Showing papers on "Fading distribution published in 2002"
TL;DR: The use of ML detection in spatial diversity reception to reduce the diversity gain penalty caused by correlation between the fading at different receivers is described.
Abstract: In free-space optical communication links, atmospheric turbulence causes fluctuations in both the intensity and the phase of the received light signal, impairing link performance. We describe several communication techniques to mitigate turbulence-induced intensity fluctuations, i.e., signal fading. These techniques are applicable in the regime in which the receiver aperture is smaller than the correlation length of fading and the observation interval is shorter than the correlation time of fading. We assume that the receiver has no knowledge of the instantaneous fading state. When the receiver knows only the marginal statistics of the fading, a symbol-by-symbol ML detector can be used to improve detection performance. If the receiver has knowledge of the joint temporal statistics of the fading, maximum-likelihood sequence detection (MLSD) can be employed, yielding a further performance improvement, but at the cost of very high complexity. Spatial diversity reception with multiple receivers can also be used to overcome turbulence-induced fading. We describe the use of ML detection in spatial diversity reception to reduce the diversity gain penalty caused by correlation between the fading at different receivers.
1,490 citations
TL;DR: Results show that empirical capacities converge to the limit capacity predicted from the asymptotic theory even at moderate n = 16, and the assumption of separable transmit/receive correlations via simulations based on a ray-tracing propagation model is analyzed.
Abstract: Previous studies have shown that single-user systems employing n-element antenna arrays at both the transmitter and the receiver can achieve a capacity proportional to n, assuming independent Rayleigh fading between antenna pairs. We explore the capacity of dual-antenna-array systems under correlated fading via theoretical analysis and ray-tracing simulations. We derive and compare expressions for the asymptotic growth rate of capacity with n antennas for both independent and correlated fading cases; the latter is derived under some assumptions about the scaling of the fading correlation structure. In both cases, the theoretic capacity growth is linear in n but the growth rate is 10-20% smaller in the presence of correlated fading. We analyze our assumption of separable transmit/receive correlations via simulations based on a ray-tracing propagation model. Results show that empirical capacities converge to the limit capacity predicted from our asymptotic theory even at moderate n = 16. We present results for both the cases when the transmitter does and does not know the channel realization.
1,039 citations
TL;DR: It is shown that well-known methods for allocating power, based on Perron-Frobenius eigenvalue theory, can be used to determine power allocations that are provably close to achieving optimal (i.e., minimal) outage probability.
Abstract: We propose a new method of power control for interference-limited wireless networks with Rayleigh fading of both the desired and interference signals Our method explicitly takes into account the statistical variation of both the received signal and interference power and optimally allocates power subject to constraints on the probability of fading induced outage for each transmitter/receiver pair We establish several results for this type of problem We establish tight bounds that relate the outage probability caused by channel fading to the signal-to-interference margin calculated when the statistical variation of the signal and interference powers is ignored This allows us to show that well-known methods for allocating power, based on Perron-Frobenius eigenvalue theory, can be used to determine power allocations that are provably close to achieving optimal (ie, minimal) outage probability We show that the problems of minimizing the transmitter power subject to constraints on outage probability and minimizing outage probability subject to power constraints can be posed as a geometric program (GP) A GP is a special type of optimization problem that can be transformed to a nonlinear convex optimization problem by a change of variables and therefore solved globally and efficiently by interior-point methods We also give a fast iterative method for finding the optimal power allocation to minimize the outage probability
644 citations
TL;DR: The utility of the new space-time correlation model is demonstrated by clarifying the limitations of a widely accepted correlation model for MIMO fading channels, and the impact of nonisotropic scattering around the user, on the capacity of a MIMo fading channel is quantified.
Abstract: Analysis and design of multielement antenna systems in mobile fading channels require a model for the space-time cross correlation among the links of the underlying multiple-input multiple-output (MIMO) channel. In this paper, we propose a general space-time cross-correlation function for mobile frequency nonselective Rice fading MIMO channels, in which various parameters of interest such as the angle spreads at the base station and the user, the distance between the base station and the user, mean directions of the signal arrivals, array configurations, and Doppler spread are all taken into account. The new space-time cross-correlation function includes all the relevant parameters of the MIMO fading channel in a clean compact form, suitable for both mathematical analysis and numerical calculations/simulations. It also covers many known correlation models as special cases. We demonstrate the utility of the new space-time correlation model by clarifying the limitations of a widely accepted correlation model for MIMO fading channels. As another application, we quantify the impact of nonisotropic scattering around the user, on the capacity of a MIMO fading channel.
537 citations
TL;DR: New envelope probability density functions (PDFs) that describe small-scale, local area fading experienced by narrow-band wireless receivers and novel PDFs that describe theLocal area fading of two specular multipath components in the presence of other diffusely propagating waves are developed.
Abstract: This paper presents new envelope probability density functions (PDFs) that describe small-scale, local area fading experienced by narrow-band wireless receivers. The paper also develops novel PDFs that describe the local area fading of two specular multipath components in the presence of other diffusely propagating waves. These PDFs are studied in the context of classical fading PDFs such as the Rayleigh, Rician, and other distributions.
367 citations
TL;DR: An improved sum-of-sinusoids simulation model is proposed for Rayleigh fading channels, which employs random initial phase, and conditional random Doppler frequency for all individual sinusoids.
Abstract: An improved sum-of-sinusoids simulation model is proposed for Rayleigh fading channels. The new model employs random initial phase, and conditional random Doppler frequency for all individual sinusoids. The second-order statistics of the new simulator match the desired ones exactly even if the number of sinusoids is a single-digit integer. Other key statistics of the new simulator approach the desired ones of Clarke's (1968) reference model as the number of sinusoids approaches infinity, while good convergence is achieved when the number of sinusoids is small. Moreover, the new simulator can be directly used to generate multiple uncorrelated fading waveforms; it is also pointed out that a class of 16 different simulators, which have identical statistical properties, can be developed for Rayleigh fading channels.
363 citations
TL;DR: All essential parameters required for the implementation of a simulation model considering the joint statistical properties of the local azimuth spread, the local delay spread, and shadow fading are provided.
Abstract: Empirical results characterizing the joint statistical properties of the local azimuth spread (AS), the local delay spread (DS), and the shadow (slow) fading component are presented. Measurement data from typical urban, bad urban, and suburban (SU) environments have been analyzed. It is found that a log-normal distribution accurately fits the distribution function of all the investigated parameters. The spatial autocorrelation function of both AS, DS, and shadow fading can be modeled with an exponential decay function. However, for SU environments the spatial autocorrelation function is better characterized by a composite of two exponential decaying functions. A positive cross correlation is found between the AS and the DS, while both parameters are negatively correlated with shadow fading. All essential parameters required for the implementation of a simulation model considering the joint statistical properties of the AS, DS, and shadow fading are provided.
243 citations
10 Dec 2002
TL;DR: A general fading distribution - the /spl alpha/-/spl mu/ distribution - that includes the Nakagami-m and the Weibull as special cases is presented.
Abstract: This paper presents a general fading distribution - the /spl alpha/-/spl mu/ distribution - that includes the Nakagami-m and the Weibull as special cases. One-Sided Gaussian, Rayleigh, and Negative Exponential distributions are also special cases of the /spl alpha/-/spl mu/ Distribution.
215 citations
TL;DR: A simple technique for the numerical calculation of the pairwise error probability (PEP) of space-time codes over fading channels and its application to the multiple antenna independent Rayleigh-fading channel and to the Rayleigh block fading channel is described.
Abstract: We describe a simple technique for the numerical calculation, within any desired degree of accuracy, of the pairwise error probability (PEP) of space-time codes over fading channels. This method applies also to the calculation of E[Q(/spl radic//spl xi/)] for any nonnegative random variable /spl xi/ whose moment-generating function /spl Phi//sub /spl xi//(s)=E[exp(-s/spl xi/)] is known. Its application to the multiple antenna independent Rayleigh-fading channel and to the Rayleigh block fading channel is discussed, and illustrated by two simple examples.
163 citations
TL;DR: A novel sum-of-sinusoids fading model is proposed and verified, which generates Rayleigh fading processes satisfying the theoretical independence requirements and providing desired power spectral densities with ideal second-order moment.
Abstract: Multiple independent Rayleigh fading waveforms are often required for the simulation of wireless communications channels. Jakes (1974) Rayleigh fading model and its derivatives based on the sum-of-sinusoids provide simple simulators, but they have major shortcomings in their simulated correlation functions. A novel sum-of-sinusoids fading model is proposed and verified, which generates Rayleigh fading processes satisfying the theoretical independence requirements and providing desired power spectral densities with ideal second-order moment. The effects of replacing sinusoids in the proposed model by their approximate waveforms are also analyzed and tested. Performance evaluation and comparison are provided, using the quality measures of the mean-square-error of autocorrelation function and the second-order moment of the power spectral density.
139 citations
07 Aug 2002
TL;DR: Apart from introducing the Weibull distribution as a useful tool for describing outdoor multipath fading, it is verified that, in many cases, the Rayleigh distribution is inadequate for describing the modern urban environment.
Abstract: We introduce the Weibull distribution as an accurate and less complex description for the outdoor multipath fading channel than some of the existing models. Using the method of moments, we compare the Weibull distribution and other statistical models, such as the Rayleigh, Rice and Nakagami distributions, with experimental results taken in urban and suburban environments. Apart from introducing the Weibull distribution as a useful tool for describing outdoor multipath fading, we verify that, in many cases, the Rayleigh distribution is inadequate for describing the modern urban environment.
30 Jun 2002
TL;DR: Results show 2-level superposition coding is adequate to achieve most of the throughput gain in a quasi-static Rayleigh fading channel.
Abstract: Coding with a single fixed rate may not achieve the maximum throughput of a compound channel if the transmitter only has access to channel state statistics. Superposition coding for broadcast channels can be employed to increase the throughput. We study the optimal rate allocation for finite level superposition coding to maximize the throughput. Results show 2-level superposition coding is adequate to achieve most of the throughput gain in a quasi-static Rayleigh fading channel.
TL;DR: The bit error probability (BEP) for coherent detection of binary signals with dual-diversity predetection equal gain combining is derived using the Beaulieu (1991) series using a correlated Rayleigh fading channel with unequal branch signal-to-noise ratios.
Abstract: The bit error probability (BEP) for coherent detection of binary signals with dual-diversity predetection equal gain combining is derived using the Beaulieu (1991) series. In particular, we consider a correlated Rayleigh fading channel with unequal branch signal-to-noise ratios. The BEP expression is in terms of the power correlation coefficient of the branches, is easy to compute, and depicts clearly the effect of correlated fading on the error performance.
TL;DR: An analytical formula is derived for the fading correlation function of a uniform circular array (UCA) when the angular energy follows a Laplacian distribution.
Abstract: We derive an analytical formula for the fading correlation function of a uniform circular array (UCA) when the angular energy follows a Laplacian distribution. The fading correlation for a UCA is a function of antenna spacing, array geometry, as well as the distribution of the received energy in terms of the angle-of-arrival (AOA). Computer simulations are carried out to verify the analytical results.
TL;DR: A new method for simulating the multiplicative fading of the narrow-band, flat wireless channel for antenna array receivers is presented, an extension of the Jakes (1974) method of simulating fading in which the appropriate correlation of the set of waveforms is accomplished by directly considering the azimuth of scatterers in a particular distribution about the mobile transmitter.
Abstract: A new method for simulating the multiplicative fading of the narrow-band, flat wireless channel for antenna array receivers is presented. The new approach produces a set of fading waveforms, one waveform associated with each receiver element, in which the waveforms are appropriately correlated to take into account the spread, or dispersion, in the azimuth (arrival angle) of the received signal. The new method is an extension of the Jakes (1974) method of simulating fading in which the appropriate correlation of the set of waveforms is accomplished by directly considering the azimuth of scatterers in a particular distribution about the mobile transmitter. The models used for this cluster of scatterers are a ring and a disk of scatterers. Further modifications of the disk model permit the generation of fading waveforms which are correlated in a manner which reflect actual field measurements of azimuth dispersion. Analytical correlation of these models is reviewed for purposes of verification with the waveforms generated by the method.
07 Aug 2002
TL;DR: Results show that the three AOA distributions give similar spatial fading correlation for the same angle spread suggesting that the variance of the distribution is more important than the actual distribution.
Abstract: In this paper, we present the comparative spatial fading correlation function of a uniform linear array (ULA) for various angle-of-arrival (AOA) distributions in a mobile radio environment. The spatial fading correlation for ULA is a function of the angle spread and distance between elements. Angle spread is a measure of the energy distribution in AOA and is defined to be the variance in this work. Three AOA distributions are considered in this work: uniform, truncated Gaussian, and Laplacian. Results show that the three AOA distributions give similar spatial fading correlation for the same angle spread suggesting that the variance of the distribution is more important than the actual distribution. Computer simulations are carried out to verify the analytical results.
17 Nov 2002
TL;DR: Using results from multivariate statistics, a tight closed-form lower-bound is derived for the ergodic capacity of Gaussian multiple-input multiple-output (MIMO) fading channels at any signal-to-noise ratio (SNR) regime.
Abstract: We consider Gaussian multiple-input multiple-output (MIMO) fading channels assuming that the channel is unknown at the transmitter and perfectly known at the receiver. Using results from multivariate statistics, we derive a tight closed-form lower-bound for the ergodic capacity of such channels at any signal-to-noise ratio (SNR). Moreover, we provide an accurate closed-form analytical approximation of ergodic capacity in the high SNR regime. Our analysis incorporates the frequency-selective Rayleigh fading case and/or spatial fading correlation, and allows Important Insights Into optimal (ergodic capacity maximizing) MIMO configurations. Finally, we verify our analytical expressions through comparison with numerical results.
Book•
15 Jun 2002TL;DR: This chapter discusses the characterization and Consequences of Multipath Radio Channels, and the distribution of Angle-of-Arrival and Time Delay Resulting by MultipATH Phenomena.
Abstract: Introduction to the Multipath Phenomena - Statistical Description of the Multipath Propagation Channels. Narrowband Signal Fading in the Space and Time Domains. Wideband Signal Fading in the Time and Frequency Domains. Fading Phenomena - Path Loss Phenomenon in Various Land Environments. Distribution of Angle-of-Arrival and Time Delay Resulting by Multipath Phenomena. Signal Power Fading in Angle and Time Domains. Spectral Properties of Multipath Phenomena. Characterization and Consequences of Multipath Radio Channels - Prediction of Multipath Characteristics for Communications and Positioning. System Aspects of Multipath.
TL;DR: In this paper, the bivariate Nakagami-m distribution with arbitrary fading parameters is derived, obtaining the probability density function, the cumulative density function and the central moments, and limitations of that distribution are discussed.
Abstract: The bivariate Nakagami-m distribution with arbitrary fading parameters is derived, obtaining the probability density function, the cumulative density function and the central moments. Additionally, limitations of that distribution are discussed.
TL;DR: Two new and interesting results of this analysis are: (1) unlike in the case of Rayleigh fading channels, increasing correlation between diversity branches may lead to better performance in Rician fading channels and (2) the phase distribution of the line-of-sight or static fading components of the desired user has a significant influence on the BEP performance in correlated diversity channels.
Abstract: This paper discusses the performance of communication systems using binary coherent and differential phase-shift keyed (PSK) modulation, in correlated Rician fading channels with diversity reception The presence of multiple Rician-faded cochannel users, which may have arbitrary and nonidentical parameters, is modeled exactly Exact bit error probability (BEP) expressions are derived via the moment generating functions (MGFs) of the relevant decision statistics, which are obtained through coherent detection with maximum ratio combining for coherent PSK modulation, and differential detection with equal gain combining (EGC) for differential modulation Evaluating the exact expressions requires a complexity that is exponential in the number of interferers To avoid this potentially time-consuming operation, we derive two low-complexity approximate methods each for coherent and differential modulation formats, which are more accurate than the traditional Gaussian approximation approach Two new and interesting results of this analysis are: (1) unlike in the case of Rayleigh fading channels, increasing correlation between diversity branches may lead to better performance in Rician fading channels and (2) the phase distribution of the line-of-sight or static fading components of the desired user has a significant influence on the BEP performance in correlated diversity channels
TL;DR: This work investigates the outage probability and spectrum efficiency performance of cellular systems with smart antennas and presents closed-form expressions when the desired signal is subject to Rician-type fading and interfering signals exhibit Rayleigh-, or, more general Nakagami- type fading.
Abstract: Relying on the distribution of noncentral multivariate F variates, we investigate the outage probability and spectrum efficiency performance of cellular systems with smart antennas. We consider interference-limited systems in which the number of interferers exceeds or is equal to the number of antenna elements, and we present closed-form expressions when the desired signal is subject to Rician-type fading and interfering signals exhibit Rayleigh-, or, more general Nakagami-type fading. When applicable, these new expressions are compared to those previously reported in the literature dealing with the performance of cellular systems without smart antenna capabilities and the performance of cellular systems with optimum combining when both the desired and interfering signals are subject to Rayleigh-type fading. Corresponding numerical results and plots are also provided and discussed.
TL;DR: An analytical expression for the probability density function of the signal-to-noise ratio (SNR) at the output of a two-branch maximal ratio and selection diversity system is given.
Abstract: An analytical expression for the probability density function of the signal-to-noise ratio (SNR) at the output of a two-branch maximal ratio and selection diversity system is given. The two branches are assumed to be Rayleigh fading, correlated, as well as of unequal average SNRs. Measurements of the cumulative distribution functions after selection and maximal ratio combining were made in Rayleigh fading channels and compared with the analytical results. Also presented are the exact analytical average probabilities of symbol error for coherent binary phase-shift keying and coherent quaternary phase-shift keying before and after two-branch maximal ratio combining for a slow and flat fading correlated Rayleigh channel.
TL;DR: The fading rate at the output of a RAKE receiver with either maximal ratio combiner or postdetection equal gain combiner, operating over a frequency-selective fading channel with different path statistics, is easily calculated using the new cf-based LCR formula.
Abstract: The level crossing rate (LCR) of a random process conveys useful information about the underlying process, and is of interest in diverse engineering fields. In wireless communications, it is related to the system characteristics such as handoff, outage probability, fading rate, average duration of fades, velocity (or maximum Doppler shift) of the mobile, and the effect of diversity on fading. The LCR formula was originally derived by Rice in terms of the joint probability density function (pdf) of the underlying process and its time derivative. In this letter, we express the LCR in terms of the joint characteristic function (cf). This new formula is useful for many cases where the joint cf is simpler to derive than the associated joint pdf. As an application and for a direct-sequence code-division multiple-access system, the fading rate at the output of a RAKE receiver with either maximal ratio combiner or postdetection equal gain combiner, operating over a frequency-selective fading channel with different path statistics, is easily calculated using the new cf-based LCR formula.
TL;DR: Good 8-PSK space-time trellis codes for two, three and four transmit antennas are reported and the performance is evaluated by simulation.
Abstract: Good 8-PSK space-time trellis codes (STTCs) for two, three and four transmit antennas are reported and the performance is evaluated by simulation The new STTCs with three and four transmit antennas achieve large performance improvements over those with two transmit antennas
TL;DR: An online signal-to-noise ratio (SNR) estimation scheme for Nakagami-m (1960) fading channels with L branch equal gain combining (EGC) diversity is proposed and the turbo decoder performance is evaluated using the SNR estimate.
Abstract: We propose an online signal-to-noise ratio (SNR) estimation scheme for Nakagami-m (1960) fading channels with L branch equal gain combining (EGC) diversity. We derive the SNR estimate based on the statistical ratio of certain observables over a block of data, and use the SNR estimates in the iterative decoding of turbo codes on Nakagami-m fading channels with L branch EGC diversity. We evaluate the turbo decoder performance using the SNR estimate under various fading and diversity scenarios (m = 0.5, 1, 5 and L = 1, 2, 3) and compare it with the performance using perfect knowledge of the SNR and the fade amplitudes.
10 Dec 2002
TL;DR: The effects of Rician fading on the capacity of multi-antenna systems designed to be optimal for Rayleigh fading are investigated under the assumption that channel state information (CSI) is available only at the receiver.
Abstract: The effects of Rician fading on the capacity of multi-antenna systems designed to be optimal for Rayleigh fading are investigated under the assumption that channel state information (CSI) is available only at the receiver. Capacity bounds for the multi-antenna Rician fading channel are also derived and numerical results for some representative situations are provided.
TL;DR: A new expression is derived for the exact bit-error probability for the detection of a coherent binary phase-shift keying signal experiencing a number of asynchronous interferers having unequal power levels in Rayleigh fading channels in terms of the coefficients of a Hermite polynomial.
Abstract: We derive a new expression for the exact bit-error probability for the detection of a coherent binary phase-shift keying signal experiencing a number of asynchronous interferers having unequal power levels in Rayleigh fading channels. The new expression is readily computed in terms of the coefficients of a Hermite polynomial.
TL;DR: The bit error rate (BER) performance of a two-dimensional (2-D) RAKE receiver, in combination with transmit diversity on the downlink of a wide-band CDMA (W-CDMA) system, is presented.
Abstract: The bit error rate (BER) performance of a two-dimensional (2-D) RAKE receiver, in combination with transmit diversity on the downlink of a wide-band CDMA (W-CDMA) system, is presented. The analyses assume correlated fading between receive antenna array elements, and an arbitrary number of independent but nonidentical resolvable multipaths combined by the RAKE receiver in the general Nakagami-m (1960) fading channel framework. The impact of the array configuration (e.g., the number of transmit antennas and receive antennas, the antenna element separation) and the operating environment parameters (such as the fading severity, angular spread and path delay profile) on the overall space-path diversity gain can be directly evaluated. In addition, the exact pairwise error probability of a convolutional coded system is obtained, and the coding gain of a space-path diversity receiver is quantified.
TL;DR: The bit error rate of a synchronous multicarrier code-division multiple-access system operating in a Rayleigh fading channel is calculated based on a moment generating function method, without any assumption on the distribution of multiple access interference.
Abstract: The bit error rate of a synchronous multicarrier code-division multiple-access system operating in a Rayleigh fading channel is calculated based on a moment generating function method, without any assumption on the distribution of multiple access interference. Two closed-form BER expressions are derived. Moreover, the BER can be accurately evaluated by using a Gauss-Chebyshev quadrature rule based numerical approach.
TL;DR: The performance for the noncoherent reception of M-ary orthogonal frequency shift keying with postdetection equal gain combining over a correlated fading channel is analyzed.
Abstract: We analyze the performance for the noncoherent reception of M-ary orthogonal frequency shift keying with postdetection equal gain combining over a correlated fading channel. Two kinds of correlated fading statistics are considered: (1) Nakagami fading in which the diversity branches can have unequal signal-to-noise ratios (SNRs) as well as different m-parameters and (2) Rician fading in which the diversity branches can have unequal SNRs. Using the characteristic function of the combiner output SNR, closed-form expressions for the symbol error probability are obtained.