Finite-SNR Diversity–Multiplexing Tradeoff for Correlated Rayleigh and Rician MIMO Channels

A nonasymptotic framework is presented to analyze the diversity-multiplexing tradeoff of a multiple-input-multiple-output (MIMO) wireless system at finite signal-to-noise ratios (SNRs). The target data rate at each SNR is proportional to the capacity of an additive white Gaussian noise (AWGN) channel with an array gain. The proportionality constant, which can be interpreted as a finite-SNR spatial multiplexing gain, dictates the sensitivity of the rate adaptation policy to SNR. The diversity gain as a function of SNR for a fixed multiplexing gain is defined by the negative slope of the outage probability versus SNR curve on a log-log scale. The finite-SNR diversity gain provides an estimate of the additional power required to decrease the outage probability by a target amount. For general MIMO systems, lower bounds on the outage probabilities in correlated Rayleigh fading and Rician fading are used to estimate the diversity gain as a function of multiplexing gain and SNR. In addition, exact diversity gain expressions are determined for orthogonal space-time block codes (OSTBC). Spatial correlation significantly lowers the achievable diversity gain at finite SNR when compared to high-SNR asymptotic values. The presence of line-of-sight (LOS) components in Rician fading yields diversity gains higher than high-SNR asymptotic values at some SNRs and multiplexing gains while resulting in diversity gains near zero for multiplexing gains larger than unity. Furthermore, as the multiplexing gain approaches zero, the normalized limiting diversity gain, which can be interpreted in terms of the wideband slope and the high-SNR slope of spectral efficiency, exhibits slow convergence with SNR to the high-SNR asymptotic value. This finite-SNR framework for the diversity-multiplexing tradeoff is useful in MIMO system design for realistic SNRs and propagation environments     

The Throughput–Reliability Tradeoff in Block-Fading MIMO Channels

We build on Zheng and Tse's elegant formulation of diversity-multiplexing tradeoff (DMT) to provide a better understanding of the asymptotic interplay between transmission rate, error probability, and signal-to-noise ratio (SNR) in block-fading multiple-input multiple-output (MIMO) channels. In particular, we identify the limitation imposed by the notion of multiplexing gain and develop a new formulation called the throughput-reliability tradeoff (TRT), that avoids this limitation. The new characterization is then used to elucidate the asymptotic trends exhibited by the outage probability curves of block-fading MIMO channels     

Diversity‐multiplexing tradeoff over correlated Rayleigh fading channels: a non‐asymptotic analysis

In this paper, we present a finite‐signal‐to‐noise ratio (finite‐SNR) framework to establish tight bounds on the diversity‐multiplexing tradeoff of a multiple input multiple output (MIMO) system. We focus on a more realistic propagation environment where MIMO channel fading coefficients are correlated and where SNR values are finite. The impact of spatial correlation on the fundamental diversity‐multiplexing tradeoff is investigated. We present tight lower bounds on the outage probability of both spatially uncorrelated and correlated MIMO channels. Using these lower bounds, accurate finite‐SNR estimates of the diversity‐multiplexing tradeoff are derived. These estimates allow to gain insight on the impact of spatial correlation on the diversity‐multiplexing tradeoff at finite‐SNR. As expected, the diversity‐multiplexing tradeoff is severely degraded as the spatial correlation increases. For example, a MIMO system operating at a spectral efficiency of R bps/Hz and at an SNR of 5 dB in a moderately correlated channel, achieves a better diversity gain than a system operating at the same spectral efficiency and at an SNR of 10 dB in a highly correlated channel, when the multiplexing gain r is greater than 0.8. Another interesting point is that provided that the spatial correlation channel matrix is of full rank, the maximum diversity gain is not affected by the spatial correlation. Copyright © 2009 John Wiley & Sons, Ltd.     

Path diversity for DS-SSMA communications in Nakagami fading channels

Average error probability and outage probability for an asynchronous direct sequence spread spectrum multiple access communications through slow nonselective Nakagami fading channels are evaluated for nondiversity and diversity receptions. Using the Gauss quadrature rule, the moments of the self-interference and the multiple access interferences are used to evaluate average error probability and outage probability. Combining the diversity technique and error correcting codes, comparisons between the uncoded nondiversity DS-SSMA system and that of the coded diversity system are shown for the Gold Code of codelength 127. Using fourth-order diversity and the Reed-Solomon code, the maximum achievable number of users is 12 percent of the codelength for Rayleigh fading, when the average probability is 10^–3. The corresponding outage probability is less than 5 percent. Performance comparisons between Rician and Nakagami fading channels are made. Since the system is interference limited, the performance seems to show no significant difference for the two fading channel models when the number of users is large.     

Error Performance of DQPSK with EGC Diversity Reception over Fading Channels

This paper derives the average bit error probability (BEP) of differential quaternary phase shift keying (DQPSK) with postdetection equal gain combining (EGC) diversity reception over independent and arbitrarily correlated fading channels. First, using the associated Legendre functions, the average BEP of DQPSK is analyzed over independent Rayleigh, Nakagami-m, and Rician fading channels. Finite-series closed-form expressions for the average BEP of DQPSK over L-branch independent Rayleigh and Nakagami-m fading channels (for integer Lm) are presented. Besides, a finite-series closed-form expression is given for the average BEP of differential binary phase shift keying (DBPSK) with EGC over independent Rician fading channels. Second, an alternative approach is propounded to study the performance of DQPSK over arbitrarily correlated Nakagami-m and Rician fading channels. Relatively simple BEP expressions in terms of a finite sum of a finite-range integral are proposed. Moreover, the penalty in signal to noise ratio (SNR) due to arbitrarily correlated channel fading is also investigated. Finally, the accuracy of the results is verified by computer simulation.     

Performance of M-PSK with GSC and EGC with Gaussian weighting errors

Using a moment-generating function (MGF)-based approach, we study the performance of M-ary phase-shift keying (M-PSK) with generalized selection combining (GSC) and equal gain combining (EGC) in fading channels (including Rayleigh, Rician, Nakagami-m, and Nakagami-q fading) with independent and identically distributed (i.i.d) branches. Analytical expressions for the error and outage probabilities, the signal-to-noise-ratio (SNR) statistics, and the channel capacity of M-PSK diversity receivers are derived, taking into account the effects of Gaussian weighting errors and all relevant system and channel parameters. Unlike the case of perfect channel-state information (CSI), the outage probability for the case of imperfect channel estimation (ICE) is not only a function of the normalized SNR with respect to the SNR threshold, but also a function of the operating SNR itself. The SNR loss of the M-PSK GSC and EGC receivers due to ICE and the relation between the receiver input and output SNRs for ICE are derived. Our results show that, even with ICE, GSC and EGC are effective in improving the output SNR and significantly reduce the error floor and the channel-capacity loss caused by ICE.     

Block-Based Performance Measures for MIMO OFDM Beamforming Systems

In this paper, we consider an adaptive modulation system with multiple-input–multiple-output (MIMO) antennas in conjunction with orthogonal frequency-division multiplexing (OFDM) operating over frequency-selective Rayleigh fading environments. In particular, we consider a type of beamforming with a maximum ratio transmission/maximum ratio combining (MRT-MRC) transceiver structure. For this system, we derive a central limit theorem for various block-based performance metrics. This motivates an accurate Gaussian approximation to the system data rate and the number of outages per OFDM block. In addition to the data rate and outage distributions, we also consider the subcarrier signal-to-noise ratio (SNR) as a process in the frequency domain and compute level crossing rates (LCRs) and average fade bandwidths (AFBs). Hence, we provide fundamental but novel results for the MIMO OFDM channel. The accuracy of these results is verified by Monte Carlo simulations, and applications to performance analysis and system design are discussed.      

General Capacity Bounds for Spatially Correlated Rician MIMO Channels

This paper considers the capacity of spatially correlated Rician multiple-input multiple-output (MIMO) channels. We consider the general case with double-sided correlation and arbitrary rank channel means. We derive tight upper and lower bounds on the ergodic capacity. In the particular cases when the numbers of transmit and receive antennas are equal, or when the correlation is single sided, we derive more specific bounds which are computationally efficient. The bounds are shown to reduce to known results in cases of independent and identically distributed (i.i.d.) and correlated Rayleigh MIMO channels. We also analyze the outage characteristics of the correlated Rician MIMO channels at high signal-to-noise ratio (SNR). We derive the mean and variance of the mutual information and show that it is well approximated by a Gaussian distribution. Finally, we present numerical results which show the effect of the antenna configuration, correlation level (angle spreads), Rician$K$-factor, and the geometry of the dominant Rician paths.     

Asymptotic analysis of multi‐branch EGC and SC over equally correlated Rician channels

Closed‐form asymptotic expressions for bit error rate and outage probability are derived for multi‐branch equal gain combining and selection combining receiver diversity over equally correlated Rician channels. Numerical results indicate that these analytical solutions can provide accurate estimation of bit error rate and outage probability in large signal‐to‐noise ratio regimes. The analytical results reveal some important insights into the performance characteristics of equal gain combining and selection combining diversity operating over equally correlated Rician fading channels. Copyright © 2013 John Wiley & Sons, Ltd.     

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.     

Analytical modelling of multiservice switching networks with multiservice sources and resource management mechanisms

In this paper, we presents an analytical link capacity and outage performance analysis of downlink multiuser diversity (MUD) in multiple-input multiple-output (MIMO) system employing maximal-ratio combining (MRC) with transmit antenna selection (TAS) in the presence of imperfect channel state information (CSI) due to feedback delay over Rayleigh fading channels. The unified achievable analysis is appropriate for MUD–MIMO with TAS/MRC systems in which effective output signal-to-noise ratio (SNR) is specified as highest order statistic of chi-square distribution. Based on this framework, the closed-form channel capacity and outage probability expressions are examined for the MUD–MIMO exploiting TAS/MRC with normalized SNR based scheduling in heterogeneous wireless networks. Further, we derive approximate upper bound capacity as well as capacity at high SNR and low SNR region under delayed feedback CSI. The upper and lower bound of outage probability under delayed feedback CSI is also evaluated. Thereafter the impact of feedback delay and antenna structures with significance on the consideration of MUD on the performance of the system has been analyzed.     

Performance of transmit diversity assisted amplify-and-forward relay system with partial relay selection in mixed Rayleigh and Rician fading channels

The performance of transmit diversity(TD)assisted amplify-and-forward(AF)relay system with partial relay selection,which experiences mixed Rayleigh and Rician fading channels,is investigated.We first investigate the closed-form expression of the cumulative distribution function for the end-to-end equivalent signal-to-noise ratio(SNR),and then the exact expressions of outage probability and average symbol error probability(SEP)are derived.The theoretical observations are verified by the Monte Carlo simulatio...     

认知选择协同分集任意信噪比中断概率的分析

选择中继已被证明是一种有效和实用的协作分集方法.但是,现有的分析主要集中在渐进高信噪比(SNR)区域,因此,研究认知选择协同分集系统任意信噪比的中断概率具有现实意义.推导了瑞利衰落信道选择中继协议的中断概率解析式,并进行了仿真.仿真结果表明,选择中继协议在任意信噪比情况下,增加中继节点可降低中断概率,而解码中继协议(DF)在低、中信噪比情况下不一定降低中断概率;同时,选择中继协议的中断性能和分集增益随频谱空穴检测能力的提高而增强.     

Channel Selection in Virtual MIMO Wireless Sensor Networks

In this paper, we present two practical algorithms for selecting a subset of channels in virtual multiple-input–multiple-output (MIMO) wireless sensor networks (WSNs) to balance the MIMO advantage consumption of sensor cooperation. If intracluster node-to-node multihop needs be taken into account, the maximum spanning tree searching (MASTS) algorithm, with respect to the cross-layer design, always provides a path connecting all sensors. When the WSN is organized in a manner of cluster-to-cluster multihop, the singular-value decomposition-QR with threshold (SVD-QR-T) approach selects the best subset of transmitters while keeping all receivers active. The threshold is adaptive by means of fuzzy c-means (FCM). These two approaches are compared by simulation against the case without channel selection in terms of capacity, bit error rate (BER), and multiplexing gain with water filling or equal transmission power allocation. Despite less multiplexing gain, when water filling is applied, MASTS achieves higher capacity and lower BER than virtual MIMO without channel selection at moderate-to-high signal-to-noise ratio (SNR), whereas SVD-QR-T by FCM provides the lowest BER at high SNR; in the case of no water filling and equal transmission power allocation, MASTS still offers the highest capacity at moderate-to-high SNR, but SVD-QR-T by FCM achieves the lowest BER. Both algorithms provide satisfying performances with reduced resource consumption.      

Approximately universal codes over slow-fading channels

Performance of reliable communication over a coherent slow-fading multiple-input multiple-output (MIMO) channel at high signal-to-noise ratio (SNR) is succinctly captured as a fundamental tradeoff between diversity and multiplexing gains. This paper studies the problem of designing codes that optimally tradeoff the diversity and multiplexing gains. The main contribution is a precise characterization of codes that are universally tradeoff-optimal, i.e., they optimally tradeoff the diversity and multiplexing gains for every statistical characterization of the fading channel. This characterization is referred to as approximate universality; the approximation is in the connection between error probability and outage capacity with diversity and multiplexing gains, respectively. The characterization of approximate universality is then used to construct new coding schemes as well as to show optimality of several schemes proposed in the space-time coding literature.     

Fading Margin Analysis for Asynchronous CDMA Systems

In this paper, a detailed theoretical analysis of fading margin in an asynchronous code division multiple access (A-CDMA) system is discussed. Rayleigh and Rician frequency-selective slowly fading channels are considered. Probability distribution and density functions of the probability of error are derived for Rayleigh and Rician fading channels. The fluctuations in the channel capacity are proved to be directly proportional to the signal-to-noise ratio (SNR) variations. Fading margin is calculated for both Rayleigh and Rician fading channels as a function of the probability of error specification and the probability of unsatisfactory operation.     

Capacity of MIMO Rician channels

This paper presents exact results on the capacity of multiple-input-multiple-output (MIMO) Rician channels when perfect channel state information (CSI) is assumed at the receiver but the transmitter has neither instantaneous nor statistical CSI. It first derives the exact expression for the average mutual information (MI) rate of MIMO Rician fading channels when the fading coefficients are independent but not necessarily identically distributed. The results for the independent and identically distributed (i.i.d.) MIMO Rician and Rayleigh fading channels are also obtained as special cases. These results are derived using a different approach than the one used by Telatar for the i.i.d. Rayleigh case. The complementary cumulative distribution function (CCDF) of the MI is also obtained using a Gaussian approximation. The CDF of MI can serve as an upper bound to the outage probability of nonergodic MIMO Rician channels. Numerical results confirm that for a fixed channel gain, a strong tine-of-sight component decreases the channel capacity due to the lack of scattering.     

Transmit antenna selection for decision feedback detection in MIMO fading channels

In this paper, we investigate a transmit antenna selection (TAS) approach for the decision-feedback detector (DFD) over Rayleigh fading channels. In particular, for a multipleinput multiple-output (MIMO) channel with M transmit and N (N ⩾ M) receive antennas, we derive a lower bound on the outage probability for the TAS approach. The selected transmit antennas are those that maximize the post-processing signalto- noise ratio (SNR) at the receiver end. It is shown that the proposed TAS approach achieves a performance close to optimal selection based on exhaustive search, introduced in the literature, but at a lower complexity. Simulation results are presented to validate and demonstrate the performance gain of the proposed TAS approach.     

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     

Impact of Spatial Correlation on the Finite-SNR Diversity-Multiplexing Tradeoff

The impact of spatial correlation on the performance limits of multielement antenna (MEA) channels is analyzed in terms of the diversity-multiplexing tradeoff (DMT) at finite signal-to-noise ratio (SNR) values. A lower bound on the outage probability is first derived. Using this bound accurate finite-SNR estimate of the DMT is then derived. This estimate allows to gain insight on the impact of spatial correlation on the DMT at finite SNR. As expected, the DMT is severely degraded as the spatial correlation increases. Moreover, using asymptotic analysis, we show that our framework encompasses well-known results concerning the asymptotic behavior of the DMT.