Showing papers on "Fading distribution published in 2003"

A performance study of dual-hop transmissions with fixed gain relays

Abstract: The paper presents a study on the end-to-end performance of dual-hop wireless communication systems equipped with non-regenerative fixed gain relays and operating over flat Rayleigh fading channels. More specifically, it first derives generic closed-form expressions for the outage probability and the average probability of error when the relays have arbitrary fixed gains. It then proposes a specific fixed gain relay that benefits from the knowledge of the first hop's average fading power and compares its performance with previously proposed relay gains that, in contrast, require knowledge of the instantaneous channel state information of the first hop. Finally, the paper investigates the effect of the relay saturation on the performance of the systems under consideration. Numerical results show that non-regenerative systems with fixed gain relays have a comparable performance to non-regenerative systems with variable gain relays. These results also show that relay saturation of these systems results in a minimal loss in performance.

Simulation models with correct statistical properties for Rayleigh fading channels

Abstract: In this paper, new sum-of-sinusoids statistical simulation models are proposed for Rayleigh fading channels. These new models employ random path gain, random initial phase, and conditional random Doppler frequency for all individual sinusoids. It is shown that the autocorrelations and cross correlations of the quadrature components, and the autocorrelation of the complex envelope of the new simulators match the desired ones exactly, even if the number of sinusoids is as small as a single-digit integer. Moreover, the probability density functions of the envelope and phase, the level crossing rate, the average fade duration, and the autocorrelation of the squared fading envelope which contains fourth-order statistics of the new simulators, asymptotically approach the correct ones as the number of sinusoids approaches infinity, while good convergence is achieved even when the number of sinusoids is as small as eight. The new simulators can be directly used to generate multiple uncorrelated fading waveforms for frequency selective fading channels, multiple-input multiple-output channels, and diversity combining scenarios. Statistical properties of one of the new simulators are evaluated by numerical results, finding good agreements.

Capacity bounds via duality with applications to multiple-antenna systems on flat-fading channels

Abstract: A technique is proposed for the derivation of upper bounds on channel capacity. It is based on a dual expression for channel capacity where the maximization (of mutual information) over distributions on the channel input alphabet is replaced with a minimization (of average relative entropy) over distributions on the channel output alphabet. We also propose a technique for the analysis of the asymptotic capacity of cost-constrained channels. The technique is based on the observation that under fairly mild conditions capacity achieving input distributions "escape to infinity." The above techniques are applied to multiple-antenna flat-fading channels with memory where the realization of the fading process is unknown at the transmitter and unknown (or only partially known) at the receiver. It is demonstrated that, for high signal-to-noise ratio (SNR), the capacity of such channels typically grows only double-logarithmically in the SNR. To better understand this phenomenon and the rates at which it occurs, we introduce the fading number as the second-order term in the high-SNR asymptotic expansion of capacity, and derive estimates on its value for various systems. It is suggested that at rates that are significantly higher than the fading number, communication becomes extremely power inefficient, thus posing a practical limit on practically achievable rates. Upper and lower bounds on the fading number are also presented. For single-input-single-output (SISO) systems the bounds coincide, thus yielding a complete characterization of the fading number for general stationary and ergodic fading processes. We also demonstrate that for memoryless multiple-input single-output (MISO) channels, the fading number is achievable using beam-forming, and we derive an expression for the optimal beam direction. This direction depends on the fading law and is, in general, not the direction that maximizes the SNR on the induced SISO channel. Using a new closed-form expression for the expectation of the logarithm of a noncentral chi-square distributed random variable we provide some closed-form expressions for the fading number of some systems with Gaussian fading, including SISO systems with circularly symmetric stationary and ergodic Gaussian fading. The fading number of the latter is determined by the fading mean, fading variance, and the mean squared error in predicting the present fading from its past; it is not directly related to the Doppler spread. For the Rayleigh, Ricean, and multiple-antenna Rayleigh-fading channels we also present firm (nonasymptotic) upper and lower bounds on channel capacity. These bounds are asymptotically tight in the sense that their difference from capacity approaches zero at high SNR, and their ratio to capacity approaches one at low SNR.

Fading correlations in wireless MIMO communication systems

Abstract: We investigate the effects of fading correlations on wireless communication systems employing multiple antennas at both the receiver and the transmitter side of the link, so called multiple-input multiple-output (MIMO) systems. It turns out that the amount of transmitter sided channel knowledge plays an important part when dealing with fading correlations. Furthermore, the possible availability of time diversity in a time-selective channel can have essential influence on performance. To study the influence of time-selectivity, the concept of sample-mean outage is introduced and applied to information theoretic measures, like capacity or cutoff rate. It will be shown, that in some cases correlated fading may offer better performance than uncorrelated fading permits, which is due to exploitable antenna gain, that will also be defined in a general form for MIMO systems.

Measurements of small-scale fading and path loss for long range RF tags

Abstract: RF modulated backscatter (RFMB), also known as modulated radar cross section or sigma modulation, is a RF transmission technique useful for short-range, low-data-rate applications, such as nonstop toll collection, electronic shelf tags, freight container identification and chassis identification in automobile manufacturing, that are constrained to have extremely low power requirements. The small-scale fading observed on the backscattered signal has deeper fades than the signal from a traditional one-way link of the same range in the same environment because the fading on the backscattered signal is the product of the fading on the off-board-generated carrier times the fading on the reflected signal. This paper considers the continuous wave (CW) type of RFMB, in which the interrogator transmitter and receiver antennas are different. This two-way link also doubles the path loss exponent of the one-way link. This paper presents the cumulative distribution functions for the measured small-scale fading and the measured path loss for short ranges in an indoor environment at 2.4 GHz over this type of link.

Performance and design of space-time coding in fading channels

Abstract: The pairwise-error probability upper bounds of space-time codes (STCs) in independent Rician fading channels are derived. Based on the performance analysis, novel code design criteria for slow and fast Rayleigh fading channels are developed. It is found that, in fading channels, the STC design criteria depend on the value of the possible diversity gain of the system. In slow fading channels, when the diversity gain is smaller than four, the code error performance is dominated by the minimum rank and the minimum determinant of the codeword distance matrix. However, when the diversity gain is larger than, or equal to, four, the performance is dominated by the minimum squared Euclidean distance. Based on the proposed design criteria, new codes are designed and evaluated by simulation.

Performance of adaptive MC-CDMA detectors in rapidly fading Rayleigh channels

Abstract: Multicarrier code-division multiple access (MC-CDMA) combines multicarrier transmission with direct sequence spread spectrum. Different approaches have been adopted which do not assume a perfectly known channel. We examine the forward-link performance of decision-directed adaptive detection schemes, with and without explicit channel estimation, for MC-CDMA systems operating in fast fading channels. We analyze theoretically the impact of channel estimation errors by first considering a simpler system employing a threshold orthogonality restoring combining (TORC) detector with a Kalman channel estimator. We show that the performance deteriorates significantly as the channel fading rate increases and that the fading rate affects the selection of system parameters. We examine the performance of more realistic schemes based on the minimum mean square error (MMSE) criterion using least mean square (LMS) and recursive least square (RLS) adaptation. We present a discussion which compares the decision-directed and pilot-aided approaches and explores the tradeoffs between channel estimation overhead and performance. We find that there is a fading rate range where each method provides a good tradeoff between performance and overhead. We conclude that the MMSE per carrier decision-directed detector with RLS estimation combines good performance in low to moderate fading rates, robustness in parameter variations, and relatively low complexity and overhead. For higher fading rates, however, only pilot-symbol-aided detectors are appropriate.

Degrees of freedom in some underspread MIMO fading channels

Abstract: Consider a multiple-input multiple-output (MIMO) fading channel in which the fading process varies slowly over time. Assuming that neither the transmitter nor the receiver have knowledge of the fading process, do multiple transmit and receive antennas provide significant capacity improvements at high signal-to-noise ratio (SNR)? For regular fading processes, recent results show that capacity ultimately grows doubly logarithmically with the SNR independently of the number of transmit and receive antennas used. We show that for the Gauss-Markov fading process in all regimes of practical interest the use of multiple antennas provides large capacity improvements. Nonregular fading processes show completely different high-SNR behaviors due to the perfect predictability of the process from noiseless observations. We analyze the capacity of MIMO channels with nonregular fading by presenting a lower bound, which we specialize to the case of band-limited slowly varying fading processes to show that the use of multiple antennas is still highly beneficial. In both cases, regular and nonregular fading, this capacity improvement can be seen as the benefit of having multiple spatial degrees of freedom. For the Gauss-Markov fading model and all regimes of practical interest, we present a communication scheme that achieves the full number of degrees of freedom of the channel with tractable complexity. Our results for underspread Gauss-Markov and band-limited nonregular fading channels suggest that multiple antennas are useful at high SNR.

Markov chain model in maximum-likelihood sequence detection for free-space optical communication through atmospheric turbulence channels

Abstract: In free-space optical communication links using intensity modulation and direct detection (IM/DD), atmospheric turbulence-induced intensity fluctuations can significantly impair link performance. Communication techniques can be applied to mitigate turbulence-induced intensity fluctuations (i.e., signal fading) in the regime in which the receiver aperture D/sub 0/ is smaller than the fading correlation length d/sub 0/ and the observation interval T/sub 0/ is smaller than the fading correlation time /spl tau//sub 0/. If the receiver has knowledge of the joint temporal statistics of the fading, maximum-likelihood sequence detection (MLSD) can be employed, but at the cost of high computational complexity. We introduce a single-step Markov chain (SMC) model for the fading correlation and use it to derive two low-complexity, suboptimal MLSD algorithms based on per-survivor processing (PSP). Simulations are presented to verify the SMC model and the performance improvement achieved using these suboptimal per-survivor processing (PSP) algorithms.

Capacity of MIMO channels: asymptotic evaluation under correlated fading

Abstract: This paper investigates the asymptotic uniform power allocation capacity of frequency nonselective multiple-input multiple-output channels with fading correlation at either the transmitter or the receiver. We consider the asymptotic situation, where the number of inputs and outputs increase without bound at the same rate. A simple uniparametric model for the fading correlation function is proposed and the asymptotic capacity per antenna is derived in closed form. Although the proposed correlation model is introduced only for mathematical convenience, it is shown that its shape is very close to an exponentially decaying correlation function. The asymptotic expression obtained provides a simple and yet useful way of relating the actual fading correlation to the asymptotic capacity per antenna from a purely analytical point of view. For example, the asymptotic expressions indicate that fading correlation is more harmful when arising at the side with less antennas. Moreover, fading correlation does not influence the rate of growth of the asymptotic capacity per receive antenna with high E/sub b//N/sub 0/.

Nakagami-m fading modeling in the frequency domain for OFDM system analysis

Abstract: Nakagami-m fading modeling in the frequency domain is investigated. For frequency-selective Nakagami-m fading channels, we show the magnitudes of the channel frequency responses to be also Nakagami-m distributed random variables with fading and mean power parameters as explicit functions of the fading and mean power parameters of the channel impulse responses. Based on this new model, the bit error rate performance of an orthogonal frequency-division multiplexing system with receive diversity over correlated Nakagami-m fading channels is analytically evaluated and some numerical results are given.

Capacity and optimal power allocation for fading broadcast channels with minimum rates

Abstract: We derive the capacity region and optimal power allocation scheme for a slowly fading broadcast channel in which minimum rates must be maintained for each user in all fading states, assuming perfect channel state information at the transmitter and at all receivers. We show that the minimum-rate capacity region can be written in terms of the ergodic capacity region of a broadcast channel with an effective noise determined by the minimum rate requirements. This allows us to characterize the optimal power allocation schemes for minimum-rate capacity in terms of the optimal power allocations schemes that maximize ergodic capacity of the broadcast channel with effective noise. Numerical results are provided for different fading broadcast channel models.

Analysis of K -Transmit Dual-Receive Diversity withCochannel Interferers over a Rayleigh Fading Channel

Abstract: The need to combat the severe effects of fading and interference in the rapidly increasing number of communication systems providing wireless services has motivated the study of diversity in the presence of interference. Hence the analysis of wireless systems with both transmit and receive diversity and subject to cochannel interference is an important tool for system design. We consider here a K-transmit dual-receive diversity communication system employing K antennas for transmission and two antennas for reception. The desired signal is corrupted by N interfering sources apart from additive white Gaussian noise. The channel is Rayleigh fading. As a result, the channel matrix for the desired signal and the propagation vectors of the interferers have zero-mean complex Gaussian entries; the entries are assumed to be independent and identically distributed. The complex receive weight vector used for combining the received signals is chosen so as to maximize the output signal-to-interference-plus-noise ratio (SINR). From the statistics of the channel matrix and the propagation vectors of the interferers, we derive a closed-form expression for the probability density function (p.d.f.) of the maximum output SINR. This p.d.f. can be used to obtain the symbol error probability for different digital modulation schemes.

Performance analysis of SIR-based dual selection diversity over correlated Nakagami-m fading channels

Abstract: Signal-to-interference-ratio (SIR)-based selection diversity is an efficient technique to mitigate fading and cochannel interference in wireless communications systems. An approach to the performance analysis of dual SIR-based selection diversity over correlated Nakagami-m fading channels with arbitrary parameters is presented. Useful formulae for the outage probability, the average output SIR, and the average error probability for coherent, noncoherent, and multilevel modulation schemes are derived. The main contribution of the paper is that, for the first time, the proposed analysis is carried out assuming correlated Nakagami-m fading with arbitrary parameters for both the desired signals and the cochannel interferers, which is the real scenario in practical dual selection diversity systems with insufficient antenna spacing. It is shown that the presented general results reduce to the specific ones for the independent fading case, previously published. Numerical and simulation results are also presented to show the effects of various parameters, such as the fading severity, input SIR unbalance, and level of correlation, to the system's performance.

Analytical performance of MIMO zero-forcing receivers in correlated Rayleigh fading environments

Abstract: Simulation results show that fading correlation between the antenna elements of a wireless system can seriously affect the symbol error rate of MIMO receivers, especially in case of linear processing. In order to gain a better understanding of the fading effects, we present an analytical framework to assess the performance of a system with zero-forcing receiver in a correlated Rayleigh fading scenario. Closed-form expressions are derived for the symbol error rate with arbitrary array sizes in case of transmit correlation only. In the presence of a fully correlated channel, we study the 2/spl times/2 case. High SNR asymptotics allow an insightful comparison of systems with transmit and receive correlation, respectively. Monte-Carlo simulations evidence the accuracy of the analysis.

Sensitivity of wireless network simulations to a two-state Markov model channel approximation

Abstract: In this paper, we investigate the appropriateness of wireless network simulations that employ a two-state Markov model to approximate a flat Rayleigh fading channel. Our approach first analyzes the statistical similarities and differences between block error processes generated by 1) an 802.11b defined communication scheme in the presence of flat Rayleigh fading and 2) a representative two-state Markov model. It is shown that, at low SNR, the Markov model does not generate an adequate frame error process. Furthermore, we quantify the effects of said statistical deviations through ns2 network simulations. This work further advances the understanding of the appropriate, and inappropriate, environments under which the two-state Markov model is a suitable approximation of a fading channel.

Capacity per unit energy of fading channels with a peak constraint

Abstract: A discrete-time single-user scalar channel with temporally correlated Rayleigh fading is analyzed. There is no side information at the transmitter or the receiver. A simple expression is given for the capacity per unit energy, in the presence of a peak constraint. The simple formula of Verdu/spl acute/ for capacity per unit cost is adapted to a channel with memory, and is used in the proof. In addition to bounding the capacity of a channel with correlated fading, the result gives some insight into the relationship between the correlation in the fading process and the channel capacity. The results are extended to a channel with side information, showing that the capacity per unit energy is one nat per joule, independently of the peak power constraint. A continuous-time version of the model is also considered. The capacity per unit energy subject to a peak constraint (but no bandwidth constraint) is given by an expression similar to that for discrete time, and is evaluated for Gauss-Markov and Clarke fading channels.

Statistical simulation models for Rayleigh and Rician fading

Abstract: New simulation models are proposed for Rayleigh and Rician fading channels First, the statistical properties of Clarke's fading model with a finite number of sinusoids are analyzed An improved Clarke's model is then proposed for the simulation of Rayleigh fading channels Based on this improved Rayleigh fading model, a novel simulation model is proposed for Rician fading channels The new Rician fading model employs a zero-mean stochastic sinusoid as the specular (line-of-sight) component, in contrast to all existing Rician fading simulators that utilize a non-zero mean deterministic specular component The statistical properties of the proposed Rician fading 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 (-/spl pi/, /spl pi/) This property is different from that of existing Rician fading models The statistical properties of the new simulators are confirmed by extensive simulation results, finding 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

Space-time signal design for time-correlated Rayleigh fading channels

Abstract: The existing construction of space-time codes or modulation has mainly focused on two ideal situations: either quasi-static or rapid fading channels. In this paper, we consider the design of robust space-time modulation for time-correlated Rayleigh fading channels. We show that the space-time signals of square size achieving full diversity in quasi-static fading channels can also achieve the full diversity in time-correlated fading channels irrespectively of the time correlation matrix. Moreover, we propose a space-time signal construction method by combining orthogonal designs with sphere packings. The simulation results show that our scheme outperforms the previously existing methods. For example, we observe a coding gain of about 1.5 dB over the conventional orthogonal design, about 2 dB over the parametric code, and about 4 dB over the cyclic code under certain fading conditions.

Performance analysis of triple selection diversity over exponentially correlated Nakagami-m fading channels

Abstract: An approach to the performance analysis of a triple selection-diversity system over exponentially correlated Nakagami-m fading channels is presented. Closed-form expressions of converged sums for both outage and average error probabilities are derived. Numerical results are presented to point out the effect of the fading correlation, the fading severity, as well as the improvement achieved by the triple selection combining compared with the corresponding dual diversity case.

Quantifying diversity and correlation in Rayleigh fading MIMO communication systems

Abstract: The performance of MIMO systems and the usefulness of the dedicated signal processing and channel coding techniques is strongly affected by the presence of fading correlation For instance, space-time block coding is favored by low fading correlation, while beam-forming techniques are advantageous at high amounts of correlation In this paper, we define an easy to compute quantitative description of fading correlation and diversity present in a MIMO channel This definition offers the possibility to build equivalence classes of channels which offers the same amount of diversity or correlation It turns out that the channels from such an equivalence class performs essentially equivalent with respect to channel capacity or throughput

Maximum ratio combining of correlated Rayleigh fading channels with imperfect channel knowledge

Abstract: The bit error probability for binary modulation and multiple correlated Rayleigh fading diversity branches is derived. The receiver performs maximum ratio combining of the diversity branches based on noisy channel estimates. Our results provide new analytical insights into performance, design, and optimization of some known communication receivers.

Selection diversity receivers in Weibull fading: outage

Abstract: Novel expressions for the probability and the cumulative density function of the signal-to-noise ratio (SNR) at the output of an L-branch selection combining receiver, operating in Weibull fading, are derived Capitalising on these expressions, the outage probability and the average output SNR are obtained in closed-form

Performance analysis of digital modulations on Weibull fading channels

Abstract: The Weibull distribution is a flexible statistical model for describing multipath fading channels in both indoor and outdoor radio propagation environments. A new closed-form expression is derived for the moment generating function of the Weibull distribution, valid when its fading parameter assumes integer values. The performance of digital linear modulations operating on Weibull channels is studied. Expressions for the signal outage and average symbol error rate are derived for single-channel reception and multi-channel diversity reception operating on Weibull fading channels.

Analysis and simulation of Nakagami fading channel with MATLAB

Abstract: The paper simulated and analyzed the statistical performance of the Nakagami fading channel in wireless communication with MATLAB, including the complex envelop of the received signal, the level crossing rates and average fade durations on the maximal-ratio combining diversity

A novel channel estimation method for OFDM transmission technique under fast time-variant fading channel

Abstract: This paper proposes a novel estimation method of channel frequency response for orthogonal frequency division multiplexing (OFDM) systems operating in fast time-variant fading channels. The proposed method enables accurate coherent demodulation without using pilot signals, which are usually required to be inserted in the data symbols periodically to cope with fast time-variant fading. Computer simulation results show that the proposed method maintains better BER performance even when the vehicle speed reaches 180 km/h.

A generic correlated Nakagami fading model for wireless communications

Abstract: A complete statistical characterization of correlated Nakagami channels is either their joint probability density function or their joint characteristic function (CHF), which is indispensable to many applications in wireless communications. The classical correlated multivariate Nakagami model in current use is subject to a restriction that the fading parameters must be identical. We derive a generic correlated Nakagami fading model, in the form of a multiple CHF, allowing for an arbitrary covariance matrix and distinct real fading parameters. The application of the new model to wireless communications is also presented.

GPS signal fading model for urban centres

Abstract: The use of GPS receivers in wireless telephones has been proposed as a means of automatically identifying the position of wireless 911 callers. GPS simulators are an efficient means of testing the accuracy of such technology but require a channel model for GPS satellite signals. This paper presents a methodology of measuring and modeling the fading distribution of GPS satellite signals received in outdoor urban centers. GPS fading data, as collected in the downtown areas of Calgary and Vancouver, Canada, are used to generate fade histograms as a function satellite elevation angle. These histograms are found to be sufficiently similar between the two cities and, therefore, lead to the conclusion that a generic fade distribution for urban centers is reasonable. Parameters for the Urban ThreeState Fade Model are estimated from the empirical fading data collected in each city. Correlation between the model parameters derived for each city is significant and also suggests that a generic model may be derived. The parameters from the two cites are averaged to produce a generic Urban ThreeState Fade Model which adequately represents the fade histograms of each city. These averaged parameters generally agree with parameters derived from data collected in Tokyo, Japan.

On two-user fading gaussian broadcast channels with perfect channel state information at the receivers

Abstract: We show that Gaussian input is optimal for a certain class of single-antenna fading Gaussian broadcast channels with perfect channel knowledge at the receivers but not at the transmitter.

Throughput Measures for Delay-constrained Communications in Fading Channels

Abstract: Fading channels, often seen in wireless systems, provide an unfavorable environment for reliable communications. Current methods for evaluating the performance of fading channels include ergodic capacity and 2-capacity. Ergodic capacity quantifies the ultimate reliable communication limit of the fading channel. It is only achievable with infinite coding delay, making it impossible to achieve in practice. 2-capacity, achievable with finite coding delay, does not provide a measure of error-free communications performance. Since practical communication systems are delay-constrained, it is possible to retransmit codewords when errors occur. We provide a new analysis framework that accounts for codeword retransmission in the analysis of fading channels. We introduce new measures, maximum zero-outage throughput and maximum 2-throughput, that predict the performance of practical systems and show that ergodic capacity and 2-capacity are special cases of our definitions. We also provide a measure that characterizes the performance of a system with more complex receiver design, using “incremental diversity” to improve