Optimal channel switching for average capacity maximization

Abstract

Optimal channel switching is proposed for average capacity maximization in the presence of average and peak power constraints. A necessary and sufficient condition is derived in order to determine when the proposed optimal channel switching approach can or cannot outperform the optimal single channel approach, which performs no channel switching. Also, it is stated that the optimal channel switching solution can be realized by channel switching between at most two different channels. In addition, a low-complexity optimization problem is derived in order to obtain the optimal channel switching solution. Numerical examples are provided to exemplify the derived theoretical results.

Optimal Channel Switching Strategy for Average Capacity Maximization

“…1 Then, the optimal 1 Channel switching can be implemented in practice by transmitting the first λ 1 Ns symbols over channel 1, the next λ 2 Ns symbols over channel 2, . .…”

“…where the inequality follows from the facts that C max (P ) is a monotone increasing function of P (please see (1) and (4)), 3 and that…”

“…, which always holds for all P ∈ [0, P pk ] due to the concavity of the capacity function, C b (P ) (see (1)). Hence, Proposition 2 applies in this scenario; that is, the optimal single channel strategy (i.e., the use of the best channel all the time at the average power limit) becomes the optimal solution.…”

“…Note that, in the case of λ * ∈ (0, 1), i = j is not possible since time sharing of different power levels over the same channel always reduces the capacity due to the convexity of the capacity function in (1).…”

“…Although the optimal channel switching problem is studied thoroughly in terms of average probability of error minimization (e.g., [7], [21], [22]) and in the context of opportunistic spectrum access (e.g., [23]- [26]), no studies in the literature have considered the channel switching problem for maximization of data rates by jointly optimizing time sharing (channel switching) factors and corresponding power levels (please see [1] for the conference version of this study). In this paper, the average Shannon capacity is considered as the main metric since it gives the maximum achievable data rates with low probability of decoding errors.…”