Multiple-input Multiple-output Relay Networks Research Articles

MIMO Relay Networks: Scheduling and Outage Probability

We study a dual-hop multiple-input multiple-output (MIMO) relay network where the traffic source uses a relay node, selected among several possible ones, to serve multiple users. Considering that the nodes deployment can be described by Poisson point processes in a sector area, we derive the distribution of the signal-to-interference-plus-noise ratio over the two communication hops. Then, assuming that the user to be served is selected according to opportunistic, proportional fair, or selective multiuser diversity scheduling, we investigate the system outage probability, and derive a closed-form tight lower bound for it. Our analysis provides useful guidelines on the system design of MIMO relay networks. Unlike existing works, our analysis accounts for the joint impact of various multiuser scheduling schemes and nodes placement.

Asymptotic Eigenvalue Density for the Quotient Ensemble of Wishart Matrices

The matrix model involving the quotient of two Wishart matrices appears naturally in the investigation of multiple-input multiple-output (MIMO) multiple-access and relay channels. The available exact result for the eigenvalue density for this matrix model involves the determinant of a matrix whose dimension is related to the number of antennas in the channel. Consequently, the exact result becomes impractical while dealing with the case of large number of antennas. In this letter, we derive a novel expression for the asymptotic eigenvalue density of the quotient matrix model. This result is analogous to the Marcenko–Pastur density and can be conveniently applied to deal with the case of large matrix dimensions. Remarkably, satisfactorily results are obtained even for small matrix dimensions. As an application of our asymptotic result, we obtain an upper bound for the ergodic capacity in a full-duplex multi-hop decode-and-forward MIMO relay network.

Precoding Design for Correlated MIMO-AF Relay Networks With Statistical Channel State Information

An iterative precoding design of a two-hop amplify-and-forward (AF) multiple-input multiple-output relay network with one source, multiple relays, and one destination is presented. To provide a solution for general scenarios, the source-to-destination direct link and double correlated Kronecker Rician fading channels are considered. Statistical channel state information is used for the average capacity formulation for the sake of its robustness and infrequent update. The source and relay precoders are optimized to maximize a closed-form upper bound of the average capacity giving a suboptimal design. The non-convex design problem is divided into three sub-problems: source precoder, relay beamforming, and relay power allocation (PA). For optimizing the source precoder subject to multiple power constraints, rather than using computationally expensive penalty type algorithms, an efficient design procedure as a type of water-filling with multiple water levels is developed. Its negative PA is handled by a simple method of determining the eigen-modes of positive power. Using the Riemannian steepest descent method and a newly proposed power adaptation to optimize the relay beamforming and relay PA, respectively, the constrained optimization problems become unconstrained. Simulations show that the developed design procedure with trivial initialization provides nearly global optimum performance with fast convergence and efficient computation. The developed methods for the source precoder and relay PA outperform upon the augmented Lagrangian method with respect to convergence and computing time. Furthermore, the generality of the proposed scheme makes the design procedure applicable to AF relay networks with different simplified Kronecker channel models and with/without the direct link.

Pilot allocation approaches for channel estimation in MIMO relay networks

Distributed-compressed sensing (DCS)-based channel estimation of multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing for relay communication is considered in this study. Specifically, the pilot allocation is addressed to optimise the channel estimation performance. All the existing works on DCS-based channel estimation pilot placement discussed on the mean square error (MSE) of the estimation probabilistically based on the mutual coherence. On the contrary, the authors try to address the MSE of the estimation directly and optimise the MSE directly and design a pilot pattern to optimise the performance of the estimation. By taking into account the optimisation approach, two combinatorial stochastic algorithms have been presented. These two algorithms utilise cross entropy approach in sequential and parallel form. Simulation results represent that the DCS-based MIMO relay channel estimation using optimised pilot placements will increase the performance from 3 to 12 dB as compared with the conventional least squares (LS) method. Furthermore, parallelism has demonstrated the performance gain. Moreover, the DCS-based MIMO relay channel estimation shows 35 % improvement in spectrum efficiency under the same bit error rate performance over the traditional LS-based channel estimation approach, respectively.

Distributed Compressed Sensing-Based Channel Estimation and Pilot Allocation for MIMO Relay Networks

Distributed compressed sensing (DCS)-based channel estimation of multiple-input–multiple-output (MIMO) orthogonal frequency-division multiplexing for relay communication is considered in this paper. Specifically, the pilot allocation is addressed to optimize the channel estimation performance. Pilot placement in all the existing works based on Compressed Sensing (CS), address the mean square error (MSE) probabilistically via mutual coherence. On the contrary, we try to address the MSE of the estimate directly and optimize the MSE directly and design a pilot pattern to maximize the performance of the estimation. By taking into account the optimization approach, a combinatorial stochastic algorithm has been presented. Simulation results represent that the DCS-based MIMO relay channel estimation using optimized pilot placements will increase the performance from 3 to 10 dB as compared with the conventional least squares (LS) method. Moreover, the DCS-based MIMO relay channel estimation shows 2.3% and 45% improvement in spectrum efficiency under the same bit error rate performance over the compressed sensing (CS)-based channel estimation and traditional LS-based channel estimation approach, respectively.

Beamforming Design for Multi-Hop Amplify-and-Forward MIMO Relay

This paper considers a multi-hop amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay network. In the multi-hop AF MIMO relay network, the performance deteriorates as the number of hops increases because the effect of noise is enhanced. To suppress the effect of noise, this paper proposes the two beamforming schemes using channel state information (CSI) for the transmit beamforming at the source, relay beamforming at the relay, and receive beamforming at the destination. The forward-and-backward-CSI based beamforming and all-CSI based beamforming schemes are designed at each node based on the minimum mean square error criterion under the source and relay transmit power constraint. The forward-and-backward-CSI based beamforming scheme is designed by using the two matrices, forward channel, and backward channel. The two matrices are designed by using the beamforming matrices and channels from the previous nodes. Unlike the forward-and-backward-CSI based beamforming scheme, the all-CSI based beamforming scheme is designed by using all channels and an iterative algorithm. In terms of the complexity, the forward-and-backward-CSI based beamforming scheme is superior to the all-CSI based beamforming scheme. However, the all-CSI based beamforming scheme has advantage over the forward-and-backward-CSI based beamforming scheme in terms of the performance.

Individual Channel Estimation Based on Blind Interference Cancellation for Two-Way MIMO Relay Networks

In this paper, we investigate an individual channel estimation problem for multiple-input multiple-output (MIMO) two-way amplify-and-forward (AF) relay networks. To avoid self-interference during the estimation of the individual MIMO channels, a novel blind interference cancellation (BIC) approach is proposed based on an orthogonal preceding framework, where a pair of orthogonal precoding matrices is utilized at the source nodes. By designing an optimal decoding scheme, we propose to decompose the bidirectional transmission into a pair of unidirectional transmissions. Unlike most existing approaches, we make the practical assumption that the nonreciprocal MIMO channel and the mutual interference of multiple antennas are both taken into consideration. Under the precoding framework, we employ an orthogonal superimposed training strategy to obtain the individual MIMO channels. However, the AF strategy causes the noise at the terminal to be the sum of the local noise and the relay-propagated noise. To remove the relay-propagated noise during the estimation of the second-hop channel, a partial noise-nulling method is designed. We also derive a closed-form expression for the total mean square error (MSE) of the MIMO channel from which we compute the optimal power allocation. The simulation results demonstrate that the analytical and simulated curves match fully.

Robust Hybrid Beamforming in Millimeter Wave Relay Networks With Imperfect CSI

Millimeter-wave (mmWave) communication offers rich spectrum resources and acts as a key enabling technology for future wireless communication systems. Hybrid (digital and analog) beamforming and relay techniques are important for mmWave implementations considering the characteristics of mmWave signals, as well as the practical limitations of equipment size, power consumption, and hardware cost. In this paper, a robust hybrid beamforming scheme is presented for mmWave multiple-input multiple-output relay networks adopting amplify-and-forward strategy at the relays. Unlike most existing designs that are based on the perfect channel-state information (CSI), CSI imperfectness is considered in the proposed robust beamforming scheme. An accurate approximation of the average received signal-to-noise ratio is derived and used as the design criterion for the developed iterative beamforming optimization at different nodes. An orthogonal matching pursuit-based algorithm is then utilized to design the hybrid beamforming schemes. Simulation results show that the proposed robust beamforming scheme with affordable computational complexities provides substantial performance gains compared with the existing non-robust designs.

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.

Power Allocation and Relay Selection in Relay Networks: A Perturbation-Based Approach

A perturbation-based power allocation and multirelay selection approach is proposed for multiple-input multiple-output relay networks in multipath fading channels. In this approach, the relays are partitioned into two groups according to Lagrangian multipliers of power constraints. The power allocation for the relays is perturbed by increasing the power for the potential relay's group, while decreasing the power of the relays in the other group. An optimization framework is then formulated as a tradeoff between the relay selection and the mean square error performance degradation. Computer simulations are used to demonstrate the performance.

Relaying strategy based on estimated information for multi-antenna cooperative networks

A sphere-based list forwarding scheme for multiple-input multiple-output (MIMO) relay networks is proposed and analyzed. Firstly, an estimate forwarding (EF) method is proposed, which forwards the minimum mean squared error (MMSE) estimate of the source data to the destination. Since it performs like amplify-and-forward (AF) and decode-and-forward (DF) for the low and high signal-to-noise ratio (SNR) regions, respectively, the EF relay thus outperforms conventional AF and DF across all SNRs without the need for switching algorithms for different SNRs. Because computational complexity is however high for relays with a large number of antennas (large MIMO) and/or high order constellations, list EF for large MIMO relay networks is proposed. It computes a list sphere decoder based MMSE estimate and retains the advantages of the exact EF relay at a negligible performance loss. The proposed list EF could offer a flexible trade-off between the performance and computational complexity.

Performance Analysis of OSTBC Transmission in Lossy Forward MIMO Relay Networks

We analyze the outage probability for the orthogonal space-time block code based multiple-input multiple-output (MIMO) relay networks, composed of one source, one relay, and a single destination. The relay forwards the decoded and interleaved information sequence even though the information part may contain error(s), according to the lossy forward strategy. In spatially independent MIMO channels, we find that the diversity order of the relay network can be interpreted and formulated by the well-known max-flow min-cut theorem . Moreover, we extend the analysis to the case of spatially correlated MIMO channels. Approximated explicit expressions for the outage probabilities are obtained in high signal-to-noise ratio regime.

A novel forwarding method for full-duplex two-way relay networks

An estimate-and-forward (EF) scheme for single-input single-output (SISO) and multiple-input multiple-output (MIMO) full-duplex two-way relay networks is proposed and analyzed. The relay estimates the received signal from two terminal nodes by a minimum mean squared error (MMSE) estimation and forwards a scaled version of the MMSE estimate to the destination. The proposed EF outperforms conventional amplify- and-forward (AF) and decode-and-forward (DF) across all signal-to-noise ratio (SNR) region. Because its computational complexity is high for relays with a large number of antennas (large MIMO) and/or high order constellations, an approximate EF scheme, called list EF, are thus proposed to reduce the computational complexity. The proposed list EF computes a candidate list for the MMSE estimate by using a sphere decoder, and it approaches the performance of the exact EF relay at a negligible performance loss. The proposed forwarding approach also could be used to other relay networks, such as half-duplex, one-way or massive MIMO relay networks.

On the Performance of Zero-Forcing Processing in Multi-Way Massive MIMO Relay Networks

We consider a multi-way massive multiple-input multiple-output relay network with zero-forcing processing at the relay. By considering the time-division duplex protocol with channel estimation, we derive an analytical approximation of the spectral efficiency. This approximation is very tight and simple, which enables us to analyze the system performance, as well as to compare the spectral efficiency with zero-forcing and maximum-ratio processing. Our results show that by using a very large number of relay antennas and with the zero-forcing technique, we can simultaneously serve many active users in the same time-frequency resource, each with high spectral efficiency.

Joint source and relay optimization for interference MIMO relay networks

This paper considers multiple-input multiple-output (MIMO) relay communication in multi-cellular (interference) systems in which MIMO source-destination pairs communicate simultaneously. It is assumed that due to severe attenuation and/or shadowing effects, communication links can be established only with the aid of a relay node. The aim is to minimize the maximal mean-square-error (MSE) among all the receiving nodes under constrained source and relay transmit powers. Both one- and two-way amplify-and-forward (AF) relaying mechanisms are considered. Since the exactly optimal solution for this practically appealing problem is intractable, we first propose optimizing the source, relay, and receiver matrices in an alternating fashion. Then we contrive a simplified semidefinite programming (SDP) solution based on the error covariance matrix decomposition technique, avoiding the high complexity of the iterative process. Numerical results reveal the effectiveness of the proposed 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.

Joint Power Allocation, Equalization, and Relay Selection for MIMO Relay Networks With Multipath Receptions

Multiple-input multiple-output (MIMO) relays can improve cell coverage and data throughput for wireless networks. The key challenge for the success of MIMO relay networks is effectively managing the intersymbol interference (ISI) and multiantenna interference (MAI) in multipath channels. In this paper, equalize-and-forward (EF) relaying strategies are employed to mitigate the interference by jointly optimizing equalizer weights and power allocation for dual-hop MIMO relay networks. Two scenarios with different channel state information (CSI) knowledge are investigated: 1) full CSI at the relays and 2) only backward CSI at the relays and the destination. By considering CSI availability and using the minimum-mean-square-error (MMSE) criterion, iterative algorithms are proposed for the joint design of equalizer weights and power allocation to resolve the interference problem. We then extend the design to a more general case, in which the direct link between the source and the destination is taken into account. Furthermore, two relay selection algorithms based on allocated power and MSE performance are investigated for the two scenarios, which attain a performance that is comparable to that of cases with brute-force search or without relay selection. The design framework can capture the impact of the available CSI at the relays and the destination on the performance of MIMO multirelay networks with multipath receptions.

Neutralizing interferences in two‐hop amplify‐and‐forward MIMO relay systems

In this paper, we present the interference neutralization technique for two‐hop multiple‐input multiple‐output (MIMO) relay systems. It enables multiple MIMO transmitters (sources) to simultaneously transmit independent data streams to their MIMO receivers (destinations) without mutual interferences, thereby improving spectral efficiency of the systems. To neutralize the mutual interferences using multiple amplify‐and‐forward (AF) MIMO relays, we establish the sufficient condition for the antenna configuration in the MIMO relay networks, and provide a filter design technique for the AF MIMO relays. The proposed method increases sum rates of the systems linearly with the number of transmitters participating in simultaneous transmission. To improve the sum rates further, this method is combined with transmit power allocation using the water‐filling algorithm. In addition, it is shown that by employing the minimum number of relays required to meet the sufficient condition, the system cost for the proposed method can be reduced without compromising the sum rate performance severely. Finally, simulation results successfully demonstrate that by exploiting radio resources such as frequency and time efficiently, the proposed method achieves a higher sum rate than the existing techniques based on interference avoidance. © 2016 Institute of Electrical Engineers of Japan. Published by John Wiley &amp; Sons, Inc.

Joint Beamforming and Antenna Subarray Formation for Nonregenerative MIMO Relay Networks

Antenna subarray formation (ASF) is a complexity-reducing technique for multiple-input–multiple-output (MIMO) receivers. For nonregenerative MIMO relay networks, we propose a joint beamforming and ASF scheme in this paper, which maximizes the achievable rate subject to transmit power constraints at the source and the relay, as well as a limited number of nonzero elements in the ASF matrix. By relaxing the constraint of limited number of nonzero elements in the ASF matrix, we decouple the joint beamforming and ASF design problem into three problems and propose to alternatively optimize beamforming matrices at the source, the relay, and the ASF matrix. We also propose a gradient projection (GP) algorithm to solve nonlinear programming of the relay beamforming design problem. Simulation results demonstrate that the proposed joint beamforming and ASF scheme outperforms the antenna selection (AS) scheme.