Capacity and power allocation for fading MIMO channels with channel estimation error

TLDR

The paper investigates how channel estimation errors affect the capacity of MIMO fading channels and derives tight mutual‑information bounds for Gaussian inputs. Assuming Gaussian inputs, the authors analytically obtain lower bounds on ergodic and outage capacities and design optimal transmitter power‑allocation strategies that achieve these bounds under perfect feedback. They find that ergodic capacity is maximized by a modified spatial–temporal waterfilling scheme that remains near‑optimal with small feedback delays but defaults to equal spatial power when delays are large, while outage capacity is optimized by spatial waterfilling combined with temporal truncated channel inversion, yielding modest ergodic gains from spatial allocation and substantial outage performance improvements from temporal adaptation.

Abstract

In this correspondence, we investigate the effect of channel estimation error on the capacity of multiple-input-multiple-output (MIMO) fading channels. We study lower and upper bounds of mutual information under channel estimation error, and show that the two bounds are tight for Gaussian inputs. Assuming Gaussian inputs we also derive tight lower bounds of ergodic and outage capacities and optimal transmitter power allocation strategies that achieve the bounds under perfect feedback. For the ergodic capacity, the optimal strategy is a modified waterfilling over the spatial (antenna) and temporal (fading) domains. This strategy is close to optimum under small feedback delays, but when the delay is large, equal powers should be allocated across spatial dimensions. For the outage capacity, the optimal scheme is a spatial waterfilling and temporal truncated channel inversion. Numerical results show that some capacity gain is obtained by spatial power allocation. Temporal power adaptation, on the other hand, gives negligible gain in terms of ergodic capacity, but greatly enhances outage performance.