In this paper, we study the degrees of freedom (DoF) of a multiple-input multiple-output (MIMO) multiway relay channel (mRC) with two relays, two clusters and K (K≥3) users per cluster. We consider a clustered full data exchange model, i.e., each user in a cluster sends a multicast (common) message to all other users in the same cluster and desires to acquire all messages from them. The DoF results of the mRC with the single relay have been reported. However, the DoF achievability of the mRC with multiple relays is still an open problem. Furthermore, we consider a more practical scenario where no channel state information at the transmitter (CSIT) is available to each user. We first give a DoF cut-set upper bound of the considered mRC. Then, we propose a distributed interference neutralization and retransmission scheme (DINR) to approach the DoF cut-set upper bound. In the absence of user cooperation, this method focuses on the beamforming matrix design at each relay. By investigating channel state information (CSI) acquisition, we show that the DINR scheme can be performed by distributed processing. Theoretical analyses and numerical simulations show that the DoF cut-set upper bound can be attained by the DINR scheme. It is shown that the DINR scheme can provide significant DoF gain over the conventional time division multiple access (TDMA) scheme. In addition, we show that the DINR scheme is superior to the existing single relay schemes for the considered mRC.

Network coding on the physical-layer has recently been widely discussed as a potentially promising solution to the wireless access problem in a relay network. However, the existing research on physical-layer network coding (PNC), usually assumes that the symbol timing of the nodes is fully synchronized and hardly investigates the unavoidable symbol timing errors. Similar to many telecommunication systems, symbol timing plays a critical role in PNC and precise alignment has to be provided for the encoding. In this work, we propose a novel symbol timing algorithm with a low oversampling factor (samples per symbol) based on the a priori knowledge of the transmitted pulse shape. The proposed algorithm has the dual advantages of the low oversampling rate and high precision. The mean square error (MSE) performance is verified by simulations to be at least one order of magnitude better than that of the conventional optimum phase (OP) algorithm for a signal noise ratio (SNR) greater than 5dB.

Information-theoretic limits of a multi-way relay channel with direct links (MWRC-DL), where multiple users exchange their messages through a relay terminal and direct links, are discussed in this paper. Under the assumption that a restricted encoder is employed at each user, an outer bound on the capacity region is derived first. Then, a decode-and-forward (DF) strategy is proposed and the corresponding rate region is characterized. The explicit outer bound and the achievable rate region for the Gaussian MWRC-DL are also derived. Numerical examples are provided to demonstrate the performance of the proposed DF strategy.

In this letter, we combine minimum-shift keying (MSK) with physical-layer network coding (PNC) to form a new scheme, i.e., MSK-PNC, for two-way relay channels (TWRCs). The signal detection of the MSK-PNC scheme is investigated, and two detection methods are proposed. The first one is orthogonal demodulation and mapping (ODM), and the second one is two-state differential detection (TSDD). The error performance of the proposed MSK-PNC scheme is evaluated through simulations.

The relay channel is the common approach to cooperative communication. Quasi-cyclic low-density parity-check (QC-LDPC) code design for the relay channel is important to cooperative communication. This paper proposes a bilayer QC-LDPC code design scheme for the relay channel. Combined with the bilayer graphical code structure, an improved Chinese remainder theorem (CRT) method, the Biff-CRT method is presented. For the proposed method we introduce a finite field approach. The good performance of the finite field based QC-LDPC code can improve the performance of its corresponding objective QC-LDPC code in the proposed scheme. We construct the FF code and the FA code by the Biff-CRT method. The FF code and the FA code are both named as their two component codes. For the FF code, the two component code are both finite field based QC-LDPC codes. For the FA code, one of the component codes is the finite field based QC-LDPC code and the other is the array code. For the existing CRT method, the shortened array code and the array code are usually used as the component codes to construct the SA code. The exponent matrices of FF code, FA code and SA code are given both for the overall graph and the lower graph. Bit error rate (BER) simulation results indicate that the proposed FF code and FA code are superior to the SA code both at the relay node and the destination node. In addition, the theoretical limit and the BER of the bilayer irregular LDPC code are also given to compare with the BER of the proposed QC-LDPC codes. Moreover, the proposed Biff-CRT method is flexible, easy to implement and effective for constructing the QC-LDPC codes for the relay channel, and it is attractive for being used in the future cooperative communication systems.

This paper describes a simple packet combining scheme with maximum likelihood detection (MLD) for multiple-input multiple-output with orthogonal frequency division multiplexing (MIMO-OFDM) in relay channels to construct reliable wireless links in wireless local area networks (LANs). Our MLD-based approach employs the multiplexed sub-stream signals in different transmit slots. The proposed scheme uses an additional combining process before MLD processing. Moreover, the proposed scheme sets the cyclic shift delay (CSD) operation in the relay terminal. We evaluate the performance of the proposed scheme by the packet error rate (PER) and throughput performance in the decode-and-forward (DF) strategy. First, we show that the proposed scheme offers approximately 4.5dB improvement over the conventional scheme in the received power ratio of the relay terminal to the destination terminal at PER =0.1. Second, the proposed scheme achieves about 1.6 times the throughput of the conventional scheme when the received power ratio of the relay terminal to the destination terminal is 3dB.

This paper proposes an opportunistic feedback and user selection method for a multiuser two-way relay channel (MU-TWRC) in a time-varying environments where a base station (BS) and a selected mobile station (MS), one of K moving MSs, exchange messages during two time slots via an amplify-and-forward relay station. Specifically, under the assumption of perfect channel reciprocity, we analyze the outage probabilities of several channel feedback scenarios, including the proposed scheme. Based on the analysis, the transmission rates are optimized and the optimal user selection method is proposed to maximize the expected sum throughput. The simulation results indicate that, with opportunistic feedback, the performance can be significantly improved compared to that without feedback. Moreover, the performance is nearly identical to that with full feedback, and close to the case of perfect channel state information at BS for low mobility MSs.

The multiple-input-multiple-output (MIMO) Gaussian wireless network with K users and an intermediate relay is investigated. In this network, each user with available local channel state information (CSI) intends to convey a multicast message to all other users while receiving all messages from other users via the relay. This model is termed the MIMO K-way relay channel with distributed CSI. For this channel, the sum capacity is shown as MK/(K-1)log(SNR)+o(SNR) where each user and the relay is equipped with M antennas. Achievability is based on the signal space alignment strategy with a K-1 time slot extension. A most general case is then considered, in which each user intends to recover all messages required within T time slots. We provide an improved scheme called fractional signal space alignment which achieves MK/(K-1) degrees of freedom in the general case and the feasibility condition is also explored.

Physical-layer network coding with binary turbo coding in a two-way relay channel is considered. A two-user turbo decoding scheme is proposed with a simplified sum trellis. For two-user iterative decoding at a relay, the component decoder with its simplified sum trellis decodes the superimposed signal to the arithmetic sum of two users' messages. The simplified sum trellis is obtained by removing one of the states in a pair of mutual symmetrical states from a sum trellis. This removal reduces the decoding complexity to half of that with the sum trellis, and does not degrade decoding performance over AWGN channel since two output sequences from the pair of mutual symmetrical states are the same.

From an information-theoretic point of view, it is well known that the capacity of relay channels comprising of three terminals is much greater than that of two terminal direct channels especially for low SNR region. Previously invented relay coding strategies have not been designed to achieve this relaying gain occurring in the low SNR region. In this paper, we propose a new simple coding strategy for a relay channel with low SNR or, equivalently, for a very noisy relay channel. The multiplicative repetition is utilized to design this simple coding strategy. We claim that the proposed strategy is simple since the destination and the relay can decode with almost the same computational complexity by sharing the same structure of decoder. An appropriate static power allocation which yields the maximum throughput close to the optimal one in low SNRs is also suggested. Under practical constraints such as equal time-sharing etc., the asymptotic performance of this simple strategy is within 0.5 dB from the achievable rate of a relay channel. Furthermore, the performance at few thousand bits enjoys a relaying gain by approximately 1 dB.

A specific physical layer network coding (PNC) scheme is proposed for the two-way relay channel. Unlike the traditional binary PNC that focuses mainly on BPSK modulation, the proposed PNC scheme is tailored for general MPSK modulation. In particular, the product of the two modulated signals is considered as a network-coded symbol. The proposed network coding operation occurs naturally in the inner or outer product of the received signal. A novel PNC-specific detection principle is then developed to estimate the network-coded symbol. Simulations show that the proposed scheme achieves almost optimal performance in terms of end-to-end bit error rate (BER), where the relay node is equipped with multiple antennas.

This letter considers a two-way relaying network where two nodes exchange their information based on the principle of physical layer network coding (PNC). We study the amplify-and-forward (AF) relay filter design with multiple-input multiple-output (MIMO) system. In order to maximize the sum-rate for information exchange, we propose a relay filter for two-way relaying network. Simulation results show that the proposed scheme performs better than the conventional schemes for two-way relay channel.

Relay, which promises to enhance the performance of future communication networks, is one of the most promising techniques for IMT-Advanced systems. In this paper, multiple-input multiple-output (MIMO) relay channels based on outdoor measurements are investigated. We focus on the link between the base station (BS) and the relay station (RS) as well as the link between the RS and the mobile station (MS). First of all, the channels were measured employing a real-time channel sounder in IMT-Advanced frequency band (2.35 GHz with 50 MHz bandwidth). Then, the parameters of multipath components (MPCs) are extracted utilizing space-alternating generalized expectation algorithm. MPC parameters of the two links are statistically analyzed and compared. The polarization and spatial statistics are gotten. The trends of power azimuth spectrum (PAS) and cross-polarization discrimination (XPD) with the separation between the RS and the MS are investigated. Based on the PAS, the propagation mechanisms of line-of-sight and non-line-of-sight scenarios are analyzed. Furthermore, an approximate closed-form expression of channel correlation is derived. The impacts of PAS and XPD on the channel correlation are studied. Finally, some guidelines for the antenna configurations of the BS, the RS and the MS are presented. The results reveal the different characteristics of relay channels and provide the basis for the practical deployment of relay systems.

In this letter, we present a closed-form bound of the average bit error rate (BER) performance for the multi-hop amplify-and-forward (AF) relaying systems with fixed gain in Rayleigh fading channel. The proposed bound is derived from the probability density function (PDF) of the overall multi-hop relay channel under the assumption of asymptotic high signal-to-noise ratio (SNR) at every intermediate relays. When intermediate relays actually operate at finite SNR, the proposed BER bound becomes looser as the SNR of the last hop increases. In order to reflect the effect of all the noise variances of relay links to the BER evaluation, a hop-indexed recursive BER approximation is proposed, in which the proposed bound of BER under asymptotic high SNR is used. The simulation results manifest that the proposed hop-indexed recursive BER approximation can not only guarantee accuracy regardless of the SNR of the last hop but also provide higher accuracy than the previous works.

In this paper, the multi-user multiple-input multiple-output (MU-MIMO) relay channel is investigated, where the source node provides multi-beams to multi-users via a multi-antenna relay node. In this scenario, linear processing matrix at the relay node is designed around block diagonal (BD) scheme to improve the system sum-rate. Compared with the traditional linear processing matrix with zero-forcing (ZF) scheme at the relay node, the proposed matrix based on BD scheme can not only eliminate the multi-user interference to the same extent as the ZF scheme, but also realize optimal power allocation at the relay node. Numerical simulations demonstrate the BD scheme outperforms the ZF scheme and can significantly improve the sum-rate performance.