Showing papers on "Fading distribution published in 2006"

A closed-form expression for the outage probability of decode-and-forward relaying in dissimilar Rayleigh fading channels

Abstract: Decode-and-forward relaying has been shown to be a viable transmission protocol for wireless networks incorporating distributed spatial diversity. Practical systems may employ relay channels that experience statistically different signal fading. The performance of decode-and-forward relaying in channels with dissimilar fading parameters is investigated. In particular, a closed-form expression for the outage probability of a system with an arbitrary number of relays is derived

Optimized transmission for fading multiple-access and broadcast channels with multiple antennas

Abstract: In mobile wireless networks, dynamic allocation of resources such as transmit powers, bit-rates, and antenna beams based on the channel state information of mobile users is known to be the general strategy to explore the time-varying nature of the mobile environment. This paper looks at the problem of optimal resource allocation in wireless networks from different information-theoretic points of view and under the assumption that the channel state is completely known at the transmitter and the receiver. In particular, the fading multiple-access channel (MAC) and the fading broadcast channel (BC) with additive Gaussian noise and multiple transmit and receive antennas are focused. The fading MAC is considered first and a complete characterization of its capacity region and power region are provided under various power and rate constraints. The derived results can be considered as nontrivial extensions of the work done by Tse and Hanly from the case of single transmit and receive antenna to the more general scenario with multiple transmit and receive antennas. Efficient numerical algorithms are proposed, which demonstrate the usefulness of the convex optimization techniques in characterizing the capacity and power regions. Analogous results are also obtained for the fading BC thanks to the duality theory between the Gaussian MAC and the Gaussian BC

On the Capacity of Fading MIMO Broadcast Channels with Imperfect Transmitter Side-Information

Abstract: A fading broadcast channel is considered where the transmitter employs two antennas and each of the two receivers employs a single receive antenna It is demonstrated that even if the realization of the fading is precisely known to the receivers, the high signal-to-noise (SNR) throughput is greatly reduced if, rather than knowing the fading realization \emph{precisely}, the trasmitter only knows the fading realization \emph{approximately} The results are general and are not limited to memoryless Gaussian fading

Novel Sum-of-Sinusoids Simulation Models for Rayleigh and Rician Fading Channels

Abstract: The statistical properties of Clarke's fading model with a finite number of sinusoids are analyzed, and an improved reference model is proposed for the simulation of Rayleigh fading channels. A novel statistical simulation model for Rician fading channels is examined. The new Rician fading simulation model employs a zero-mean stochastic sinusoid as the specular (line-of-sight) component, in contrast to existing Rician fading simulators that utilize a non-zero deterministic specular component. The statistical properties of the proposed Rician fading simulation model are analyzed in detail. It is shown that the probability density function of the Rician fading phase is not only independent of time but also uniformly distributed over [-pi, pi). This property is different from that of existing Rician fading simulators. The statistical properties of the new simulators are confirmed by extensive simulation results, showing good agreement with theoretical analysis in all cases. An explicit formula for the level-crossing rate is derived for general Rician fading when the specular component has non-zero Doppler frequency

Outage probability of cooperative relay networks in Nakagami-m fading channels

Abstract: It is well known that the cooperation among nodes can improve the performance of a wireless network. In this letter we analyze the outage probability behaviour of a relay network in Nakagami-m fading channels. A closed-form solution for the outage probability is derived. When m=1, the results are applicable for Rayleigh fading. Computer simulations confirm the presented mathematical analysis

A useful integral for wireless communication theory and its application to rectangular signaling constellation error rates

Abstract: A useful integral, representing the average over Rayleigh fading of the product of two Gaussian Q-functions, is solved in closed-form. A closed-form solution for the symbol-error probability of general rectangular quadrature amplitude modulation in Rayleigh fading is derived.

The α-η-μ and α-κ-μ Fading Distributions

Abstract: In this paper two new fading distributions, the α-η-μ Distribution and α-κ-μ Distribution, are presented. The α-η-μ distribution includes the α-μ, Nakagami-m, Nakagami-q, Weibull, Hoyt, Rayleigh, Exponential, and the One-Sided Gaussian distributions as special cases. The α-κ-μdistribution includes the α-μ, Nakagami-m, Weibull, Rice, Rayleigh, Exponential, and the One-Sided Gaussian distributions as special cases. Furthermore, it proposes estimators for the involved parameters and uses field measurements to validate the distributions.

Multipath fading in wireless sensor networks: measurements and interpretation

Abstract: Multipath fading heavily contributes to the unreliability of wireless links, causing fairly large deviations from link quality predictions based on path loss models; its impact on wireless sensor networks is considerable. Although analytical models provide a probabilistic description, multipath fading is a deterministic phenomenon. Moreover, in the case of static nodes, fading is time-invariant. We illustrate its spatial nature with experimental evidence obtained using lower-end sensing node hardware. We also show the limitations of the supposed immunity of wideband radios to multipath fading in indoor deployments.

Diversity analysis of space-time coding in cascaded Rayleigh fading channels

Abstract: Cascaded Rayleigh distribution is used to model multipath fading in mobile-to-mobile communication scenarios and provides a better fit to experimental data in such scenarios compared to the conventional Rayleigh channel model. In this letter, we derive an exact expression for the pairwise error probability (PEP) of space-time trellis codes over the cascaded Rayleigh fading channel, which is in the form of a simple single finite-range integral. Through the derived PEP expression, we present the maximum diversity order achievable over such channels and demonstrate the performance degradation in comparison to conventional Rayleigh channels. Monte-Carlo simulations are further demonstrated to confirm the analytical results.

Performance Analysis of Diversity Combining Algorithms in Shadowed Fading Channels

Abstract: A compound fading model incorporating short term fading and shadowing proposed recently is used to analyze the performance of wireless systems employing microscopic diversity to mitigate the effects of flat fading. This model can account for the presence of different levels of fading and shadowing and provide an analytical solution for the probability density function of the signal-to-noise ratio. Using that model, the performances of MRC and SC diversity combining algorithms were studied. The amount fading (AF) following diversity implementation was calculated and it is seen that the decline in the amount of fading is bound by the level of shadowing present, with the MRC providing a larger decrease in the amount of fading than the SC algorithm. The effect on the error rates was studied using the example of the coherent BPSK modem. Results show that the performances of wireless systems can be analyzed using the compound model for the shadowed fading channels.

Accurate error-rate performance analysis of OFDM on frequency-selective Nakagami-m fading channels

Abstract: Error rates of orthogonal frequency-division multiplexing (OFDM) signals in multipath slow fading Nakagami-m fading channels are considered. The exact probability density function of a sum of Nakagami-m random phase vectors is used to derive a closed-form expression for the error rates of OFDM signals. The precise error-rate analysis is extended to a system using multichannel reception with maximal ratio combining. An asymptotic error-rate analysis is also provided. For a two-tap channel with finite values of Nakagami-m fading parameters, our analysis and numerical results show that the asymptotic error-rate performance of an OFDM signal is similar to that of a single carrier signal transmitted over a Rayleigh fading channel. On the other hand, our analysis further shows that a frequency-selective channel that can be represented by two constant taps has similar asymptotic error-rate performance to that of a one-sided Gaussian fading channel. It is observed that, depending on the number of channel taps, the error-rate performance does not necessarily improve with increasing Nakagami-m fading parameters.

Performance analysis for MIMO systems using zero forcing detector over fading channels

Abstract: In the paper, the performance of multiple-input-multiple-output (MIMO) systems using a zero forcing detector is studied over Rayleigh and Rice fading channels. Approximation to the distribution of non-central complex Wishart distribution is used to derive the distribution of the post-detection signal-to-noise (SNR) ratio. A closed-form expression of bit error rate is obtained in terms of the hypergeometric and Gamma functions. The performance of MIMO systems under the scenario that the individual sub-channels are correlated is also investigated. It is shown that, for the exponential correlation channel model, an increase in channel correlation between the transmission paths results a decrease in SNR at the receiver. It is concluded that with the same SNR at the receiver, the performance of MIMO systems over a Rice fading channel degrades compared to that over an independent and identical distributed (i.i.d.) Rayleigh fading channel.

On the performance analysis of equal-gain diversity receivers over generalized gamma fading channels

Abstract: A versatile envelope distribution which generalizes many commonly used models for multipath and shadow fading is the so-called generalized Gamma (GG) distribution. By considering the product of N GG random variables (RV)s, novel expressions for its moments-generating, probability density, and cumulative distribution functions are obtained in closed form. These expressions are used to derive a closed-form union upper bound for the distribution of the sum of GG distributed RVs. The proposed bound turns out to be an extremely convenient analytical tool for studying the performance of TV-branch equal-gain combining receivers operating over GG fading channels. For such receivers, first the moments of the signal-to-noise (SNR) at the output, including average SNR and amount of fading, are obtained in closed form. Furthermore, novel union upper bounds for the outage and the average bit error probability are derived and evaluated in terms of Meijer's G-functions. The tightness of the proposed bounds is verified by performing comparisons between numerical evaluation and computer simulations results

Optimal Training and Pilot Pattern Design for OFDM Systems in Rayleigh Fading

Abstract: This paper deals with two major considerations for pilot symbol assisted orthogonal frequency division multiplexing (PSA-OFDM) systems when operated over Rayleigh fading channels. One of them is to decide how many pilot symbols should be used and the other is where to place these pilot symbols, i.e. pilot pattern. Incorporating linear interpolation and choosing appropriate system parameters, we first derive analytically the bit-error-rate (BER) for frequency-selective fading, time-selective fading and correlated fading, respectively. Based on the theoretical BER, the optimal training can be determined numerically for a specific fading environment. Furthermore, we propose a new and simple pilot pattern for PSA-OFDM system and its performance is analyzed in terms of the BER. The proposed scheme clusters two neighboring pilots together so as to increase the channel estimate accuracy by averaging over the two pilot symbols. Analytical and simulation results show that this clustered pilot pattern gives better performance in terms of BER than the existing equi-spaced pilot pattern when the channel SNR is moderate, without sacrificing the bandwidth efficiency

On the symbol error probability of general order rectangular qam in nakagami-m fading

Abstract: Recently, Beaulieu, following an ingenious concept, presented a closed-form expression for a useful integral, which was used for the evaluation of the symbol error probability (SEP) of general order rectangular quadrature amplitude modulation (QAM) in slow Rayleigh fading. In this letter, these results are extended to Nakagami-m fading channels, deriving a novel closed-form formula for the average over Nakagami-m fading of the product of two Gaussian Q-functions, which can be efficiently used to study the impact of fading severity on the error performance of general rectangular QAM constellations

SNR Analysis of OFDM Systems in the Presence of Carrier Frequency Offset for Fading Channels

Abstract: This letter analyzes the effect of the carrier frequency offset on orthogonal frequency division multiplexing (OFDM) systems for multipath fading channels. A simple approximate expression for the average signal-to-noise ratio (SNR) is derived. This approximate expression is shown to be an upper bound of the average SNR for flat fading channels and an exact expression for the AWGN channel. The approximate average SNR expression is validated using Monte Carlo simulation for both flat fading channels and frequency-selective fading channels

Impact of double-Rayleigh fading on system performance

Abstract: Double-Rayleigh amplitude distribution, induced by double scattering in the radio channel, occurs in a variety of propagation scenarios, including propagation via diffracting wedges. It is unknown, however, how double scattering affects communication link performance. In this paper, an expression for symbol error probability for some common communication schemes over double-Rayleigh fading wireless channels is derived. It is shown that double scattering results in severe degradation in symbol error probability. Interestingly, our analysis suggests that for the double-Rayleigh channel there exists no meaningful diversity order for the SNR values of practical interest.

Capacity of correlated nakagami-m fading channels with diversity combining techniques

Abstract: We derive closed-form expressions for the capacity of dual-branch maximal ratio combining, equal gain combining, selection combining, and switch and stay combining (SSC) diversity systems over correlated Nakagami-m fading channels. Because the final capacity expressions contain infinite series, we truncate the series and present upper bounds on the truncation errors. We also derive an expression that can be used to numerically determine the optimum adaptive switching threshold for the capacity of a dual-branch SSC system over correlated Nakagami-m fading channels. However, a closed-form expression for the optimum adaptive switching threshold is derived for the case of independent branches. The corresponding expressions for Rayleigh fading are obtained as a special case of Nakagami-m fading. Finally, numerical examples are presented for illustration.

A new simulation model for mobile-to-mobile Rayleigh fading channels

Abstract: A new statistical sum-of-sinusoids simulation model is proposed for mobile-to-mobile Rayleigh fading channels and compared with existing simulation models. The new proposed model has a lower variance of the auto-correlation functions, i.e., it converges faster and has a lower correlation between the in-phase and quadrature components of the complex faded envelope than existing simulation models. This model yields adequate statistics with only 30 simulation runs

The fading number of single-input multiple-output fading channels with memory

Abstract: We derive the fading number of stationary and ergodic (not necessarily Gaussian) single-input multiple-output (SIMO) fading channels with memory. This is the second term, after the double-logarithmic term, of the high signal-to-noise ratio (SNR) expansion of channel capacity. The transmitter and receiver are assumed to be cognizant of the probability law governing the fading but not of its realization. It is demonstrated that the fading number is achieved by independent and identically distributed (i.i.d.) circularly symmetric inputs of squared magnitude whose logarithm is uniformly distributed over an SNR-dependent interval. The upper limit of the interval is the logarithm of the allowed transmit power, and the lower limit tends to infinity sublogarithmically in the SNR. The converse relies inter alia on a new observation regarding input distributions that escape to infinity. Lower and upper bounds on the fading number for Gaussian fading are also presented. These are related to the mean squared-errors of the one-step predictor and the one-gap interpolator of the fading process respectively. The bounds are computed explicitly for stationary mth-order autoregressive AR(m) Gaussian fading processes.

A Shannon-Theoretic Perspective on Fading Multihop Networks

Abstract: We consider a frequency-flat fading multihop network with a single active source-destination pair terminals communicating over multiple hops through a set of intermediate relay terminals. We use Shannon-theoretic tools to analyze the tradeoff between energy efficiency and spectral efficiency (known as the power-bandwidth tradeoff) for a simple communication protocol based on time-division decode-and-forward relaying in meaningful asymptotic regimes of signal-to-noise ratio (SNR) under a system-wide power constraint on source and relay transmissions. The impact of multi-hopping and channel fading on the key performance measures of the high and low SNR regimes is investigated to shed new light on the possible enhancements in power/bandwidth efficiency and link reliability. In contrast to the common belief that in fading environments communicating over multiple hops suffers significantly in performance due to the worst link limitation, our results indicate that hopping could significantly improve the outage behavior over slow-fading networks and stabilize links against the random channel fluctuations. In particular, we prove that there exists an optimal number of hops that minimizes the end-to-end outage probability and characterize the dependence of this optimal number on the fading statistics and target energy and spectral efficiencies.

Diversity analysis of space-time coding in cascaded Rayleigh fading channels

Abstract: Cascaded Rayleigh distribution is used to model multipath fading in mobile-to-mobile communication scenarios and provides a better fit to experimental data in such scenarios compared to the conventional Rayleigh channel model. In this letter, we derive an exact expression for the pairwise error probability (PEP) of space-time trellis codes over the cascaded Rayleigh fading channel, which is in the form of a simple single finite-range integral. Through the derived PEP expression, we present the maximum diversity order achievable over such channels and demonstrate the performance degradation in comparison to conventional Rayleigh channels. Monte-Carlo simulations are further demonstrated to confirm the analytical results

Outage Theorems for MIMO Block-Fading Channels

Abstract: The connection between the average codeword or frame error probability (FEP) of space-time codes and the outage probability over general block-fading multiple-input multiple-output (MIMO) channels is established. Three archetypal problems are considered under general fading distributions in a single framework wherein the receiver has channel state information whereas the transmitter knows a) the fading distribution but not the channel realization b) the channel realization but must follow a short term (per codeword) average power constraint, and c) the channel realization but is constrained only by a long-term average power constraint. Three telescoping sets of space-time codes are defined for a given rate and it is shown that average FEPs arbitrarily close to the respective outage probabilities for each of the three cases a)-c) can be achieved by codes in each set for sufficiently large frame lengths. For the smallest set among the three which contains codes with a spectral norm constraint that is stricter than the average or maximum energy constraints commonly assumed, firm sphere-packing lower bounds on the FEP are obtained, and, consequently, strong converse theorems are proved which assert that the respective outage probabilities also represent the best achievable FEP in the large frame-length limit. Moreover, the set of spectral norm constrained codes are also shown to be large enough to contain universal codes that can communicate reliably over any channel realization for which the mutual information exceeds the information rate of the code

Performance of generalized selection combining over Weibull fading channels

Abstract: The literature is relatively sparse in performance analysis of diversity combining schemes over Weibull fading channels, despite the fact that the Weibull distribution is often found to be suitably fit for empirical fading channel measurements. In this paper, we capitalize on some interesting results due to Lieblein on the order statistics of Weibull random variables to derive exact closed-form expressions for the combined average signal-to-noise ratio (SNR) as well as amount of fading (AF) at a generalized selection combining (GSC) output over Weibull fading channels. We also use some simple AF-based mappings between the fading parameters of the Weibull distribution and those of the Nakagami, Rice, and Hoyt distributions to obtain the approximate but accurate average SNR and AF of GSC over these types of channels. The mathematical equations are validated and illustrated by some numerical examples for scenarios of practical interest. Copyright © 2006 John Wiley & Sons, Ltd.

Performance of DS-CDMA receivers with MRC in nakagami-m fading channels with arbitrary fading parameters

Abstract: The receivers that combine spatial antenna diversity with temporal multipath diversity are known as two-dimensional (2-D) RAKE receivers. In this paper, we consider the outage probability and the bit error rate performance of a coherent binary phase shift keying 2-D RAKE receiver in the context of an asynchronous direct sequence (DS)-code division multiple access (CDMA) system operating in a Nakagami-m fading channel with real and arbitrary fading parameters. The closed-form expressions derived for the two wireless performance measures are easily evaluated numerically and enable the link designer to examine the effects of system parameters, such as the number of receive antennas, RAKE fingers per antenna, and asynchronous CDMA users in the cell, as well as channel conditions, such as the amount of fading in the combined paths and the multipath intensity profile of the channel on the link performance. In addition, the diversity loss due to correlated fading among the spatially separated RAKE fingers is quantified.

Optimal Layered Transmission Over Quasi-Static Fading Channels

Abstract: We consider layered transmission of a successively refinable complex Gaussian source over a quasi-static fading channel. For a given number of source coding layers, we propose an efficient algorithm to calculate the optimal rate assignment for each layer, as well as the optimal size of each layer. The optimality of the algorithm is proved and numerical results for a multiple antenna Rayleigh fading channel are presented. It is numerically shown that a small number of layers is usually sufficient to achieve most of the layering gain.

Two New Methods for the Generation of Multiple Uncorrelated Rayleigh Fading Waveforms

Abstract: This paper deals with the design of a set of multiple uncorrelated Rayleigh fading waveforms. The Rayleigh fading waveforms are mutually uncorrelated, but each waveform is correlated in time. The waveforms are generated by using the sum-of-sinusoids principle. Two new closed-form solutions are presented for the computation of the model parameters. Analytical and numerical results show that the resulting sum-of-sinusoids-based channel simulator fulfills all main requirements imposed by the reference model with given correlation properties derived under two-dimensional isotropic scattering conditions. The proposed methods are useful for the design of simulation models for diversity-combined Rayleigh fading channels, frequency-selective channels, and multiple-input multiple-output (MIMO) channels.

Outage-based optimal power control for generalized multiuser fading channels

Abstract: We address the problem of achieving outage probability constraints on the uplink of a code-division multiple-access (CDMA) system employing power control and linear multiuser detection, where we aim to minimize the total expended power. We propose a generalized framework for solving such problems under modest assumptions on the underlying channel fading distribution. Unlike previous work, which dealt with a Rayleigh fast-fading model, we allow each user to have a different fading distribution. We show how this problem can be formed as an optimization over user transmit powers and linear receivers, and, where the problem is feasible, we provide conceptually simple iterative algorithms that find the minimum power solution while achieving outage specifications with equality. We further generalize a mapping from outage probability specifications to average signal-to-interference-ratio constraints that was previously applicable only to Rayleigh-faded channels. This mapping allows us to develop suboptimal, computationally efficient algorithms to solve the original problem. Numerical results are provided that validate the iterative schemes, showing the closeness of the optimal and mapped solutions, even under circumstances where the map does not guarantee that constraints will be achieved.

M-ary frequency shift keying communications over an underwater acoustic channel: Performance comparison of data with models

Abstract: The bit error rate (BER) is modeled for M-ary frequency-shift-keying (MFSK) signals in a fading channel using different envelope amplitude statistics and compared with frequency-hopping (FH) FSK signaling data collected during the TREX04 experiment, which used Binary FSK (BFSK) for each symbol. The BER data is found to be significantly higher than that of a Rayleigh fading channel and is found to agree with that modeled with a K-distribution amplitude fading distribution. Using the parameters of the K-distribution, independently measured from the M-sequence data collected in the same experiment, the modeled BER as a function of the signal-to-noise ratio (SNR) agrees well with the measured BER within the SNR of the data. This suggests that the BER of FH-FSK signaling can be predicted given some prior channel characterization measurements.

Performance of correlation-based frequency estimation methods in the presence of multiplicative noise

Abstract: This paper provides a comprehensive performance evaluation of a correlation-based frequency estimator under different fading channel conditions. The efficiency of the estimator in terms of the Cramer-Rao lower bound (CRB) is investigated for different fading conditions, i.e., slow fading, fast fading, Rayleigh fading, and Ricean fading. The asymptotic CRB, which provides an insight to the frequency estimation in fading channels, has been evaluated via a frequency-domain approach. The optimal correlation lag value suitable for frequency estimation under different fading conditions is determined, and closed-form expressions for the variance of the estimates are provided. For proper implementation of the estimator, the Doppler spread of the signal is also estimated. It is shown that using the Doppler spread information, frequency estimation accuracy at low signal-to-noise ratios can be improved using multiple lags of correlations