Capacity analysis of MMSE pilot-aided transmission for doubly selective channels

In previous work, we established necessary and sufficient conditions on pilot/data patterns that minimize the mean-squared error of pilot-aided channel estimates, given a pilot power constraint and a general linear time-varying channel model. Here we derive upper and lower bounds on the ergodic channel capacity of these MSE-optimal pilot-aided transmission (PAT) schemes. These bounds may be used to allocate power between pilot and data, as well as to choose among MSE-optimal pilot/data patterns. For example, the bounds show that frequency-domain PAT achieves higher capacity than time-domain PAT, or vice-versa, depending on the relative time- and frequency-dispersion of the channel.