Multi-hop Multiple-input Multiple-output Research Articles

Precoder Design for Multi-Hop Cognitive MIMO Relay Systems With Finite-Alphabet Inputs

This paper investigates the precoder design in a multi-hop multiple-input multiple-output (MIMO) relay system with cognitive radio. We assume that the source node (secondary user) sends data to the destination node (secondary user) by means of multiple relay nodes (secondary users), and that the source and relays simultaneously share the same frequency band with primary users. Unlike previous research, this paper assumes the inputs to be practical finite-alphabet signals, such as phase shift keying (PSK). Our objective is to maximize the mutual information of the overall system by optimizing the precoders at the source and relays under the constraints of the transmit power at each node and the interference power to the primary users. The precoder designs in two channel state information (CSI) cases, where the nodes know the perfect or statistical CSI, are both investigated. The formulated optimization problems are nondeterministic polynomial-time (NP)-hard and nonconvex, so the global optimal solution cannot be found within the polynomial time. However, by exploiting the structures of the optimization problems, we develop a new framework, which combines the iterative rank penalty (IRP) algorithm with the customized Uzawa algorithm, to solve them. Simulation results are provided to verify the efficacy of the proposed precoding algorithms.

Performance analysis of multi-hop underwater wireless optical communication system with space-time block codes considering the impact of beam spread function

The average bit error rate (ABER) performance of the decode-and-forward-based multiple-input multiple-output (MIMO) multi-hop underwater wireless optical communication (UWOC) systems has been investigated over the composite exponential-generalized gamma (EGG) fading channel with space-time block coding (STBC). The impacts of absorption, scattering, and the misalignment caused by spatial spreading in the sea, which are modeled by the beam spread function, as well as the turbulence-induced fading are all taken into account in this work. With the help of the moment generating function, Meijer’s-G function, and Gauss–Laguerre quadrature numerical methods, the approximate closed-form expressions of ABER for the UWOC system with binary phase shift keying are mathematically derived. Furthermore, numerical analyses are provided to investigate the effects of various hops, temperature gradients, air bubbles levels, STBC schemes, and turbulence severity on the performance of the multi-hop MIMO UWOC system. In addition, Reed–Solomon (RS) codes are adopted to improve the UWOC system performance. Results reveal that the ABER performance of this multi-hop UWOC system would degrade as the temperature gradients, hop numbers, and bubble levels (BLs) increases, which could be improved considerably by employing the STBC scheme. The ABER performance over the composite EGG distribution is mainly limited by the environmental parameters, whereas the fading can be significantly improved by RS codes. The ABERs of EGG distribution are compared with exponential-gamma and exponential-lognormal distributions in oceanic turbulence under different temperature gradients and BLs, respectively. These analytical results are also verified by Monte Carlo simulations. This work is beneficial for the design of UWOC system.

Performance of multi-hop cognitive MIMO relaying networks with joint constraint of intercept probability and limited interference

In this paper, we propose a multi-hop multiple input multiple output (MIMO) decode-and-forward relaying protocol in cognitive radio networks. In this protocol, a multi-antenna secondary source attempts to send its data to a multi-antenna secondary destination with assistance of multiple intermediate multi-antenna nodes, in presence of a multi-antenna secondary eavesdropper. A primary network includes a primary transmitter and a primary receiver which are equipped with multiple antennas, and use transmit antenna selection (TAS) and selection combining (SC) to communicate with each other. Operating on the underlay spectrum sharing method, the secondary source and relay nodes have to adjust their transmit power so that the outage performance of the primary network is not harmful and satisfy the quality of service (QoS). Moreover, these secondary nodes also reduce their transmit power so that the intercept probability (IP) at the eavesdropper at each hop is below a desired value. To improve the outage performance of the secondary network under the joint constraint of IP and limited interference, the TAS/SC method is employed to relay the source data hop-by-hop to the destination. We derived exact closed-form expressions of the end-to-end (e2e) outage probability (OP) and IP of the proposed protocol over Rayleigh fading channels. Monte Carlo simulations are then performed to verify the theoretical derivations.

Robust Transceiver Design for Multi-Hop AF MIMO Relay Multicasting From Multiple Sources

In this article, the transceiver design optimization problem is investigated for multi-hop multicasting amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay systems, where multiple source nodes broadcast their message to multiple destination nodes via multiple serial relay nodes. Multiple antennas are installed at the sources, relays, and the destination nodes. In the transceiver design, we consider the mismatch between the true and the estimated channel state information (CSI), where the CSI mismatch follows the Gaussian-Kronecker model. A robust transceiver design algorithm is developed to jointly optimize the source, relay, and destination matrices to minimize the maximal weighted mean-squared error (WMSE) of the received message at all destination nodes. In particular, the WMSE is made statistically robust against the CSI mismatch by averaging through the distributions of the true CSI. Moreover, the WMSE decomposition is exploited to reduce the computational complexity of the transceiver optimization. Numerical simulations show a better performance of the proposed robust transceiver design against the channel mismatch.

Optimal Best Path Selection Algorithm for Cluster-Based Multi-Hop MIMO Cooperative Transmission for Vehicular Communications

Multiple-input multiple-output (MIMO) cooperation in cluster-to-cluster communication has shown improved network quality of services by utilizing less transmission power over the fading environment. This is an enhancement from the traditional cluster-based single-input single-output multi-hop relaying used in vehicular communications. In this paper, we deploy multi-hop MIMO clustering relay into vehicular communication for a two-lane road transportation scenario. We deploy precoder and receiver filter in each MIMO link that is characterized by a narrowband classical three-dimensional time-varying channel. With the aid of the precoder and minimum mean square error receiver filtering algorithm in MIMO communication, we derive the end-to-end network signal-to-noise ratio to find the optimal best path using max-min theory with equal power allocation in precoder matrices that minimizes the network mean square error. A low-cost close-optimal best path selection method is also proposed through mathematical modeling. Computer simulation results demonstrate the validity of the theoretical investigations in this work.

PARATUCK semi-blind receivers for relaying multi-hop MIMO systems

In this paper, two receivers are proposed for a multiple-input multiple-output (MIMO) relaying multi-hop communication system using a Khatri-Rao space-time (KRST) coding at the source and amplify-and-forward (AF) relays. It is shown that the third-order tensor of signals received at the destination satisfies a PARATUCK-(K+1) tensor model, where K is the number of relays. After formulating the system model, the expressions of the Cramér-Rao bound (CRB) for the communication channels are derived for the particular case of a two-hop system, i.e., K=1. The presented tensorial modeling enables a joint semi-blind estimation of the transmitted symbols and the channels. The first proposed estimation algorithm is a non-iterative technique based on a rearrangement of the Kronecker product, while the second proposed receiver is based on the alternating least squares (ALS) algorithm. The uniqueness of the tensor decomposition and the identifiability conditions of the proposed algorithms are discussed. The performance of these receivers is evaluated by means of Monte Carlo simulations.

The performance analysis of multi-hop MIMO free space optical communications with space–time block codes over exponentiated Weibull fading channels

The symbol error rate (SER) performance of decode-and-forward (DF) based multiple-input multiple-output (MIMO) multi-hop free-space optical (FSO) systems is investigated with space–time block coding (STBC) over the exponentiated Weibull (EW) fading channel. The moment generating function (MGF) and Gauss–Laguerre quadrature rule are adopted to derive the end-to-end (EE) analytical SER expressions for this considered FSO communication system. The SER performance is further studied under various hops, STBC schemes, and turbulence conditions detailly. In addition, the asymptotic EE SER expressions are obtained to evaluate the diversity orders. Results show that the SER performances of this FSO system under EW atmospheric turbulence distribution can be improved considerably by employing the STBC scheme, and the diversity order depends not only on the numbers of transmitting and receiving antennas, but also on the channel fading parameters. The SERs of EW distribution are compared with Lognormal (LN) and gamma–gamma (G–G) distributions in weak and strong turbulence atmosphere, respectively. We also verify these analytical results through Monte Carlo simulations. This work is beneficial to the design of FSO system.

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.

Space shift keying for multi-hop multi-branch networks

In this paper, we propose two different multi-hop multiple-input multiple-output (MIMO) space shift keying (SSK) schemes and investigate their error performance. In the first scheme, we consider a multi-hop multi-branch SSK system, in which the source and destination are equipped with multiple transmit and receive antennas, respectively. In this scheme, SSK is applied by using the source transmit antennas. Moreover, in each branch, single-antenna relays are used to amplify the transmitted signal from the source and forward it to the next relay until it reaches to the destination. In the second scheme, we consider a multi-hop MIMO-SSK system with path selection. In this scheme, the best path is selected among multiple branches and a multiple-antenna source communicates with a multiple-antenna destination via the relays of the selected path. Each relay is equipped with multiple transmit and receive antennas. Moreover, the source and all relays employ SSK modulation to transmit information bits and each relay in each path follows the decode-and-forward protocol. Approximate theoretical error probability expressions are derived for both schemes. Furthermore, an asymptotic symbol error probability performance analysis is also performed for the multi-hop MIMO-SSK system with path selection. It is shown that the proposed multi-hop SSK systems outperform conventional multi-hop M-PSK systems in terms of the error performance for especially high data rates and sufficient number of receive antennas at the receiving nodes.

Underlay Cognitive Multihop MIMO Networks With and Without Receive Interference Cancellation

This paper investigates the impact of primary network interference on the performance of cognitive multihop secondary network under various multiple-input multiple-output (MIMO) approaches per hop. Specifically, the cognitive system involves a secondary network with MIMO relays that use the amplify-and-forward protocol, and each of which shares the same spectrum resources of multiple primary users (PUs) transmit and receive stations. Two different receive array conditions, and hence processing approaches, per hop in the secondary network are treated separately, which are maximal ratio combining for sufficiently spaced receive antennas to provide receive diversity gain and interference cancellation (IC) for insufficiently spaced antennas to reduce the effect of PUs interference. The latter approach involves two different algorithms that vary in terms of complexity and achieved performance, which are dominant receive IC and adaptive receive IC. Moreover, for both approaches, the transmit array gain is achieved per hop through the low-complexity transmit antenna selection. In doing so, new analytical results for multihop secondary network’s end-to-end outage probability are developed. Moreover, simple asymptotic results for this outage performance in high SNR regime are provided, from which the achieved diversity and coding gains and the diversity-multiplexing tradeoff can be extracted. In addition, to further enhance the secondary network, optimal power allocation among hops is obtained based on the asymptotic outage performance under the constraints of transmit power of a secondary transmit station and interference limit on the primary network. The developed analytical results in this paper are validated through numerical and simulation results.

Optimal Energy-Efficient Joint Resource Allocation for Multi-Hop MIMO-AF Systems

Energy efficiency is a key enabler for the next generation of communication systems. Equally, resource allocation and cooperative communication are effective techniques for improving the communication system performance. In this paper, we propose an optimal energy-efficient joint resource allocation method for the multi-hop multiple-input-multiple-output (MIMO) amplify-and-forward (AF) system. We define the joint source and multiple relays optimization problem and prove that its objective function, which is not generally quasiconvex, can be lower bounded by a convex function. Moreover, all the minima of this objective function are strict minima. Based on these two properties, we then simplify the original multivariate optimization problem into a single variable problem and design a novel approach for optimally solving it in both the unconstraint and power constraint cases. In addition, we provide a sub-optimal approach with reduced complexity; the latter reduces the computational complexity by a factor of up to 40 with a near-optimal performance. We finally utilize our novel approach for comparing the optimal energy-per-bit consumption of multi-hop MIMO-AF and MIMO systems; the results indicate that MIMO-AF can help to save energy when the direct link quality is poor.

Performance of Multi-Hop Cooperative Networks Subject to Timing Synchronization Errors

In this paper, we propose a mathematical model for timing synchronization errors in a cascaded virtual multi-hop multiple-input multiple-output (MIMO) system that incorporates cooperation at each hop using decode-and-forward (DF) algorithm. Specifically, the DF relays are grouped to form clusters and one cluster transmits the same data to the next cluster over orthogonal fading channels. The proposed error model is used to study the statistics of the timing error from one cluster to the next and it has been shown that the variance of the timing errors gradually increases as the data traverse the multi-hop network. The effects of the timing errors on the bit error probability (BEP) performance of the system have been quantified. For that purpose, the closed-form expressions of the BEP for the network are derived for every hop with a particular number of nodes per hop. The results indicate that the BEP performance of the system degrades as the data propagates from hop to hop. We quantify the minimum required SNR and the optimal number of relays per cluster that guarantee successful traversal of data to a specified number of hop while keeping overall BEP below a defined threshold.

Performance Analysis of Space-Shift Keying in Decode-and-Forward Multihop MIMO Networks

In this paper, space-shift keying (SSK) is considered for multihop multiple-input-multiple-output (MIMO) networks. In SSK, only one among $n_{s} = \hbox{2}^{m}$ available transmit antennas, chosen on the basis of $m$ information bits, is activated during transmission. We consider two different systems of multihop cooperation, where each node has multiple antennas and employs SSK. In system I, a multihop diversity relaying scheme is considered. In system II, a multihop multibranch relaying scheme is considered. In both systems, we adopt decode-and-forward (DF) relaying, where each relay forwards the signal only when it correctly decodes. We analyze the end-to-end bit error rate (BER) and diversity order of both the systems with SSK. For binary SSK $(n_{s} = \hbox{2})$ , our analytical BER expression is exact, and our numerical results show that the BERs evaluated through the analytical expression overlap with those obtained through Monte Carlo simulations. For nonbinary SSK $(n_{s} > \hbox{2})$ , we derive an approximate BER expression, where the analytically evaluated BER results closely follow the simulated BER results. We show the comparison of the BERs of SSK and conventional phase-shift keying (PSK) and also show the instances where SSK outperforms PSK. We also present the diversity analyses for SSK in systems I and II, which predict the achievable diversity orders as a function of system parameters.

Distributed CSMA Algorithms for Link Scheduling in Multihop MIMO Networks Under SINR Model

In this paper, we study distributed scheduling in multihop multiple-input-multiple-output (MIMO) networks. We first develop a model that provides the upper layers a set of rates and signal-to-interference-plus-noise ratio (SINR) requirements that capture the rate-reliability tradeoff in MIMO communications. The main thrust of this paper is then dedicated to developing distributed carrier sense multiple access (CSMA) algorithms for MIMO-pipe scheduling under the SINR interference model. We choose the SINR model over the extensively studied protocol-based interference models because it more naturally captures the impact of interference in wireless networks. The coupling among the links caused by the interference under the SINR model makes the problem of devising distributed scheduling algorithms very challenging. To that end, we explore the CSMA algorithms for MIMO-pipe scheduling from two perspectives. We start with an idealized continuous-time CSMA network, where control messages can be exchanged in a collision-free manner, and devise a CSMA-based link scheduling algorithm that can achieve throughput optimality under the SINR model. Next, we consider a discrete-time CSMA network, where the message exchanges suffer from collisions. For this more challenging case, we develop a scheduling algorithm by imposing a more stringent SINR constraint on the MIMO-pipe model. We show that the proposed conservative scheduling achieves an efficiency ratio bounded from below.

Multiuser Multi-Hop MIMO Relay Systems with Correlated Fading Channels

In this letter, we address multiuser multi-hop multiple-input multiple-output (MIMO) relay communication systems with correlated MIMO fading channels. In particular, we consider the practical scenario where the channel fading is fast and thus the instantaneous channel state information (CSI) is only available at the destination node, but unknown at all users and all relay nodes. We derive the structure of the optimal user precoding matrices and relay amplifying matrices that maximizes the users-destination ergodic sum mutual information. Compared with existing works, our results are more general, since we address multiuser scenarios, consider MIMO relays with a finite dimension, and take into account the noise vector at each relay node.

On Uplink-Downlink Duality of Multi-Hop MIMO Relay Channel

For two-hop amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay systems, the uplink-downlink duality has been recently investigated. In this paper, we establish the duality between uplink and downlink multi-hop AF-MIMO relay channels with any number of hops and any number of antennas at each node, which is a further generalization of several previously established results. We show that in the downlink relay system, signal-to-interference-noise ratios (SINRs) identical to those in the uplink relay system, and vice versa, can be achieved by two approaches. First, with the same total network transmission power constraint, one simply applies Hermitian transposed uplink relay amplifying matrices at relay nodes in the downlink system. Second, with transmission power constraint at each node of the relay network, one can use scaled and Hermitian transposed uplink relay amplifying matrices in the downlink system, with scaling factors obtained by switching power constraints at different nodes of the uplink system. As an application of the uplink-downlink duality, we propose an optimal design of the source precoding matrix and relay amplifying matrices for multi-hop MIMO relay system with a dirty paper coding (DPC) transmitter at the source node.

Capacity and resource allocation of cooperative MIMO in ad hoc networks

Cooperative MIMO (Multiple Input–Multiple Output) allows multiple nodes share their antennas to emulate antenna arrays and transmit or receive cooperatively. It has the ability to increase the capacity for future wireless communication systems and it is particularly suited for ad hoc networks. In this study, based on the transmission procedure of a typical cooperative MIMO system, we first analyze the capacity of single-hop cooperative MIMO systems, and then we derive the optimal resource allocation strategy to maximize the end-to-end capacity in multi-hop cooperative MIMO systems. The study shows three implications. First, only when the intra-cluster channel is better than the inter-cluster channel, cooperative MIMO results in a capacity increment. Second, for a given scenario there is an optimal number of cooperative nodes. For instance, in our study an optimal deployment of three cooperative nodes achieve a capacity increment of 2 bps/Hz when compared with direct transmission. Third, an optimal resource allocation strategy plays a significant role in maximizing end-to-end capacity in multi-hop cooperative MIMO systems. Numerical results show that when optimal resource allocation is applied we achieve more than 20% end-to-end capacity increment in average when compared with an equal resource allocation strategy.

Multihop Nonregenerative MIMO Relays— QoS Considerations

For nonregenerative multihop multiple-input multiple-output (MIMO) relay communication systems, the optimal source precoding matrix and the optimal relay amplifying matrices have been recently established for a broad class of objective functions subjecting to the transmission power constraint at each node. However, existing works do not consider any quality-of-service (QoS) constraints, which are important in practical communication systems. In this paper, we derive the optimal source and relay matrices of a multihop MIMO relay system that guarantee the predetermined QoS criteria be attained with the minimal total transmission power. In particular, we consider two types of receivers at the destination node: the linear minimal mean-squared error (MMSE) receiver and the nonlinear decision feedback equalizer (DFE) based on the MMSE criterion. We show that for both types of receivers, the solution to the original optimization problem can be upper-bounded by using a successive geometric programming (GP) approach and lower-bounded by utilizing a dual decomposition technique. Simulation results show that both bounds are tight, and to obtain the same QoS, the MIMO relay system using the nonlinear MMSE-DFE receiver requires substantially less total transmission power than the linear MMSE receiver-based system.

Optimal Linear Non-Regenerative Multi-Hop MIMO Relays with MMSE-DFE Receiver at the Destination

In this paper, we study multi-hop non-regenerative multiple-input multiple-output (MIMO) relay communications with any number of hops. We design the optimal source precoding matrix and the optimal relay amplifying matrices for such relay network where a nonlinear minimal mean-squared error (MMSE)-decision feedback equalizer (DFE) is used at the destination node. We first derive the structure of the optimal source and relay matrices. Then based on the link between most commonly used MIMO system design objectives and the diagonal elements of the MSE matrix, we classify the objective functions into two categories: Schur-convex and Schur-concave composite objective functions. We show that when the composite objective function is Schur-convex, the MMSE-DFE receiver together with the optimal source and relay matrices enable an arbitrary number of source symbols to be transmitted at one time, and yield a significantly improved BER performance compared with non-regenerative MIMO relay systems using linear receivers at the destination. We also show that for Schur-concave composite objective functions, the optimal source and relay matrices, and the optimal feed-forward matrix at the destination node jointly diagonalize the multi-hop MIMO relay channel, and thus in such case, the nonlinear MMSE-DFE receiver is essentially equivalent to a linear MMSE receiver.

Outage Performance of Multi-Hop Decouple-and-Forward Relaying in Spatially Correlated MIMO Channels

In this letter, the outage performance of multi-hop multiple-input multiple-output (MIMO) relaying systems is analyzed for spatially correlated Rayleigh fading channels. We focus on nonregenerative MIMO decouple-and-forward (DCF) relaying in orthogonal space-time block code (OSTBC) transmission and provide its outage probability given the assumption of ideal relay gain. The outage obtained here is shown a lower bound for using practical gains, which gets tight at high SNR. We conduct numerical studies to assess the impact of the spatial correlation between antennas on the outage probability.