Multiple-input Multiple-output Relay Channel Research Articles

Information Rate Optimization for the Non-Regenerative Linear MIMO Relay Channel With a Direct Link and Variable Duty Cycle

We consider the optimization of a two-hop linear relay channel based on an amplify-and-forward Multiple-Input Multiple-Output (MIMO) relay. The relay is assumed to derive the output signal by applying a Relay Transform Matrix (RTM) applied to the input signal. Assuming perfect channel state information about the channel at the relay and iid transmitted symbols, the RTM is optimized according to two different criteria: <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i)</i> MIMO information rate; <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ii)</i> information rate based on Orthogonal Space–Time Block Codes. The two assumptions have been addressed in part in the literature. The optimization problem is reduced to a manageable convex form, whose KKT equations are explicitly solved. Then, a parametric solution is given, which yields the power constraint and the information rate achieved with uncorrelated transmitted symbols as functions of a positive indeterminate. The solution for a given average power constraint at the relay is amenable to a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">water-filling-like</i> algorithm, and extends earlier literature results addressing the case without the direct link. The duty cycle of the two-hop relaying process is also addressed in the general form of the achievable rate. Simulation results are reported, which are relevant to a Rayleigh fading MIMO relay channel and the role of the direct link SNR is precisely assessed. Duty cycle optimization is also considered by a numerical example.

Performance Optimization of Polarized MIMO Relay Channels Based on the COST 2100 Channel Model

Polarization selectivity has a great impact on multiple-input–multiple-output (MIMO) relay channels. In this letter, the channel capacity of MIMO relay channels is analyzed, revealing the polarization dependency of multipath components. Polarization optimization schemes are proposed, including a regular optimization and a dynamic weight particle swarm optimization (DWPSO) for MIMO relay channels. The performance analysis shows that the DWPSO can significantly improve the link capacity of MIMO relay channels based on the COST 2100 channel model. This study indicates that it is necessary to optimize the polarization direction of MIMO relay channels.

Two-Timescale Uplink Channel Estimation for Dual-Hop MIMO Relay Multi-User Systems

Multiple-input multiple-output (MIMO) relay systems have received great attention for the development of future wireless networks, since they can be invoked for improving system capacity and extending the coverage area. Considering the fixed base station (BS) and relay station (RS) and the highly mobile users (UEs), the dual-hop MIMO relay channel possesses the two-timescale characteristics, i.e., the UEs-RS channel varies in a short-timescale manner whereas the RS-BS channel varies in a long-timescale manner. In order to acquire the knowledge of all individual channels at the BS directly, we propose two-timescale channel estimation algorithms with one-stage training (OST) scheme based on the above time-varying channel characteristics. Specifically, the two-timescale channel estimation problem is firstly formulated as an approximate maximum likelihood (AML) problem. Then, we design batch algorithm to solve the resultant optimization problem. Moreover, to overcome the drawbacks of batch algorithm, a low-complexity online algorithm is also proposed based on the two-stage stochastic optimization framework. Finally, simulation results are provided to verify the effectiveness of the proposed two-timescale channel estimation algorithms.

Maximizing the Partial Decode-and-Forward Rate in the Gaussian MIMO Relay Channel

It is known that circularly symmetric Gaussian signals are the optimal input signals for the partial decode-and-forward (PDF) coding scheme in the Gaussian multiple-input multiple-output (MIMO) relay channel, but there is currently no method to find the optimal covariance matrices nor to compute the optimal achievable PDF rate since the optimization is a non-convex problem in its original formulation. In this paper, we show that it is possible to find a convex reformulation of the problem by means of an approximation and a primal decomposition. We derive an explicit solution for the inner problem as well as an explicit gradient for the outer problem, so that the efficient cutting-plane method can be applied for solving the outer problem. Based on these ingredients, we propose a convergent algorithm whose output is an approximation of the globally optimal solution along with a certificate of accuracy in terms of a maximum distance to the true global optimum. In numerical simulations, this distance converged to values close to zero in all considered instances of the problem, showing that the proposed method manages to find the global optimum in all these instances.

Gaussian MIMO relay channel with orthogonal channel components

Abstract The Gaussian multiple-input multiple-output (MIMO) orthogonal relay channel (ORC) is investigated. The transmission from source to relay is done over a channel that is orthogonal to source-destination and relay-destination channels. Practically, this assumption is made such that many communication devices from different technologies are exploited in relaying the source’s signal into its destination. For this channel model, the capacity is initially derived. Thereafter, we propose a transmission algorithm to achieve the derived capacity. Further, to support our theoretical results, many numerical examples are presented.

Improving MIMO relay compressed sensing-based channel estimation and pilot allocation

Increasing the data rate of communication systems together with the performance are main goals of the communication networks in the future. Multiple-input multiple-output (MIMO)-orthogonal frequency division multiplexing (OFDM) relay networks as a key technology is one the main techniques to maintain the performance and data rate. Being influenced by fading channels, the MIMO-OFDM relay networks need some reliable approaches to estimate the channel response. Compressed sensing (CS) is one of the critical approaches to maintain the accuracy together with the spectral efficiency. In this paper, we have utilized CS-based approaches to estimate the MIMO-OFDM relay channel. Specifically, forward backward prediction (FBP) is used to estimate the fading channels. This approach benefits from backward correction which distinguishes it from other iterative approaches and helps interestingly in channel estimation accuracy. Moreover, in order to improve the channel estimation, pilot allocation approaches are proposed based on the system model and probability function. Furthermore, a cross entropy-based approach is utilized to propose two different approaches called sequential cross entropy self-coherence (SCE-SC) and parallel cross entropy self-coherence. Actually, mutual coherence is divided into two parts namely cross coherence and self coherence. It is demonstrated that in FBP-based approach self-coherence is important in mutual coherence. Consequently, the computations are interestingly decreased. The superiority of the method is represented using comparing simulations with other well-known approaches.

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.

Robust Hybrid Transceiver Design for AF Relaying in Millimeter Wave Systems Under Imperfect CSI

In this paper, we present a robust hybrid transceiver design for millimeter-wave communication systems operating in amplify-and-forward multiple-input multiple-output relay channels. Unlike most of current works that assume the perfect or partial channel state information (CSI) at the transceivers in the design, the CSI uncertainty is taken into consideration to design a robust transceiver. To achieve that end, the average received signal-to-noise ratio (SNR) is adopted as the objective function. To produce a tractable expression, an accurate approximation of the average received SNR is derived and used as the design criterion. An alternating maximization algorithm is proposed to optimize the design criterion, in which an orthogonal matching pursuit-based algorithm is utilized to design the transceiver at the relay. Simulations show that the algorithm takes a few iterations to produce converged transceivers for the source, relay, and destination nodes. Numerical results demonstrate the substantial performance gains of the proposed scheme, compared with the existing non-robust designs.

On the Exact and Approximate Eigenvalue Distribution for Sum of Wishart Matrices

The sum of Wishart matrices has an important role in multiuser communication employing multiantenna elements, such as multiple-input multiple-output (MIMO) multiple access channel (MAC), MIMO Relay channel, and other multiuser channels where the mathematical model is best described using random matrices. In this paper, the distribution of linear combination of complex Wishart distributed matrices has been studied. We present a new closed form expression for the marginal distribution of the eigenvalues of a weighted sum of K complex central Wishart matrices having covariance matrices proportional to the identity matrix. The expression is general and allows for any set of linear coefficients. As an application example, we have used the marginal distribution expression to obtain the ergodic sum-rate capacity for the MIMO-MAC network, and the cut-set upper bound for the MIMO-Relay case, both as closed form expressions. We also present a very simple expression to approximate the sum of Wishart matrices by one equivalent Wishart matrix. All of our results are validated by means of Monte Carlo simulations. As expected, the agreement between the exact eigenvalue distribution and simulations is perfect, whereas for the approximate solution the difference is indistinguishable.

Cutset Bounds on the Capacity of MIMO Relay Channels

We analyze the ergodic capacity of multiple-input multiple-output (MIMO) Rayleigh-fading relay channels. We first derive the probability density function of a sum of independent complex central Wishart matrices—called the central hyper-Wishart matrix —and its joint eigenvalue density. We then derive a trace representation for the max-flow min-cut upper bound on the ergodic capacity of general full-duplex MIMO relay channels where each communicating node is equipped with $ N$ antennas and has access only to respective receive channel state information. We also establish the Schur monotonicity theorem for this cutset bound as a functional of the signal-to-noise ratios (SNRs) of three communication links. We further characterize the exact ergodic capacity in the regularity SNR regime where the upper and lower bounds coincide.

Artificial-Noise-Aided Secure MIMO Full-Duplex Relay Channels With Fixed-Power Transmissions

This letter studies the physical-layer security of a full-duplex (FD) multiple-input multiple-output relay channel. A legitimate source node (Alice) communicates with her destination node (Bob) through an FD relay node in the presence of a cooperative FD jammer and a potential eavesdropper (Eve). The cooperative jammer is assumed to be an FD node that is solely charged by the ambient radio-frequency transmissions. We investigate the self-energy recycling at the cooperative jammer and derive a sufficient condition for the cooperative jammer to operate as a node with reliable energy supply. Without knowing the eavesdropper’s channel state information at the legitimate nodes, we propose a precoded artificial-noise (AN) injection scheme to secure the legitimate transmissions. The numerical results demonstrate that our proposed AN-aided secure scheme achieves a significant average secrecy rate improvement compared with the case of no cooperative jammer.

Enhancing the PHY-Layer Security of MIMO Buffer-Aided Relay Networks

We investigate the physical-layer security of a buffer-aided multiple-input multiple-output relay channel. The wireless network under investigation is composed of one legitimate source node (Alice), one legitimate half-duplex relay node, and one legitimate destination node (Bob). Alice communicates with both relay and Bob in the presence of a potential passive multi-antenna eavesdropper (Eve). Without knowing the instantaneous eavesdropper’s channel state information at the legitimate nodes, we propose a precoded artificial-noise injection scheme to enhance the security of the legitimate transmissions. The relay is equipped with a finite buffer to store the unsuccessfully decoded packets at Bob. We analyze the Markov chain of the relay’s queue and derive its steady-state distributions. Our optimization problem is formulated such that the average end-to-end secure throughput is maximized under the secrecy outage probability constraint on the Alice-relay link. Our numerical results demonstrate that our proposed buffer-aided relaying scheme achieves a significant improvement in the secure throughput compared with the conventional bufferless relaying scheme, where the time slot is divided equally between the source and the relay for their data transmissions.

Perfect Secrecy in Physical-Layer Network Coding Systems From Structured Interference

Physical-layer network coding (PNC) has been proposed for next generation networks. In this paper, we investigate PNC schemes with embedded perfect secrecy by exploiting structured interference in relay networks with two users and a single relay. In a practical scenario where both users employ finite and uniform signal input distributions, we establish upper bounds (UBs) on the achievable perfect secrecy rates and make these explicit when pulse amplitude modulation modems are used. We then describe two simple, explicit encoders that can achieve perfect secrecy rates close to these UBs with respect to an untrustworthy relay in the single antenna and single relay setting. Last, we generalize our system to a multiple-input multiple-output relay channel, where the relay has more antennas than the users and study optimal precoding matrices, which maintain a required secrecy constraint. Our results establish that the design of PNC transmission schemes with enhanced throughput and guaranteed data confidentiality is feasible in next generation systems.

Blind channel estimation and signal retrieving for MIMO relay systems

In this paper, we propose a blind channel estimation and signal retrieving algorithm for two-hop multiple-input multiple-output (MIMO) relay systems. This new algorithm integrates two blind source separation (BSS) methods to estimate the individual channel state information (CSI) of the source-relay and relay-destination links. In particular, a first-order Z-domain precoding technique is developed for the blind estimation of the relay-destination channel matrix, where the signals received at the relay node are pre-processed by a set of precoders before being transmitted to the destination node. With the estimated signals at the relay node, we propose an algorithm based on the constant modulus and signal mutual information properties to estimate the source-relay channel matrix. Compared with training-based MIMO relay channel estimation approaches, the proposed algorithm has a better bandwidth efficiency as no bandwidth is wasted for sending the training sequences. Numerical examples are shown to demonstrate the performance of the proposed algorithm.

Optimal Cooperative Beamforming Design for MIMO Relay Channels

Motivated by the rapid growth of wireless applications with multiple antenna terminals, multiple input multiple output (MIMO) relaying has gained much attention now a days due to its improved data rate, coverage extension and improved signal to noise ratio (SNR). In this paper, a transmit beamforming design for MIMO decode-and-forward (DF), MIMO amplify-and-forward (AF) and MIMO compress-and-forward (CF) half-duplex two-hop relay channels with a direct source–destination link is considered. Network model consist of source, relay and destination. Design includes four different cases in terms of the number of antennas deployed at source, relay and destination node which contains 2:2:1 scenario, Ns:1:1 scenario, Ns:Nr:1 scenario and Ns:Nr:Nd scenario. Here, beamforming design is based on exact capacity formulation and low-complexity explicit expressions are used. Effect of parameter such as number of antennas on the performance of MIMO relay channels is also investigated. Optimal beamforming design for MIMO AF relaying scheme achieves high performance gain and higher information rates than MIMO DF and MIMO CF relaying scheme.

On the Maximum Achievable Partial Decode-and-Forward Rate for the Gaussian MIMO Relay Channel

This paper considers the so-called partial decode-and-forward (DF) strategy for the Gaussian multiple-input multiple-output (MIMO) relay channel. Unlike for the DF strategy or point-to-point (P2P) transmission from source to destination, for which Gaussian channel inputs are known to maximize the achievable rates, the input distribution that attains the maximum achievable partial DF rate for the Gaussian MIMO relay channel has remained unknown so far. For some special cases, e.g., for relay channels where the partial DF strategy reduces to the DF or P2P transmission, it could be deduced that Gaussian inputs maximize the rate that can be achieved with the partial DF strategy. For the general case, however, the problem has remained open until now. In this paper, we solve this problem by proving that the maximum achievable partial DF rate for the Gaussian MIMO relay channel is always attained by Gaussian channel inputs. Our proof relies on the channel enhancement technique, which was originally introduced by Weingarten et al. to derive the (private message) capacity region of the Gaussian MIMO broadcast channel. By combining this technique with a primal decomposition approach, we first establish that jointly Gaussian source and relay inputs maximize the achievable partial DF rate for the aligned Gaussian MIMO relay channel. Subsequently, we use a limiting argument to extend this result from the aligned to the general Gaussian MIMO relay channel.

Outage Probability for MIMO Relay Channel

The channel capacity for the multiple-input multiple-output (MIMO) relay channel is still an open problem. In view of this gap, upper and lower bounds were found by Wang et al., 2005. This paper presents an extensive study of mutual information and outage probability of Rayleigh fading MIMO relay channels based on the eigenvalues distribution for the sum of complex Wishart matrices. Interestingly, for certain scenarios, upper and lower bounds are coincident providing the real channel capacity. To compute outage probability, a Gaussian approximation for mutual information has been used. Furthermore, it was proposed an equivalent distribution for the sum of Wishart matrices, which proves to be excellent in all scenarios. Closed-form expressions for probability density function and outage probability have been found for the general case of any number of antennas and any SNR values. Analytical expressions have been validated by means of Monte Carlo simulations.

On Optimal Gaussian Signaling in MIMO Relay Channels With Partial Decode-and-Forward

For Gaussian multiple-input multiple-output (MIMO) relay channels with partial decode-and-forward, the optimal type of input distribution is still an open question in general. Recent research has revealed that in some other scenarios with unknown optimal input distributions (e.g., interference channels), improper (i.e., noncircular) Gaussian distributions can outperform proper (circular) Gaussian distributions. In this paper, we show that this is not the case for partial decode-and-forward in the Gaussian MIMO relay channel with Gaussian transmit signals, i.e., we show that a proper Gaussian input distribution is the optimal one among all Gaussian distributions. In order to prove this property, an innovation covariance matrix is introduced, and a decomposition is performed by considering the optimization over this matrix as an outer problem. A key point for showing optimality of proper signals then is a reformulation that reveals that one of the subproblems is equivalent to a sum rate maximization in a two-user MIMO broadcast channel under a sum covariance constraint, for which the optimality of proper signals can be shown.

A Low Complexity Antenna Switching for Joint Wireless Information and Energy Transfer in MIMO Relay Channels

In this paper, we investigate a low-complexity technique for simultaneous wireless information and energy transfer in multiple-input multiple-output relay channels. The proposed technique exploits the array configuration at the relay node and uses the antenna elements either for conventional decoding or for rectifying (rectennas). In order to keep the complexity low, a dynamic antenna switching between decoding/rectifying is proposed based on the principles of the generalized selection combiner (GSC); the L strongest paths are allocated for decoding while the remaining channel paths for rectifying (and vice versa). The optimal L as well as the allocation strategy that minimizes the outage probability are investigated via theoretical and numerical results. In addition, two performance bounds that provide the optimal performance without the limitation of GSC are proposed by solving a linear programming and a binary knapsack problem, respectively. The proposed technique is extended to scenarios with multi-user interference, where a zero-forcing receiver is used at the relay node; closed-forms expressions for the outage probability are also derived.