Multiple-input Multiple-output Relay Research Articles

MIMO Relaying: Distributed TAS/MRC in Nakagami-m Fading

We develop a unified framework for the symbol error rate (SER) of distributed transmit antenna selection with receiver maximal-ratio combining (TAS/MRC) in multiple-input multiple-output (MIMO) relay networks. We focus on nonregenerative relaying with N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</sub> , N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</sub> , and N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</sub> antennas at the source, relay, and destination, respectively. We consider the general fading scenario of Nakagami-m fading with distinct m fading parameters in the source-to-relay and the relay-to-destination links. We present new analytical expressions for the statistics of the end-to-end signal-to-noise ratio (SNR). Specifically, we derive exact expressions and first order expansions for the cumulative distribution function and moment generating function of the end-to-end SNR. Based on these, we derive new closed-form expressions for the asymptotic SER under M-ary phase-shift keying (M-PSK) and M-ary quadrature amplitude modulation (M-QAM). Our asymptotic solutions accurately identify the diversity order and the array gain as two key design components of the network.

Cooperative Partial Detection Using MIMO Relays

Using multiple-input multiple-output (MIMO) relays in cooperative communication improves the data rate and reliability of the communication. The MIMO transmission, however, requires considerable resources for the detection in the relay. In particular, if a full detect-and-forward (FDF) strategy is employed, the relay needs to spend considerable resources to perform the full MIMO detection. We propose a novel cooperative partial detection (CPD) strategy to partition the detection task between the relay and the destination. CPD modifies the tree traversal of the tree-based sphere detectors in a way where there is no need to visit all the levels of the tree and only a subset of the levels; thus, a subset of the transmitted streams are visited. The destination, then, combines the source signal and the partial relay signal to perform the final detection step and recover the transmitted vector. We study and compare the performance and complexity of FDF and CPD and show that by using the CPD approach, the relay can avoid the considerable overhead of MIMO detection while helping the source-destination link to improve its performance. More specifically, in the case of a 4 × 4 system, the relay complexity can be reduced by up to 80% of the conventional relaying scheme.

Precoder Design for MIMO Relay Networks with Direct Link and Decision Feedback Equalisation

In this letter we derive the source and relay precoders for a multiple-input multiple-output (MIMO) relay system with zero-forcing (ZF) decision feedback equalisation (DFE) when a direct link exists between the source and destination. Assuming full channel state information (CSI) is available at each node in the network, the processors are optimised for a large class of objective functions subject to the ZF condition and average power constraints at both the source and relay terminals. Simulation results show that the proposed design outperforms existing techniques in terms of bit error ratio (BER).

Balanced Linear Precoding in Decode-and-Forward Based MIMO Relay Communications

This paper proposes a linear precoding technique for multiple-input multiple-output (MIMO) decode-and-forward (DF) based relay communications. The proposed precoder is constructed by linearly combining two independently designed precoders that maximize data rates at relay and destination, respectively. Contrary to conventional precoding in DF relay communications, the proposed precoding balances direct and relay links and maximize the achievable rate of the overall system. We also propose a distributed precoder design method using limited information. The proposed algorithms are shown to significantly reduce computation complexity of precoder design. The numerical results show that the proposed precoders with full information and limited information achieve significantly higher data rates than conventional precoding neglecting a direct link and comparable data rate to the optimal precoding even when the coefficients for linear combining are restricted to real numbers.

Statistically robust design of linear filter for non-regenerative MIMO relay systems

This paper addresses the robust linear filter design issues for non-regenerative multiple input multiple output (MIMO) relay systems with imperfect channel state information (CSI) in both or partial hops. By considering statistical Kronecker channel model involving channel mean and antenna correlation, the robust linear processing schemes in imperfect CSI scenario for both hops are first derived based on mean squared error (MSE) criterion. In addition to this, the result is also extended to two practical scenarios, i.e. imperfect CSI for relay link with perfect CSI for access link and imperfect CSI for access link with perfect CSI for relay link. Simulation results show that the proposed scheme is capable of mitigating the performance degradation caused by the imperfect CSI.

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.

On the Throughput of MIMO Relay Wireless Network with Receive Antenna Selection

In this letter, we consider a single-relay and K users multiple-input multiple-output (MIMO) system with the channel state information (CSI)-assisted amplify-and-forward (CAF) protocol, where each node is equipped with N antennas. We propose one antenna selection scheme for the multiuser wireless relay network. According to the order statistics, we derive the exact expressions for the probability density functions (PDF) and use them to evaluate the average throughput. The numerical results show that for a N = 2 and K = 3 relay channel the antenna selection scheme results about 2dB SNR loss compared to the full antenna case.

Robust Design for Linear Non-Regenerative MIMO Relays With Imperfect Channel State Information

In this correspondence, we address statistically robust multiple-input multiple-output (MIMO) relay design problems under two imperfect channel state information (CSI) scenarios: (1) a ll nodes have imperfect CSI and (2) the destination node knows the exact CSI, while the other nodes have imperfect CSI. For each scenario, we develop robust source and relay matrices by considering a broad class of frequently used objective functions in MIMO system design and the averaged transmission power constraints. Simulation results demonstrate the improved robustness of the proposed algorithms against CSI errors.

Joint precoding and power allocation for multiuser transmission in MIMO relay networks

This paper proposes a joint precoding and power allocation strategy to maximize the sum rate of multiuser multiple-input multiple-output (MIMO) relay networks. A two-hop relay link working on amplify-and-forward (AF) mode is considered. Precoding and power allocation are designed jointly at the base station (BS). It is assumed that there are no direct links between the BS and users. Under individual power constraints at the BS and relay station, precoders designed based on zero forcing, minimum mean-square error and maximum ratio transmission are derived, respectively. Optimal power allocation strategies for these precoders are given separately. To demonstrate the performance of the proposed strategies, we simulate the uncoded bit error rate performance of the underlined system. We also show the difference of the sum rate of the system with the optimal power allocation strategies and with average power transmission. The simulation results show the advantages of the proposed joint precoding and power allocation strategies as expected. Copyright © 2011 John Wiley & Sons, Ltd.

Capacity Enhanced Transmission for the MIMO Relay Channel

For the classic three-node multiple-input multiple-output (MIMO) relay channel, a capacity enhanced transmission is proposed, using simple half-duplex tow-hop relaying based on symbol level decode-and-forward (DF) mode. For higher capacity to the destination, we assume the source node equipped with more antennas and propose the transmission strategy, where using channel precoding, the source transmits the data to the relay and destination respectively in the first hop and retransmits part of data to destination jointly with relay in the second hop. Additionally, the power allocation is designed to maximize the system capacity. Simulation results are then presented for illustration of the capacity enhancement.

Exact and Asymptotic SER of Distributed TAS/MRC in MIMO Relay Networks

We propose distributed transmit antenna selection with receiver maximal-ratio combining (TAS/MRC) for use in a two-hop multiple-input multiple-output (MIMO) relay network. The network under consideration is equipped with N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</sub> , N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</sub> , and N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</sub> antennas at the source, relay, and destination, respectively. First, we derive a new closed-form expression for the exact cumulative distribution function (cdf) of the end-to-end SNR. Based on this, we present a new closed-form expression for the exact symbol error rate (SER). Our analytical results are further evaluated in the high SNR regime, leading to practical design insights. Our asymptotic expressions are concise and have the added advantage of explicitly characterizing the diversity order and the array gain of the network. Our exact and asymptotic results are valid for general operating scenarios with distinct average received SNRs in each hop.

Outage Performance of Heterogeneous MIMO Relaying in OSTBC Transmission over Spatially Correlated Nakagami Fading Channels

In this letter, we investigate a heterogeneous multi-hop relaying system in which relay nodes (RNs) use different relaying methods due to the different versions or the cost structure of deployed RN equipments. Especially, we provide the outage performance of heterogeneous multiple-input multiple-output (MIMO) relaying of orthogonal space-time block code (OSTBC) transmission for spatially correlated Nakagami fading channels. In this letter, the heterogeneous RNs are comprised of decouple-and-forward (DCF) and decode-and-forward (DF) relays. The outage probability is obtained by assuming an ideal amplifying gain for DCF relaying and then verified with numerical investigation. The numerical results also show the impact of various combinations of DCF and DF RNs on the outage performance.

On the MAC-BC duality of multiuser non-regenerative MIMO relay systems

Multiple input multiple output (MIMO) relaying techniques can greatly improve the spectral efficiency and extend network coverage for future wireless systems. This article investigates a multiuser MIMO relay channel, where a base station (BS) with multiple antennas communicates with multiple mobile stations (MS) via a relay station (RS) with multiple antennas. The RS applies linear processing to the received signal and then forwards the processed signal. The dual channel conditions between MIMO relay multiple access channel (MAC) and broadcast channel (BC) are first developed for single-relay scenario with white Gaussian noise. Then the MAC-BC duality for MIMO relay systems is established by proving that the capacity region of MIMO relay MAC is equal to that of dual MIMO relay BC under the same total network transmit power constraint. In addition, the duality is also extended to multi-relay scenario with arbitrary noise. Finally, several simple general numerical examples are provided to better illustrate the effectiveness of the MIMO relay MAC-BC duality.

Peroformance analysis of decode-and-forward MIMO relay channels with OSTBCs

Performance analysis is presented for multiple-input multiple-output (MIMO) relay channels employing transmit antenna diversity with orthogonal space-time block codes (OSTBCs), where the source and the destination are equipped with N s and N d antennas, and communicate with each other with the help of a multiple-antenna relay operating in decode-and-forward (DF) mode. Over independent, not necessarily identical Rayleigh fading channels, exact closed-form symbol error rate (SER) expressions are derived for various digital modulation formats for both the OSTBC transmission with and without the direct link. The moment generating functions (MGFs) for overall system signal-noise ratios (SNRs) are also derived, based on which we present a unified SER analysis. The analysis shows that full spatial diversity order can be achieved for the DF MIMO relay channel by adopting OSTBC transmissions and maximal ratio combining (MRC) receptions. All the analytical results are confirmed through comparison with the results obtained using Mento Carlo simulations.

Polarization and Spatial Statistics of Wideband MIMO Relay Channels in Urban Environment at 2.35 GHz

Relay, which promises to enhance the performance of future communication networks, is one of the most promising techniques for IMT-Advanced systems. In this paper, multiple-input multiple-output (MIMO) relay channels based on outdoor measurements are investigated. We focus on the link between the base station (BS) and the relay station (RS) as well as the link between the RS and the mobile station (MS). First of all, the channels were measured employing a real-time channel sounder in IMT-Advanced frequency band (2.35GHz with 50MHz bandwidth). Then, the parameters of multipath components (MPCs) are extracted utilizing space-alternating generalized expectation algorithm. MPC parameters of the two links are statistically analyzed and compared. The polarization and spatial statistics are gotten. The trends of power azimuth spectrum (PAS) and cross-polarization discrimination (XPD) with the separation between the RS and the MS are investigated. Based on the PAS, the propagation mechanisms of line-of-sight and non-line-of-sight scenarios are analyzed. Furthermore, an approximate closed-form expression of channel correlation is derived. The impacts of PAS and XPD on the channel correlation are studied. Finally, some guidelines for the antenna configurations of the BS, the RS and the MS are presented. The results reveal the different characteristics of relay channels and provide the basis for the practical deployment of relay systems.

Joint source-and-relay power allocation in multiple-input multiple-output amplify-and-forward relay systems: a non-convex problem and its solution

In this study, the joint source-and-relay power allocation (JPA) problem in multiple-input multiple-output (MIMO) relay systems is investigated. It is revealed for the first time that the JPA problem based on the mean squared error (MSE) minimisation or the achievable rate maximisation criterion possesses a partial convexity, that is, the cost function is convex with respect to (w.r.t.) part of the optimisation parameters only. It is then proved that a better partial convexity, namely, a partial convexity w.r.t. a larger subset of the optimisation parameters, can be achieved by relaxing the cost function with an upper or lower bound of the MSE or achievable rate. By exploiting the partial convexity properties disclosed, two iterative algorithms are proposed to solve the non-convex JPA problem. It is shown that the convergence of the proposed iterative algorithms is guaranteed because of the fact that each iteration follows a convex optimisation w.r.t. the partial parameters. Finally, it is shown by Monte Carlo simulations that the proposed algorithms outperform several existing methods including our own prior work.

Robust Joint Linear Precoding for AF MIMO Relay Broadcast Systems with Limited Feedback

This letter proposes a robust joint linear precoding scheme based on the minimum mean squared error (MMSE) criterion for amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay broadcast systems with limited feedback, where only the quantized channel direction information (CDI) of the forward channel is available for the base station (BS) and the relay station (RS). The proposed scheme employs an iterative algorithm which alternately optimizes the BS and RS precoders to jointly minimize the expected MSE conditioned on the quantized CDI.

Two-Way MIMO Relay Precoder Design with Channel State Information

In this paper, a two-way relay precoder is designed for multiple-input multiple-output (MIMO) distributed cooperative relay systems. A constrained optimization problem with respect to (w.r.t.) the relay precoder is formulated for the most general relay and antenna scenario, namely, multiple relays each with multiple antennas, It is shown that due to the difficulty of two-way distributed relaying mechanism as well as the block-diagonal nature of the relay precoding matrix, this optimization problem cannot be solved by existing one-way relaying methods. It is then proved that with full channel state information available at relays, the underlying problem can be converted to a convex optimization w.r.t. the non-zero entries of the relay precoding matrix only, such that the Lagrangian multiplier method is applicable to the relay precoder design, leading to a closed-form relay precoding solution. A simulation study is conducted to justify the superior performance of the proposed two-way relaying scheme.

Cooperative Transmission Using Quasi-Orthogonal Space-Time Block Codes with Adaptive Decode-and-Forward Relaying Protocol

In this paper, we propose a cooperative transmission scheme using quasi-orthogonal space-time block codes (QOSTBCs) for multiple-input multiple-output (MIMO) relay networks. Comparing with the conventional cooperative transmission scheme using orthogonal space-time block codes (OSTBCs), the proposed scheme can achieve higher bandwidth efficiency with the same decoding complexity. Moreover, an adaptive decode-and-forward (ADF) relaying protocol is proposed based on one-bit channel state information (CSI) feedback. According to the CSI feedback, a better transmission mode can be selected between the direct transmission and decode-and-forward (DF) cooperative transmission. In addition, the outage performance of the proposed scheme is investigated and a closed-form upper bound on the outage probability is derived. The performance analysis shows that the proposed scheme can achieve a full diversity order, which is higher than that of the direct and DF cooperative transmissions.

A Two-Stage Antenna Subset Selection Scheme for Amplify-and-Forward MIMO Relay Systems

A two-stage antenna subset selection scheme is proposed to maximize the channel capacity of amplify-and-forward multiple-input multiple-output relay systems. To reduce the computational complexity of the antenna selection process, the receive and transmit antenna selections are separated in a two-stage algorithm. In stage 1, a subset of receive antennas is selected at the relay node. A subset of transmit antennas is then selected at the relay node in stage 2. The simulation results demonstrate that the proposed scheme achieves nearly the same channel capacity with a reduced amount of computational complexity as compared to an exhaustive search.