MIMO Relay Networks Research Articles

Null‐space beamforming strategy for secrecy rate balancing of two‐way MIMO relay networks

AbstractHere, the issue of physical layer security in a two‐way multi‐antenna relay network) is studied. In such a network, two multi‐antenna transceivers attempt to exchange their secret messages via a multi‐antenna relay node in the presence of an eavesdropper. Throughout the first hop, two sources send their messages to the relay node, while an eavesdropper tries to overhear these messages. Then, in the second hop, the relay attempts to send its signal in the null‐space direction of relay‐to‐eavesdropper channel to prevent eavesdropping. The main goal is to obtain effective receive and transmit beamforming vectors at transceivers as well as the beamforming matrix at the relay node to address the secrecy rate balancing problem. The underlying problem is not convex in general. To overcome this issue, the original problem is divided into three subproblems. In the first subproblem the beamforming design at the relay is optimized while in the second subproblem the receive beamforming in a closed form solution is obtained. Finally, in the last subproblem the transmit beamforming is solved using the semi‐definite relaxation and Taylor series expansion. Numerical results represent the effectiveness of the proposed method compared to the previous works in the literature.

On performance of short-packet ultra-reliable and low-latency communications NOMA MIMO relay networks

This paper proposes and analyzes the performance of a multi-antenna NOMA relay system over the Nakagami-m fading channel, in which the size of signal packets is finite. Based on the application of the Gaussian–Chebyshev quadrature, Riemann integral and incomplete Gamma function, the exact and asymptotic closed-form expressions of the block error rate (BLER), throughput, goodput of the proposed finite block-length multi-antenna NOMA relay system are derived. Moreover, in order to improve the BLER, throughput, and goodput of the proposed system, maximal-ratio combining and maximal-ratio transmission are applied to receivers and transmitters, respectively. The provided analysis and simulation results indicate that the proposed system meets the requirements of ultra-reliable and low-latency communications (URLLC). Especially, the reliability is higher than 99.99%, i.e., the BLER is less than 10−4. The accuracy of analysis results is verified by simulation results. Furthermore, the number of transmission bits and power allocation coefficients are optimized to maximize the throughput, and goodput and minimize the BLER.

Performance Analysis and Optimization of Multihop MIMO Relay Networks in Short-Packet Communications

This work investigates the multiple-input multiple-output system in the context of the selective decode-and-forward multihop relay network under short-packet communications to facilitate not only ultra-reliability, but also low-latency communications. For the transmit and receive diversity techniques, we analyze the transmit antenna selection (TAS) and maximum-ratio transmission (MRT) schemes at the transmit side, whereas the selection-combining (SC) and maximum-ratio combining (MRC) schemes are leveraged at the receive side. For quasi-static Rayleigh fading channels and the finite-blocklength regime, we derive the approximate closed-form expressions of the end-to-end (e2e) block error rate (BLER) for the TAS/MRC, TAS/SC, and MRT/MRC schemes. The asymptotic performance in the high signal-to-noise ratio regime is derived, from which the comparison among diversity schemes in terms of the diversity order, e2e BLER loss, and SNR gap is provided. Furthermore, based on the asymptotic results, we develop power-allocation, relay-location, and joint simplified optimizations to minimize the asymptotic e2e BLER under the system constraints. The e2e latency and throughputs are also analyzed for the considered schemes. The correctness of our analysis is confirmed via Monte Carlo simulations.

Distributed Learning for MIMO Relay Networks

This paper studies a multi-antenna multi-user and multi-relay network, where the radio frequency (RF) power amplifiers (PA) of the nodes are subject to instantaneous power constraints. To optimize the nonlinear transceivers of the distributed nodes, we introduce a novel perspective of relating a relay network to an artificial neural network (ANN). With this perspective, we propose a distributed learning-based relay beamforming (DLRB) scheme. Based on a set of pilot sequences, the DLRB scheme can optimize the transceivers to minimize the mean squared error (MSE) of the data stream in a distributed manner. It can effectively coordinate the distributed relay nodes to form a virtual array to suppress interferences, even assuming neither the channel state information (CSI) nor information exchange between the relay nodes or between the users. We also present a frame design to support the DRLB so that it can adapt well with time-varying channels. Extensive simulations verify the effectiveness of the proposed scheme.

Impairments-Aware Resource Allocation for FD Massive MIMO Relay Networks: Sum Rate and Delivery-Time Optimization Perspectives

In this paper, we investigate the resource allocation problem for a full-duplex (FD) massive multiple-input-multiple-output (mMIMO) multi-carrier (MC) decode and forward (DF) relay system which serves multiple MC single-antenna half-duplex (HD) nodes. In addition to the prior studies focusing on maximizing the sum-rate and energy efficiency, we focus on minimizing the overall delivery time for a given set of communication tasks to the user terminals. As our system is an FD MC system, we consider the impact of hardware distortions resulting in residual self-interference and inter-carrier leakage. We also consider that only limited channel state information is available. A joint power and sub-carrier allocation problem to maximize the sum-rate of the system is then formulated. Due to the intractable nature of the underlying problem, an iterative solution is proposed, employing the successive inner approximation (SIA) framework, with guaranteed convergence to the point that satisfies the Karush-Kuhn-Tucker (KKT) conditions. For the energy efficiency maximization problem, a two-stage iterative algorithm which follows the SIA and Dinkelbach algorithm is proposed. The operation of an FD mMIMO MC DF relay system is evaluated for different system parameters using numerical simulations. We also show the importance of considering delivery time minimization rather than sum-rate maximization, i.e., maximizing the sum-rate of the system does not necessarily minimize the overall delivery time. Numerical results show the significance of distortion-aware design for such systems and also the significant gain in terms of different objectives such as sum-rate, energy efficiency, and delivery time compared to its HD counterpart.

On the ergodic capacities of decode‐and‐forward MIMO relay network with simultaneous wireless information and power transfer

AbstractIn this article, simultaneous wireless information and power transfer (SWIPT) has been studied for point‐to‐point decode‐and‐forward (DF) based multiple‐input‐multiple‐output (MIMO) relay network with an energy‐constrained relay. This relay is capable of harvesting energy from the wireless signals received from the source terminal. In particular, three different SWIPT schemes, that is, time switching, power splitting, and antenna switching are considered for EH at relay. New closed‐form approximations for the sum ergodic capacity of a DF MIMO relay network have been derived with spatial multiplexing at source, zero‐forcing receivers at relay and destination. Based on the sum capacity approximations, optimal splitting coefficients for aforementioned SWIPT schemes that maximize the sum capacity are presented. Moreover, the impact of system parameters on these optimal coefficients has been studied. In addition to this, first optimization problems for the number of antennas at relay have been formulated and then these problems are transformed into concave form by relaxing constraints to be defined over positive real numbers instead of taking only discrete values. New closed‐form solutions for the optimum number of antennas at relay have been derived. Furthermore, new closed‐form approximations for the ergodic capacities in the presence of an external co‐channel interference are also presented. Numerical results show that approximations for the sum capacity match well with the exact ones obtained through Monte‐Carlo simulations, particularly when the channel hardening effect kicks in, that is, for large degrees of freedom. Finally, the solutions for the optimization problems have also been validated by the numerical examples.

Tensor-Based Joint Channel Estimation and Symbol Detection for AF MIMO Relay Networks

A study on the joint channel and symbol estimation issue is provided for two hop relay networks which employ the amplify-and-forward (AF) relaying approach. The encoding scheme at the source node introduces the time-domain spreading with a time-varying linear constellation precoding. Then, a set of amplifying factors matrices is utilized by the relays to amplify and forward the received data to the destination. The received signal at the destination can be constructed as a fourth-order tensor model, which is referred to as the nested parallel factor (PARAFAC) model. And then, we present a novel Levenberg-Marquardt (LM) algorithm based on this tensor model. The proposed method does not require complex signal processing at the relay, which effectively reduces the burden of relay. As a semi-blind method, which does not require the pilot signal, the proposed receiver can jointly recover the channels and information symbols. Moreover, the proposed semi-blind receiver is robust as it can work in different wireless channel scenarios. Simulations are conducted to demonstrate the efficiency of the proposed semi-blind approach.

Coexistence of Direct and Relayed Transmission Users in Multi-Cell Massive MIMO Systems

In this paper, we investigate the uplink performance of a multi-cell massive MIMO relay network, where the base stations (BSs) and the relay stations (RSs) are equipped with large scale antennas and conventional number of antennas, respectively. In each cell, a portion of users communicate with the BS directly while others are aided by the RSs, which are called direct transmission users (DTUs) and relayed transmission users (RTUs), respectively. The two types of users and RSs of all cells share the same time-frequency resource and thus interfere with each other. After describing the system model, we investigate linear minimum mean-squared error channel estimation for the DTUs and RTUs and derive tractable expressions of channel estimation accuracy. With maximal ratio combining and zero-forcing detections based on the estimated channel state information (CSI), we derive the closed-form lower bound and approximation of the achievable rates for DTUs and RTUs to reveal their mutual impact, including intra- and inter-cell interference and pilot contamination. Then, we propose the power scaling law, which proves to be a simple and energy-efficient way to enable the coexistence of DTUs and RTUs in all cells. Furthermore, an optimal power allocation (OPA) scheme is designed based on the proposed power scaling law to maximize the system sum rate. Numerical results verify the accuracy of our theoretical analysis and the effectiveness of the OPA scheme to guarantee performance improvement and fairness simultaneously.

A Hybrid Optimization Approach for Interference Alignment in Multi-User MIMO Relay Networks Under Different CSI

For the next generation of wireless communication network, a heterogeneous network architecture with macro cells, small cells, and relays offers numerous advantages, such as higher spectrum efficiency, better fairness in resource allocation, and energy efficient usage as well as optimal coverage. However, this approach encounters various network management challenges, including interference mitigation techniques. In this paper, we consider a multi-user half-duplex amplify-and-forward-MIMO relay system, where a macro basis station communicates with edge cell users via relays and each node has multiple antennas. In this context, we propose two interference alignment (IA) schemes, for which a hybrid approach of the problem formulation based on zero-forcing (ZF) and minimum-mean-square-error optimization criteria was developed to deal with interferences in perfect and imperfect channel state information (CSI) cases. In the case of perfect CSI, simulation results show that this approach provides a SNR gain of about 4 dB regarding BER performance in comparison to that achieved by the reference approach, where all filters are determined solely based on ZF criterion. Furthermore, the achieved capacity and effective signal-to-interference-plus-noise ratio at each edge node are improved by around 5 dB. Having CSI errors, the system performance is significantly improved using the robust design IA approach by minimizing the expected value of cost functions.

Multi-User Massive MIMO Relay Networks With Space-Constrained 2-D Antenna Arrays

The detrimental effects of spatially correlated fading are investigated for multi-user massive multiple-input multiple-output relay networks with maximal-ratio combining detectors. To this end, the achievable sum rates are derived in closed form for quantifying the cumulative effects of: 1) imperfect channel state information and 2) spatially correlated fading at the co-located space-constrained 2-D antenna arrays with increasingly many antenna elements for 3-D fading channels. The achievable sum rate for the uncorrelated fading and the corresponding asymptotic sum rate limit are derived. Our results reveal that the correlated fading in 2-D antenna arrays significantly degrades the achievable sum rate even in the finite antenna regime. The sum rate loss gradually increases, and hence, the achievable sum rate becomes infinitesimal in the asymptotic regime of 2-D antenna arrays with finite dimensions over 3-D correlated fading channels.

Spectral and Energy Efficiency of Multi-Pair Massive MIMO Relay Network With Hybrid Processing

We consider a multi-pair massive multiple-input multiple-output relay network, where the relay is equipped with a large number, N, of antennas, but driven by a far smaller number, L, of radio-frequency (RF) chains. We assume that K pairs of users are scheduled for simultaneous transmission, where K satisfies 2K=L. A hybrid signal processing scheme is presented for both uplink and downlink transmissions of the network. Analytical expressions of both spectral efficiency (SE) and energy efficiency (EE) are derived with respect to the RF chain number under imperfect channel estimation. It is revealed that, under the condition N>⌊4L <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> /π⌋, the transmit power of each user and the relay can be, respectively, scaled down by 1/√N and 2K/√N if pilot power scales with signal power, or they can be, respectively, scaled down by 1/N and 2K/N if the pilot power is kept fixed, while maintaining an asymptotically unchanged SE. While regarding EE of the network, the optimal EE is shown to be achieved when P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> = 2K P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> , where P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> and P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> , respectively, refer to the transmit power of the relay and each source terminal. We show that the network EE is a quasi-concave function with respect to the number of RF-chains which, therefore, admits a unique globally optimal choice of the RF-chain number. Numerical simulations are conducted to verify our observations.

Outage analysis of TAS/MRC in dual hop full-duplex MIMO relay networks with co-channel interferences

In this paper, we investigate the outage performance of transmit antenna selection (TAS) and maximal-ratio combining (MRC) in dual hop full-duplex (FD) amplify-and-forward (AF) relay network over Rayleigh fading channels. In the analysis, Rayleigh faded multiple co-channel interferers (CCIs) are also taken into account at the relay. In the network, source and destination are equipped with multiple antennas, and relay is equipped with one receive and one transmit antennas, respectively and source-destination link is not available. While the TAS is applied at the source without considering residual self-interference (RSI) effect, received signals at the destination are combined based on the MRC technique. For the analysis, we consider three approaches at the relay. In the first, we consider the received signal at the relay is corrupted by faded RSI and noise, in the second one, the RSI is considered as non-fading. In the last one, the noise is neglected. In all cases, the relay suffers from multiple Rayleigh faded CCIs. Outage probability (OP) expression related to all the cases is derived and obtained in single integral forms in case of the faded/non-fading RSI and in closed form in case of the noise neglected approach. Moreover, we also find asymptotic OPs and conduct effective diversity order analysis. The analytical results are verified by the Monte Carlo simulations. Results show that TAS decreases error floor at high signal-to-noise ratio (SNR) region and MRC provides diversity gain at low SNR region. In addition, approaches II and III are good approximations to approach I at low and high SNR regions, respectively.

Toward Green and Secure Communications over Massive MIMO Relay Networks: Joint Source and Relay Power Allocation

In this paper, we address the problem of green and secure communications under adverse conditions, i.e., no instantaneous eavesdropper channel state information (CSI) and imperfect instantaneous legitimate CSI. The benefits of a massive multiple-input multiple-output relay are exploited to significantly improve the secrecy energy efficiency (bit per Joule), which is defined as the ratio of secrecy outage capacity and total power consumption. The focus of this paper is on joint power allocation at the source and the relay to maximize the secrecy energy efficiency. Accordingly, two energy-efficient power allocation schemes are proposed under joint and distributed source and relay power constraints. We show that the two schemes asymptotically approach the same saturated energy efficiency. Finally, simulation results validate the advantage of the proposed energy-efficient schemes compared with several baseline schemes.

Relaying Strategies for Wireless-Powered MIMO Relay Networks

This paper investigates relaying schemes in an amplify-and-forward multiple-input multiple-output relay network, where an energy-constrained relay harvests wireless power from the source information flow and can be further aided by an energy flow (EF) in the form of a wireless power transfer at the destination. However, the joint optimization of the relay matrix and the source precoder for the energy-flow-assisted (EFA) and the non-EFA (NEFA) schemes is intractable. The original rate maximization problem is transformed into an equivalent weighted mean square error minimization problem and optimized iteratively, where the global optimum of the nonconvex source precoder subproblem is achieved by semidefinite relaxation and rank reduction. The iterative algorithm finally converges. Then, the simplified EFA and NEFA schemes are proposed based on channel diagonalization, such that the matrices optimizations can be simplified to power optimizations. Closed-form solutions can be achieved. Simulation results reveal that the EFA schemes can outperform the NEFA schemes. Additionally, deploying more antennas at the relay increases the dimension of the signal space at the relay. Exploiting the additional dimension, the EF leakage in the information detecting block can be nearly separated from the information signal, such that the EF leakage can be amplified with a small coefficient.

Statistical Analysis of Multiantenna Relay Systems and Power Allocation Algorithms in a Relay With Partial Channel State Information

The performance of a dual-hop MIMO relay network is studied in this paper. The relay is assumed to have access to the statistical channel state information of its preceding and following channels and it is assumed that fading at the antennas of the relay is correlated. The cumulative density function (cdf) of the received SNR at the destination is first studied and closed-form expressions are derived for the asymptotic cases of the fully-correlated and non-correlated scenarios; moreover, the statistical characteristics of the SNR are further studied and an approximate cdf of the SNR is derived for arbitrary correlation. The cdf is a multipartite function which does not easily lend itself to further mathematical calculations, e.g., rate optimization. However, we use it to propose a simple power allocation algorithm which we call "proportional power allocation". The algorithm is explained in detail for the case of two antennas and three antennas at the relay and the extension of the algorithm to a relay with an arbitrary number of the antennas is discussed. Although the proposed method is not claimed to be optimal, the result is indistinguishable from the benchmark obtained using exhaustive search. The simplicity of the algorithm combined with its precision is indeed attractive from the practical point of view.

Degrees of Freedom in Cached MIMO Relay Networks

It is well known that conventional cooperative relay schemes cannot provide Degrees of Freedom (DoF) gains due to the cut-set bound. In this paper, we propose a physical layer (PHY) caching scheme for relay networks to achieve DoF gains over conventional relay schemes. By properly caching some popular content at the relay station (RS), the proposed PHY caching can opportunistically transform the unfavorable relay channel topology into a more favorable MIMO broadcast channel topology (cache-induced MIMO cooperation opportunity) and enjoy a large DoF gain. Specifically, we first propose a maximum distance separable (MDS) coded PHY caching scheme to significantly improve the MIMO cooperation opportunity induced by PHY caching. Then we propose a global optimal cache content placement solution to maximize the DoF gain. We also propose a low complexity cache content placement algorithm to find a near-optimal solution without explicit knowledge of the popularity of the content files. Finally, we quantify the DoF gain w.r.t. some important system parameters. Simulations show that the proposed scheme can achieve significant throughput gains over various baselines.

Geometric programming applied to multipoint-to-multipoint MIMO relay networks

In this paper, we consider a relaying system which employs a single relay in a wireless network with distributed sources and destinations. Here, all source, destination, and relay nodes are equipped with multiple antennas. For amplify-and-forward relay systems, we confirm the achievable sum rate through a joint multiple source precoders and a single relay filter design. To this end, we propose a new linear processing scheme in terms of maximizing the sum rate performance by applying a blockwise relaying method combined with geometric programming techniques. By allowing the global channel knowledge at the source nodes, we show that this joint design problem is formulated as a standard geometric program, which can guarantees a global optimal value under the modified sum rate criterion. Simulation results show that the proposed blockwise relaying scheme with the joint power allocation method provides substantial sum rate gain compared to the conventional schemes.

Precoding of Space–Time Block Codes for Relay Networks over Correlated MIMO Channels

In this paper, we consider the precoder design at both the source and relay nodes of MIMO relay networks to minimize the symbol error rate (SER) based on the statistical channel state information. First compact SER expressions are derived, then the optimization problem of designing the precoding matrices is formulated. This problem is highly nonlinear and nonconvex. We propose a two-step method by exploiting the correlations of the source-relay and relay-destination links. In the first step the two precoding matrices are proved to be in the eigenvector directions of the transmit correlation matrices. In the second step, the original joint problem is decomposed into two independent sub-problems which can be solved in lower complexity. Simulation results show that the precoding system combined with orthogonal space---time block codes (STBC) outperforms the STBC-only system in terms of SER, especially at low signal-to-noise ratios.

Degrees of Freedom of MIMO Multiway Relay Channel With Clustered Pairwise Exchange

In this paper, we consider a symmetric multiple-input-multiple-output (MIMO) multiway relay channel (mRC) with L clusters and K users per cluster operating in clustered pairwise data exchange. Each user is equipped with M antennas, and the relay is equipped with N antennas. The degrees of freedom (DoF) of the MIMO mRC has recently attracted much research interest. The DoF results under certain configurations of (L,K,M,N) have been reported. However, the DoF capacity of the MIMO mRC with an arbitrary network configuration is, in general, far from being well understood. In this regard, the main contribution of this paper is to propose a systematic signal alignment approach to jointly design the beamforming matrices at the users and the relay. Based on that, an achievable DoF is derived for the MIMO mRC with an arbitrary network configuration of (L,K,M,N). Our analysis revealed that the derived achievable DoF is piecewise linear in M and N alternately. Moreover, we showed that the DoF capacity can be achieved for M/N ∈ [1/LK(K-1) + 1/2, ∞) and M/N ∈ (0, Lq/LK(Lq-1)], where q = 2 ⌈K/2⌉.We further derived the asymptotic DoF as K or L → ∞. The DoF analysis in this paper can provide insights on the practical design of efficient communication mechanisms over multiterminal MIMO relay networks.

Diversity Analysis of Lattice-Reduction Aided Linear Equalizers in Decode and Forward MIMO Relay Networks

Cooperation among distributed multiple-input-multiple-output (MIMO) nodes allows a relay network to improve the performance, enhance the coverage, and increase the capacity by exploiting the available space diversity. In this paper, considering the practical relay detect-and-forward strategy, we propose a lattice-reduction aided linear equalizer at the destination of the MIMO relay network to collect diversity when the cooperating relay adopts a zero forcing equalizer with a well-known adaptive power scaling strategy. We analytically prove that this link adaptive system design is capable of collecting the maximum available receive diversity. The theoretical analysis is corroborated with numerical simulations.