Optimal tracking and power allocation over an additive white noise channel

In this paper, we study the optimal tracking performance of multiple-input multiple-output (MIMO), linear and time-invariant system over a parallel additive white noise (AWN) channel. We adopt the power of the tracking error as a measure of the performance and examine the best achievable performance by all two-parameter stabilizing controllers. In addition, we investigate a scaling scheme of the channel to counter the noise and achieve better performance. We show explicitly that the tracking performance is constrained by the plant unstable poles, as well the power constraint and the channel noise level. Furthermore, we examine the power allocation strategy across the sub-channels under this optimal control scheme. It is also found that for decentralized plant with independently designed scaling factors, the tracking system distributes more power to the more demanding sub-channels.