Capacity of MIMO channels: asymptotic evaluation under correlated fading

This paper investigates the asymptotic uniform power allocation capacity of frequency nonselective multiple-input multiple-output channels with fading correlation at either the transmitter or the receiver. We consider the asymptotic situation, where the number of inputs and outputs increase without bound at the same rate. A simple uniparametric model for the fading correlation function is proposed and the asymptotic capacity per antenna is derived in closed form. Although the proposed correlation model is introduced only for mathematical convenience, it is shown that its shape is very close to an exponentially decaying correlation function. The asymptotic expression obtained provides a simple and yet useful way of relating the actual fading correlation to the asymptotic capacity per antenna from a purely analytical point of view. For example, the asymptotic expressions indicate that fading correlation is more harmful when arising at the side with less antennas. Moreover, fading correlation does not influence the rate of growth of the asymptotic capacity per receive antenna with high E/sub b//N/sub 0/.     

Capacity scaling and spectral efficiency in wide-band correlated MIMO channels

The dramatic linear increase in ergodic capacity with the number of antennas promised by multiple-input multiple-output (MIMO) wireless communication systems is based on idealized channel models representing a rich scattering environment. Is such scaling sustainable in realistic scattering scenarios? Existing physical models, although realistic, are intractable for addressing this problem analytically due to their complicated nonlinear dependence on propagation path parameters, such as the angles of arrival and delays. In this paper, we leverage a recently introduced virtual representation of physical models that is essentially a Fourier series representation of wide-band MIMO channels in terms of fixed virtual angles and delays. Motivated by physical considerations, we propose a D-connected model for correlated channels defined by a virtual spatial channel matrix consisting of D nonvanishing diagonals with independent and identically distributed (i.i.d.) Gaussian entries. The parameter D provides a meaningful and tractable measure of the richness of scattering. We derive general bounds for the coherent ergodic capacity and investigate capacity scaling with the number of antennas and bandwidth. In the large antenna regime, we show that linear capacity scaling is possible if D scales linearly with the number of antennas. This, in turn, is possible if the number of resolvable paths grows quadratically with the number of antennas. The capacity saturates for linear growth in the number of paths (fixed D). The ergodic capacity does not depend on frequency selectivity of the channel in the wide-band case. Increasing bandwidth tightens the bounds and hastens the convergence of scaling behavior. For large bandwidth, the capacity scales linearly with the signal-to-noise ratio (SNR) as well. We also provide an explicit characterization of the wide-band slope recently proposed by Verdu. Numerical results are presented to illustrate the key theoretical results.     

Optimum transmit-receive beamforming with noisy channel estimates for correlated MIMO Rayleigh channels

In this paper, we design jointly optimum transmitter and receiver beamforming structures in correlated MIMO Rayleigh fading channels with noisy channel estimates, and evaluate their performance through a closed-form expression for the probability of error. At the receiver, an estimate of the channel is obtained based on the transmitted pilot symbols. The knowledge of the estimate is then made available to the transmitter through a feedback channel. It is assumed that spatial correlation exists, either at the transmitter or at the receiver. A new exact closed-form expression for the probability of error is derived and the joint effects of diversity order and channel estimation accuracy on system performance are analyzed.     

相关Rician衰落信道下紧凑MIMO系统的容量分析

研究了Rician衰落信道下采用紧凑型双偶极子阵列的MIMO系统容量,建立了相关Rician衰落信道下紧凑MIMO系统的模型,深入分析了天线互耦、空间相关性、功率分配方案以及信道衰落环境对信道容量的影响。数值结果表明天线间距较小时,互耦和相关性会导致信道容量的损失,而在某些情况下互耦和相关性的影响会使信道容量有所增加。     

Adaptive spatial modulation and thresholds optimization for MIMO systems in correlated Rayleigh channels

Spatial modulation (SM) is a simple and spectral efficient modulation technique that has received much interest recently. In this paper, an adaptive SM (ASM) scheme is presented by combining adaptive modulation with conventional SM. The performance of ASM is analyzed in spatially correlated Rayleigh fading channels. In order to reduce the computational complexity of average bit error rate (BER), an approximate expression of error probability of the antenna index estimation, which contributes one of two components of the average BER, is derived by using the fitting method and matches well with simulation results in the SNR range of interest. With the above results, the closed-form spectrum efficiency (SE) and overall average BER are obtained, respectively. Besides, the optimized switching thresholds for maximizing SE under an average BER constraint are achieved by means of the Karush Kuhn Tucker conditions, and the resultant SE performance can be improved greatly when compared to the ASM system with fixed thresholds. Simulations indicate that the theoretical SE and BER are effective and agree well with the corresponding simulations. Moreover, the SE and BER performance of ASM under spatially correlated channel are poorer than those under spatially independent channel because of the influence of spatial correlation.     

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.     

Decision-directed estimation of MIMO time-varying Rayleigh fading channels

This paper presents a decision-directed (DD) maximum a posteriori probability (MAP) channel-estimation scheme for multiple-input multiple-output (MIMO) time-varying fading channels. With the estimate of the channel matrix for the current symbol interval, a zero-forcing (ZF) receiver is applied to detect the spatially multiplexed data on a symbol-by-symbol basis. Symbol decisions are then fed to the channel predictor for estimation of channel coefficients in future symbol intervals. Simulated error performance of a ZF receiver with the DD MAP and perfect channel estimates is provided and compared.     

Rayleigh环境下MIMO系统容量分析

研究了多输入多输出(MIMO)系统Rayleigh衰落信道矩阵的特征值以及天线空间相关性对信道容量的影响.Monte-Carlo数值仿真结果表明:MIMO系统能极大提高Rayleigh衰落环境中的系统容量,且容量随最小收发天线数目的增加而线性增加,但由于相关性对信道矩阵特征值及其统计分布的影响较大,因此可导致MIMO系统容量的损失.     

Some remarkable properties of diagonally correlated MIMO channels

This paper investigates so-called diagonally correlated multiple input-multiple output (MIMO) channels, which provide higher ergodic capacity than independent and identically distributed (i.i.d.) fading channels. The presented analysis details physical scenarios leading to such channels, some properties of the channel matrix, and an analytical expression for its ergodic capacity.     

Closed-form capacity expressions of orthogonalized correlated MIMO channels

Space-time block codes are known to orthogonalize the multiple-input multiple-output (MIMO) wireless channel, thus reducing the space-time vector detection to a simpler scalar detection problem. The capacity over orthogonalized ergodic correlated Rayleigh and Ricean flat-fading MIMO channels has so far only been given in integral form. This letter derives a closed form capacity expression over such channels, hence avoiding numerical integrations or Monte Carlo simulations.     

Robust space-time codes for correlated Rayleigh fading channels

Space-time (ST) coding has emerged as an effective strategy to enhance performance of wireless communications in fading environments. Many different ST coding schemes have been proposed to achieve reliable communications in independent fading channels. However, a design of robust ST codes for correlated fading channels has not been addressed. We propose a simple robust ST coding scheme that achieves robust performance over a wide range of fading conditions. The key to achieve robust performance is to formulate code design criteria that are not dependent on the channel correlation statistics. A provably robust scheme can be formulated by concatenating a full-rank ST block code with an outer encoder. We derive several robust code examples via the concatenated orthogonal ST block code and TCM construction. The simulation results show that some traditional ST codes perform poorly, whereas the proposed codes achieve robust performance over a broad range of fading conditions.     

Approximate distribution of capacity of Rayleigh fading MIMO channels

Approximate closed-form density and distribution functions for the capacity of multiple-input multiple-output (MIMO) radio systems in spatially semi-correlated Rayleigh fading channels are derived. The approximations are given in terms of the Meijer G-function, hence allowing easy numerical evaluation of capacity outage probabilities with, for example, Maple or Mathematica.     

Capacity lower bound and energy efficiency of training‐based MIMO systems over correlated channels

The behavior of training‐based multiple‐input multiple‐output wireless communications over correlated channels is studied in the low signal‐to‐noise ratio (SNR) regime from an energy efficiency perspective. To start with, a relaxed but analytically more tractable capacity lower bound is derived where the impacts of channel spatial correlation are considered simply through the ranks of correlation matrices. It shows that, different from the independent and identically distributed case, the optimal training length no longer equals the number of transmit antennas but is just the same as the rank of transmit correlation matrix. Next, the bit energy requirements are analyzed based on the derived capacity lower bound. It shows that the minimum bit energy required for reliable communication is achieved at a nonzero SNR value below, which the bit energy grows to infinity with a zero‐approaching wideband slope. Flash training and transmission scheme is also studied and shown to improve the energy efficiency. In addition, the impacts of spatial correlation, channel coherence interval and antenna number on the energy efficiency are analyzed. It shows that stronger spatial correlation leads to less bit energy, i.e. higher‐energy efficiency. The minimum bit energy is achieved at lower SNR in a more correlated channel. Spatial correlation also helps to reduce the signal peakiness in the flash scheme. And larger coherence interval always improves energy efficiency at all SNR. Finally, the validity of the proposed results is verified by numerical simulations. Copyright © 2009 John Wiley & Sons, Ltd.     

DWT-based joint antenna selection for correlated MIMO channels

This paper proposes a new discrete wavelet transform (DWT)-based joint antenna selection scheme for spatially correlated multiple-input multiple output (MIMO) channels. To reduce the severe performance degradation of the traditional antenna selection schemes in correlated channels, a new scheme which employ joint antenna selection (JAS) at both link ends algorithm and embed DWT operations in the receiver-end RF chains is proposed. Through extensive simulations it is demonstrated that the proposed DWT-based joint antenna selection has significant improvement of the capacity for both i.i.d and correlated MIMO channels, while requiring only a minor hardware overhead and low computational complexity for the DWT operations. Moreover, it is shown that the capacity associated with DWT-based JAS is higher than the system employing DWT-based receive antenna selection (RAS) only. This is achieved in i.i.d. and correlated MIMO channels.     

空间相关MIMO信道下的有限反馈预编码

对于独立同分布的瑞利衰落信道,Grassmann码本可以取得良好的系统性能,但是当MIMO信道存在空间相关性时,该码本不可避免的带来性能损失,本文针对空间相关的MIMO信道,通过用发送相关矩阵的平方根对传统Grassmann码本进行旋转,然后再量化,得到适用于空间相关信道下的新码本,并通过实验仿真阐释了新得到的码本对于传统码本在误码率和信道容量方面等方面的性能优势。     

Iterative diversity detection for correlated continuous-time Rayleigh fading channels

An antenna array is proposed as a means of achieving a space-diversity effect that partly overcomes the severity of continuous-time Rayleigh fading channels. The investigated channel is assumed to be frequency-nonselective with correlated diversity links, where the correlation is related to the array geometry and the spatial and Doppler dispersions. Further, the error performance is improved by bit interleaving and channel coding, where the encoders/channel is viewed as a serially concatenated system: a convolutional code constitutes the outer code, whereas a differential encoder and the fading channel (having truncated memory) form a joint inner code. In order to obtain a practical detector structure it is desirable to perform iterative decoding by applying some a posteriori probability (APP) algorithms. For this purpose, we propose a novel generalization of the well-known Bahl-Cocke-Jelinek-Raviv (1974) algorithm that calculates the APPs over channels having memory. Numerical results indicate that iterative decoding becomes more powerful when the exploited channel memory depth is extended. Also, the error performance is significantly improved by introducing multiple antennas. The interleaver gain is, however, seen to be quite moderate, in contrast to additive white Gaussian noise channels.     

A trellis-coded DS-CDMA system in correlated Rayleigh fading channels

We present the trellis-coded code-division multiple-access (TC-CDMA) system based on a multisequence signaling, called orthogonal plane sequence modulation (OPSM), in correlated Rayleigh fading channels and derive its pairwise error probability with different degrees of channel state information. Numerical results show that the OPSM-based TC-CDMA system outperforms conventional convolutionally coded CDMA or TC-CDMA systems.     

On the capacity of spatially correlated MIMO Rayleigh-fading channels

In this paper, we investigate the capacity distribution of spatially correlated, multiple-input-multiple-output (MIMO) channels. In particular, we derive a concise closed-form expression for the characteristic function (c.f.) of MIMO system capacity with arbitrary correlation among the transmitting antennas or among the receiving antennas in frequency-flat Rayleigh-fading environments. Using the exact expression of the c.f., the probability density function (pdf) and the cumulative distribution function (CDF) can be easily obtained, thus enabling the exact evaluation of the outage and mean capacity of spatially correlated MIMO channels. Our results are valid for scenarios with the number of transmitting antennas greater than or equal to that of receiving antennas with arbitrary correlation among them. Moreover, the results are valid for an arbitrary number of transmitting and receiving antennas in uncorrelated MIMO channels. It is shown that the capacity loss is negligible even with a correlation coefficient between two adjacent antennas as large as 0.5 for exponential correlation model. Finally, we derive an exact expression for the mean value of the capacity for arbitrary correlation matrices.     

Pilot-symbol-assisted LDPC coded BICM over correlated Rayleigh fading channels

Pilot-symbol-assisted low-density parity-check (LDPC)-coded bit-interleaved coded modulation (BICM) is analyzed using the density evolution (DE) and the extrinsic information-transfer (EXIT) chart for correlated Rayleigh fading channels. The key parameter (the power correlation coefficient) is identified, and the threshold degradation is quantified. The optimal tradeoff of energy allocation between pilots and coded symbols is found to be sensitive to the normalized Doppler spread of the channel, the interpolation filter, the modulation scheme, and the pilot selection. In addition, a simple upper bound on the performance of any receiver that performs joint iterative decoding and channel estimation is derived. Extension to irregular code design is also discussed.