On the capacity of OFDM-based spatial multiplexing systems

This paper deals with the capacity behavior of wireless orthogonal frequency-division multiplexing (OFDM)-based spatial multiplexing systems in broad-band fading environments for the case where the channel is unknown at the transmitter and perfectly known at the receiver. Introducing a physically motivated multiple-input multiple-output (MIMO) broad-band fading channel model, we study the influence of physical parameters such as the amount of delay spread, cluster angle spread, and total angle spread, and system parameters such as the number of antennas and antenna spacing on ergodic capacity and outage capacity. We find that, in the MIMO case, unlike the single-input single-output (SISO) case, delay spread channels may provide advantages over flat fading channels not only in terms of outage capacity but also in terms of ergodic capacity. Therefore, MIMO delay spread channels will in general provide both higher diversity gain and higher multiplexing gain than MIMO flat fading channels     

Linear dispersion codes for MIMO systems based on frame theory

Multiple-input multiple-output (MIMO) wireless communication systems provide high capacity due to the plurality of modes available in the channel. Existing signaling techniques for MIMO systems have focused primarily on multiplexing for high data rate or diversity for high link reliability. In this paper, we present a new linear dispersion code design for MIMO Rayleigh fading channels. The proposed design bridges the gap between multiplexing and diversity and yields codes that typically perform well both in terms of ergodic capacity as well as error probability. This is important because, as we show, designs performing well from an ergodic capacity point of view do not necessarily perform well from an error probability point of view. Various techniques are presented for finding codes with good error probability performance. Monte Carlo simulations illustrate performance of some example code designs in terms of ergodic capacity, codeword error probability, and bit error probability.     

Asymptotic Ergodic Capacity of Multidimensional Vector-Sensor Array MIMO Channels

We analyze asymptotic ergodic capacity of multidimensional vector-sensor array MIMO (PMD-MIMO) channels established by the use of dual-polarized antennas in the form of 1D, 2D and/or 3D MIMO arrays. Based on the identification of the decomposition of PMD-MIMO channels into multiple independently-fading and scaled classical MIMO channels in parallel, we consequently derive corresponding asymptotic ergodic capacities analytically via tools out of free probability theory. The analysis of derived asymptotic ergodic capacity expressions in terms of antenna locus aspect ratio ?, average symbol SNR per antenna ˉ?s and cross-polar discrimination XPD as well as comparison with asymptotic ergodic capacity of classical MIMO channels present important gains in using compact multidimensional vector-sensor array MIMO systems in asymptotic regimes.     

Capacity Bounds for MIMO Nakagami- $m$ Fading Channels

This paper studies the ergodic capacity limits of multiple-input multiple-output (MIMO) antenna systems with arbitrary finite number of antennas operating on general fading environments. Through the use of majorization theory, we first investigate in detail the ergodic capacity of Nakagami- $m$ fading channels, for which we derive several ergodic capacity upper and lower bounds. We then show that a simple expression for the capacity upper bound is possible for high signal-to-noise ratio (SNR), which permits to analyze the impact of the channel fading parameter $m$ on the ergodic capacity. The asymptotic behavior of the capacity in the large-system limit in which the number of antennas at one or both side(s) goes to infinity, is also addressed. Results demonstrate that the capacity scaling laws for Nakagami-$m$ and Rayleigh-fading MIMO channels are identical. Finally, we employ the same technique to distributed MIMO (D-MIMO) systems undergoing composite log-normal and Nakagami fading, where we derive similar ergodic capacity upper and lower bounds. Monte Carlo simulation results are provided to verify the tightness of the proposed bounds.      

Beneficial impact of channel correlations on MIMO capacity

The potential beneficial impact of channel correlations on the capacity of MIMO systems is investigated. In contrast to most previous work, the present analysis is based on a comprehensive model of the channel correlation structure. It is therefore illustrated that fading cross-correlations may increase the ergodic capacity, sometimes even beyond the supposedly ideal case of independent channels. Starting from considerations on an analytical upper bound of the capacity, the study is then supported by simulation results of the actual ergodic capacity in arbitrary MIMO channels using a simple geometry-based stochastic model.     

分布式MIMO系统信道容量分析

首先推导了分布式MIMO点对点链路遍历信道容量的近似表达式或理论下界,然后给出小区平均遍历容量的表达式.在此基础上,研究D-MIMO与C-MIMO系统分别在BT和ST两种天线选择机制下的平均遍历容量.最后通过仿真,证明了所推导理论表达式的正确性,同时比较了两种MIMO系统的信道容量.     

On the Ergodic Capacity of Rank-1 Ricean-Fading MIMO Channels

This paper investigates the ergodic capacity of Ricean-fading multiple-input-multiple-output (MIMO) channels with rank-1 mean matrices under the assumption that the channel is unknown at the transmitter and perfectly known at the receiver. After introducing the system model and the concept of ergodic capacity of MIMO channels, we derive the explicit expressions for the expected values of the determinant and log-determinant of complex noncentral Wishart matrices. Subsequently, we obtain new upper and lower bounds on the ergodic capacity of rank-1 Ricean-fading MIMO channels at any signal-to-noise ratio (SNR). We show that our bounds are tighter than previously reported analytical bounds, and discuss the impact of spatial fading correlation and Ricean K-factor with the help of these bounds. Furthermore, we extend the analysis of ergodic capacity to frequency selective spatially correlated Ricean-fading MIMO channels. We demonstrate that the calculation of ergodic capacity of frequency selective fading MIMO channels can be converted to the calculation of the one of equivalent frequency flat-fading MIMO channels. Finally, we present numerical results that confirm the theoretical analysis     

基于OFDM的宽带MIMO信道容量研究

研究在发射端和接收端两端都分布有散射体的情况下基于OFDM的MIMO信道容量,推导了归一化信道功率情形下信道容量的上限,分析了各种参数对容量的影响,仿真结果表明:MIMO-OFDM信道容量不仅受到天线数目的限制,同时还受到延时扩展、簇角度扩展、相邻天线间距等因素的影响。     

Performance analysis and design optimization of LDPC-coded MIMO OFDM systems

We consider the performance analysis and design optimization of low-density parity check (LDPC) coded multiple-input multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) systems for high data rate wireless transmission. The tools of density evolution with mixture Gaussian approximations are used to optimize irregular LDPC codes and to compute minimum operational signal-to-noise ratios (SNRs) for ergodic MIMO OFDM channels. In particular, the optimization is done for various MIMO OFDM system configurations, which include a different number of antennas, different channel models, and different demodulation schemes; the optimized performance is compared with the corresponding channel capacity. It is shown that along with the optimized irregular LDPC codes, a turbo iterative receiver that consists of a soft maximum a posteriori (MAP) demodulator and a belief-propagation LDPC decoder can perform within 1 dB from the ergodic capacity of the MIMO OFDM systems under consideration. It is also shown that compared with the optimal MAP demodulator-based receivers, the receivers employing a low-complexity linear minimum mean-square-error soft-interference-cancellation (LMMSE-SIC) demodulator have a small performance loss (< 1dB) in spatially uncorrelated MIMO channels but suffer extra performance loss in MIMO channels with spatial correlation. Finally, from the LDPC profiles that already are optimized for ergodic channels, we heuristically construct small block-size irregular LDPC codes for outage MIMO OFDM channels; as shown from simulation results, the irregular LDPC codes constructed here are helpful in expediting the convergence of the iterative receivers.     

Introducing Space into MIMO Capacity Calculations

The large spectral efficiencies promised for multiple-input multiple-output (MIMO) wireless fading channels are derived under certain conditions which do not fully take into account the spatial aspects of the channel. Spatial correlation, due to limited angular spread or insufficient antenna spacing, significantly reduces the performance of MIMO systems. In this paper we explore the effects of spatially selective channels on the capacity of MIMO systems via a new capacity expression which is more general and realistic than previous expressions. By including spatial information we derive a closed-form expression for ergodic capacity which uses the physics of signal propagation combined with the statistics of the scattering environment. This expression gives the capacity of a MIMO system in terms of antenna placement and scattering environment and leads to valuable insights into the factors determining capacity for a wide range of scattering models.     

On the Ergodic Capacity and Energy Efficiency for Fading MIMO NOMA Systems

Non-orthogonal multiple access (NOMA) is expected to be a promising multiple access techniques for 5G networks due to its superior spectral efficiency (SE). Previous research mainly focus on the design to improve the SE performance with instantaneous channel state information (CSI). In this paper, we consider the fading MIMO channels with only statistical CSI at the transmitter, and explore the potential gains of MIMO NOMA scheme in terms of both ergodic capacity and energy efficiency (EE). The ergodic capacity maximization problem is first studied for the fading multiple-input multiple-output (MIMO) NOMA systems. We derive the optimal input covariance structure and propose both optimal and low complexity suboptimal power allocation schemes to maximize the ergodic capacity of MIMO NOMA system. For the EE maximization, the optimization problem is formulated to maximize the system EE (defined by ergodic capacity under unit power consumption) under the total transmit power constraint and the minimum rate constraint of the weak user. By transforming the EE maximization problem into an equivalent one-dimensional optimization problem, the optimal power allocation for EE design is proposed. To further reduce the computation complexity, a near-optimal solution based on golden section search and suboptimal closed form solution are proposed as well. Numerical results show that the proposed NOMA schemes significantly outperform the traditional orthogonal multiple access scheme with traditional orthogonal multiple access transmission in terms of both SE and EE.     

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.     

分布式MIMO系统小区平均遍历容量分析

针对分布式MIMO系统的圆形小区平均遍历容量展开研究.文章首先建立了包含快衰落、阴影衰落和路径损耗的复合衰落信道模型;然后,对分布式天线采用覆盖式（BT）传输策略,并在高信噪比条件下,导出给定移动台位置时,区上、下行点对点链路遍历容量表达式.最后,考虑移动台在小区内任意分布特点,进一步推导出小区平均遍历容量闭合近似表达式.仿真结果表明,所推导的近似表达式可很好的反应系统的实际性能.导的近似表达式可很好的反应系统的实际性能.     

On the bounds of frequency-selective channel capacity with doubly correlated geometrical MIMO channel model

The multi-input multi-output (MIMO) technology plays an important role in link transmissions. This article considers the general case for the ergodic capacity in doubly correlated frequency-selective MIMO channel. In the study, the geometrical MIMO channel model is presented. Based on the formula of MIMO ergodic capacity, the capacity limits are studied with arbitrary finite number of antennas in the frequency-selective MIMO channel. It first derives the exact expressions for the upper bound and lower bound in doubly correlated MIMO channel. The results for the single-ended correlation and independent identically distributed (i.i.d.) MIMO channel are also obtained as special cases. Then the simple expressions of the capacity bounds are attained at high SNR. Finally, results are provided by Monte Carlo simulations to verify the tightness of the derived bounds.     

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.     

On the capacity of MIMO relay channels

We study the capacity of multiple-input multiple- output (MIMO) relay channels. We first consider the Gaussian MIMO relay channel with fixed channel conditions, and derive upper bounds and lower bounds that can be obtained numerically by convex programming. We present algorithms to compute the bounds. Next, we generalize the study to the Rayleigh fading case. We find an upper bound and a lower bound on the ergodic capacity. It is somewhat surprising that the upper bound can meet the lower bound under certain regularity conditions (not necessarily degradedness), and therefore the capacity can be characterized exactly; previously this has been proven only for the degraded Gaussian relay channel. We investigate sufficient conditions for achieving the ergodic capacity; and in particular, for the case where all nodes have the same number of antennas, the capacity can be achieved under certain signal-to-noise ratio (SNR) conditions. Numerical results are also provided to illustrate the bounds on the ergodic capacity of the MIMO relay channel over Rayleigh fading. Finally, we present a potential application of the MIMO relay channel for cooperative communications in ad hoc networks.     

Ergodic capacity formula of MIMO-OFDM systems under correlated frequency selective Rayleigh fading channels

An explicit formula for the ergodic capacity of Orthogonal Frequency Division Multiplexing (OFDM)-based Multiple-Input Multiple-Output (MIMO) systems under correlated frequency selective Rayleigh channels is derived,by simplifying the channel response matrix in frequency domain into the so-called Kronecker model composed of three kinds of correlations,i.e.multipath tap gain correlation and spatial fading correlations at both transmitter and receiver.The derived formula is very simple and convenient for one to estimate the effects of all three kinds of correlations on MIMO-OFDM capacity.If taps are independent,there is a very simple expression for the ergodic capacity.In case of tap correlation,the capacity formula could be further given in an integral expression.The validity of the new formula is verified and the effects of correlations,delay spread as well as the number of subcarriers on the ergodic capacity are evaluated via Monte Carlo simulations.     

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.     

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.     

Performance analysis of orthogonal space-time block codes in spatially correlated MIMO Nakagami fading channels

Orthogonal space-time block coding (STBC) is an open-loop transmit diversity scheme that decouples the multiple-input multiple-output (MIMO) channel, thereby reducing the space-time decoding into a scalar detection process. This characteristic of STBC makes it a powerful tool, achieving full diversity over MIMO fading channels, and requiring little computational cost for both the encoding and decoding processes. In this paper, we exploit the single-input single-output equivalency of STBC in order to analyze its performance over nonselective Nakagami fading channels in the presence of spatial fading correlation. More specifically, we derive exact closed-form expressions for the outage probability and ergodic capacity of STBC, when the latter is employed over spatially correlated MIMO Nakagami fading channels. Moreover, we derive the exact symbol error probability of coherent M-PSK and M-QAM, when these modulation schemes are used along with STBC over such fading channels. The derived formulae are then used to assess the robustness of STBC to spatial correlation by considering general MIMO correlation models and analyzing their effects on the outage probability, ergodic capacity, and symbol error probability achieved by STBC.