Performance Analysis of Quantized Beamforming MIMO Systems

Multiple-input multiple-output (MIMO) wireless systems can achieve significant diversity and array gain by using single-stream transmit beamforming and receive combining. A MIMO beamforming system with feedback using a codebook based quantization of the beamforming vector allows practical implementation of such a strategy in a single-user scenario. The performance of this system in uncorrelated Rayleigh flat fading channels is studied from the point-of-view of signal-to-noise ratio (SNR) and outage probability. In this paper, lower bounds are derived on the expected SNR loss and the outage probability of systems that have a single receive antenna or two transmit antennas. For arbitrary transmit and receive antennas, approximations for the SNR loss and outage are derived. In particular, the SNR loss in a quantized MIMO beamforming system is characterized as a function of the number of quantization bits and the number of transmit and receive antennas. The analytical expressions are proved to be tight with asymptotically large feedback rate. Simulations show that the bounds and approximations are tight even at low feedback rates, thereby providing a benchmark for feedback system design     

On the Diversity Order of Spatial Multiplexing Systems With Transmit Antenna Selection: A Geometrical Approach

In recent years, the remarkable ability of multiple-input-multiple-output (MIMO) wireless communication systems to provide spatial diversity or multiplexing gains has been clearly demonstrated. For MIMO diversity schemes, it is well known that antenna selection methods that optimize the postprocessing signal-to-noise ratio (SNR) can preserve the diversity order of the original full-size MIMO system. On the other hand, the diversity order achieved by antenna selection in spatial multiplexing systems, especially those exploiting practical coding and decoding schemes, has not thus far been rigorously analyzed. In this paper, a geometrical framework is proposed to theoretically analyze the diversity order achieved by transmit antenna selection for separately encoded spatial multiplexing systems with linear and decision-feedback receivers. When two antennas are selected from the transmitter, the exact achievable diversity order is rigorously derived, which previously only appears as conjectures based on numerical results in the literature. If more than two antennas are selected, we give lower and upper bounds on the achievable diversity order. Furthermore, the same geometrical approach is used to evaluate the diversity-multiplexing tradeoff in spatial multiplexing systems with transmit antenna selection     

Spatial multiplexing with transmit antenna and constellation selection for correlated MIMO fading channels

We consider spatial multiplexing systems in correlated multiple-input multiple-output (MIMO) fading channels with equal power allocated to each transmit antenna. Under this constraint, the number and subset of transmit antennas together with the transmit symbol constellations are determined assuming knowledge of the channel correlation matrices. We first consider a fixed data rate system and vary the number of transmit antennas and constellation such that the minimum margin in the signal-to-noise ratio (SNR) is maximized for linear and Vertical Bell Laboratories Layered Space-Time (V-BLAST) receivers. We also derive transmit antenna and constellation selection criteria for a successive interference cancellation receiver (SCR) with a fixed detection order and a variable number of bits transmitted on each substream. Compared with a system using all available antennas, performance results show significant gains using a subset of transmit antennas, even for independent fading channels. Finally, we select a subset of transmit antennas to maximize data rate given a minimum SNR margin. A lower bound on the maximum outage data rate is derived. The maximum outage data rate of the SCR receiver is seen to be close to the outage channel capacity.     

Capacity of multiple-antenna fading channels: spatial fading correlation, double scattering, and keyhole

The capacity of multiple-input multiple-output (MIMO) wireless channels is limited by both the spatial fading correlation and rank deficiency of the channel. While spatial fading correlation reduces the diversity gains, rank deficiency due to double scattering or keyhole effects decreases the spatial multiplexing gains of multiple-antenna channels. In this paper, taking into account realistic propagation environments in the presence of spatial fading correlation, double scattering, and keyhole effects, we analyze the ergodic (or mean) MIMO capacity for an arbitrary finite number of transmit and receive antennas. We assume that the channel is unknown at the transmitter and perfectly known at the receiver so that equal power is allocated to each of the transmit antennas. Using some statistical properties of complex random matrices such as Gaussian matrices, Wishart (1928) matrices, and quadratic forms in the Gaussian matrix, we present a closed-form expression for the ergodic capacity of independent Rayleigh-fading MIMO channels and a tight upper bound for spatially correlated/double scattering MIMO channels. We also derive a closed-form capacity formula for keyhole MIMO channels. This analytic formula explicitly shows that the use of multiple antennas in keyhole channels only offers the diversity advantage, but provides no spatial multiplexing gains. Numerical results demonstrate the accuracy of our analytical expressions and the tightness of upper bounds.     

Capacity bounds for Cooperative diversity

In a cooperative diversity network, users cooperate to transmit each others' messages; to some extent nodes therefore collectively act as an antenna array and create a virtual or distributed multiple-input multiple-output (MIMO) system. In this paper, upper and lower bounds for the information-theoretic capacity of four-node ad hoc networks with two transmitters and two receivers using cooperative diversity are derived. One of the gains in a true MIMO system is a multiplexing gain in the high signal-to-noise ratio (SNR) regime, an extra factor in front of the log in the capacity expression. It is shown that cooperative diversity gives no such multiplexing gain, but it does give a high SNR additive gain, which is characterized in the paper     

Adaptive MIMO Transmission for Exploiting the Capacity of Spatially Correlated Channels

We consider a novel low-complexity adaptive multiple-input multiple-output (MIMO) transmission technique. The approach is based on switching between low-complexity transmission schemes, including statistical beamforming, double space-time transmit diversity, and spatial multiplexing, depending on the changing channel statistics, as a practical means of approaching the spatially correlated MIMO channel capacity. We first derive new ergodic capacity expressions for each MIMO transmission scheme in spatially correlated channels. Based on these results, we demonstrate that adaptive switching between MIMO schemes yields significant capacity gains over fixed transmission schemes. We also derive accurate analytical approximations for the optimal signal-to-noise-ratio switching thresholds, which correspond to the crossing-points of the capacity curves. These thresholds are shown to vary, depending on the spatial correlation, and are used to identify key switching parameters. Finally, we propose a practical switching algorithm that is shown to yield significant spectral efficiency improvements over nonadaptive schemes for typical channel scenarios     

Space-time modulation and coding over transmit correlated fading channels

Multi-dimensional space-time modulation schemes can be classified by the manner in which signal dimensions are shared among transmit antennas. In aggregate transmit antenna (ATA) systems, a generalization of Tarokh, Seshadri, Calderbank's (TSC) approach, there is total sharing of dimensions. In orthogonal transmit antenna (OTA) systems, a generalization of many traditional diversity schemes, there is no sharing of dimensions. In partially orthogonal transmit antennas (POTA), a combination of ATA with OTA, subsets of available dimensions are shared by subsets of transmit antennas. This letter considers such coded schemes for spatially correlated fading channels. Over strongly transmit correlated channels, in addition to coding and diversity gains, ATA and POTA can harvest a transmit beamforming-like gain. This letter presents a scheme, POTARep, designed to provide beamforming-like gain as well as diversity and coding gains, yielding improved performance over a highly transmit correlated channel.     

Characterizing the statistical properties of mutual information in MIMO channels

We consider Gaussian multiple-input multiple-output (MIMO) frequency-selective spatially correlated fading channels, assuming that the channel is unknown at the transmitter and perfectly known at the receiver. For Gaussian codebooks, using results from multivariate statistics, we derive an analytical expression for a tight lower bound on the ergodic capacity of such channels at any signal-to-noise ratio (SNR). We show that our bound is tighter than previously reported analytical lower bounds, and we proceed to analytically quantify the impact of spatial fading correlation on ergodic capacity. Based on a closed-form approximation of the variance of mutual information in correlated flat-fading MIMO channels, we provide insights into the multiplexing-diversity tradeoff for Gaussian code books. Furthermore, for a given total number of antennas, we consider the problem of finding the optimal (ergodic capacity maximizing) number of transmit and receive antennas, and we reveal the SNR-dependent nature of the maximization strategy. Finally, we present numerical results and comparisons between our capacity bounds and previously reported bounds.     

Adaptive antennas for space-time codes in outdoor channels

Space-time codes have been introduced to improve mobile system performance in a multipath fading environment. We consider a multiple-input multiple-output (MIMO) system with m mobile antennas and n base station antennas, in which there are L multipaths at the base station at distinct angles of arrival. We show that when the channel has no intersymbol interference (ISI), then adaptive antennas in the form of beamforming, can be combined with space-time coding, to achieve a diversity gain of mL and a large signal-to-noise ratio (SNR) gain whenever n/spl ges/L. When the channel has ISI, beamforming can be used by the MIMO systems to achieve an SNR gain over a single-input multiple-output system, although both systems have the same diversity gain.     

The Downlink Capacity of Single-User SA-MIMO System

In this paper, a novel multiple antenna system framework, which combines smart antennas (SA) with multiple-input-multiple-output (MIMO) at the transmitter, is proposed. The downlink capacity of the single-user SA-MIMO wireless systems is investigated. The joint optimization problem corresponding to the capacity is deduced. After that, upper bounds of the capacity are given in general case and in the case of equal power allocation, respectively. Furthermore, in the case of equal power allocation and the same direction of departure from one transmit smart antenna to all antenna arrays at the receiver the closed-form expression of the capacity is obtained. Some numerical results are given to show that smart antennas can bring significant capacity gain for the MIMO systems due to the smart antennas gain, without additional spatial degrees of freedom, especially at high SNR with strong correlation among the MIMO channel links or at low SNR.     

Outage probability of multi-hop MIMO relaying with transmit antenna selection and ideal relay gain over rayleigh fading channels

We present a study on the outage probability of multi-hop wireless communication systems with multiple-input multiple-output (MIMO) link based on the transmit antenna selection and the maximal-ratio combining (MRC) at the receiver. A nonregenerative system (NS) is investigated with an ideal amplifying gain. MIMO channels are assumed in uncorrelated Rayleigh fading.We derive a moment generating function (MGF) of the reciprocal of the end-to-end signal-to-noise ratio (SNR) and obtain a closed-form approximation on the outage probability through the numerical inversion of a Laplace transform. Numerical results show that the presented outage is exactly matched with the outage probability when assuming the ideal relay gain. For more practical gains, the result is shown to be a lowerbound that gets tight at high average SNR as well as for a small number of hops and/or of antennas. We also compare the outage probabilities of nonregenerative MIMO relaying with a regenerative counterpart for multiple hops.     

基于最大比合并的MIMO分集系统递增天线选择算法

MIMO分集系统天线选择技术可以在不增加系统射频链路的情况下,达到与全天线几乎相同的分集增益.针对发送端采用最大比发送,接收端采用最大比合并的MIMO分集系统,提出了一种递增天线选择方法,每次增加一根天线,并使得它与已选出的天线结合起来具有最大的信噪比增益.相对于对所有可用天线集进行遍历的最优算法,它减小了需要搜索的范围和每次搜索的计算量,降低了复杂度;相对于功控天线选择算法,它考虑了新增天线与已选出天线集之间的相关性,改善了性能.仿真结果表明,在误比特率、信道容量和信噪比增益方面,此算法和最优算法性能相近,且不随可用天线数和选出天线数的改变而改变.     

MIMO Broadcast Channels With Finite-Rate Feedback

Multiple transmit antennas in a downlink channel can provide tremendous capacity (i.e., multiplexing) gains, even when receivers have only single antennas. However, receiver and transmitter channel state information is generally required. In this correspondence, a system where each receiver has perfect channel knowledge, but the transmitter only receives quantized information regarding the channel instantiation is analyzed. The well-known zero-forcing transmission technique is considered, and simple expressions for the throughput degradation due to finite-rate feedback are derived. A key finding is that the feedback rate per mobile must be increased linearly with the signal-to-noise ratio (SNR) (in decibels) in order to achieve the full multiplexing gain. This is in sharp contrast to point-to-point multiple-input multiple-output (MIMO) systems, in which it is not necessary to increase the feedback rate as a function of the SNR     

Error performance of transmit beamforming with delayed and limited feedback

Feedback delay can severely affect the performance of transmit beamforming (TB) and the analytical quantification of the performance degradation has attracted much research interest recently. In this letter, we study the effect of delayed and limited-rate codebook index feedback on the error rate performance of TB systems over Rayleigh fading channels. We derive closed-form expressions for the moment generating function (MGF) and the probability density function (PDF) of the receiver output signal-to-noise ratio (SNR) including the effects of outdated and finite-rate feedback and further provide accurate analytical error rate expressions, which are verified by simulation results. The coding gain gap between the full-rate and limited-rate feedback and the coding gain advantage of multiple transmit antennas to the single antenna are analyzed, for limited and delayed feedback. These results are simple and concise and provide new analytical insight into the achievable diversity and combining gains and the loss caused by feedback delay for different system parameters and modulation formats.     

Performance Analysis of Multiuser Diversity in MIMO Systems with Antenna Selection

In this paper, a framework is presented to analyze the performance of multiuser diversity (MUD) in multiuser point-to-multipoint (PMP) MIMO systems with antenna selection. Based on this framework, the tight closed-form expressions of outage capacity and average symbol error rate are derived for the multiuser transmit antenna selection with maximal-ratio combining (TAS/MRC) system, by which we show how and with what characteristics antenna selection gains, MIMO antenna configurations and fading gains impact on the system performance, with an emphasis on the study of multiuser diversity influence. From both theoretical and simulation results, our study shows that in multiuser PMP TAS/MRC systems an diversity order equals to the product of the number of transmit antennas, number of receive antennas and number of users can be achieved; what's more, users plays a key role in the system performance and can be viewed as equivalent 'virtual" transmit antennas, which is the source of the multiuser diversity inherent exists in the multiuser system. This kind of diversity can be efficiently extracted in the design of multiantenna systems.     

Energy spreading transform based iterative signal detection for mimo fading channels

Multiple transmit and receive antenna arrays can be used to form multiple input and multiple output (MIMO) systems for diversity and multiplexing in wireless communications. In this paper, we develop iterative signal-detection schemes based on energy spreading transform (EST) (T. Hwang and Y. Li) for MIMO channels. The EST in a MIMO system improves signal-detection performance by spreading the symbol energy over the space and time domain. It also enables iterative signal detection without employing channel coding. Analytical and simulation results demonstrate that the performance of the proposed schemes is very close to that of the genie-aided receiver when there are a sufficiently large number of receive antennas and signal-to-noise ratio (SNR) is above a threshold     

On strategies of multiuser MIMO transmit signal processing

In this letter, we introduce five different strategies of linear transmit signal processing for multiuser multiple-input multiple-output (MIMO) systems and provide performance comparisons in terms of maximum throughput in both uncorrelated and correlated channels when the number of transmit antennas is much larger than the number of receive antennas. It is shown that the multiuser MIMO schemes are preferable to time-division multiple-access (TDMA)-based MIMO schemes, hence demonstrating the power of multiuser MIMO signal processing. Our work also indicates possibilities for future research in finding efficient suboptimal algorithms. As an example, we show that our multiuser MIMO decomposition scheme can improve the maximum throughput compared to TDMA-based MIMO schemes for large number of transmit antennas or high transmit power.     

Interference Mitigation in MIMO Systems by Subset Antenna Transmission

This paper investigates subset antenna transmission (SAT) for multiple-input multiple-output (MIMO) systems in the presence of strong dominant co-channel interferer. The capacity gain from SAT is investigated in the context of optimal antenna subset selection and power allocation. The SAT does not require channel state information of the co-channel interference, and achieves capacity gains by distributing the transmit power equally over a selected subset of the transmit antennas. The capacity gain of the SAT method is analyzed in terms of transmit power and eigenvalues of channel matrix, and its performance in V-BLAST MIMO systems with various signal constellations is evaluated by computer simulation.     

基于MIMO系统的准正交空时分组码的容量分析

应用于MIMO系统的准正交空时分组码可以获得较大的容量,同时能够提供较低的误码率。文中比较了MIMO系统的准正交空时分组码的容量与SIMO系统的容量。结果显示,在低SNR和接收天线数少的情况下,应用于MIMO系统的准正交空时分组码会产生较大的容量增益,但随着SNR和天线数目的增加,容量增益越来越不明显。另外,文中比较了MIMO系统中准正交空时分组码和正交空时分组码的容量,仿真结果表明前者的容量明显高于后者。     

Equal gain transmission in multiple-input multiple-output wireless systems

Multiple-input multiple-output (MIMO) wireless systems are of interest due to their ability to provide substantial gains in capacity and quality. The paper proposes equal gain transmission (EGT) to provide diversity advantage in MIMO systems experiencing Rayleigh fading. The applications of EGT with selection diversity combining, equal gain combining, and maximum ratio combining are addressed. It is proven that systems using EGT with any of these combining schemes achieve full diversity order when transmitting over a memoryless, flat-fading Rayleigh matrix channel with independent entries. Since, in practice, full channel knowledge at the transmitter is difficult to realize, a quantized version of EGT is proposed. An algorithm to construct a beamforming vector codebook that guarantees full diversity order is presented. Monte-Carlo simulation comparisons with various beamforming and combining systems illustrate the performance as a function of quantization.