low latency communication, e.g. vehicular network. These techniques modulate data bits by selecting a certain vector from a predefined permutation set. In this work, we first prove that generating such a permutation set is NP-complete. With the required throughput and reliability, a greedy algorithm is then proposed to efficiently design the permutation set. Theoretical analysis shows that this algorithm can achieve optimal performance in most practical cases. In addition to the permutation generation algorithm, we also generalize SPM by constructing the virtual transmit antennas, i.e., the combination vectors used to concurrently activate multiple antennas. Numerical results demonstrate the optimality of the proposed algorithm for the generation of permutation set and the superior of such generalized SPM using the permutation set acquired by the proposed algorithm.