Showing papers on "Fading distribution published in 2000"

Fading correlation and its effect on the capacity of multielement antenna systems

Abstract: We investigate the effects of fading correlations in multielement antenna (MEA) communication systems. Pioneering studies showed that if the fades connecting pairs of transmit and receive antenna elements are independently, identically distributed, MEAs offer a large increase in capacity compared to single-antenna systems. An MEA system can be described in terms of spatial eigenmodes, which are single-input single-output subchannels. The channel capacity of an MEA is the sum of capacities of these subchannels. We show that the fading correlation affects the MEA capacity by modifying the distributions of the gains of these subchannels. The fading correlation depends on the physical parameters of MEA and the scatterer characteristics. In this paper, to characterize the fading correlation, we employ an abstract model, which is appropriate for modeling narrow-band Rayleigh fading in fixed wireless systems.

Digital Communication over Fading Channels: A Unified Approach to Performance Analysis

Abstract: FUNDAMENTALS. Fading Channel Characterization and Modeling. Types of Communication. MATHEMATICAL TOOLS. Alternative Representations of Classical Functions. Useful Expressions for Evaluating Average Error Probability Performance. New Representations of Some PDF's and CDF's for Correlative Fading Applications. OPTIMUM RECEPTION AND PERFORMANCE EVALUATION. Optimum Receivers for Fading Channels. Performance of Single Channel Receivers. Performance of Multichannel Receivers. APPLICATION IN PRACTICAL COMMUNICATION SYSTEMS. Optimum Combining: A Diversity Technique for Communication Over Fading Channels in the Presence of Interference. Direct--Sequence Code--Division Multiple Access. FURTHER EXTENSIONS. Coded Communication Over Fading Channels. INDEX.

Adaptive Modulation over Nakagami Fading Channels

Abstract: We first study the capacity of Nakagami multipath fading (NMF) channels with an average power constraint for three power and rate adaptation policies. We obtain closed-form solutions for NMF channel capacity for each power and rate adaptation strategy. Results show that rate adaptation is the key to increasing link spectral efficiency. We then analyze the performance of practical constant-power variable-rate M-QAM schemes over NMF channels. We obtain closed-form expressions for the outage probability, spectral efficiency and average bit-error-rate (BER) assuming perfect channel estimation and negligible time delay between channel estimation and signal set adaptation. We also analyze the impact of time delay on the BER of adaptive M-QAM.

Long-range prediction of fading signals

Abstract: It was previously proposed to adapt several transmission methods, including modulation, power control, channel coding, and antenna diversity to rapidly time variant fading channel conditions. Prediction of the channel coefficients several tens-to-hundreds of symbols ahead is essential to realize these methods in practice. We describe a novel adaptive long-range fading channel prediction algorithm (LRP) and its utilization with adaptive transmission methods. The LRP is validated for standard stationary fading models and tested with measured data and with data produced by our novel realistic physical channel model. Both numerical and simulation results show that long-range prediction makes adaptive transmission techniques feasible for mobile radio channels.

A space-frequency transmitter diversity technique for OFDM systems

Abstract: A transmitter diversity technique for wireless communications over frequency selective fading channels is presented. The proposed technique utilizes orthogonal frequency division multiplexing (OFDM) to transform a frequency selective fading channel into multiple flat fading subchannels on which space-frequency processing is applied. Simulation results verify that in a slow fading environment the proposed space-frequency OFDM (SF-OFDM) transmitter diversity technique has the same performance as a previously reported space-time OFDM (ST-OFDM) transmitter diversity system but shows better performance in the more difficult fast fading environments. Other implementation advantages of SF-OFDM over the ST-OFDM transmitter diversity technique are also discussed.

Efficient simulation of Ricean fading within a packet simulator

Abstract: Packet level network protocol simulators use simple channel models for computational efficiency. A typical method for doing this is to compute a packet error probability assuming a certain fading distribution without taking into account time-correlation. This paper introduces work that has been done to model the effect of small-scale fading (Rayleigh and Ricean) within the ns network simulator. It allows for the faithful simulation of a complete fading envelope. The fading models have the appropriate statistics and also time correlational properties obtained from the Doppler spectrum. An efficient implementation based on a simple table lookup is described.

Performance analysis of maximal ratio combining and comparison with optimum combining for mobile radio communications with cochannel interference

Abstract: The performance of maximal ratio combining for space diversity reception in digital cellular mobile radio systems is studied for communications in the presence of multiple cochannel interference (CCI) sources and is compared to optimum combining. The main contribution of the paper is that the analysis accounts for fading of the signal of interest (SOI) as well as the cochannel interference (CCI). The paper considers BPSK signalling in flat, quasi-static channels. Rayleigh or Rice fading is assumed for the SOI, while CCI is assumed subject to Rayleigh fading. Channels associated with interference sources are assumed independent and identically distributed. Using a multivariate statistical analysis approach and assuming equal-power interference sources, analytical expressions are derived for the density function of the array output signal-to-interference ratio (SIR), the outage probability, and the average probability of bit error with maximal ratio combining. Earlier results obtained for optimum combining and Rayleigh fading are extended to the case when the SOI is subject to Rice fading. A limited analysis of the equal gain combiner is also presented.

Outage probability of diversity systems over generalized fading channels

Abstract: Outage probability is an important performance measure of communication systems operating over fading channels. Relying on a simple and accurate algorithm for the numerical inversion of the Laplace transforms of cumulative distribution functions, we develop a moment generating function-based numerical technique for the outage probability evaluation of maximal-ratio combining (MRC) and postdetection equal-gain combining (EGC) in generalized fading channels for which the fading in each diversity path need not be independent, identically distributed, nor even distributed according to the same family of distributions. The method is then extended to coherent EGC but only for the case of Nakagami-m fading channels. The mathematical formalism is illustrated by applying the method to some selected numerical examples of interest showing the impact of the power delay profile and the fading correlation on the outage probability of MRC and EGC systems.

Shannon-theoretic approach to a Gaussian cellular multiple-access channel with fading

Abstract: Shannon-theoretic limits on the achievable throughput for a simple infinite cellular multiple-access channel (MAC) model (Wyner 1994) in the presence of fading are presented. In this model, which is modified to account for flat fading, the received signal, at a given cell-site's antenna, is the sum of the faded signals transmitted from all users within that cell plus an attenuation factor /spl alpha//spl isin/[0,1] times the sum of the faded signals received from the adjacent cells, accompanied by Gaussian additive noise. This model serves as a tractable model providing considerable insight into complex and analytically intractable real-world cellular communications. Both linear and planar cellular arrays are considered with exactly K active users in each cell. We assume a hyper-receiver, jointly decoding all of the users, incorporating the received signals from all of the active cell-sites. The hyper-receiver is assumed to be aware of the codebooks and realizations of the fading processes of all the users in the system. In this work we consider the intracell time-division multiple-access (TDMA) and the wideband (WB) protocols. We focus on the maximum reliably transmitted equal rate. Bounds to this rate are found for the intracell TDMA protocol by incorporating information-theoretic inequalities and the Chebyshev-Markov moment theory as applied to the limiting distribution of the eigenvalues of a quadratic form of tridiagonal random matrices. We demonstrate our results for the special case where the amplitudes of the fading coefficients are drawn from a Rayleigh distribution, i.e., Rayleigh fading. For this special case, we observe the rather surprising result that fading may increase the maximum equal rate, for a certain range of /spl alpha/ as compared to the nonfaded case. In this setting, the WB strategy, which achieves the maximum reliable equal rate of the model, is proved to be superior to the TDMA scheme. An upper bound to the maximum equal rate of the WB scheme is also obtained. This bound is asymptotically tight when the number of users is large (K/spl Gt/1). The asymptotic bound shows that the maximum equal rate of the WB scheme in the presence of fading is higher than the rate which corresponds to the nonfaded case for any intercell interference factor /spl alpha//spl isin/[0,1] signal-to-noise ratio (SNR) values. This result is found to be independent of the statistics of the fading coefficients.

Performance of space-time codes in the presence of spatial fading correlation

Abstract: Previous work on space-time coding has been restricted to the idealistic case of uncorrelated spatial fading. In practice, however insufficient antenna spacing or lack of scattering cause the individual antennas to be correlated. In this paper we study the impact of spatial fading correlation on the performance of space-time codes. In particular we quantify the loss in diversity gain and coding gain as a function of angle spread and antenna spacing. We furthermore show that if a space-time code achieves full diversity in the uncorrelated case, the diversity order achieved in the correlated case is given by the product of the rank of the transmit correlation matrix and the rank of the receive correlation matrix. Finally, we provide simulation results demonstrating the impact of spatial fading correlation on the symbol error rate of space-time codes.

A decomposition technique for efficient generation of correlated Nakagami fading channels

Abstract: Correlated Nakagami m-fading is commonly encountered in wireless communications. Its generation in a laboratory environment is therefore of theoretical and practical importance. However, no generic technique for this purpose is available in the literature. Correlated Rayleigh fading is easy to simulate since it has a simple relationship with a complex Gaussian process. Unfortunately, this is not the case for Nakagami fading. The difficulty lies in that the fading parameter can be a real number and there is no general theory linking a Nakagami vector to a finite set of correlated Gaussian vectors. In this paper, by introducing a direct-sum decomposition principle and determining the statistical mapping between the correlated Nakagami process and a set of Gaussian vectors for its generation, a simple general procedure is derived for the generation of correlated Nakagami channels with arbitrary parameters. A key parameter in the statistical mapping can be determined by using an iterative method. The validity of the new technique is examined through the generation of a correlated Nakagami sequence, as encountered in U.S. digital cellular, and a multibranch vector channel as encountered in diversity reception.

Generation of correlated Rayleigh fading envelopes for spread spectrum applications

Abstract: A procedure for generating N Rayleigh fading envelopes with any desired covariance matrix is given. This method, numerical in nature, enables researchers to simulate correlated fading envelopes, for use in: (1) the study of the impact of correlation on diversity system performance and (2) the study of multicarrier CDMA (MC-CDMA), where the number of carriers notably exceeds the degree of system diversity.

A Markov model for the mobile propagation channel

Abstract: A finite-state Markov model is fitted to the mobile propagation channel by the use of contingency tables. Narrow-band Rayleigh and Ricean fading are considered in detail, but the techniques extend to other types of fading. Several criteria may indicate that a first-order finite-state Markov model sufficiently characterizes the channel behavior. The parameters of the model are obtained both from theoretical analysis and simulation. Functional dependence between the transition probabilities and the steady-state probabilities is found in the slow fading case.

Exponential-type bounds on the generalized Marcum Q-function with application to error probability analysis over fading channels

Abstract: Strict upper and lower bounds of exponential-type are derived for the generalized (mth order) Marcum Q-function which enable simple evaluation of a tight upper bound on the average bit-error probability performance of a wide class of noncoherent and differentially coherent communication systems operating over generalized fading channels. For the case of frequency selective fading with arbitrary statistics per independent fading path, the resulting upper hound on performance is expressed in the form of a product of moment generating functions of the instantaneous power random variables that characterize these paths.

The /spl kappa/-/spl mu/ distribution: a general fading distribution

Abstract: This paper presents a general fading distribution-the /spl kappa/-/spl mu/ distribution-that includes the Rice and the Nakagami-m distributions as special cases. Therefore the one-sided Gaussian and the Rayleigh distributions also constitute special cases and the lognormal distribution may be well-approximated by the /spl kappa/-/spl mu/ distribution. Preliminary results show that the /spl kappa/-/spl mu/ distribution provides a very good fitting to experimental data.

Comparison of the level crossing rate and average fade duration of Rayleigh, Rice and Nakagami fading models with mobile channel data

Abstract: Level crossing rate (LCR) and average fade duration (AFD) of the signal envelope are two important second-order channel statistics, which convey useful information about the dynamic temporal behavior of multipath fading channels. In this paper and for a general non-isotropic scattering scenario, in which the mobile receives signal only from particular directions with different probabilities, we derive expressions for the LCR and AFD of Rayleigh, Rice and Nakagami (1960) fading models, including the effect of non-uniform signal angle-of-arrival distribution. The merits and limitations of all the above models in describing the first- and second-order statistics of multipath fading channels are explored through an extensive comparison of theoretical results with narrowband measurements taken in urban and suburban areas at 910.25 MHz.

A simulation model for Nakagami-m fading channels, m<1

Abstract: This paper proposes a mathematical model for simulating a Nakagami-m (1960) fading channel, m<1. It is shown that the m fading process can be expressed as a product of a square-root-beta process and a complex Gaussian process. Extension of the proposed model to simulate correlated diversity channels is also given. Numerical results demonstrate that the statistical properties of the samples generated from the proposed model are close to the required ones.

A space-time model for frequency nonselective Rayleigh fading channels with applications to space-time modems

Abstract: This paper extends the traditional Clarke/Jakes (1968, 1974) model for a frequency flat fading process in a land mobile radio system to facilitate the examination of coherent space-time demodulation systems. The work develops a space-time correlation function using a ring of scatterers model around the mobile unit. The resulting correlation function permits the investigation of a variety of issues concerning base station configurations in space-time systems. The interrelationship of the fading process between the space and the time domain is explored. A detailed example regarding the effects of antenna separation in a receiver diversity system is considered. A set of design rules for interleaving depth and antenna separation in a space-time modem is presented and quantified.

Performance analysis of MMSE receivers for DS-CDMA in frequency-selective fading channels

Abstract: The performance of the minimum mean-squared error (MMSE) receiver for the detection of direct sequence code division multiple access is considered in various fading channel models. Several modifications to the basic MMSE receiver structure which have been previously proposed for use on nonselective fading channels are reviewed and shown to represent different approximations to a single common form. The performance of this general structure is analyzed as well as various extensions suitable for frequency-selective fading channels. Particular attention is given to the performance advantage gained through knowledge of the fading parameters of the various transmission paths of each user's signal. It is shown that having this knowledge is not particularly useful on a flat fading channel unless the loading is very heavy and even then the difference in performance is only minimal. On the other hand, having this knowledge is crucial in a multipath fading channel and the inability to learn the fading channel parameters will lead to substantial degradation in capacity. A heuristic explanation to support this result based on a dimensionality argument is also presented.

Comparison of DPSK and MSK bit error rates for K and Rayleigh-lognormal fading distributions

Abstract: The composite Rayleigh-lognormal distribution is mathematically intractable for the analytical evaluation of such a communication system performance metric as bit error rate. The composite K distribution closely approximates the Rayleigh-lognormal and is potentially useful for analytical manipulations. In this contribution we derive the bit error rates of differential phase-shift keying (DPSK) and minimum shift keying (MSK), in manageable closed forms, for the K distribution model of multipath fading and shadow fading, and show, numerically, the close agreement between these results and those based on the Rayleigh-lognormal distribution.

Performance evaluation and analysis of space-time coding in unequalized multipath fading links

Abstract: This paper investigates the use of space-time (ST) coding for high-speed data transmission, as well as studies the effect of time delay spread on such scheme over unequalized fading channels. Using a random variable decomposition technique, we present an analytical model and obtain an approximate bound of the pairwise-error probability for ST coded systems over multipath and time-dispersive fading channels. It is shown that the presence of multipath does not reduce the diversity gain provided by the original design criteria, which is adopted to construct specific ST codes in quasi-static flat fading, but the coding gain diminishes due to the effect of multipath fading.

Theoretical analysis and measurement results of vegetation effects on path loss for mobile cellular communication systems

Abstract: This paper reports on studies of propagation in an urban forested park area to investigate the statistical nature of the time fading for frequencies ranging from 0.9 GHz to 1.8 GHz, as well as to examine the range dependence and the base station height gain. Measurements of the received signal over 30 s intervals for a stationary mobile were used to construct the distribution functions for the fading. In most cases, the distribution could be approximated by a Rician distribution, whose K-factor was found to depend on transmitter height.

Exact bit-error probability for optimum combining with a Rayleigh fading Gaussian cochannel interferer

Abstract: We derive expressions for the exact bit-error probability (BEP) for the detection of coherent binary phase-shift keying signals of the optimum combiner employing space diversity when both the desired signal and a Gaussian cochannel interferer are subject to flat Rayleigh fading. Two different methods are employed to reach two different, but numerically identical, expressions. With the direct method, the conditional BEP is averaged over the fading of both signal and interference, With the moment generating function based method, expressions are derived from an alternative representation of the Gaussian Q-function.

Error performance analysis of space-time codes over Rayleigh fading channels

Abstract: Space-time coding is a bandwidth and power efficient method of communication over fading channels that realizes the benefits of multiple transmit and receive antennas. This novel technique has attracted much attention recently. However, currently the only analytical guide to the performance of space-time codes is an upper bound [1] which could be quite loose in many cases. In this paper, an exact pairwise error probability is derived for space-time codes operating over Rayleigh fading channels. Based on this expression, an analytical estimate for bit error probability is computed, taking into account dominant error events. Simulation results indicate that the estimates are of high accuracy in a broad range of signal-to-noise ratios.

Effect of mobile velocity on communications in fading channels

Abstract: In a fading channel, it is well known that the rate of channel variation is dependent on the velocity of the mobile. Consequently, depending on the channel correlation, successive symbols transmitted over the channel can suffer from very similar or possibly very different fading conditions. In this paper, we present an analytical model to evaluate the effect of mobile velocity on the performance of a communication system operating in a multipath fading channel. To incorporate the effect of velocity, a Markov process is used which captures the correlated nature of the channel. An error recursion is then developed which considers the effect of closed-loop power control, channel coding, and finite interleaving. In the numerical analysis, we use the analytical model to investigate the tradeoffs when these various schemes are used. We demonstrate how the performance of these different schemes is sensitive to mobile velocity.

Average SNR of dual selection combining over correlated Nakagami-m fading channels

Abstract: We investigate the effect of fading correlation and branch gain imbalance on the average output signal-to-noise ratio (SNR) in conjunction with dual selection combining (SC). In particular, starting with the moment generating function of the dual SC output SNR, we derive a closed-form expression for the average output SNR in the general case of correlated unbalanced Nakagami-m fading channels. We then show that the generic result can be further simplified for the special cases of Rayleigh fading, uncorrelated branches, and/or equal average SNRs. Because of their simple form, the given expressions readily allow numerical evaluation for cases of practical interest.

Generation of bivariate Rayleigh and Nakagami-m fading envelopes

Abstract: The paper presents an algorithm for generating bi-variate Nakagami-m distributed fading envelopes with any desired power cross correlation. For this algorithm, the fading index m should be a positive integer (m=1 for Rayleigh fading). Its applications include dual-branch selection combining diversity, dual-branch switch diversity systems, and wireless channel modeling.

A systematic approach to detecting OFDM signals in a fading channel

Abstract: We derive the maximum a posteriori probability (MAP) receiver for orthogonal frequency-division multiplexed signals in a fading channel. As the complexity of the MAP receiver is high, we obtain a low-complexity, suboptimal receiver and evaluate its performance.

A transmit diversity scheme for frequency selective fading channels

Abstract: We propose a transmit diversity scheme for frequency selective fading channels using orthogonal frequency division multiplexing (OFDM). The transmit diversity scheme proposed by Alamouti (see IEEE JSAC, vol.16, no.8, p.1451-58, 1998) for flat fading channels is extended to the case when the channel has a delay spread. There is no loss in receive SNR due to the delay spread in the channel. A diversity order of 2N can be achieved by using two transmit and N receive antennas. We discuss several interesting aspects of the approach and compare it with other extensions of the Alamouti scheme for delay spread channels.

Modified Jakes' model for simulating multiple uncorrelated fading waveforms

Abstract: Two ways for modifying the classical Jakes' (1974) fading simulator to generate multiple uncorrelated fading waveforms are proposed. The 1/sup st/ and 2/sup nd/ order statistics of individual output waveforms are shown to agree well with theoretical expectations. The cross correlation between different waveforms is nearly zero. These fading simulators are expected to be useful in the investigations of frequency-selective and diversity-combined multipath fading channels.