MIMO decode-and-forward relay beamforming for secrecy with cooperative jamming

A multiple-input multiple-output (MIMO) relay network is composed of source, relay, and destination nodes, each of which is equipped with multiple antennas. Network information theory has shown that the use of multiple relay nodes in source and destination (S-D) communication makes the capacity of the S-D system logarithmically increase with the number of relay nodes. In [13], we proposed a MIMO relay scheme for a relay network with single source and destination pair; each of the multiple relay nodes performs QR decomposition of backward and forward channels in conjunction with phase control (QR-P-QR). In this paper, we extend this scheme to the MIMO relay network with multiple source and destination pairs. For this aim, we use the group nulling approach to decompose the multiple S-D MIMO relay channel to parallel independent S-D MIMO relay channels, and apply the QR-P-QR scheme in each of the decomposed MIMO relay links. Numerical examples show that the proposed relay scheme offers higher capacity than the existing zero-forcing (ZF) relaying scheme

Multiple input multiple output (MIMO) relay networks are wireless communication systems comprising of multiple nodes, each of which is equipped with multiple antennas. Information theories have shown that using multiple nodes to simultaneously relay a message can improve the capacity of source-to-destination communications. In this paper, we propose new relaying schemes for MIMO relay networks. The major concept behind the proposed schemes is to transform each of the MIMO relay channels into an equivalent triangular channel with positive real diagonal entries. By doing so, the resultant MIMO relay channel can simultaneously offer both distributed array gain (diversity gain obtained among relay nodes) and intranode array gain (diversity gain realized by multiple antennas of individual relay node) while maintaining the maximum spatial multiplexing gain (number of parallel data pipes). Based on this concept, three relaying schemes are derived that perform QR decomposition and phase control. Numerical results confirm that at least one of the proposed schemes outperforms the amplify-and-forward and the zero-forcing relaying schemes under various conditions. Moreover, we show that ratios of noise power level at relay and destination node have a great impact on capacities.

A two-hop multiple-input multiple-output (MIMO) relay network which comprises a multiple antenna source, an amplify-and-forward MIMO relay and many potential users are studied in this paper. Consider the achievable sum rate as the performance metric, a joint design method for the processing units of the BS and relay node is proposed. The optimal structures are given, which decompose the multiuser MIMO relay channel into several parallel single-input single-output relay channels. With these structures, the signal-to-noise ratio at the destination users is derived; and the power allocation is proved to be a convex problem. We also show that high sum rate can be achieved by pairing each link according to its magnitude. The sum rate of three broadcast strategies, time division multiple access (TDMA) to the strongest user, dirty paper coding (DPC), and beamforming (BF) are investigated. The sum rate bounds of these strategies and the sum capacity (achieved by DPC) gain over TDMA and BF are given. With these results, it can be easily obtained that how far away TDMA and BF are from being optimal in terms of the achievable sum rate.

In this paper, capacity performance analysis is presented for multiple-input multiple-output (MIMO) relay channels with transmit antenna selection and maximal-ratio combining receive (TAS/MRC) in amplify-and-forward (AF) relay networks operating over flat Rayleigh fading channels. Assuming that the source and destination are equipped with Ns and Nd antennas, respectively, and communicate with each other with the help of a single-antenna relay, we derive the cumulative distribution function (CDF), probability density function (PDF) and moment generation function (MGF) for the system end-to-end SNR. Based on these, we then present closed-form analytical expressions for the calculation of the ergodic capacity and outage capacity for the AF MIMO relay channels with TAS/MRC. Numerical results show that all the derived analytical expressions are very tight and are valid for evaluations of the ergodic and outage capacity under various antenna configurations. The results also show how the number of transmit antennas and receives antennas affect the overall channel capacity under fading channel environments.

We consider Multiple-input multiple-output (MIMO) wiretap channel with one transmitter, one receiver, one cooperative jammer, and one eavesdropper, where each node equips with multiple antennas. Eigenbeam-space division multiplexing (E-SDM) and cooperative jamming are known as the techniques improving secrecy rate. E-SDM enables the transmitter and the legitimate receiver to communicate with each other in parallel using channel state information (CSI) known to them to maximize the legitimate receiver's mutual information. On the other hand, cooperative jamming is to jam only the eavesdropper to degrade eavesdropper's mutual information. However, co-channel interference and residual interference from the cooperative jammer are caused by channel estimation error, which degrades legitimate receiver's mutual information. How these interference influence on the secrecy rate has not been clarified. In this paper, we derive lower and upper bounds on secrecy rate using legitimate receiver's mutual information in the presence of channel estimation error and eavesdropper's mutual information who uses minimum mean square error (MMSE) receiver. We analyze the effect of co-channel interference and residual interference from the cooperative jammer on the secrecy rate.

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.

In multi-hop wireless networks where links are prone to be broken or degraded, it is important to guarantee the network connectivity as well as satisfy the performance requirements. Observing the promising features of Multiple-Input Multiple-Output (MIMO) techniques for improving the transmission capacity and reliability, in this paper, we make the very first attempt to deploy MIMO nodes as relays to assist weak links in wireless networks, with the aim of reducing the number of relay nodes and providing performance provisioning. We identify the specific constraints of MIMO relay nodes for assisting weak links, and take advantage of the MIMO ability to flexibly select among different transmission strategies. The constrains and flexibility, however, make the MIMO deployment problem different from conventional single-antenna deployment schemes and much more challenging. Based on the constraints, we formulate the MIMO relay deployment problem, and provide a polynomial-time approximation scheme (PTAS) algorithm, as well as a distributed heuristic algorithm. The performance of the proposed algorithms is evaluated through simulations and demonstrated to be very effective.

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.

Relay communication networks increase the spectral efficiency and remote availability with the support of Multiple-Input Multiple-Output (MIMO). Channel estimation in the MIMO relay communication networks is mandatory to enhance the represented capabilities. Hence, developing channel estimation approaches in MIMO relay communication networks is one of the noteworthy aspects of recent researches. Besides, compressed sensing (CS) as a spectral efficient signal processing approach is attractive for estimators. Hence, in this paper, we have used CS based channel estimation method to improve the accuracy and spectral efficiency of channel estimation for MIMO-OFDM relay network. As represented, having a proper pilot allocation will increase the efficiency, and to this end, we are encountered with a combinatorial optimization which is dealt with Geometrical Differential Evolution (GDE) and Population-Based Incremental Learning (PBIL) in this paper. These are population-based evolutionary optimization. GDE is utilized for its speed and accuracy of convergence. Besides, PBIL is used for its probability nature which makes it capable of escaping from local minimum trapping. The illustrated result of simulations represents the superiority of the proposed methods in defining the pilot allocation sequences.

In this paper, the mutual information outage probability (P) for dual-hop decode-and-forward multiple-input multiple-output (MIMO) relay channel is obtained. Rayleigh distribution is used to model MIMO channels, and both full-duplex and half-duplex modes are investigated. Co-channel interference at relay and destination nodes has been considered. Our assumption is based on the result of [1], which establishes that MIMO channel mutual information can be well approximated by a Gaussian distribution. We have found a closed form expression for P given as a function of bivariate Gaussian cumulative density function. The results show for low-medium interference regime that full-duplex performs better than half-duplex mode. On the other hand, when relay self-interference increases, half-duplex outperforms full-duplex mode. Regarding the number of antennas, full-duplex mode performs better than half-duplex mode when number of antennas increases, even in high interference scenario. All the results are validated by numerical Monte Carlo simulations.

In this paper, we investigate the impact of the outdated Channel State Information (CSI) and the Co-Channel Interference (CCI) on the performance of Transmit Antenna Selection with Selective Combining (TAS/SC) in a dual-hop amplify-and-forward (AF) Multiple-Input Multiple-Output (MIMO) relay network. We derive the exact closed-form and asymptotic expressions for the outage probability in the cases of perfect and outdated CSI, respectively. The simulation results match the theoretical analysis well. The findings suggest that the outdated CSI and CCI have significant impacts on the outage probability of an AF MIMO relay system with TAS/SC.

The authors propose a full-duplex relay (FDR) based on a block diagonalisation (BD) method in multiple-input multiple-output (MIMO) relay channels. The BD method is employed to suppress the self-interference in MIMO FDR as well as to transmit multiple data streams to multiple users at the same time. The authors also derive the optimal power allocation strategy for MIMO FDR operation. Numerical results show that the use of the proposed FDR with BD can provide enhanced system performance compared with the FDR with zero-forcing beamforming.

Multiple-input multiple-output (MIMO) amplify-and- forward (AF) relaying is designed for secure communication between a source-destination pair in the presence of multiple eavesdroppers. Assuming statistical knowledge of the eavesdroppers' channel state information (ECSI) errors, we introduce a probabilistically robust design method, which aims to optimize the source transmission power and AF relaying matrix by maximizing the received signal-to- interference-plus-noise ratio (SINR) at the destination, while satisfying a set of intercept probability constraints. The resultant optimization problem becomes nonconvex, and hence we propose a conservative two-step solution, where the source transmission power and the relaying matrix are sequentially optimized. Our simulation results demonstrate the improved secrecy of the proposed relaying design against eavesdropping and its robustness against the channel uncertainties.

This paper investigates a three-node amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay network, where an autonomous relay harvests power from the source information flow and is further helped by an energy flow in the form of a wireless power transfer (WPT) at the destination. An energy-flow-assisted two-phase relaying scheme is proposed, where a source and relay joint optimization is formulated to maximize the rate. By diagonalizing the channel, the problem is simplified to a power optimization, where a relay channel pairing problem is solved by an ordering operation. The proposed algorithm, which iteratively optimizes the relay and source power, is shown to converge. Closed-form solutions can be obtained for the separate relay and source optimizations. Besides, a two-phase relaying without energy flow is also studied. Simulation results show that the energy-flow-assisted scheme is beneficial to the rate enhancement, if the transmit power of the energy flow is adequately larger than that of the information flow. Otherwise, the scheme without energy flow would be preferable.

Closed form expressions for the bit error rate (BER) for a multiple input multiple output (MIMO) relay system employing maximum likelihood (ML) based decode and forward (DF) cooperative diversity are obtained. The DF operation at the relay involves maximal ratio combining (MRC) on the source-relay link and space-time coding (STC) on the relay-destination link. Exact expressions of the BER are obtained for the case of a single relay supporting two antennas. For a system employing a large number of relays, each having two antennas, approximate expressions for the BER are obtained using the piecewise linear (PL) approximation for the ML detector. This is done by finding the statistics of conditionally Gaussian random variables, that appear in the decision variable. The validity of the analytical expressions is then verified through simulations. Through numerical results obtained from the BER expressions for large number of relays, it is then shown that the loss in diversity order due to DF can be compensated by using multiple antennas at the relay.