Symmetric capacity of nonlinearly modulated finite alphabet signals in MIMO random channel with waveform and memory constraints

The paper shows a procedure for evaluating the symmetric ergodic capacity of nonlinearly modulated finite alphabet signals in the MIMO random channel. We first investigate informationally an equivalent signal space representation for finite alphabet signals. The signals are allowed to be multidimensional per one antenna to reflect the modulation nonlinearity. The informationally equivalent signal space representation allows a factorization per one eigenmode (depending purely on one marginal eigenvalue) in the capacity evaluation in the MIMO channel. The evaluation complexity does not depend on the MIMO dimensions. We consider two types of channel signal constraints. (1) A constraint on the waveform only. (2) A constraint on the waveform and memory (modeled as a Markov chain). The mean symmetric capacity for the former one is derived. For the latter one, we derive lower and upper bounds based on the entropy rate approximation.