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.
For an OFDM system as a typical example of multi-channel systems, the concept of CP was first introduced independently in @cite_21 and @cite_0 for a dual-hop AF relaying system where heuristic algorithms for pairing based on the order of channel quality were proposed. For relaying without the direct source-destination link available, @cite_21 used integer programming to find the optimal pairing that maximizes the sum SNR. From a system-design perspective, the sorted-SNR CP scheme was proposed in @cite_0 and was shown optimal for the noise-free relaying case, under the assumption of uniform power allocation.
@cite_0 @cite_21
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Amplify-and-Forward (AF) is a simple but effective relaying concept for multihop networks that combines transparency regarding modulation format and coding scheme with ease of implementation. Conventional AF, however, does not take into account the transfer function of the first and the second hop channels. For OFDM based systems, this appears to be sub-optimum. In this paper an AF relaying scheme is proposed that adapts to the transfer functions of both channels. The relay estimates the transfer functions and rearranges the subcarriers in each OFDM packet such that an optimum coupling between subcarriers of the first and the second hop channels occurs. Additionally, a signaling scheme is developed that allows for an efficient transfer of the necessary information. Simulations show that the proposed relaying scheme achieves significant SNR gains over conventional OFDM relaying. The paper considers a source-relay-destination link in which the relay node is allowed to reassign the input subchannels to different output subchannels. In particular, we consider a channel-aware relay node and compute the subchannel reassignment that optimizes a selected performance criterion. The numerical results suggest that optimized subchannel reassignment is particularly beneficial in frequency-selective channels and in channels where interference information is available at transmitter.