Joint optimization of communication rates and linear systems

We consider a linear system, such as a controller or estimator, in which several signals are transmitted over communication channels with bit rate limitations. We model the effect of bit rate limited wireless channels by conventional uniform quantization, and use a standard white-noise model for quantization errors. We focus on finding the allocation of communication resources such as transmission powers, bandwidths, or time-slot fractions, that yields optimal system performance. We show that if the linear system is fixed, the problem of allocating communication resources is often convex. We discuss optimization algorithms that exploit the problem structure, and present efficient heuristics for obtaining integer-valued solutions. The problem of jointly allocating communication resources and designing the linear system is in general not convex, but can be solved heuristically in a way that exploits the problem structure and appears to work well in practice.