Average Capacity Maximization via Channel Switching in the Presence of Additive White Gaussian Noise Channels and Switching Delays

Abstract

The optimal channel switching problem is studied for average capacity maximization in the presence of additive white Gaussian noise channels and channel switching delays. First, an optimization problem is formulated for the maximization of the average channel capacity considering channel switching delays and constraints on average and peak powers. Then, an equivalent optimization problem is obtained to facilitate theoretical investigations. The optimal strategy is derived and the corresponding average capacity is specified when channel switching is performed among a given number of channels. Based on this result, it is shown that channel switching among more than two different channels is not optimal. In addition, the maximum average capacity achieved by the optimal channel switching strategy is formulated as a function of the channel switching delay parameter and the average and peak power limits. Then, scenarios under which the optimal strategy corresponds to the exclusive use of a single channel or to channel switching between two channels are described. Furthermore, sufficient conditions are obtained to determine when the optimal single channel strategy outperforms the optimal channel switching strategy. Numerical results are presented to provide examples of the theoretical results and to illustrate effects of channel switching delays.

Optimal channel switching in multiuser systems under average capacity constraints

“…Compared to this manuscript, the studies in [30] and [31] do not consider the multi-user scenario and consequently the optimal channel strategies obtained in those studies are not applicable for a communication system in which multiple users communicate with each other. Even though the studies in [30] and [31] do not provide any approaches for multi-user communication systems, they constitute a fundamental aspect for the optimal channel switching strategies obtained in this manuscript. Therefore, the methods and approaches employed in this study bear a certain level of resemblance to those in [30] and [31].…”

“…In the presence of multiple channels in a communication system, time sharing (i.e., channel switching) can be employed to enhance certain performance metrics such as average probability of error, average number of correctly received symbols, and channel capacity [28][29][30][31]. The channel switching problem is studied in [28] for M-ary communication systems in which a transmitter communicates with a receiver by employing a stochastic signaling approach in order to minimize the average probability of error under an average power constraint.…”

“…It is proved that the optimal strategy corresponds to channel switching either among at most three different channels with full channel utilization (i.e., no idle periods), or between at most two different channels with partial channel utilization. Unlike the studies in [28] and [29], the channel switching strategy is employed together with power allocation in order to enhance the capacity of a communication system in [30,31]. In [30], the optimal channel switching strategies are investigated for a communication system in which a single transmitter communicates with a single receiver in the presence of the average and peak power constraints.…”

“…It is obtained that the optimal channel switching strategy corresponds to the exclusive use of a single channel or to channel switching between two channels. In [31], the study in [30] is extended for a communication system where the channel switching delays (costs) are considered due to hardware limitations. It is shown that any channel switching strategy consisting of more than two different channels cannot be optimal.…”

“…Even though the studies in [30] and [31] do not provide any approaches for multi-user communication systems, they constitute a fundamental aspect for the optimal channel switching strategies obtained in this manuscript. Therefore, the methods and approaches employed in this study bear a certain level of resemblance to those in [30] and [31]. On the other hand, it is important to note that the contributions of this study to the literature are significantly different from the ones in [30] and [31].…”