For multiple-input multiple-output (MIMO) channels with phase modulation, we recently proposed a method of unitarily transforming the channel matrix into a certain row-echelon form, by which the original MIMO channel can be converted into a certain number of scalar sub-channels with two phase inputs, thereby forming an annulus constellation geometry, and corrupted by both the additive white Gaussian noise and weak self-interference. In this paper, several bounds are derived to evaluate the fundamental limit of such a specific transceiver architecture. Two upper bounds are obtained by upper-bounding the capacity of a scalar channel with an annulus support constraint from the perspective of the convex geometry, while a lower bound is obtained by the standard entropy power inequality. Numerical results show that the gaps between these bounds are small at high signal-to-noise ratios for the MIMO phase-modulated channels over the Rayleigh fading and the single-input multiple-output symbiotic communication system assisted by a reconfigurable intelligent surface.

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