  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
\revv{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.
