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.
These works sparked interests for more research in this area. In the absence of the direct source-destination link, for the practical case of noisy-relay, by using the property of L-superadditivity of the rate function, the authors of @cite_20 proved that the sorted-SNR CP still remains optimal for sum-rate maximization in dual-hop AF relaying OFDM system. Subsequently, it was further proved in @cite_5 , through a different approach, that the sorted-SNR CP scheme is optimal for both AF and DF relaying in the same setup. When the direct source-destination link is available, @cite_3 presented two suboptimal CP schemes. For the same setup, a low complexity optimal CP scheme was later established in @cite_10 for dual-hop AF relaying, and the effect of direct path on the optimal pairing was characterized. In addition, it was shown in @cite_10 that, under certain conditions on relay power amplification, among all possible linear processing at the relay, the channel pairing is optimal.
@cite_5 @cite_3 @cite_10 @cite_20
2113418259 1987847589 1713504836 2098255692
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. In this paper, a two-hop amplify-and-forward cooperative diversity system using OFDM modulation was considered. We proposed an associated waterfllling power allocation scheme under separate power constraints at source and relay, which allocated source and relay power in an associated fashion. The scheme first allocated power to subcarriers uniformly, then gave an approximate equivalent channel gain model, and last employed the classic waterfilling algorithm to optimize the power allocation at relay and source, respectively. Moreover, we investigated the subcarrier pairing problem and presented a modified sorted subcarrier pairing algorithm, which considered the effect of source-destination link as well as source-relay link. The simulation results show that the associated waterfilling power allocation scheme and the modified sorted subcarrier pairing algorithm both could achieve higher average rate alone, and that the combination of them could improve the performance further. In this paper, we consider the amplified-and-forward relaying in an OFDM system with unitary linear processing at the relay. We proposed a general analytical framework to find the unitary linear processing matrix that maximizes the system achievable rate. We show that the optimal processing matrix is a permutation matrix, which implies that a subcarrier pairing strategy is optimal. We further derived the optimal subcarrier pairing schemes for scenarios with and without the direct source-destination path for diversity. Simulation results are presented to demonstrate the achievable gain of optimal subcarrier pairing compared with non-optimal linear processing and non-pairing. The paper studies subchannel assignment in a two-hop OFDM relay system in which the transmitting nodes (source and relay) have access to channel information and interference-related information. We show that with L-superadditive relay (performance) functions a simple ranking of subchannels leads to the optimal assignment with a very low computational complexity. Numerical results quantify the benefit of subchannel assignment in a frequency-selective channel.