University of Oulu

R. F. Siregar, N. Rajatheva and M. Latva-Aho, "Permutation Matrix Modulation," in IEEE Transactions on Wireless Communications, vol. 22, no. 7, pp. 4947-4961, July 2023, doi: 10.1109/TWC.2022.3231011.

Permutation Matrix Modulation

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Author: Siregar, Rahmat Faddli1; Rajatheva, Nandana1; Latva-Aho, Matti1
Organizations: 1Centre for Wireless Communications, University of Oulu, 90570 Oulu, Finland
Format: article
Version: published version
Access: open
Online Access: PDF Full Text (PDF, 1.8 MB)
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Language: English
Published: Institute of Electrical and Electronics Engineers, 2023
Publish Date: 2023-09-01


We propose a novel scheme that allows MIMO system to modulate a set of permutation matrices to send more information bits, extending our initial work on the topic. This system is called Permutation Matrix Modulation (PMM). The basic idea is to employ a permutation matrix as a precoder and treat it as a modulated symbol. We continue the evolution of index modulation in MIMO by adopting all-antenna activation and obtaining a set of unique symbols from altering the positions of the antenna transmit power. We provide the analysis of the achievable rate of PMM under Gaussian Mixture Model (GMM) distribution and finite cardinality input (FCI). Numerical results are evaluated by comparing PMM with the other existing systems. We also present a way to attain the optimal achievable rate of PMM by solving a maximization problem via interior-point method. A low complexity detection scheme based on zero-forcing (ZF) is proposed, and maximum likelihood (ML) detection is discussed. We demonstrate the trade-off between simulation of the symbol error rate (SER) and the computational complexity where ZF performs worse in the SER simulation but requires much less computational complexity than ML.

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Series: IEEE transactions on wireless communications
ISSN: 1536-1276
ISSN-E: 1558-2248
ISSN-L: 1536-1276
Volume: 22
Issue: 7
Pages: 4947 - 4961
DOI: 10.1109/TWC.2022.3231011
Type of Publication: A1 Journal article – refereed
Field of Science: 213 Electronic, automation and communications engineering, electronics
Funding: This work was supported by the Academy of Finland, 6G Flagship Program, under Grant 346208.
Academy of Finland Grant Number: 346208
Detailed Information: 346208 (Academy of Finland Funding decision)
Copyright information: © 2022. The Authors. This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see