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In this paper, we investigate the quantization and the feedback of downlink spatial covariance matrix for massive multiple-input multiple-output (MIMO) systems with cascaded precoding. Massive MIMO has gained a lot of attention recently because of its ability to significantly improve the network performance. To reduce the overhead of downlink channel estimation and uplink feedback in frequency-division duplex massive MIMO systems, cascaded precoding has been used to convert high-dimensional physical channels into low-dimensional effective channels. For the cascaded precoding, the inner precoder is determined by the downlink spatial covariance matrix, which is unknown in the base station (BS). To address this issue, we propose a spatial spectrum-based approach for the quantization and the feedback of the spatial covariance matrix. In this manner, the BS can obtain partial information on the downlink spatial covariance matrix. Our result shows that the inner precoder based on the proposed approach can be viewed as modulated discrete prolate spheroidal sequences and thus achieves much smaller spatial leakage than the traditional discrete Fourier transform submatrix-based precoding. Practical issues for the application of the proposed approach are also addressed in this paper. [ABSTRACT FROM PUBLISHER]

In this paper, we address the ordering of transmit antennas according to reliability for unequal error protection (UEP) in spatially multiplexed (SM) multiple-input multiple-output (MIMO) systems with joint detection at the receiver. When zero-forcing (ZF) detection is adopted, the reliabilities of transmit antennas are explicitly expressed as postequalization signal-to-noise ratios (SNRs). Thus, multiantenna UEP can be implemented by assigning data of high priority to transmit antennas with a high postequalization SNR. Unfortunately, the overall error performance is generally unsatisfactory. Various joint signal detection techniques that achieve maximum likelihood (ML) or near-ML performance have been developed as alternatives to ZF, but it is not obvious how to discriminate the reliabilities of the transmit antennas or the jointly detected symbols. Recently, an ordering technique for antenna reliabilities was proposed that exploits the structure of the previous near-optimal QR-decomposition-based least-reliable-layer joint detection. In this paper, we divide the log-likelihood ratio of each symbol into collaborative and individual components, assuming joint ML detection. We derive a statistical connection between the magnitude order of each component of the multiple symbols (or the corresponding transmit antennas) and the post-ZF-equalization SNRs. Based on the statistical connections, we propose the use of post-ZF-equalization SNR as a criterion for antenna reliability ordering of SM MIMO with various near-optimal, as well as optimal, joint detections. The differentiated error performance of transmit antennas is also shown to be mainly attributed to the difference of individual components, and the tendency becomes stronger as the constellation size increases. Simulations demonstrate that the proposed ordering technique better meets the UEP requirement with lower computational complexity than the conventional ordering. Assuming N_t \times N_t MIMO systems, the previous ordering and the proposed ordering require \mathcal{O}(N_t^3)+\sum_{N=2}^{N_t-1}\mathcal{O}(NN_t^2+N^3) and \mathcal{O}(N_t^3)$, respectively. [ABSTRACT FROM PUBLISHER]

In this paper, we propose a novel receiver scheme for multiple-input–multiple-output (MIMO) single-carrier frequency-division multiple access (SC-FDMA) systems. Various optimal and near-optimalMIMO detection techniques developed for flat-fading channels are not readily applied to MIMO SC-FDMA systems due to the large dimensions of the effective channels. Recently, the system equation of single-input–single-output (SISO) SC-FDMA systems was divided into a number of disjoint subsystems with moderate dimensions, and a previous MIMO detection technique was applied to the subsystems. In this paper, instead of naively extending the previous scheme for SISO SC-FDMA to MIMO SC-FDMA systems, we first express the large system equation of MIMO SC-FDMA, such that the effective channels are block circulant for an arbitrary number of transmit and receive antennas. The block circulant channel structure is then exploited to lower the computational complexity of projections to construct nonoverlapping subsystems. The proposed circulant projection also takes advantage of the sparse channel structure, offering higher postprojection signal-to-noise ratios (SNRs) of the resulting subsystems than those of a naive projection that does not exploit the channel structure. The simulations confirm the desirable performance of the proposed scheme when a relatively small number of subcarriers are used. The proposed technique is also compared with the previous iterative block decision feedback equalization (IB-DFE) and minimum-mean-square-error–prewhitened-maximum-likelihood (MMSE-prewhitened-ML) detection techniques. [ABSTRACT FROM PUBLISHER]

Channel state information (CSI) is critical for the performance of cooperative multicell transmission. In this paper, the performances of cooperative multicell precoding under global CSI and local individual CSI are analyzed and compared in the large dimensional regime. Using theoretical results from large random matrix theory, we derive large dimensional approximations of signal-to-interference-plus-noise ratio for both precoding cases. Such approximations depend only on the slow fading channel statistics instead of the fast fading channel realizations. It is easy to quantify the performance loss caused by local individual CSI in the large dimensional regime. Two different massive MIMO scenarios are considered. When the number of antennas and that of users go large at the same rate, there is a constant gap between the two CSI cases. When the number of antennas goes large, while the number of users is fixed, the performances of both CSI cases are the same. This means that the impact of limited local individual CSI vanishes. Numerical results validate the theoretical analysis and show that there is constant performance loss due to the price of limited CSI. Also, the performance of precoding with local individual CSI almost decreases linearly with the increased number of BSs for the first scenario. [ABSTRACT FROM PUBLISHER]

We investigate the performance of multiuser multiple-input-single-output (MU-MISO) downlink in the presence of the mutual coupling effect at the transmitter. Contrary to traditional approaches that aim at eliminating this effect, in this paper we propose a joint analog–digital (AD) beamforming scheme that exploits this effect to further improve the system performance. A jointly optimal AD beamformer is first obtained by iteratively maximizing the minimum received signal-to-interference-plus-noise ratio in the digital domain, followed by an optimization on the load impedance of each antenna element in the analog domain. We further introduce a decoupled low-complexity approach, with which existing closed-form beamforming schemes can also be efficiently applied. For the consideration of hardware imperfections in practice, we study the case where the analog load values are quantized, and propose a sequential search scheme based on greedy algorithm to efficiently obtain the desired quantized load values. Moreover, we also investigate the imperfect channel state information (CSI) scenarios, where we prove the optimality for closed-form beamformers, and further propose the robust schemes for two typical CSI error models. Simulation results show that with the proposed schemes the mutual coupling effect can be exploited to further improve the performance for both perfect CSI and imperfect CSI. [ABSTRACT FROM PUBLISHER]

In this paper, we study multiple-input multiple-output (MIMO) systems with a large number of antennas at a base station serving a number of users in a cell. The antennas at the base station are assembled into multiple antenna arrays (MAA), which are well separated to keep independence between the arrays, but in each array, antennas are densely installed. The MAA can be viewed as a flexible configuration of multiple antennas to reduce the space for installing the antennas and benefit from beamforming. In order to determine how dense the MAA can be designed, we define antenna area efficiency, that is the ratio of the achievable rate and the 2-D space required for installing the antennas. Then, we analyze the achievable rate of the massive MIMO system with $K$ uplink users and NM$ antenna elements at the base station placed in N$ square arrays and each array having antennas densely deployed. Specifically, the analytical uplink sum rate is first derived. Then, the sum rate in the low-SNR and high-SNR regimes is studied. A case study is provided to show how dense MAA can be designed in a massive MIMO system. Our analytical and simulations results show that, for ten users in low SNR, a single dense antenna array with $11\times 11$ antennas in a square requires only $1/200$ of the area of conventional 100 independent antennas to achieve the same rate. For ten users in high SNR, we find that two $8\times 8$ square arrays can achieve the highest antenna area efficiency in comparison with one $16\times 16$ antenna array, four $5\times 5$ antenna arrays, and 100 independent antennas. [ABSTRACT FROM PUBLISHER]

This paper investigates the secrecy outage performance of buffer-aided multirelay multiple-input multiple-output cooperative systems in the presence of a passive eavesdropper. Due to the unavailability of the channel state information of eavesdropper's channel, a buffer-aided joint transmit antenna and relay selection scheme based on the main channel is proposed to enhance the secrecy performance. Specifically, we model the evolution of the relay buffers as a Markov chain and derive new exact and asymptotic closed-form expressions for the secrecy outage probability, which provides an efficient way to assess the effect of system parameters on the secrecy outage probability. Moreover, simple asymptotic results are further exploited under two special scenarios, i.e., $L \rightarrow \infty$ and L \not\rightarrow \infty$ (where L$ denotes the size of the relay buffers), for characterizing the achievable secrecy diversity gain, the secrecy coding gain, and the secrecy diversity-multiplexing tradeoff. Our results reveal that: 1) a secrecy diversity gain of is achieved when $L \not\rightarrow \infty$, however, when $L \rightarrow \infty$, the secrecy diversity gain increases to $N_RM(N_S+N_D)$, where $N_S$, $N_R$ , and $N_D$ represent the number of antennas at the source, each of $M$ relays and the destination, respectively. 2) The eavesdropper's channel does not affect the secrecy diversity gain but only the secrecy coding gain in both the two scenarios. [ABSTRACT FROM AUTHOR]

This paper considers channel estimation and system performance for the uplink of a single-cell massive multiple-input multiple-output system. Each receiver antenna of the base station is assumed to be equipped with a pair of one-bit analog-to-digital converters to quantize the real and imaginary part of the received signal. We first propose an approach for channel estimation that is applicable for both flat and frequency-selective fading, based on the Bussgang decomposition that reformulates the nonlinear quantizer as a linear function with identical first- and second-order statistics. The resulting channel estimator outperforms previously proposed approaches across all SNRs. We then derive closed-form expressions for the achievable rate in flat fading channels assuming low SNR and a large number of users for the maximal ratio and zero forcing receivers that takes channel estimation error due to both noise and one-bit quantization into account. The closed-form expressions, in turn, allow us to obtain insight into important system design issues such as optimal resource allocation, maximal sum spectral efficiency, overall energy efficiency, and number of antennas. Numerical results are presented to verify our analytical results and demonstrate the benefit of optimizing system performance accordingly. [ABSTRACT FROM PUBLISHER]

In this paper, we investigate secure transmission over the large-scale multiple-antenna wiretap channel with finite alphabet inputs. First, we investigate the case where instantaneous channel state information (CSI) of the eavesdropper is known at the transmitter. We show analytically that a generalized singular value decomposition (GSVD)-based design, which is optimal for Gaussian inputs, may exhibit a severe performance loss for finite alphabet inputs in the high signal-to-noise ratio regime. In light of this, we propose a novel Per-Group-GSVD (PG-GSVD) design, which can effectively compensate the performance loss caused by the GSVD design. More importantly, the computational complexity of the PG-GSVD design is by orders of magnitude lower than that of the existing design for finite alphabet inputs while the resulting performance loss is minimal. Then, we extend the PG-GSVD design to the case where only statistical CSI of the eavesdropper is available at the transmitter. Numerical results indicate that the proposed PG-GSVD design can be efficiently implemented in large-scale multiple-antenna systems and achieves significant performance gains compared with the GSVD design. [ABSTRACT FROM PUBLISHER]

In this paper, we characterize the total degrees of freedom (DoFs) of the full-duplex asymmetric multiple-input multiple- output (MIMO) three-way channel. Each node has a separate-antenna full-duplex MIMO transceiver with a different number of antennas, where each antenna can be configured for either signal transmission or reception. We study this system under two message configurations; the first configuration is when each node has two unicast messages to be delivered to the two other nodes, while the second configuration is when each node has two unicast messages as well as one broadcast message to be delivered to the two other nodes. For each configuration, we first derive upper bounds on the total DoF of the system. Cut-set bounds in conjunction with genie-aided bounds are derived to characterize the achievable total DoF. Afterward, we analytically derive the optimal number of transmit and receive antennas at each node to maximize the total DoF of the system, subject to the total number of antennas at each node. Finally, the achievable schemes for each configuration are constructed. The proposed schemes are mainly based on zero-forcing and null-space transmit beamforming. We show that the derived outer and inner bounds on the total DoF are tight for each message configuration. [ABSTRACT FROM PUBLISHER]

Cooperative diversity systems with optimal and suboptimal antenna and relay selection have been paid significant attention for more than half a decade. However, optimal antenna and relay selection strategies require global channel state information (CSI), which is a cumbersome process. In this paper, we propose a diversity-optimal and three suboptimal transmit–receive antenna and relay selection strategies, named S1, S2, and S3, for decode-and-forward cooperative relaying systems, equipped with Nt and Nr antennas at the source (S) and the destination (D), respectively, and considering a multirelay scenario. Furthermore, we study the symbol error probability (SEP) for these strategies, assuming M-ary phase-shift keying signaling over Rayleigh fading channels. In addition, we perform diversity order analysis through closed-form asymptotic SEP expressions. Since the proposed suboptimal strategies, i.e., S2 and S3, involve the so-called switch-and-examine combining scheme, we compare the complexity of S1, S2, and S3 in terms of the average number of CSI required at D to select the best transmit–receive antenna pair and relay. From the derived SEP expressions, it can be concluded that all three suboptimal strategies achieve the same diversity order of N_{t}N_{r}+N, where N$ is the number of relays, except for the case when the switching threshold signal-to-noise ratio (SNR) is much lower than the average SNR in S2 and S3. Finally, the diversity-optimal strategy achieves full diversity order of N_{t}N_{r}+N\min(N_{t},N_{r}). [ABSTRACT FROM AUTHOR]

In this paper, we consider a dual-hop amplify-and-forward (AF) multiple-input–multiple-output (MIMO) relay network, where the source, relay, and destination are each equipped with multiple antennas. The relay is untrusted if it is willing to forward the signal to the destination and, at the same time, acts as a potential eavesdropper to interpret the message from the source. Since there exists no direct link between the source and the destination, a positive secrecy rate cannot be obtained. Addressing this issue, we propose a joint destination-aided cooperative jamming and precoding at both the source and the relay scheme: joint source, relay, and destination precoding (JP). We target at maximizing the secrecy rate by jointly designing the source, relay, and destination precoding matrices and propose an alternating iterative optimization algorithm to tackle the nonconvex problem. Then, a comprehensive study on the asymptotic performance is conducted in a high signal-to-noise ratio (SNR) regime. In particular, we present simple closed-form expressions for the two key performance parameters in the asymptotic secrecy rate, i.e., the high-SNR slope and the high-SNR power offset. Finally, numerical results are conducted to demonstrate the validity of the proposed secure scheme and its performance analysis. [ABSTRACT FROM PUBLISHER]

This paper investigates a transmission scheme that is suitable for short-range multiple-input–multiple-output (MIMO) transmission. Since the distance between two array antennas that face each other is comparable with the size of the array antenna aperture in short-range MIMO, the propagation characteristics are greatly different from those in conventional MIMO. Unlike conventional MIMO, the optimal element spacing, which maximizes channel capacity, exists in short-range MIMO. Moreover, the channel capacity with optimal antenna spacing exceeds the ergodic capacity of independent identically distributed (i.i.d.) channels since optimal eigenvalue distribution, which can maximize channel capacity, is obtained in the short-range MIMO. In this paper, we focus on the actual transmission methods, because complex transmission schemes such as eigenmode transmission or maximum-likelihood detection are required to obtain ideal channel capacity. We clarify that the channel capacity obtained by zero forcing (ZF) at the receiver without beamforming at the transmitter is almost the same as that using eigenmode transmission when considering the optimal element spacing. The effectiveness of short-range MIMO communication is also clarified using a 4 \times 4 MIMO testbed with actual signals based on the IEEE 802.11n standard. Simulated and measured results show that optimal element spacing is a key parameter in the short-range MIMO communication. We found that designing antenna arrays with optimal element spacing is a very effective approach to achieving a simple hardware configuration. [ABSTRACT FROM PUBLISHER]

Secrecy capacity is a fundamental information-theoretic performance metric to predict the maximum data rate of reliable communication, while the intended message is not revealed to the eavesdropper. Motivated by this consideration in this paper, a unified communication-theoretic framework for the analysis of the probability of nonzero secrecy capacity, the secrecy outage probability, and the secrecy capacity of multiple-antenna systems over fading channels is proposed. Specifically, a powerful frequency-domain approach is first developed in which the integrals involved in the evaluation of the probability of nonzero secrecy capacity and secrecy outage probability are transformed into the frequency domain, by employing Parseval’s theorem. A generic approach for the evaluation of the asymptotic secrecy outage probability at high signal-to-noise ratio (SNR) region is also introduced, thus providing useful insight as to the parameters affecting the secrecy performance. Finally, a unified numerical approach for computing the average secrecy capacity of multiple-antenna systems under arbitrary fading environments is developed. The proposed framework is general enough to accommodate any well-known multiantenna transmission technique and fading model. Finally, the secrecy performance of several multiple-antenna system setups is assessed, in the presence of generalized fading conditions and arbitrary antenna correlation, while various numerical and computer simulation results are shown and compared to substantiate the proposed mathematical analysis. [ABSTRACT FROM AUTHOR]

In this paper, we give a unified performance analysis of interference alignment (IA) over multiple-input–multiple-output (MIMO) interference channels. Rather than the asymptotic characterization, i.e., degree of freedom (DOF) at high signal-to-noise ratio (SNR), we focus on the other practical performance metrics, namely, outage probability, ergodic rate, and symbol error rate (SER). In particular, we consider imperfect IA because the transmitters usually have only imperfect channel state information (CSI) in a practical scenario. By characterizing the impact of imperfect CSI, we derive the exact closed-form expressions of outage probability, ergodic rate, and SER in terms of CSI accuracy, transmit SNR, channel condition, number of antennas, and the number of data streams of each communication pair. Furthermore, we obtain some important guidelines for performance optimization of IA under imperfect CSI by minimizing the performance loss over IA with perfect CSI. Finally, our theoretical claims are validated by simulation results. [ABSTRACT FROM PUBLISHER]

Massive multiple-input–multiple-output (MIMO) antenna system implies the use of a large number of base station (BS) antennas to serve a relatively small number of user terminals (UTs) for extraordinary spectral efficiency. However, its performance is limited by pilot contamination due to unavoidable reuse of pilot sequences from UTs in different cells. In this paper, we analyze the performance of massive MIMO zero-forcing (ZF) systems using the time-shifted pilot scheme, which was known to combat pilot contamination effectively using conjugate beamforming if there is a very large number of antennas. We derive expressions for achievable sum rates and the signal-to-interference-plus-noise ratios (SINRs) of forward and reverse links if the number of BS antennas is finite. Then, the impact of system parameters, such as cell radius, transmit power, group number (a parameter related to the time-shifted pilot scheme), BS antenna number, etc., on the system performance are revealed. Our model embraces a series of previous works as special cases. Moreover, we compare the performance of conjugate and ZF precoders, from which a simple but effective large-scale fading-based UT scheduling scheme is proposed to enhance the system throughput. [ABSTRACT FROM PUBLISHER]

This paper proposes an alignment based interference cancellation scheme for a multi-cell network with multiple-input multiple-output users under a Gaussian Interference compounded broadcast channel scenario. The basic idea is to split up the role of the transmit beamforming matrix according to the type of interference caused by each base station. It will be shown that, for a network of L base stations, the proposed method would result in achieving (L-1) degrees of freedom per user and convert the multi-cell multi-user MIMO channel into a set of single-cell single-user MIMO channels. Finally, we derive the relationship between all the relevant network elements as N_t=(L-d_s+1)K^\primeN_r+1, where N_t and $N_r$ are the numbers of transmit and receive antennas, respectively, L$ and d_s$ denote the number of cells and the number of data streams transmitted from each base station, and is the number of users per cell defined under the proposed system model. Hence, we show that the proposed scheme makes it possible to implement interference alignment using less antenna resources. [ABSTRACT FROM PUBLISHER]

In this paper, we propose transmit antenna selection with maximal ratio combining (TAS/MRC) in dual-hop decode-and-forward spectrum-sharing relaying networks with the primary user's interference and outdated channel state information (CSI). In this network, a single antenna that maximizes the received SNR is selected at the secondary transmitter, and the MRC is adopted at the secondary receiver. To efficiently evaluate the impact of key parameters on the system performance, we derive the exact analytical expression for the outage probability of the secondary network in a Rayleigh fading channel. Moreover, we present simple asymptotic expressions for the outage probability in a high SNR regime, which reveal practical insights on the achievable diversity order and coding gain. The findings suggest that whether the outdated CSI concerning the secondary transmission links has significant impact on the outage probability of the system depends on the interference power constraint at primary receivers. Specifically, under the proportional interference power constraint, the achievable diversity order is affected by imperfect CSI regarding the secondary transmission links, and the diversity–multiplexing tradeoff is independent of the primary network. However, under the fixed interference power constraint, the error floor is displayed, and the achievable diversity order reduces to zero regardless of the CSI concerning the secondary transmission links. [ABSTRACT FROM AUTHOR]

Modern communications systems use multiple-input multiple-output (MIMO) and high-order QAM constellations for maximizing spectral efficiency. However, as the number of antennas and the order of the constellation grow, the design of efficient and low-complexity MIMO receivers possesses big technical challenges. For example, symbol detection can no longer rely on maximum likelihood detection or sphere-decoding methods, as their complexity increases exponentially with the number of transmitters/receivers. In this paper, we propose a low-complexity high-accuracy MIMO symbol detector based on the Expectation Propagation (EP) algorithm. EP allows approximating iteratively at polynomial-time the posterior distribution of the transmitted symbols. We also show that our EP MIMO detector outperforms classic and state-of-the-art solutions reducing the symbol error rate at a reduced computational complexity. [ABSTRACT FROM PUBLISHER]

This paper investigates the power allocation problem for artificial noise (AN) secure precoding systems, and proposes closed-form solutions for maximizing the achievable secrecy rate. It is assumed that the transmitter knows the full channel information at the legitimate receiver, and knows only the statistics of the channel information at the eavesdropper. Lower bounds are derived for the secrecy rates in multiple-input single-output channels with single or multiple eavesdroppers and multiple-input multiple-output channels with multiple eavesdroppers. When the number of transmit antennas is sufficiently large, the bounds are tight, and closed-form solutions can be derived from these bounds. The analytical results suggest simple and yet informative solutions as follows: Let the numbers of receive antennas at the legitimate receiver and at the eavesdropper be Nr and Nr,e, respectively. The system should distribute Nr,e/(Nr+Nr,e) of the power to AN in the high SNR regime, and distribute zero power to AN in the low SNR regime; the rate loss due to the eavesdropper is -Nr\log(Nr/(Nr+Nr,e))-Nr,e\log(Nr,e/(Nr+Nr,e)) bits/sec/Hz in the high SNR regime and nearly negligible in the low SNR regime. The derived results also show that equal power and water-filling power allocations lead to similar solutions and rate loss. Simulation results corroborate the theoretical results. [ABSTRACT FROM PUBLISHER]

In this paper, we propose two relay antenna selection (RAS) schemes in multiple-input–multiple-output (MIMO) two-way relay networks, where an NA-antenna source and an NB-antenna source exchange information via an NR-antenna amplify-and-forward (AF) relay. The proposed RAS schemes maximize the minimum of the two overall end-to-end signal-to-noise ratio (SNR) values. In the first RAS scheme, transmit and receive beamforming (BF) is adopted at the two sources using all antennas. In the second RAS scheme, transmit and receive antenna selection (AS) is adopted at the two sources using one antenna. To conduct a performance comparison of the proposed RAS-BF and RAS-AS schemes, we first derive new expressions for the exact outage probability over independent but not necessarily identically distributed Nakagami- m fading channels. We then derive new closed-form lower and upper bounds on the outage probability to offer an efficient computation. We further derive new compact expressions for the asymptotic outage probability to characterize the performance in the high-SNR regime. Notably, we demonstrate that RAS-BF and RAS-AS achieve the full outage diversity order of \min\{N_{\rm A}N_{\rm R}m_{\rm A}, N_{\rm B}N_{\rm R}m_{\rm B}\}, where m_{\rm A} and mB denote the Nakagami- m fading parameters between the NA-antenna source and relay and between the NB-antenna source and relay, respectively. Based on asymptotic results, we determine a concise solution for the optimal power allocation among the sources and the relay to maximize the performance under the assumption that both the sources have the same transmit power. To quantify the effect of spatial correlation at the sources, we derive new closed-form expressions for the asymptotic outage probability over correlated Nakagami- $m$ fading channels. The results indicate that the spatial correlation has no impact on the outage diversity order but significantly deteriorates the outage array gain. [ABSTRACT FROM PUBLISHER]

This paper considers the ergodic noncoherent capacity of a multiple-input multiple-output frequency-flat block Rayleigh fading full duplex relay channel at high signal-to-noise ratios (SNRs). It is shown that, for these SNRs, restricting the input distribution to be isotropic on a compact Grassmann manifold maximizes an upper bound on the cut-set bound. Furthermore, it is shown that, from a degrees of freedom point of view, no relaying is necessary and Grassmannian signalling at the source achieves the upper bound within an SNR-independent gap. When the source-relay channel is sufficiently stronger than the source-destination and relay-destination channels, it is shown that, with the number of relay transmit antennas appropriately chosen, a Grassmannian decode-and-forward scheme, which is devised herein, achieves the ergodic noncoherent capacity of the relay channel within an approximation gap that goes to zero as the SNR goes to infinity. Closed-form expressions for the optimal number of relay transmit antennas indicate that this number decreases monotonically with the source transmit power. [ABSTRACT FROM AUTHOR]

This paper presents simple throughput models for multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems with hybrid automatic repeat request (HARQ). In particular, we consider the long term evolution (LTE) systems. Antenna correlations and power imbalances are implicitly included in the models. In order to explicitly characterize the antenna effects on throughput, we resort to the spatial multiplexing (SM) efficiency. The SM efficiencies of a MIMO antenna with zero forcing (ZF), minimum mean square error (MMSE), and maximum likelihood (ML) receivers are studied via numerical simulations using the throughput models. To verify the throughput models, the throughputs of two LTE terminals (including antenna correlations and power imbalances) are measured in a reverberation chamber (RC). Good agreements between the measured and modeled throughputs are observed. [ABSTRACT FROM PUBLISHER]

We present bounds and a closed-form high-SNR expression for the capacity of multiple-antenna systems affected by Wiener phase noise. Our results are developed for the scenario where a single oscillator drives all the radio-frequency circuitries at each transceiver (common oscillator setup), the input signal is subject to a peak-power constraint, and the channel matrix is deterministic. This scenario is relevant for line-of-sight multiple-antenna microwave backhaul links with sufficiently small antenna spacing at the transceivers. For the 2x 2 multiple-antenna case, for a Wiener phase-noise process with standard deviation equal to 6^°, and at the medium/high SNR values at which microwave backhaul links operate, the upper bound reported in the paper exhibits a 3\dB gap from a lower bound obtained using 64-QAM. Furthermore, in this SNR regime the closed-form high-SNR expression is shown to be accurate. [ABSTRACT FROM PUBLISHER]

In recent years, reconfigurable antennas have been sought to improve the performance of multiple-input multiple-output (MIMO) wireless communication systems. Their ability to dynamically reconfigure their radiation pattern adds diversity in a manner that is not possible with fixed antennas. This paper investigates the performance benefits provided by pattern reconfigurable receiving antennas with uniform beam steering capability. Their potential performance is first estimated using simulations, and for the first time, the effect of uniform beam steering on MIMO system performance is evaluated in a real indoor channel using two electrically steerable passive array radiator (ESPAR) antennas. Performance comparison is made against a pair of monopole antennas using a hardware bit error rate (BER) test-bed that incorporates statistical spatial averaging in order to assess performance improvements in a more realistic way, and analyze the effect of antenna diversity on the overall system performance. The MIMO-ESPAR system reduces BER with certain pattern combinations and excels in capacity evaluations. The ESPAR antennas improve the spatially averaged channel capacity by as much as 37% at 10 dB transmit SNR, and gain an additional 1 bit/s/Hz in peak capacity at 10 dB receive SNR from diversity gain alone. These improvements make pattern reconfigurable antennas promising options in MIMO-related applications. [ABSTRACT FROM PUBLISHER]

This paper experimentally demonstrates that, for two representative indoor distributed antenna system (DAS) scenarios, existing radio-over-fiber (RoF) DAS installations can enhance the capacity advantages of broadband 3 \times 3 multiple-input–multiple-output (MIMO) radio services without requiring additional fibers or multiplexing schemes. This is true for both single- and multiple-user cases with a single base station and multiple base stations. First, a theoretical example is used to illustrate that there is a negligible improvement in signal-to-noise ratio (SNR) when using a MIMO DAS with all N spatial streams replicated at N RAUs, compared with a MIMO DAS with only one of the N streams replicated at each RAU for N \leq \4. It is then experimentally confirmed that a 3 \times 3 MIMO DAS offers improved capacity and throughput compared with a 3 \times 3 MIMO collocated antenna system (CAS) for the single-user case in two typical indoor DAS scenarios, i.e., one with significant line-of-sight (LOS) propagation and the other with entirely non-line-of-sight (NLOS) propagation. The improvement in capacity is 3.2% and 4.1%, respectively. Then, experimental channel measurements confirm that there is a negligible capacity increase in the 3 \times 3 configuration with three spatial streams per antenna unit over the 3 \times 3 configuration with a single spatial stream per antenna unit. The former layout is observed to provide an increase of \sim1% in the median channel capacity in both the single- and multiple-user scenarios. With 20 users and three base stations, a MIMO DAS using the latter layout offers median aggregate capacities of 259 and 233 bit/s/Hz for the LOS and NLOS scenarios, respectively. It is concluded that DAS installations can further enhance the capacity offered to multiple users by multiple 3 \times 3 MIMO-enabled base stations. Further, designing future DAS systems to support broadband 3 \times 3 MIMO systems may not require significant upgrades to existing installations for small numbers of spatial streams. [ABSTRACT FROM PUBLISHER]

Opportunistic resource allocation for multiple users utilizing multiple-input multiple-output (MIMO) channel in orthogonal frequency division multiple access (OFDMA) is used to attain the spectral efficiency required in future wireless communications networks. In this paper, we express analytical outage capacity results and average capacity results with optimal rate adaptation for MIMO-OFDMA systems with limited feedback. A resource block (RB)-wise SNR quantization feedback scheme and a best-M feedback method are studied for RB allocation. Feedback based transmit antenna selection (AS) is considered in the analysis. An imperfect feedback channel has a significant impact on the performance of practical feedback based communication. The proposed analysis also considers imperfect feedback in the RB allocation and AS. [ABSTRACT FROM PUBLISHER]

In this paper, we present the efficient pilot patterns and channel estimations for a high-rate multi-input multi-output orthogonal frequency division multiplexing (MIMO-OFDM) system. In particular, we propose the scattered pilot (SP), edge pilot (EP), and continuous pilot (CP) by exploiting a basic orthogonal property of a unitary matrix. From the orthogonal property, we then propose the efficient channel frequency response (CFR) and channel impulse response (CIR) estimations. Finally, we evaluate the efficiency of the proposed schemes by comparing with a multi-input single-output OFDM (MISO-OFDM) system. [ABSTRACT FROM AUTHOR]

In most multiple-input multiple-output (MIMO) systems, the family of waterfall error curves, calculated at different spectral efficiencies, are asymptotically parallel at high signal-to-noise ratio. In other words, most MIMO systems exhibit a single diversity value for all fixed rates. The MIMO minimum mean square error (MMSE) receiver does not follow this pattern and exhibits a varying diversity in its family of error curves. This paper analyzes this interesting behavior of the MMSE MIMO receiver and produces the MMSE MIMO diversity at all rates. The diversity of the quasi-static flat-fading MIMO channel consisting of any arbitrary number of transmit and receive antennas is fully characterized, showing that full spatial diversity is possible if and only if the rate is within a certain bound which is a function of the number of antennas. For other rates, the available diversity is fully characterized. At sufficiently low rates, the MMSE receiver has a diversity similar to the maximum likelihood receiver (maximal diversity), while at high rates, it performs similarly to the zero-forcing receiver (minimal diversity). Linear receivers are also studied in the context of the MIMO multiple-access channel. Then, the quasi-static frequency selective MIMO channel is analyzed under zero-padding and cyclic-prefix (CP) block transmissions and MMSE reception, and lower and upper bounds on diversity are derived. For the special case of SIMO under CP, it is shown that the aforementioned bounds are tight. [ABSTRACT FROM PUBLISHER]

Large-scale propagation effect plays an important role in multiple-input multiple-output (MIMO) relay systems. In particular, the position of the relay (between the source and destination) determines the path-loss effects of adjacent hops, which will further affect the performance of each hop and thus the relay system. In this paper, by minimizing the outage probability of a decode-and-forward (DF) MIMO relay system with orthogonal space-time block coding, we show that relay position optimization improves the finite-SNR (signal-to-noise ratio) diversity gain of a relay system whose adjacent hops have different diversity orders (unbalanced system). Specifically, with relay position optimization, the diversity gain is no longer bounded by that of the weaker hop, i.e., the hop with a lower diversity order, but approaches the diversity order of the stronger hop. This diversity improvement provides a dramatic improvement for the end-to-end outage probability. It will also be shown that although power allocation has no effects on the achievable diversity order, it provides some SNR gains. [ABSTRACT FROM AUTHOR]

This paper proposes a low complexity protocol that preserves full diversity in multiuser amplify-and-forward relay networks with NS antennas at the source, NR antennas at the relay, and ND antennas at each of the K destinations. In the proposed protocol, a two-fold diversity is guaranteed: 1) multi-antenna diversity via transmit antenna selection with maximal-ratio combining (TAS/MRC), and 2) multiuser diversity via opportunistic scheduling. Under perfect feedback with precise channel state information (CSI), we derive new exact and asymptotic symbol error rate (SER) expressions in closed-form for the general case of Nakagami-m fading. We prove that the full diversity order of NSNDKmX+ min{NSNRmY,NRNDKmZ} is guaranteed, where mX, mY, and mZ denote the fading parameters of the source-destination, source-relay, and relay-destination links, respectively. To examine the impact of delayed feedback, we next derive new exact and asymptotic SER expressions in closed-form. We prove that in the presence of delayed feedback, outdated CSI degrades the diversity order to NDmX+ min{NRmY,NDmZ}. In addition, based on our asymptotic expressions, we determine the optimal power allocation between the source and the relay such that the SER is minimized. We show that optimal power allocation offers superior performance over uniform power allocation; highlighting a pivotal design choice for maximizing network performance without investing additional resources. [ABSTRACT FROM AUTHOR]

In this paper, we consider a secrecy relaying communication scenario where all nodes are equipped with multiple antennas. An eavesdropper has the access to the global channel state information (CSI), and all the other nodes only know the CSI not associated with the eavesdropper. A new secrecy transmission protocol is proposed, where the concept of interference alignment is combined with cooperative jamming to ensure that artificial noise from transmitters can be aligned at the destination, but not at the eavesdropper due to the randomness of wireless channels. Analytical results, such as ergodic secrecy rate and outage probability, are developed, from which more insightful understanding of the proposed protocol, such as multiplexing and diversity gains, can be obtained. A few special cases, where outage probability cannot be decreased to zero regardless of SNR, are also discussed. Simulation results are provided to demonstrate the performance of the proposed secrecy transmission protocol. [ABSTRACT FROM AUTHOR]

In this paper, we propose a linear precoder for the downlink of a multi-user MIMO system with multiple users that potentially act as eavesdroppers. The proposed precoder is based on regularized channel inversion (RCI) with a regularization parameter α and power allocation vector chosen in such a way that the achievable secrecy sum-rate is maximized. We consider the worst-case scenario for the multi-user MIMO system, where the transmitter assumes users cooperate to eavesdrop on other users. We derive the achievable secrecy sum-rate and obtain the closed-form expression for the optimal regularization parameter αLS of the precoder using large-system analysis. We show that the RCI precoder with αLS outperforms several other linear precoding schemes, and it achieves a secrecy sum-rate that has same scaling factor as the sum-rate achieved by the optimum RCI precoder without secrecy requirements. We propose a power allocation algorithm to maximize the secrecy sum-rate for fixed α. We then extend our algorithm to maximize the secrecy sum-rate by jointly optimizing α and the power allocation vector. The jointly optimized precoder outperforms RCI with αLS and equal power allocation by up to 20 percent at practical values of the signal-to-noise ratio and for 4 users and 4 transmit antennas. [ABSTRACT FROM AUTHOR]

In this paper, we study K-user multiple-input multiple-output (MIMO) interference channels (IC) in the presence of antenna correlations. Although interference alignment (IA) achieves the maximum multiplexing gain, i.e., degrees of freedom (DOF), the actual performance is degraded due to ill-conditioned channels caused by the antenna correlations. To enhance the overall system performance, we thus consider a transmission mode selection scheme which adaptively determines the number of data streams at each transmitter-receiver pair in a distributed fashion using local channel state information (CSI). A filter update process is exploited in order to estimate the performance regarding each transmission mode successively by considering the actual channel conditions as well as signal-to-noise ratio (SNR). Simulation results show that our mode selection scheme enhances the sum rate performance compared to the conventional full data stream transmissions in spatially correlated MIMO IC. [ABSTRACT FROM PUBLISHER]

In this paper, we compute two important information-theoretic quantities which arise in the application of multiple-input multiple-output (MIMO) antenna wireless communication systems: the distribution of the mutual information of multiantenna Gaussian channels, and the Gallager random coding upper bound on the error probability achievable by finite-length channel codes. We show that the mathematical problem underpinning both quantities is the computation of certain Hankel determinants generated by deformed versions of classical weight functions. For single-user MIMO systems, it is a deformed Laguerre weight; for multiuser MIMO systems, it is a deformed Jacobi weight. We apply two different methods to characterize each of these Hankel determinants. First, we employ the ladder operators of the corresponding monic orthogonal polynomials to give an exact characterization of the Hankel determinants in terms of Painlevé differential equations. This turns out to be a Painlevé V for the single-user MIMO scenario and a Painlevé VI for the multiuser scenario. We then introduce Coulomb fluid linear statistics methods to derive closed-form approximations for the MIMO mutual information distribution and the error probability which, although formally valid for large matrix dimensions, are shown to give accurate results even when the matrix dimensions are small. Focusing on the single-user mutual information distribution, we then employ the exact Painlevé V representation with the help of the Coulomb fluid linear statistics approximation to yield deeper insights into the scaling behavior in terms of the number of antennas and signal-to-noise ratio (SNR). Among other things, these results allow us to study the asymptotic Gaussianity of the distribution as the number of antennas increase, and to investigate when and why such approximations break down as the SNR increases. Based on the Painlevé, we also derive recursive formulas for explicitly computing in closed form any desired number of correction terms to the asymptotic mean and variance, as well as closed-form asymptotic expressions for any desired number of higher order cumulants. Using these cumulants, we propose new closed-form approximations to the mutual information distribution which are shown to be very accurate, not only in the bulk but also in the tail region of interest for the outage probability. [ABSTRACT FROM PUBLISHER]

In this paper, we investigate the secrecy rate of finite-alphabet communications over multiple-input–multiple-output–multiple-antenna eavesdropper (MIMOME) channels. Traditional precoding designs based on Gaussian input assumption may lead to substantial secrecy rate loss when the Gaussian input is replaced by practical finite-alphabet input. To address this issue, we investigate linear precoding designs to directly maximize the secrecy rate for MIMOME systems under the constraint of finite-alphabet input. By exploiting the theory of Karush–Kuhn–Tucker (KKT) analysis and matrix calculus, we first present necessary conditions of the optimal precoding design when instantaneous channel-state information (CSI) of the eavesdropper is known at the transmitter. In this light, an iterative algorithm for finding the optimal precoding matrix is developed, utilizing a gradient decent method with backtracking line search. Moreover, we find that the beamforming design in MIMONE systems, which is a secrecy-capacity-achieving approach for Gaussian signaling, no longer provides the maximum secrecy rate for finite-alphabet input data. This case is substantially different from the Gaussian input case. In addition, we derive the closed-form results on the precoding matrix, which maximizes the secrecy rate in the low signal-to-noise ratio (SNR) region, and reveal the optimal precoding structure in the high-SNR region. A novel jamming signal generation method that draws on the CSI of the eavesdropper to additionally increase the secrecy rate is further proposed. The precoding design with only statistical CSI of the eavesdropper available at the transmitter is also considered. Numerical results show that the proposed designs provide significant gains over recent precoding designs through a power control policy and the precoding design with the Gaussian input assumption in various scenarios. [ABSTRACT FROM PUBLISHER]

This paper investigates transmit antenna selection for linearly precoded multiuser multiple-input–multiple-output (MU-MIMO) systems. First, in some precoded single-user MIMO systems, using all transmit antennas does not always lead to the best performance due to ill-conditioned channel matrices. This condition motivates us to investigate whether a similar result can be obtained in MU-MIMO systems. Based on the derived analytical results, we found that, for a given number of transmit antennas, decreasing the number of active transmit antennas [number of radio frequency (RF) units] always degrades system performance in the linearly precoded MU-MIMO systems. However, in practical systems, RF units are expensive. To reduce the hardware cost, antenna selection is usually used to reduce the number of RF units. Thus, we further analyze the performance loss due to transmit antenna selection (TAS). These analytical results provide good design references for using TAS in practical systems. Moreover, based on the analytical results, we proposed several simple TAS algorithms for linearly precoded MU-MIMO systems. Complexity analysis and simulation results show that the computational complexity of the proposed algorithms can significantly be reduced, whereas the performance is still comparable with the optimal selection scheme. As a result, the analyzed results enable us to better understand how TAS affects the MU-MIMO systems. In addition, the proposed algorithms make TAS more feasible to be used in practical systems. [ABSTRACT FROM PUBLISHER]

Transmit antenna selection with receive maximal-ratio combining (TAS/MRC) and transmit antenna selection with receive selection combining (TAS/SC) are two attractive multiple-input–multiple-output (MIMO) protocols. In this paper, we present a framework for the comparative analysis of TAS/MRC and TAS/SC in a two-hop amplify-and-forward relay network. In doing so, we derive exact and asymptotic expressions for the symbol error rate (SER) in Nakagami-m fading. Using the asymptotic expressions, the SNR gap between the two protocols is quantified. Given that the two protocols maintain the same diversity order, we show that the SNR gap is entirely dependent on the array gain. Motivated by this, we derive the SNR gap as a simple ratio of the respective array gains of the two protocols. This ratio explicitly takes into account the impact of the number of antennas and the fading severity parameter m. In addition, we address the fundamental question of “How to allocate the total transmit power between the source and the relay in such a way that the SER is minimized?” Our answer is given in the form of new compact expressions for the power allocation factor, which is a practical design tool that optimally distributes the total transmit power in the network. [ABSTRACT FROM PUBLISHER]

In this paper, we consider transmit beamforming (BF) design under per-antenna power constraint (PPC) for multiple-input–single-output (MISO) frequency-selective channels. Both cyclic-prefixed (CP) single carriers and orthogonal frequency-division-multiplexing (OFDM) systems are investigated. Since there is no closed-form expression for the optimal PPC BF coefficients, and the optimization tools employed to find the PPC solution are usually complicated, here, we propose three computationally more effective suboptimal solutions to minimize the arithmetic mean of the effective error probabilities. Moreover, we address the issue of limited-rate feedback, and a simple codebook design method for frequency-selective channels is proposed. Unlike conventional methods where the codebook is directly designed for BF vectors, here, we construct codebooks for the amplitude and phase of the time-domain channel state information (CSI) to reduce the rate of feedback. Further, the nonuniform feedback strategy is investigated. Simulation results show that the proposed suboptimal solutions have much lower complexities than the convex optimization-based PPC solutions. The effectiveness of the proposed uniform and nonuniform limited-rate feedback methods is also demonstrated via simulations. [ABSTRACT FROM PUBLISHER]

This paper introduces some novel upper and lower bounds on the achievable sum rate of multiple-input multiple-output (MIMO) systems with zero-forcing (ZF) receivers. The presented bounds are not only tractable but also generic since they apply for different fading models of interest, such as uncorrelated/correlated Rayleigh fading and Ricean fading. We further formulate a new relationship between the sum rate and the first negative moment of the unordered eigenvalue of the instantaneous correlation matrix. The derived expressions are explicitly compared with some existing results on MIMO systems operating with optimal and minimum mean-squared error (MMSE) receivers. Based on our analytical results, we gain valuable insights into the implications of the model parameters, such as the number of antennas, spatial correlation and Ricean-K factor, on the sum rate of MIMO ZF receivers. [ABSTRACT FROM AUTHOR]

Opportunistic beamforming is a promising technique for downlink channels in cellular systems. When opportunistic beamforming is to support multiple users at a time, it is important to form multiple beams with as little interference as possible. In the conventional approach with limited feedback of channel state information from users, the best beamforming matrix can be selected from a set of multiple beamforming matrices. Thus, at each time when a different set of users are selected by a scheduler, a new beamforming matrix has to be found, which may require excessive complexity. To avoid this problem, in this paper, we propose an opportunistic beamforming approach with a single fixed beamforming matrix for stationary users. Since the beams are fixed, we only need to perform user selection (and power allocation if necessary). It is also shown that the proposed approach is suited for a distributed virtual antenna array built by multiple base station or access point units, since the intercorrelation between the users' channel vectors in this case allows effective opportunistic beamforming based on user classification in conjunction with a single beamforming matrix. [ABSTRACT FROM PUBLISHER]

Distributing the construction of a multiple-input multiple-output (MIMO) system among more than one mobile user reduces hardware and processing complexity at the terminal end, and may result in improved channel propagation conditions, particularly those related to spatial correlation. In this paper, measured outdoor propagation data is used to study a 4\,\times\,4 virtual MIMO system formed from a two-user 4\,\times\,4 classical system using only two of the antennas at each constituent user. The capacity, K-factor, and spatial correlation are evaluated for 226 possible pairs of users whose channels were measured while standing and walking. The proportions of pairings that result in a capacity increase and K-factor and correlation reductions over both, only one and neither of the constituents are determined. It is found that correlation reduction appears to be a stronger sign of capacity improvement than is K-factor reduction. When choosing a partner for a given single user, results show that it is easier to improve these three parameters as the user's value of them becomes poorer, so thresholds applicable to this data set are found which specify values of capacity, K, and correlation beyond which at least 50% of possible pairings improve matters. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the effects of channel estimation error on the receiver of multiple-input–multiple-output (MIMO) amplify-and-forward (AF) two-way relaying. The estimation is conducted via training using known pilot symbols transmitted from the terminals, which is a method commonly referred to as pilot symbol-aided modulation. In this context, linear minimum mean square estimation (LMMSE) of composite and individual channels is analyzed. We show that orthogonal pilots, i.e., pilot sequences that are orthogonal over the antenna arrays and the communicating terminals, minimize the composite and individual mean square errors. Using notions of worst-case noise, we obtain lower bounds on the sum rate of information transmission in both directions of the bidirectional relay link and show that the orthogonal pilots perform well against the bound. [ABSTRACT FROM PUBLISHER]

In this paper, we investigate the performance of a wireless relay network with each of its nodes equipped with N antennas and the same orthogonal space–time block coding (OSTBC) scheme adopted at its destination and relays for transmission. By deriving the performance expressions for a single-relay system, we obtain the maximum diversity order achievable by the channel-state information (CSI)-assisted amplify-and-forward (CAF) protocol. Then, by focusing on CAF multirelay systems subject to a total power constraint, we derive a simple approximate symbol error rate (SER) expression for the multiple-relay channels with and without relay selection revealing a higher achievable diversity order by using relay selection than its counterpart with fixed relay configuration. [ABSTRACT FROM PUBLISHER]

This paper provides a systematic characterization of Zero-Forcing (ZF) detectors over multiple-input multiple-output (MIMO) channels that experience both small and large-scale fading. In particular, we consider the generic K distribution (Rayleigh/gamma distribution) to model the composite fading fluctuations and also assume the general case of semi-correlated small-scale fading. In the following, novel exact analytical expressions for the achievable sum rate are derived, followed by asymptotic expressions in the high and low Signal-to-Noise ratio (SNR) regimes. In these limiting cases, two common and insightful affine expansions are studied followed by new, closed-form upper and lower bounds on the sum rate that remain tight for all SNRs. In the second part of the paper, we present exact tractable expressions along with first-order expansions for the symbol error rate (SER) and outage probability; we also quantify the performance of ZF detectors in terms of diversity order and array (or coding) gain. The implications of the model parameters on the ZF detector performance are investigated via Monte-Carlo simulations which also validate the theoretical analysis. [ABSTRACT FROM AUTHOR]

In this paper, we propose a general framework to quantify the average error probability of the minimum mean squared error based precoding schemes in amplify-and-forward relay networks where all nodes are equipped with multiple antennas. Especially, we investigate spatial multiplexing schemes which transmit multiple data streams simultaneously. Due to difficulty in finding an exact expression of the average error rate, we exploit the high signal-to-noise-ratio (SNR) based approach which allows a simple and accurate characterization of the performance. Then, we derive new closed form expressions for bit error rate performance of both the optimal source-relay joint precoding schemes and the optimal relay only precoding schemes in terms of a coding gain as well as a diversity gain. Taking a different pathloss in each hop into consideration, we evaluate the performance in a generalized environment. Through our analysis, we discuss several interesting observations and provide a helpful guideline for designing MMSE-based relaying systems. Monte-Carlo simulations show that our analytical work accurately predicts numerical results. [ABSTRACT FROM PUBLISHER]

In this paper, we address the issue of multiaccess communication through multi-hop linear non-regenerative relays, where all users, all relay nodes, and the destination node may have multiple antennas. Using a linear minimal mean-squared error (MMSE) receiver at the destination node, we demonstrate that the optimal amplifying matrix at each relay node can be viewed as a linear MMSE filter concatenated with another linear filter. As a consequence, the MSE matrix of the signal waveform estimation at the destination node is decomposed into the sum of the MSE matrices at all relay nodes. We show that at a high signal-to-noise ratio (SNR) environment, this MSE matrix decomposition significantly simplifies the solution to the problem of optimizing the source precoding matrices and relay amplifying matrices. Simulation results show that even at the low to medium SNR range, the simplified optimization algorithms have only a marginal performance degradation but a greatly reduced computational complexity and signalling overhead compared with the existing optimal iterative algorithm, and thus are of great interest for practical relay systems. [ABSTRACT FROM AUTHOR]