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Abstract
Physical-layer network coding (PNC) has attracted much attention in the past decade. The intuitive idea behind PNC is to exploit the network coding operation that occurs naturally in superimposed electromagnetic waves. In a two-way relay channel (TWRC), where two users exchange messages with the assistance of a relay, the PNC strategy can harness the interference in the multiple-access transmission phase and double the system throughput. In this thesis, we focus on the design and analysis of PNC schemes in multiple-input multiple-output (MIMO) TWRCs.
It is critical to provide a theoretical analysis of the error performance of PNC in MIMO TWRCs, which is the first part of our research on PNC. We consider a general system model of Rayleigh faded MIMO TWRCs, where the two users may have different numbers of antennas and different signal-to-noise ratios to the relay. Transmit antenna selection is applied at the two users. We derive the closed-forms of the upper and lower bounds on the uplink error probability of PNC based on maximum-likelihood (ML) detection. To provide insight, the upper and lower bounds on the error probabilities for two special cases are derived, i.e., the TWRC with the single-antenna users and multiple-antenna relay (referred to as the SIMO TWRC), and the TWRC with the multiple-antenna users and single-antenna relay (referred to as the MISO TWRC). It is shown that our bounds are tight to Monte-Carlo simulations. Both the theoretical analysis and simulation results demonstrate that the PNC scheme can achieve transmit/receive diversity.
Considering that space-time block coding can achieve transmit diversity when there is no channel side information available at the transmitter, we investigate PNC with the Alamouti scheme in a Rayleigh faded MISO TWRC, where each user has two antennas and the relay has a single antenna. We propose the design criterion for constructing the network codewords which allows each user to recover the other user's messages. Based on ML detection, we find eighteen types of network codewords that satisfy the proposed criterion. We also derive new tight upper bounds on the error probabilities achieved by these network codewords, based on which the PNC scheme with these network codewords is found to achieve full diversity. We then propose new linear decoders to reduce the complexity incurred by ML detection. Through analyzing the error performance, we find that the proposed linear decoders cannot achieve full diversity. To enhance the error performance of the proposed linear decoders, we develop modified linear decoding algorithms, referred to as the log-likelihood ratio (LLR) equal gain combining (EGC), LLR selection combining (SC), network codewords selection (NCS) with EGC, and NCS with SC based decoding algorithms. Numerical results show that the modified decoding algorithms significantly outperform the linear decoders. In addition, we also developed the NCS based ML detection, which slightly outperforms the ML decoder.
While the binary code and binary phase-shift-keying modulation are used in most of research works on PNC, nested lattice codes provide an important solution to the design of PNC schemes with high level modulations. We propose two relay computation schemes for SIMO TWRCs with lattice network coding, referred to as compute-and-forward with receive antenna selection (CF-RAS) and compute-and-forward with receive antenna combining (CF-RAC). For CF-RAS, we propose that the relay selects the antenna with the highest computation rate, which is a straightforward scheme and serves as a benchmark. For CF-RAC, the received signals at all relay antennas are linearly combined with a scaling vector. We derive the optimal scaling vector with respect to the computation rate and present the conditional error probability for CF-RAC. Numerical results show that CF-RAC outperforms CF-RAS significantly and approaches full diversity.