Estimating the Ergodic Capacity of Log-Normal Channels

In this paper, we first provide a very accurate estimation of the capacity of a single-input single-output system operating in a log-normal environment. Then, hinging on the fact that the sum of log-normal Random Variables (RV) is well approximated by another log-normal RV, we apply the obtained results to find the capacity of Maximum Ratio Combining and Equal Gain Combining in a log-normal environment. The capacity in an interference-limited environment is also investigated in this paper. The analytical expressions obtained match perfectly the capacity given by simulations.     

Error performance of a pulse amplitude and position modulated ultra-wideband system over lognormal fading channels

In this paper, the error performance of an ultra-wideband (UWB) system with a hybrid pulse amplitude and position modulation (PAPM) scheme over indoor lognormal fading channels is analyzed. In the PAPM UWB system, input data is modulated onto both the pulse amplitudes and pulse positions. The receiver employs a RAKE to combine energy contained in the resolvable multipath components. Derivation of closed-form error rate expressions of the system in lognormal fading channels is based on approximating a sum of independent lognormal random variables (RV) as another lognormal RV using the Wilkinson method. Given the same delay spread of the channel, the proposed PAPM scheme can provide a higher throughput than the binary pulse amplitude or pulse position modulation scheme.     

A Tight Closed-Form Approximation of the Log-Normal Fading Channel Capacity

The log-normal probability distribution has been commonly used in wireless communications to model the shadowing and, recently, the small-scale fading for indoor ultrawideband (UWB) communications. In this paper, a tight closedform approximation of the ergodic capacity over log-normal fading channels is derived. This expression can be easily used to evaluate and compare the ergodic capacities of communication systems operating over log-normal fading channels. We also utilize this expression to show that the capacity of a multi-antennas UWB system operating over the IEEE 802.15.3a channel can be improved mainly through receive diversity.     

BPSK Bit Error Outage over Nakagami-m Fading Channels in Lognormal Shadowing Environments

In this letter, we address the problem of finding a tractable expression for the bit-error outage (BEO) defined as the probability to observe a given average bit error rate (BER) over a fading channel in a shadowing environment. Our contribution is two-fold: (1) a simple yet tight approximation of the bit error probability (BEP) for binary phase shift keying (BPSK) over a frequency-flat Nakagami-m fading channel is derived, which (2) facilitates the derivation of a tight lower bound of the BEO in presence of lognormal shadowing in closed form. Theoretical results are corroborated by means of simulation results, confirming the tightness of the bounds.     

Numerical calculation of symmetric capacity of Rayleigh fadingchannel with BPSK/QPSK

In this letter, we develop a simple series representation for the symmetric capacity of a Rayleigh fading channel with BPSK/QPSK when perfect channel state information is available at the receiver. This series expansion provides a simple and numerically efficient way to calculate the capacity. We also note that the bounds on the capacity developed in the paper by Baccarelli and Fasano (2000) are loose under the cases considered in this letter     

最大比宏分集下的CDMA系统反向容量分析

本文综合考虑快衰落,阴影衰落和路径衰减的影响,建立了最大比宏分集下CDMA系统反向信道分析模型并推导出了中断率(outage probability)表达式.数值结果表明,采用宏分集后反向容量随参与宏分集基站数的增加而大大提高了,而且移动台的反向性能和其位置有关,在小区边界处性能最佳.     

Tight closed-form approximation for the ergodic capacity of orthogonal STBC

In this letter we derive a simple and tight closed-form approximation for the ergodic capacity of orthogonal space-time block coding in arbitrary fading channels. The expression is an analytical function of the power covariance matrix of the channel. In the case of uncorrelated channels the expression only depends on the variances of the channel power gains. These channel statistics can be easily obtained from both analytical and physical fading channel models. Simulations results show the accuracy of the proposed expression     

System Capacity Analysis and Antenna Placement Optimization for Downlink Transmission in Distributed Antenna Systems

System capacity and antenna placement play crucial roles in wireless communication systems, and they are of great value to network planning. In this paper, we are motivated to analyze the system capacity and optimize the antenna placement in distributed antenna systems. This paper establishes a composite channel model which takes path loss, lognormal shadowing and Rayleigh fading into consideration. To reduce the computational complexity, an approximate theoretical expression of system capacity is derived with selective transmission at the transmitter and maximal ratio combining at the receiver. An antenna placement optimization problem is formulated, and then a genetic algorithm (GA) based searching scheme is proposed to solve the proposed optimization problem. The computational complexity analysis indicates that the proposed GA-based searching scheme is computationally efficient in terms of both running time and storage space. Numerical results show that the approximate theoretical expression of system capacity can provide a very good approximation to the simulation results, and the proposed GA-based searching scheme for solving the antenna placement optimization problem can consistently offer a large capacity gain over other existing schemes.     

复合k-m/Gamma衰落信道下的平均信道容量

A new analytical expression is presented for the instantaneous power Probability Density Function (PDF) of receiver signals over composite κ-μ/gamma fading channels. Moreover, the exact expression of channel capacity is derived in the form of an infinite series, while an accurate approximation expression is obtained in closed form. To reveal the implications of the model parameters on capacity, we provide an expression for the case of a high-SNR environment. The relationship of the presented results with previously reported results on generalised-K and K fading chan-nels is also discussed. Finally, numerical and simulation results are presented to prove the correctness of our derived expressions.     

Transactions Letters - Outage Capacity and Optimal Power Allocation for Multiple Time-Scale Parallel Fading Channels

In this paper, we address the optimal power allocation problem for minimizing capacity outage probability in multiple time-scale parallel fading channels. Extending ideas from the work of Dey and Evans (2005), we derive the optimal power allocation scheme for parallel fading channels with fast Rayleigh fading, as a function of the slow fading gains. Numerical results are presented to demonstrate the outage performance of this scheme for lognormal slow fading on two parallel channels.     

Downlink System Capacity Analysis in Distributed Antenna Systems

This paper focuses on the downlink system capacity in distributed antenna systems (DAS). Due to the complexity of actual wireless environments, a composite channel model is established which takes into account three factors, i.e., path loss, lognormal shadowing and Rayleigh fading. Based on the channel model, the probability density function (PDF) of the output signal-to-noise ratio (SNR) is derived. To facilitate the analysis, the distribution of the output SNR is approximated by a lognormal distribution. After that, by making use of selective diversity (SD) scheme for distributed antennas, an approximate analytical expression of the capacity for a mobile station (MS) over a given position is derived. Furthermore, considering the distribution of MSs in the system, a closed-form expression of the system capacity is obtained. Numerical results show that the closed-form expression can evaluate the system capacity performance of DAS very accurately.     

分布式天线系统混合SC/MRC分集中断概率性能

在频率选择性复合Nakagami/lognormal衰落信道条件下,研究了层叠分布式天线系统(Cascade Distributed Antenna System--CDAS)采用混合SC/MRC分集的中断概率性能.针对中断概率性能,分析了多径密度函数(Multipath Intensity Profile MIP)衰减因子、空时分集维数、活动用户数、每比特平均接收信噪比以及衰落因子对系统性能的影响.仿真表明CDAS系统可以有效对抗衰落,提高系统容量,削弱对数正态阴影衰落影响.     

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.      

Another look at the performance of MRC schemes in Nakagami-m fading channels with arbitrary parameters

In this letter, we take a close look at the performance of maximal ratio combining (MRC) schemes operating in a flat-Nakagami-m fading environment with arbitrary fading parameters. We derive an expression for the probability density function (pdf) of the output signal-to-noise ratio (SNR) by expressing the moment generating function of the output SNR in the form of multiple Barnes-type contour integrals. By evaluating the inverse transform and converting the multiple contour integrals into infinite series, we are able to derive an expression for the pdf of the output SNR when the Nakagami fading parameters along the diversity branches take on real and arbitrary values. Consequently, the average bit-error rate can now be expressed in terms of Lauricella's multivariate hypergeometric function, which can be easily evaluated numerically. Special cases of the main results reduce to known results in the literature. The results, which apply to independent as well as correlated diversity branches, will be useful for predicting the system performances when the Nakagami fading parameters are real and arbitrary.     

Bounds on the Distribution of a Sum of Correlated Lognormal Random Variables and Their Application

The cumulative distribution function (cdf) of a sum of correlated or even independent lognormal random variables (RVs), which is of wide interest in wireless communications, remains unsolved despite long standing efforts. Several cdf approximations are thus widely used. This letter derives bounds for the cdf of a sum of 2 or 3 arbitrarily correlated lognormal RVs and of a sum of any number of equally-correlated lognormal RVs. The bounds are single-fold integrals of readily computable functions and extend previously known bounds for independent lognormal summands. An improved set of bounds are also derived which are expressed as 2-fold integrals. For correlated lognormal fading channels, new expressions are derived for the moments of the output SNR and amount of fading for maximal ratio combining (MRC), selection combining (SC) and equal gain combining (EGC) and outage probability expressions for SC.     

M-ary symbol error outage over Nakagami-m fading channels in shadowing environments

This letter addresses the problem of finding a tractable expression for the symbol error outage (SEO) in flat Nakagami-m fading and shadowing channels. We deal with M-ary phase shift keying (M-PSK) and quadrature amplitude modulation (M-QAM) which extends our previous results on BPSK signaling. We propose a new tight approximation of the symbol error probability (SEP) holding for M-PSK and M-QAM signals which is accurate over all signal to noise ratios (SNRs) of interest. We derive a new generic expression for the inverse SEP which facilitates the derivation of a tight approximation of the SEO in a lognormal shadowing environment.     

The Impact of Shadowing and the Severity of Fading on the First and Second Order Statistics of the Capacity of OSTBC MIMO Nakagami-Lognormal Channels

This article presents a thorough statistical analysis of the capacity of orthogonal space-time block coded (OSTBC) multiple-input multiple-output (MIMO) Nakagami- lognormal (NLN) channels. The NLN channel model allows to study the joint effects of fast fading and shadowing on the statistical properties of the channel capacity. We have derived exact analytical expressions for the probability density function (PDF), cumulative distribution function (CDF), level-crossing rate (LCR), and average duration of fades (ADF) of the capacity of MIMO NLN channels. It is observed that an increase in the MIMO dimension or a decrease in the severity of fading results in an increase in the mean channel capacity, while the variance of the channel capacity decreases. On the other hand, an increase in the shadowing standard deviation increases the spread of the channel capacity, however the shadowing effect has no influence on the mean channel capacity. We have also presented approximation results for the statistical properties of the channel capacity, obtained using the Gauss-Hermite integration method. It is observed that approximation results not only reduce the complexity, but also have a very good fitting with the exact results. The presented results are very useful and general because they provide the flexibility to study the impact of shadowing on the channel capacity under different fading conditions. Moreover, the effects of severity of fading on the channel capacity can also be studied. The correctness of theoretical results is confirmed by simulations.     

Highly accurate simple closed-form approximations to lognormal sum distributions and densities

Sums of lognormal random variables occur extensively in wireless communications, in part, because a shadowing environment is well modeled by a lognormal distribution. A closed-form expression does not exist for the sum distribution and, furthermore, it is difficult to numerically calculate the distribution. Numerous approximations exist that are based on approximating a sum of lognormal random variables as another lognormal random variable. A new paradigm to calculate an approximation to the lognormal sum distribution, based on curve fitting on lognormal probability paper, is introduced in this letter. Highly accurate, simple closed-form approximations to lognormal sum distributions are presented.     

Closed-form approximation for the outage capacity of orthogonal STBC

In this letter we derive a tight analytical approximation for the outage capacity of orthogonal space-time block codes (STBC's). The proposed expression is a simple closed-form function of the power covariance matrix of the channel. In the case of uncorrelated channels, the expression only depends on the variances of the channel power gains that can be expressed analytically for the most common fading distributions: Rayleigh, Rice, Nakagami, Weibull, etc. Furthermore, the approximation encompasses different fading distributions and gains between different pairs of transmit and receive antennas, which can occur in distributed STBC networks.     

Optimal channel reuse in cellular radio systems with multiplecorrelated log-normal interferers

The probability of co-channel interference (PCI) due to multiple correlated log-normal signals is calculated for cellular radio systems operating in Rayleigh fading and lognormal shadowing environment. The effects on the PCI of the correlation between the signals, the standard deviation due to shadowing, the number of interferers, the co-channel protection ratio, and the traffic load is investigated. The results are used for analyzing the optimal channel reuse, the cluster size, and the spectrum efficiency in terms of these parameters