Analysis of microdiversity and dual channel macrodiversity in shadowed fading channels using a compound fading model

Wireless channels are affected by short-term fading and long-term fading (shadowing). A compound fading model was proposed for the modeling of shadowed fading channels which resulted in a closed form solution for the probability density function (pdf) of the signal-to-noise ratio (SNR). This model is applied to a case where both micro- and macro-diversity schemes are implemented to mitigate short-term fading and shadowing, respectively. Using the compound fading model, it is shown that the pdf of the signal-to-noise ratio after the implementation of maximal ratio combining (MRC) at the micro level and selection combining (SC) at the macro level can be expressed in analytical form. Even when branch correlation exists, the pdf still can be expressed in analytical form. Thus, the compound pdf model offers significant improvement over approaches which use lognormal pdf for shadowing. The performance of a coherent binary phase shift keying (BPSK) modem is evaluated using this approach. The results demonstrate the simplicity and usefulness of the compound pdf in the performance analyses of shadowed fading channels even when branch correlation exists at the base station or correlation exists between base stations.     

Effect of macrodiversity on average-error probabilities in a Ricianfading channel with correlated lognormal shadowing

The effect of correlated lognormal shadowing on the average probability of error performance of narrow-band mobile communication systems with micro- and macrodiversity reception in a Rician fading channel is studied by considering a constant correlation model for the shadowed signals at the base stations. The performance degradation due to correlated shadowing is illustrated by considering both coherent and differentially coherent binary phase-shift keying schemes. Numerical results presented show that when the base stations in a cellular system are very closely spaced, the effect of correlated shadowing on system performance cannot be ignored     

Error Rates in Generalized Shadowed Fading Channels

Most of the existing models to describe the shadowed fading channels use either the Suzuki or Nakagami-lognormal probability density function (pdf), both based on lognormal shadowing. However, these two density functions do not lead to closed form solutions for the received signal power, making the computations of error rates and outages very cumbersome. A generalized or compound fading model which takes into account both fading and shadowing in wireless systems, is presented here. Starting with the Nakagami model for fading, shadowing is incorporated using a gamma distribution for the average power in the Nakagami fading model. This compound pdf developed here based on a gamma-gamma distribution is analytically simpler than the two pdfs based on lognormal shadowing and is general enough to incorporate most of the fading and shadowing observed in wireless channels. The performance of coherent BPSK is evaluated using this compound fading model.     

Performance analysis of hexagonal cellular networks in fading channels

This paper analyzes the location‐dependent performance metrics of coverage probability and spectral efficiency in hexagonal cellular networks under Rayleigh fading with a general distribution for shadowing and also including two special cases of no shadowing and lognormal shadowing. The effects of system parameters such as frequency reuse factor, transmission probability of base stations, and signal‐to‐interference‐plus‐noise ratio gap from Shannon capacity are accurately characterized. The proposed approach is applied to fractional frequency reuse (FFR) scheme where the impact of FFR on spectral efficiency is evaluated. Numerical results show that (i) in a lognormal‐shadowed Rayleigh fading channel with the shadowing standard deviation of 12 dB, the cell area wide spectral efficiency is degraded by approximately 40% compared with when there is Rayleigh fading without shadowing; (ii) the improvement in spectral efficiency achieved by FFR over the universal frequency reuse increases as the transmission probability increases and the shadowing becomes less severe; and (iii) in Rayleigh fading without shadowing environment where all the base stations are actively transmitting, FFR achieves approximately 20% improvement in spectral efficiency in the cell edge area. Interestingly, this improvement increases to about 30% if a 3‐dB signal‐to‐interference‐plus‐noise ratio gap from Shannon capacity is further accounted. Copyright © 2015 JohnWiley & Sons     

Outage analysis in wireless channels with multiple interferers subject to shadowing and fading using a compound pdf model

Wireless communication systems are subject to short- and long-term fading of the channel. Instead of the commonly used Nakagami–lognormal model to account for the conditions existing in these shadowed fading channels, a compound probability density function (pdf) model is used to evaluate the performance of wireless systems. While the Nakagami–lognormal lacks a closed-form solution to the pdf of the received power in shadowed fading channels, the compound pdf has an analytical expression for the pdf of the received signal power. The synergy between these two models for the analysis of wireless systems is explored by calculating the bit error rate in a DPSK modem as well as the outage probability in a wireless system in a shadowed fading channel. This is followed by the computation of the outage probability in the general case where both the desired and cochannels are subject to shadowing and fading. The analyses were carried out for both fixed number of cochannels and random number of cochannels. Results demonstrate the usefulness of the compound pdf model for the performance analyses of wireless systems in shadowed fading channels.     

Second‐order statistics of system with N‐branch microdiversity and L‐branch macrodiversity operating over gamma shadowed Nakagami‐m fading channels

The problem concerning short‐term fading and long‐term fading (shadowing) and their deleterious effects on wireless systems performance has been in focus for a long time. In this paper, motivated by the results of propagation measurements in land‐mobile and indoor‐mobile systems, and by the fact that gamma distribution can describe shadowing reliably, Nakagami‐m distribution is used to model the signal envelope and gamma distribution is used to model the average signal power. Receive diversity with maximal‐ratio combining and selection combining is implemented at the microlevel and macrolevel, respectively. The general case is explored, which assumes that microdiversity and macrodiversity are provided through arbitrary number of channels. Because shadowing has larger correlation distance than short‐term fading, correlated macrodiversity channels are studied. This paper investigates the dynamics of the received signal. A novel rapidly converging infinite‐series expression for average level crossing rate and average fade duration are obtained. Numerical results are graphically presented to examine the impact of fading severity, shadowing severity, number of diversity branches at the microlevel, number of base stations and correlation between base stations to the system's performance. Computer simulations are also performed to verify the validity and the accuracy of proposed theoretical analysis. Copyright © 2012 John Wiley & Sons, Ltd.     

考虑混合SC/MRC分集的层叠分布式天线系统SER性能分析

针对Nakagami/lognormal复合衰落信道,研究了层叠分布式天线系统(Cascade Distributed Antenna System-CDAS)在CDMA网络中的平均误符号率性能.推导出了采用混合SC/MRC分集接收机的层叠分布式天线系统平均误符号率性能公式.利用推导出的平均误符号率表达式,分析了多径密度函数(Multipath Intensity Profile-MIP)衰减因子、空时分集维数、活动用户数以及阴影衰落因子对平均误符号率性能的影响.仿真表明层叠分布式天线系统可以有效对抗衰落,提高系统容量以及削弱对数正态阴影衰落的影响.     

DS/CDMAM-ary orthogonal signalling in a shadowed Rayleigh channel for mobile communications

In this paper a modified RAKE receiver is studied for a frequency selective mobile radio channel. The reverse link (Mobile to base station) is analysed, assuming lognormal shadowing and Rayleigh fading andK asynchronous users, withM orthogonal sequences per user. The analysis is based on the consideration of the quadrature components of the signal and noise, taking advantage of the multipath effects. The performance evaluation is carried out in terms of both the bit error rate and outage probability in order to qualify completely the proposed receiver. The positive results assure the possibility of applying this system in a microcellular mobile radio environment.     

Performance analysis of microcellular mobile radio systems with shadowed cochannel interferers

A study is presented of microcellular mobile radio systems where the desired signal has Rician statistics and cochannel interferers experience lognormal shadowing as well as Rayleigh fading. This implies a Rician/Rayleigh-plus-lognormal microcell interference model. The probability density function of the signal-to-interference ratio is derived and used to evaluate the performance of microcellular systems in terms of the outage probability.<>     

Micro- and macrodiversity MDPSK on shadowed frequency-selectivechannels

The performance of M-ary differential phase shift keying (MDPSK) on frequency-selective slow Rayleigh fading, lognormal shadowed channels with diversity combining is analyzed for mobile and portable applications. The use of L-branch equal gain postdetection microdiversity combining to mitigate the effects of fading and P-port macrodiversity to alleviate the effects of shadowing are investigated. Four performance criteria are considered for a frequency-selective multipath fading, intersymbol interference channel. These are, the short term bit error rate (BER), the irreducible BER, the complementary distribution over the lognormal shadowing of the average BER, and the probability that the instantaneous BER exceeds a threshold value, averaged over a spatial environment. Closed-form expressions for the four performance criteria are obtained. The BER and outage performance results show that diversity combining is an effective method for improving the system performance (and hence system reliability), when the normalized delay spread is not large. It is also seen that, in most cases, 4DPSK gives the best performance followed by 8DPSK and 2DPSK, respectively, for a given information throughput     

Effects of Rician faded and log-normal shadowed signals on spectrumefficiency in microcellular radio

An assessment of spectrum efficiency for a microcellular land mobile radio system is presented by considering the desired signal as (fast) Rician fading with (slow) log-normal shadowing and cochannel interfering signals as uncorrelated (fast) Rayleigh fading superimposed over (slow) log-normal shadowing. Spectrum efficiency is defined in terms of reuse distance, i.e., cluster size, traffic intensity, bandwidth of the system, and area of a cell by considering cochannel interference probability. The expression for cochannel interference probability is derived using appropriate path-loss law for microcells for four different cases: Rician plus log-normal desired signal and Rayleigh plus log-normal interfering signals; Rician desired signal and Rayleigh fading plus log-normal shadowing interfering signals; Rician desired signal and Rayleigh interfering signals; and both desired and interfering signals as Rician fading. The performance of a microcellular system is compared with that of a conventional macrocellular system     

Closed‐Form Expressions for Selection Combining System Statistics over Correlated Generalized‐K Fading Channels in the Presence of Interference

This paper considers the effects of simultaneous correlated multipath fading and shadowing on the performances of a signal‐to‐interference ratio (SIR)‐based dual‐branch selection combining (SC) diversity receiver. This analysis includes the presence of cochannel interference. A generalized fading/shadowing channel model in an interference‐limited correlated fading environment is modeled by generalized‐K distribution. Closed‐form expressions are obtained for probability density function and cumulative distribution function of the SC output SIR, as well as for the outage probability. Based on this, the influence of various fading and shadowing parameter values and the correlation level on the outage probability is examined.     

Performance analysis of lognormally shadowed generalized Gamma fading channels

A new composite channel model is proposed for the performance analysis of shadowed fading channels. This model is represented as a mixture of generalized Gamma (GG) multipath fading and lognormal shadowing. GG distribution includes the Rayleigh, Nakagami, and Weibull as special cases; hence the presented model, which is referred to as GG‐L, is a generic model that covers many well‐known composite fading models, including the Rayleigh–lognormal (R‐L), Nakagami–lognormal (N‐L), and Weibull–lognormal (W‐L). The main drawback of the lognormal‐based composite models is that the composite probability density function (PDF) is not in closed form, thereby making the performance evaluation of communication links in these channels cumbersome. To bypass this problem, an approximation method is developed which makes it possible to derive a closed‐form, analytical expression for GG‐L composite distribution. The proposed method only needs the mean and the variance of the underlying lognormal distribution, and hence, bypasses the required complicated integration needed to calculate the PDF of the received signal envelope in GG‐L channel. Based on this method, the most statistical characteristics, such as cumulative density function (CDF) and moments of the GG‐L composite distribution, are derived and used for the performance analysis of a single receiver operating over GG‐L fading channel. Copyright © 2010 John Wiley & Sons, Ltd.     

Interference Modelling in DS/CDMA Cellular Systems Operating in a General Fading Environment

Multiple access interference and the mobile radio environment are the primary limitations on the performance of DS/CDMA cellular systems. This paper presents the analysis of a DS/CDMA cellular system operating in a general fading environment. In particular the issues of signal fading, multiple access interference, and power control are addressed. A computationally efficient statistical method is used in the estimation of system performance. It is assumed that the variability of each received signal can be represented by fast Nakagami_m fading plus slower log-normal shadowing. Average bit-error-rate (BER) and outage probability are estimated as system performance indicators. The analysis shows, that as the variability of the fast fading of the received signal reduces, the performance of the system improves. However, when the signal undergoes both fast fading and shadowing, it is largely the shadowing that determines system performance. Use of forward link power control (that compensates for the variability due to shadowing) results in minimal performance improvement. However, in the reverse link significant improvement in performance can be achieved using a similar power control scheme.     

Outage probability for lognormal-shadowed Rician channels

A new general outage probability expression for a Rician signal received among L Rician interferers is derived. This result is shown to cover previous published expressions involving Rayleigh signal/interferers as special cases. A new method is then applied to further extend the result to include the effect of lognormal shadowing on the outage probability (for microcellular mobile radio systems in Rician/Rician fading environments). New Rician/Rician outage probability curves against the normalized reuse distance and cluster size with and without lognormal shadowing effect are presented and discussed     

无线光中继通信在弱湍流时的性能估计方法

对数正态信道是描述弱湍流条件下无线光通信衰落的有力数学工具.然而精确的对数正态信道性能表达式带有无法化简的多重积分,难以揭示信道参数和性能的联系,不利于性能估计.针对该问题,Wilkinson和Fenton近似被广泛应用于对数正态信道的性能分析,但Wilkinson和Fenton近似的应用范围却缺乏标准,这导致了系统设...     

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.     

Optimum number of secondary users in collaborative spectrum sensing considering resources usage efficiency

The optimum number of secondary users in collaborative spectrum sensing is derived for lognormal shadowing channels, static additive white Gaussian noise channels and Rayleigh fading channels, when the efficiency of resources usage is considered in the system design. By weighting the detection performance and the usage efficiency in a target function that is maximized with respect to the number of secondary users, it is shown that the optimum number of secondary users decreases when the weighting coefficient of the usage efficiency increases, the sample correlation increases, or the SNR increases.     

Outage possibilities in mobile radio systems suffering cochannelinterference

Mobile radio systems are usually designed on the basis of providing adequate reception quality to a specified area. The outage probability equations are used to determine the quality of radio reception when that quality is limited by a minimum required signal level, interference from a cochannel transmitter, and variability in the received signal levels. Considering Rayleigh fading and lognormal shadowing as joint causes of signal variation, average outage probability expressions are derived for mobile radio systems of a uniform nature. These expressions are used to investigate the influence of various system and propagation characteristics on reception quality     

Characteristic‐Function‐Based Analysis of MIMO Systems Applying Macroscopic Selection Diversity in Mobile Communications

Multiple‐input multiple‐output (MIMO) systems can provide significant increments in capacity; however, the capacity of MIMO systems degrades severely when spatial correlation among multipath channels is present. This paper demonstrates that the influence of shadowing on the channel capacity is more substantial than that of multipath fading; therefore, the shadowing effect is actually the dominant impairment. To overcome the composite fading effects, we propose combining macroscopic selection diversity (MSD) schemes with MIMO technology. To analyze the system performance, the capacity outage expression of MIMO‐based MSD (MSD‐MIMO) systems using a characteristic function is applied. The analytic results show that there are significant improvements when MSD schemes are applied, even for the two‐base‐station diversity case. It is also observed that the effect of spatial correlation due to multipath fading is almost negligible when multiple base stations cooperatively participate in the mobile communication topology.