We study the problem of channel pairing and power allocation in a multichannel multihop relay network to enhance the end-to-end data rate. Both amplify-and-forward (AF) and decode-and-forward (DF) relaying strategies are considered. Given fixed power allocation to the channels, we show that channel pairing over multiple hops can be decomposed into independent pairing problems at each relay, and a sorted-SNR channel pairing strategy is sum-rate optimal, where each relay pairs its incoming and outgoing channels by their SNR order. For the joint optimization of channel pairing and power allocation under both total and individual power constraints, we show that the problem can be decoupled into two subproblems solved separately. This separation principle is established by observing the equivalence between sorting SNRs and sorting channel gains in the jointly optimal solution. It significantly reduces the computational complexity in finding the jointly optimal solution. It follows that the channel pairing problem in joint optimization can be again decomposed into independent pairing problems at each relay based on sorted channel gains. The solution for optimizing power allocation for DF relaying is also provided, as well as an asymptotically optimal solution for AF relaying. Numerical results are provided to demonstrate substantial performance gain of the jointly optimal solution over some suboptimal alternatives. It is also observed that more gain is obtained from optimal channel pairing than optimal power allocation through judiciously exploiting the variation among multiple channels. Impact of the variation of channel gain, the number of channels, and the number of hops on the performance gain is also studied through numerical examples.
The related problem of optimal PA for a dual-hop OFDM system was studied by many @cite_23 @cite_11 @cite_24 for different relay strategies and power constraints. The problem of jointly optimizing CP and PA was studied in a dual-hop OFDM system for AF and DF relaying in @cite_4 and @cite_18 , respectively, where the direct source-destination link was assumed available. The joint optimization problems were formulated as mixed integer programs and solved in the Lagrangian dual domain. Exact optimality under arbitrary number of channels was not established. Instead, by adopting the time-sharing argument @cite_22 in their systems, the proposed solutions were shown to be optimal in the limiting case as the number of channels approaches infinity.
@cite_18 @cite_4 @cite_22 @cite_24 @cite_23 @cite_11
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We consider multi-hop OFDM relaying systems employing either decode-and-forward (DF) or amplify-and-forward (AF) relaying protocols in this paper. We propose adaptive power allocation (PA) algorithms under joint transmit power constraint at source and relays in order to maximize system capacity with channel state information (CSI) known at all nodes. The paring of subcarriers is also discussed. Simulation results show that the proposed adaptive PA algorithms achieve higher system capacity than uniform PA algorithms. If paring techniques are employed, system capacity can be further enhanced. In this paper, a point-to-point orthogonal-frequency- division multiplexing (OFDM) system with a decode-and- forward (DF) relay is considered. The transmission consists of two hops. The source transmits in the first hop, and the relay transmits in the second hop. Each hop occupies one time slot. The relay is half-duplex, and capable of decoding the message on a particular subcarrier in one time slot, and re-encoding and forwarding it on a different subcarrier in the next time slot. Thus, each message is transmitted on a pair of subcarriers in two hops. It is assumed that the destination is capable of combining the signals from the source and the relay pertaining to the same message. The goal is to maximize the weighted sum rate of the system by jointly optimizing subcarrier pairing and power allocation on each subcarrier in each hop. The weighting of the rates is to take into account the fact that different subcarriers may carry signals for different services. Both total and individual power constraints for the source and the relay are investigated. For the situations where the relay does not transmit on some subcarriers because doing so does not improve the weighted sum rate, we further allow the source to transmit new messages on these idle subcarriers. To the best of our knowledge, such a joint optimization inclusive of the destination combining has not been discussed in the literature. The problem is first formulated as a mixed integer programming problem. It is then transformed to a convex optimization problem by continuous relaxation, and solved in the dual domain. Based on the optimization results, algorithms to achieve feasible solutions are also proposed. Simulation results show that the proposed algorithms almost achieve the optimal weighted sum rate and outperform the existing methods in various channel conditions. We consider a two-hop relaying network in which orthogonal frequency division multiplexing (OFDM) is employed for the source-to-destination, the source-to-relay and the relay- to-destination links. Amplify-and-forward (AF) and decode-and- forward (DF) policies are both discussed with or without two-hop diversity, respectively, for the relaying network with a sum-power constraint. An unified approach is used for optimal power allocation in the four different relaying scenarios. First, equivalent channel gains are developed for any given subcarrier pair in each scenario, and then optimal power allocation can be obtained by applying the classic water-filling method. Moreover, we provide the proof to the optimality of sorted subcarrier pairing for AF and DF relaying without diversity, which, combined with optimal power allocation, can offer further performance gain. The combination of a multihop relay system and orthogonal frequency-division multiplexing (OFDM) modulation is a promising way to increase the capacity and coverage area. For the OFDM two-hop relay system with separate power constraints, joint subcarrier matching and power allocation is considered in this paper, which uses the ldquodecode-and-forwardrdquo relay strategy. The aforementioned problem can be formulated as a mixed binary integer programming problem, which is prohibitive when trying to find the global optimum. By separating the subcarrier matching and the power allocation, the optimal scheme, i.e., the optimal joint subcarrier matching and power allocation, is presented in this paper. After that, a suboptimal scheme with less complexity is also proposed, which can also be used to better understand the effects of power allocation. Simulation results show that the capacity of the optimal scheme is almost equivalent to the upper bound of the system capacity, and the capacity of the suboptimal scheme is close to that of the optimal scheme. In addition, simulation results also show that the one-to-one subcarrier matching is almost optimal, although it simplifies the system architecture.