Multi-way Relay Networks Research Articles

Performance Analysis of Massive MIMO Multi-Way Relay Networks With Low-Resolution ADCs

High power consumption and hardware cost have motivated using low-resolution analog-to-digital converters (ADCs) for practical massive multiple-input multiple-output (mMIMO) systems. In this paper, we consider a general mMIMO multi-way relaying system with a multi-level mixed-ADC architecture in which each antenna is connected to an ADC pair with an arbitrary resolution. By leveraging on Bussgang's decomposition theorem and Lloyd-Max algorithm for quantization, tight closed-form approximations are derived for the average achievable rates of zero-forcing (ZF) relaying considering both perfect and imperfect channel state information (CSI). To handle such a challenging setup, we develop a novel method for the achievable rate analysis using distributions of the singular values of Gaussian matrices and properties of Haar matrices. We demonstrate that the average achievable rate has an almost linear relation with the square of the average of quantization coefficients pertaining to the ADC resolution profile. In addition, in the medium to high SNR region, the ADC resolutions have a more significant effect on the rate compared to the number of antennas. Our work also reveals that the performance gap between the perfect and imperfect CSI cases is smaller for lower ADC resolutions, hence imperfect CSI is better tolerated at lower resolutions.

NOMA-Aided Multi-Way Massive MIMO Relaying

For a multi-way relay network (MWRN) with K users, K time slots are needed for full data exchange. Thus, the overall spectral efficiency, due to the 1/K pre-log factor, declines as number of users grows. It has recently been improved to roughly K/2 time slots, but even this improvement does not arrest the decline. Herein, we reduce this task to just two time slots regardless of K. To do this, we exploit the performance gains of non-orthogonal multiple-access (NOMA) and a massive multiple-input multiple-output (MIMO) relay. First, the users transmit their signals to the relay, which uses maximal ratio combining reception. Next, the relay transmits a superposition-coded signal for all users by using maximal ratio transmission. Each user then performs successive interference cancellation (SIC) decoding of data symbols of the other K - 1 user nodes. We use the so-called worst-case Gaussian approximation to derive the overall sum rate and demonstrate significant spectral-efficiency gains and energy-efficiency gains over the existing MWRN counterparts. We also design the relay power allocation matrix to maximize the minimum among the user rates, thus maximizing the user fairness. Furthermore, the effects of imperfect SIC and imperfect channel state information (CSI) on the sum rate are analyzed.

LDPC based Network Coded Cooperation Design for Multi-way Relay Networks

In this paper, we focus on the reliable network coded cooperation design for multi-way relay network (MWRN) with m users and one single relay, in which every user is supposed to exchange data with all the other m - 1 users (full data exchange) by the assistance of the relay. By reformulating the multi-way relaying network in the framework of error control coding, the LDPC based network coded cooperation design issue for MWRNs is presented. On the basis, the requirements, design criteria, and practical design were proposed to demonstrate how to devise reliable network coded cooperation scheme, such that every user is capable of reliably exchanging data with the other m - 1 users. Our analysis shows that the proposed LDPC based network coded cooperation design exhibits powerful error correction capability, especially when compared with the existing schemes. And the overall required number of time slots to accomplish the proposed LDPC based network coded cooperation scheme is 2m.

Energy-efficient power allocation for massive MIMO-enabled multi-way AF relay networks with channel aging

In this paper, we consider a massive MIMO-enabled multi-way amplify-and-forward relay network with channel aging, where multiple users mutually exchange information via an intermediate relay equipped with massive antennas. For this system, we propose an energy-efficient power allocation scheme for the optimization of energy efficiency (EE). Specifically, we firstly derive accurate closed-form expressions of the system sum rate with aged channel state information (CSI) and predicted CSI. Secondly, based on the derived analytical results, a unified power allocation optimization problem with aged/predicted CSI is formulated for maximizing the system EE. To solve this challenging problem, the successive convex approximation technique is invoked to transform the original optimization problem into a tractable concave fractional programming problem. Then, Dinkelbach’s algorithm and Lagrangian dual method are adopted to find the optimal solution. In addition, to strike a balance between the computational complexity and the optimality, the EE maximization problem using the equal power allocation scheme is solved by extreme value theorem, leading to a closed-form optimal solution. Numerical results demonstrate the accuracy of our analytical results and the effectiveness of the proposed algorithms. Moreover, the impact of several important system parameters on the system performance achieved by the proposed algorithms is also illustrated.

A closed-form sum-rate lower bound for amplify-and-forward multi-way relay networks

In this letter, we investigate the sum-rate performance of the multi-way relay network (MWRN) with amplify-and-forward (AF) relaying, where multiple users exchange information with the help of a relay node. We consider a full exchange scenario where each user has to decode messages form all the other users. We analyze the sum-rate lower and upper bounds of the AF MWRN, and derive a closed-form expression for the average sum-rate low bound when the number of users is sufficient large. Numerical results show that the derived bound is tight.

English

English

Joint Relay Beamforming and Receiver Processing for Multi-Way Multi-Antenna Relay Networks

We consider a multi-way relay network with multiple users exchanging information with each other via a multi-antenna relay. The multi-way relaying strategy consists of one multiple access phase and multiple broadcast phases. We jointly design relay beamforming matrices and users’ linear processing receivers in the broadcast phases to maximize the minimum signal-to-interference-and-noise ratio (SINR) under the relay power budget. For the non-convex joint optimization problem, we propose to solve it by iteratively optimizing the relay beam matrices and receiver processing matrices in two sub-problems. For the receiver processing, both maximum-ratio-combining (MRC) receiver and zero-forcing (ZF) receiver are designed. We show that our iterative approach with the MRC receiver leads to a local maximum for the original joint optimization problem, while the ZF receiver has the computational advantage with a lower complexity. To further improve the performance, we design the successive interference cancellation at each user’s receiver based on the SINR criterion to sequentially decode symbols from other users. Simulation shows that our proposed algorithm for joint design provides substantial improvement in the sum rate than the existing methods that use the sum rate as the design objective. Finally, we investigate the performance of our proposed algorithm under partial channel state informations (CSIs). We show in simulation that using quantized CSIs at each receiver only incurs a small performance loss for the typical range of relay channel quality.

Generalized Multiway Relay Network: Proposition and Effective Rate Analysis

A multiway relay network (mRN), which is widely employed in the literature, is extended to represent a larger number of practical scenarios, such as a vehicular ad hoc network (VANET). For the proposed system, generalized multiway relay network (g-mRN), three transmission strategies are presented and analyzed in terms of effective rate, for different numbers of users. Assuming that the average signal-to-noise ratio (SNR) is known to the transmitters, the maximum effective rate is obtained through the optimal choice of the message rates. We also derive the effective rate for fixed message rates. Numerical results show that the best strategy under the optimal message rates is the one in which all users transmit simultaneously in the multiple access phase. But when considering fixed message rates, the best transmission strategy depends upon the SNR. These results are important in that they can be used as guidelines for selecting the right strategy and message rates depending on the situation.

Partial Zero-Forcing for Multi-Way Relay Networks

The ever increasing demands for mobile network access have resulted in a significant increase in bandwidth usage. By improving the system spectral efficiency, multi-way relay networks (MWRNs) provide promising approaches to address this challenge. In this paper, we propose a novel linear beamforming design, namely partial zero-forcing (PZF), for MWRNs with a multiple-input-multiple-output (MIMO) relay. Compared to zero-forcing (ZF), PZF relaxes the constraints on the relay beamforming matrix such that only partial user-interference, instead of all, is canceled at the relay. The users eliminate the remaining interferences through self-interference and successive interference cancellation. A sum-rate maximization problem is formulated and solved to exploit the extra degrees-of-freedom resulted from PZF. Simulation results show that the proposed PZF relay beamforming design achieves significantly higher network sum-rates than the existing linear beamforming designs.

Distributed Energy Beamforming and Information Transfer for Multiway Relay Networks

In this paper, we propose a distributed energy beamforming and information transfer (DEBIT) scheme for realizing simultaneous wireless information and power transfer (SWIPT) in multiway relay networks (MWRNs), where multiple users exchange messages with the help of an energy-constrained relay node. We investigate the sum-rate maximization as well as the harvested power maximization problems for the proposed scheme. The resultant sum-rate maximization problem is non-convex and the global optimal solution can be obtained through a 3-D search in combination with convex optimization. To reduce the computation complexity, a suboptimal DEBIT scheme is also proposed, for which the optimization problem becomes linear programming. The achievable sum-rate performance is analyzed and a closed-form lower bound is derived for the MWRN with a large number of users. Furthermore, we consider the harvested-power maximization problem under a target sum-rate constraint and derive a lower bound of the average harvested power for MWRNs with a large number of users. Numerical results show that the DEBIT scheme significantly outperforms the conventional SWIPT and the derived lower bounds are tight.

On the Degrees of Freedom of the Symmetric Multi-Relay MIMO Y Channel

In this paper, we study the degrees of freedom (DoF) of the symmetric multi-relay multiple-input multiple-output (MIMO) Y channel, where three user nodes, each with M antennas, communicate via K geographically separated relay nodes, each with N antennas. For this model, we establish a general DoF achievability framework based on linear precoding and post-processing methods. The framework poses a nonlinear problem with respect to user precoders and post-processors, as well as relay precoders. To solve this problem, we adopt an uplink-downlink asymmetric strategy, where the user precoders are designed for signal alignment and the user post-processors are used for interference neutralization. With the user precoder and post-processor designs fixed as such, the original problem then reduces to a problem of relay precoder design. To address the solvability of the system, we propose a general method for solving matrix equations. This method is also useful to the DoF analysis of many other multiway relay networks. Together with the techniques of antenna disablement and symbol extension, an achievable DoF of the symmetric multi-relay MIMO Y channel is derived for an arbitrary setup of (K, M, N). We show that, for K >= 2, the optimal DoF is achieved for M/N in [0, max{sqrt(3K)/3,1}) and [(3K+sqrt(9K^2-12K))/6,infinity). We also show that the uplink-downlink asymmetric design proposed in this paper considerably outperforms the conventional approach based on uplink-downlink symmetry.

Multicell Multiway Massive MIMO Relay Networks

A generic performance analysis framework is developed for multicell amplify-and-forward (AF) multiway massive multiple-input multiple-output (MIMO) relay networks. The detrimental effects of imperfect channel state information (CSI), including channel estimation errors and outdated/delayed CSI for multicell massive MIMO AF multiway relay networks, are investigated. Thereby, for the first time in the open literature in the context of massive MIMO relay networks, the cumulative detrimental effects of pilot contamination and channel aging caused by the reuse of nonorthogonal pilot sequences and relative movements of user nodes, respectively, are quantified. The asymptotic signal-to-interference-plus-noise ratio and the achievable spectral efficiency expressions corresponding to three transmit power scaling laws at the user nodes and relay are derived whenever the number of antennas at the relay is substantially higher than the number of user nodes. The asymptotic performance analysis is generic in the sense that the individual effects of the practical transmission impairments, such as cochannel interference, pilot contamination, and channel aging, can be decomposed. The average symbol error rate (SER) and asymptotic SER are derived in closed form. The optimal pilot sequence length, which maximizes the achievable spectral efficiency, is derived in closed form. Our asymptotic analysis for the perfect CSI case reveals that the detrimental effects of cochannel interference can be asymptotically mitigated. Nevertheless, the performance degradation caused due to the cumulative effects of pilot contamination and channel aging cannot be mitigated, even in the limit of infinitely many relay antennas.

Error Performance Analysis of a Clustered Multiway Relay Network

In this paper, we propose a new clustered structure for a multiway relay network (MWRN) with $G$ clusters, $N$ users per cluster, one intracluster relay per cluster, and a single intercluster relay. The proposed structure allows private information exchange among users within a certain cluster through the corresponding intracluster relay and only public information exchange among users in different clusters through the intercluster relay. In this paper, we quantify the dominating error events in the proposed clustered MWRN and derive the expressions for the probability of these error events. Then, we use these expressions to derive the average bit error rate (BER) of a clustered MWRN. It is shown that clustering in an MWRN improves the error performance by reducing the number of dominating error events and, in effect, reducing error propagation, compared with the nonclustered counterpart. The analysis proves that the average BER of a clustered MWRN is minimized when the number of clusters and the number of users per cluster are chosen to be the closest possible factors of the total number of users, i.e., $L=GN$ . Finally, numerical simulation results are provided to verify the validity of the analysis.

SER analysis of multi-way relay networks with M-QAM modulation in the presence of imperfect channel estimation

Multi-way relay networks (MWRNs) allow multiple users to exchange information with each other through a single relay terminal. MWRNs are often incorporated with capacity achieving lattice codes to enable the benefits of high-rate signal constellations to be extracted. In this paper, we analytically characterize the symbol error rate (SER) performance of a functional de- code and forward (FDF) MWRN in the presence of channel estimation errors. Considering M-ary quadrature amplitude modulation (QAM) with square constellations as an important special case of lattice codes, we obtain asymptotic expressions for the average SER for a user in FDF MWRN. The accuracy of the analysis at high signal-to-noise ratio is validated by comparison with the simulation results. The analysis shows that when a user decodes other users with better channel conditions than itself, the decoding user experiences better error performance. The analytical results allow system designers to accurately assess the non-trivial impact of channel estimation errors and the users� channel conditions on the SER performance of a FDF MWRN withM-QAM modulation.

Achievable rate and error performance of an amplify and forward multi‐way relay network in the presence of imperfect channel estimation

In this paper, we investigate the impact of channel estimation error on the achievable common rate and error performance of amplify and forward (AF) multi-way relay networks (MWRNs). Assuming lattice codes with large dimensions, we provide the analytical expressions for the end-to-end SNR at the users and obtain upper bounds on the achievable common rate for an AF MWRN. Moreover, considering binary phase shift keying (BPSK) modulation as the simplest case of lattice codes, we obtain the average bit error rate (BER) for a user in an AF MWRN. The analysis shows that the average BER is a linearly increasing function and the achievable common rate is a linearly decreasing function of the channel estimation error. On the other hand, the average BER decreases and the achievable common rate increases with increasing correlation between the true and the estimated channel. Also, we observe that the AF protocol is robust against increasing number of users in terms of error performance. We show that when the decoding user has better channel conditions compared to other users, AF relaying gives a better error performance and common rate. Finally, simulation results are provided to verify the validity of our analysis.

Massive Multiway Relay Networks Applying Coded Random Access

This paper considers full data exchange for massive uncoordinated multiway relay networks (mu-mRN) applying coded random access for flexible topology changes and capable of serving massive number of users. We aim to maximize the normalized throughput of the mu-mRN using the multiuser detection (MUD) technique with MUD capability of $K > 1$ . Specifically, our goal is multiple times improvement, i.e., ten times improvement, from the maximum normalized throughput of the mu-mRN applying slotted ALOHA (SA). First, we present a network capacity bound of the mu-mRN with general $K$ . Then, we optimize many degree distributions for the MUD-based mu-mRN. However, as $K$ increases, the distributions are no longer optimal to achieve the network capacity bound. We propose doubly irregular coded SA (dir-CSA) to solve the problem. Asymptotically, the mu-mRN applying dir-CSA with $K = 4$ can achieve the ten times throughput improvement. However, for finite number of time slots, we propose to exploit side information (SI) from neighboring users to improve the normalized throughput of the mu-mRN. The results show that the mu-mRN applying dir-CSA with SI and having optimal physical encoding can achieve ten times throughput improvement, compared with the conventional SA scheme.

Simple and efficient novel multi-way relay network coding scheme

Simple and efficient novel multi-way relay network coding scheme

A novel user pairing scheme for functional decode-and-forward multi-way relay network

In this paper, we consider a functional decode and forward (FDF) multi-way relay network (MWRN) where a common user facilitates each user in the network to obtain messages from all other users. We propose a novel user pairing scheme, which is based on the principle of selecting a common user with the best average channel gain. This allows the user with the best channel conditions to contribute to the overall system performance. Assuming lattice code based transmissions, we derive upper bounds on the average common rate and the average sum rate with the proposed pairing scheme. Considering M-ary quadrature amplitude modulation with square constellation as a special case of lattice code transmission, we derive asymptotic average symbol error rate (SER) of the MWRN. We show that in terms of the achievable rates, the proposed pairing scheme outperforms the existing pairing schemes under a wide range of channel scenarios. The proposed pairing scheme also has lower average SER compared to existing schemes. We show that overall, the MWRN performance with the proposed pairing scheme is more robust, compared to existing pairing schemes, especially under worst case channel conditions when majority of users have poor average channel gains.

Optimal User Pairing to Improve the Sum Rate of a Pairwise AF Multi-Way Relay Network

In this letter, we propose a novel user pairing scheme for improving the average sum rate in an amplify and forward (AF) multi-way relay network (MWRN). We consider generalized lattice code based transmissions and derive upper bounds on the common rate and sum rate with the proposed scheme. We prove that pairing each user with the maximum average channel gain user is the optimal pairing scheme for an AF MWRN in terms of the average sum rate. Our results show that improving the overall channel conditions of the users results in greater benefits in terms of the average common rate and sum rate for the proposed pairing scheme, compared to the existing scheme.

The Solution for Cooperative Beamforming Design in MIMO Multi-way Relay Networks

In this paper, we study the design of network coding for the generalized transmit scheme in multiple input multiple output Y channel, where K users wish to exchange specified and shared information with each other within two slots. Signal space alignment at each user and the relay is carefully constructed to ensure that the signals from the same user pair are grouped together. The cross-pair interference can be canceled during both multiple accessing channel phase and broadcasting channel phase. The proposed signal processing scheme achieves the degrees of η(K)=K2 freedom of with fewer user antennas.