Performance Analysis of Adaptive Physical Layer Network Coding for Wireless Two-way Relaying

The analysis of modulation schemes for the physical layer network-coded two way relaying scenario is presented which employs two phases: Multiple access (MA) phase and Broadcast (BC) phase. It was shown by Koike-Akino et. al. that adaptively changing the network coding map used at the relay according to the channel conditions greatly reduces the impact of multiple access interference which occurs at the relay during the MA phase. Depending on the signal set used at the end nodes, deep fades occur for a finite number of channel fade states referred as the singular fade states. The singular fade states fall into the following two classes: The ones which are caused due to channel outage and whose harmful effect cannot be mitigated by adaptive network coding are referred as the \textit{non-removable singular fade states}. The ones which occur due to the choice of the signal set and whose harmful effects can be removed by a proper choice of the adaptive network coding map are referred as the \textit{removable} singular fade states. In this paper, we derive an upper bound on the average end-to-end Symbol Error Rate (SER), with and without adaptive network coding at the relay, for a Rician fading scenario. It is shown that without adaptive network coding, at high Signal to Noise Ratio (SNR), the contribution to the end-to-end SER comes from the following error events which fall as $\text{SNR}^{-1}$: the error events associated with the removable singular fade states, the error events associated with the non-removable singular fade states and the error event during the BC phase. In contrast, for the adaptive network coding scheme, the error events associated with the removable singular fade states contributing to the average end-to-end SER fall as $\text{SNR}^{-2}$ and as a result the adaptive network coding scheme provides a coding gain over the case when adaptive network coding is not used.Comment: 10 pages, 5 figure

Transmit Antenna Selection for Physical-Layer Network Coding Based on Euclidean Distance

Physical-layer network coding (PNC) is now well-known as a potential candidate for delay-sensitive and spectrally efficient communication applications, especially in two-way relay channels (TWRCs). In this paper, we present the error performance analysis of a multiple-input single-output (MISO) fixed network coding (FNC) system with two different transmit antenna selection (TAS) schemes. For the first scheme, where the antenna selection is performed based on the strongest channel, we derive a tight closed-form upper bound on the average symbol error rate (SER) with $M$-ary modulation and show that the system achieves a diversity order of 1 for $M > 2$. Next, we propose a Euclidean distance (ED) based antenna selection scheme which outperforms the first scheme in terms of error performance and is shown to achieve a diversity order lower bounded by the minimum of the number of antennas at the two users.Comment: 15 pages, 4 figures, Globecom 2017 (Wireless Communications Symposium

Space-Time Coded Spatial Modulated Physical Layer Network Coding for Two-Way Relaying

Using the spatial modulation approach, where only one transmit antenna is active at a time, we propose two transmission schemes for two-way relay channel using physical layer network coding with space time coding using Coordinate Interleaved Orthogonal Designs (CIOD's). It is shown that using two uncorrelated transmit antennas at the nodes, but using only one RF transmit chain and space-time coding across these antennas can give a better performance without using any extra resources and without increasing the hardware implementation cost and complexity. In the first transmission scheme, two antennas are used only at the relay, Adaptive Network Coding (ANC) is employed at the relay and the relay transmits a CIOD Space Time Block Code (STBC). This gives a better performance compared to an existing ANC scheme for two-way relay channel which uses one antenna each at all the three nodes. It is shown that for this scheme at high SNR the average end-to-end symbol error probability (SEP) is upper bounded by twice the SEP of a point-to-point fading channel. In the second transmission scheme, two transmit antennas are used at all the three nodes, CIOD STBC's are transmitted in multiple access and broadcast phases. This scheme provides a diversity order of two for the average end-to-end SEP with an increased decoding complexity of $\mathcal{O}(M^3)$ for an arbitrary signal set and $\mathcal{O}(M^2\sqrt{M})$ for square QAM signal set.Comment: 9 pages, 7 figure

User-Antenna Selection for Physical-Layer Network Coding based on Euclidean Distance

In this paper, we present the error performance analysis of a multiple-input multiple-output (MIMO) physical-layer network coding (PNC) system with two different user-antenna selection (AS) schemes in asymmetric channel conditions. For the first antenna selection scheme (AS1), where the user-antenna is selected in order to maximize the overall channel gain between the user and the relay, we give an explicit analytical proof that for binary modulations, the system achieves full diversity order of $min(N_A , N_B ) \times N_R$ in the multiple-access (MA) phase, where $N_A$, $N_B$ and $N_R$ denote the number of antennas at user $A$, user $B$ and relay $R$ respectively. We present a detailed investigation of the diversity order for the MIMO-PNC system with AS1 in the MA phase for any modulation order. A tight closed-form upper bound on the average SER is also derived for the special case when $N_R = 1$, which is valid for any modulation order. We show that in this case the system fails to achieve transmit diversity in the MA phase, as the system diversity order drops to $1$ irrespective of the number of transmit antennas at the user nodes. Additionally, we propose a Euclidean distance (ED) based user-antenna selection scheme (AS2) which outperforms the first scheme in terms of error performance. Moreover, by deriving upper and lower bounds on the diversity order for the MIMO-PNC system with AS2, we show that this system enjoys both transmit and receive diversity, achieving full diversity order of $\min(N_A, N_B) \times N_R$ in the MA phase for any modulation order. Monte Carlo simulations are provided which confirm the correctness of the derived analytical results.Comment: IEEE Transactions on Communications. arXiv admin note: text overlap with arXiv:1709.0445

Low-complexity energy-efficient resource allocation for delay-tolerant two-way orthogonal frequency-division multiplexing relays

Energy-efficient wireless communication is important for wireless devices with a limited battery life and cannot be recharged. In this study, a bit allocation algorithm to minimise the total energy consumption for transmitting a bit successfully is proposed for a two-way orthogonal frequency-division multiplexing relay system, whilst considering the constraints of quality-of-service and total transmit power. Unlike existing bit allocation schemes, which maximise the energy efficiency (EE) by measuring ‘bits-per-Joule’ with fixed bidirectional total bit rates constraint and no power limitation, their scheme adapts the bidirectional total bit rates and their allocation on each subcarrier with a total transmit power constraint. To do so, they propose an idea to decompose the optimisation problem. The problem is solved in two general steps. The first step allocates the bit rates on each subcarrier when the total bit rate of each user is fixed. In the second step, the Lagrangian multipliers are used as the optimisation variants, and the dimension of the variant optimisation is reduced from 2N to 2, where N is the number of subcarriers. They also prove that the optimal point is on the bounds of the feasible region, thus the optimal solution could be searched through the bounds

Two–Way Relaying Communications with OFDM and BICM/BICM-ID

Relay-aided communication methods have gained strong interests in academic community and been applied in various wireless communication scenarios. Among different techniques in relay-aided communication system, two-way relaying communication (TWRC) achieves the highest spectral efficiency due to its bi-directional transmission capability. Nevertheless, different from the conventional point-to-point communication system, TWRC suffers from detection quality degradation caused by the multiple-access interference (MAI). In addition, because of the propagation characteristics of wireless channels, fading and multipath dispersion also contribute strongly to detection errors. Therefore, this thesis is mainly concerned with designing transmission and detection schemes to provide good detection quality of TWRC while taking into account the negative impacts of fading, multipath dispersion and multiple-access interference. First, a TWRC system operating over multipath fading channels is considered and orthogonal frequency-division multiplexing (OFDM) is adopted to handle the inter-symbol interference (ISI) caused by the multipath dispersion. In particular, adaptive physical-layer network coding (PNC) is employed to address the MAI issue. By analyzing the detection error probability, various adaptive PNC schemes are discussed for using with OFDM and the scheme achieving the best trade-off among performance, overhead and complexity is suggested. In the second part of the thesis, the design of distributed precoding in TWRC using OFDM under multipath fading channels is studied. The objective is to design a distributed precoding scheme which can alleviate MAI and achieve multipath diversity to combat fading. Specifically, three types of errors are introduced when analyzing the error probability in the multiple access (MA) phase. Through analysis and simulation, the scheme that performs precoding in both time and frequency domains is demonstrated to achieve the maximum diversity gains under all types of errors. Finally, the last part of the thesis examines a communication system incorporating forward error correction (FEC) codes. Specifically, bit-interleaved code modulation (BICM) without and with iterative decoding (BICM-ID) are investigated in a TWRC system. Distributed linear constellation precoding (DLCP) is applied to handle MAI and the design of DLCP in a TWRC system using BICM/BICM-ID is discussed. Taking into account the multiple access channel from the terminal nodes to the relay node, decoding based on the quaternary code representation is introduced. Several error probability bounds are derived to aid in the design of DLCP. Based on these bounds, optimal parameters of DLCP are obtained through analysis and computer search. It is also found that, by combining XORbased network coding with successful iterative decoding, the MAI is eliminated and thus DLCP is not required in a BICM-ID system