Optimal Channel Switching Over Gaussian Channels Under Average Power and Cost Constraints

Optimal channel switching that provides the highest performance over a set of Gaussian channels with variable utilization costs is investigated in the presence of average power and average cost constraints. First, generic cost functions are considered, and it is shown that the optimal channel switching strategy performs channel switching (time sharing) among at most three different channels and always operates at the average power and average cost limits. Also, for channel switching between two channels, relations between the optimal power levels are obtained depending on the average power limit, and it is proved that the ratio of the optimal power levels is upper bounded by the ratio of the larger noise variance to the smaller one. In addition, for logarithmic cost functions, the convexity properties of the error probability are investigated as a function of power and cost, and the optimal channel switching strategy is shown to employ at most two channels, which can easily be determined based on specific formulas, when the average power limit is larger than a certain threshold. Numerical examples are presented to provide illustrations of the theoretical results.