Showing papers on "Fading distribution published in 1999"

Finite-state Markov model for Rayleigh fading channels

Abstract: We form a finite-state Markov channel model to represent Rayleigh fading channels. We develop and analyze a methodology to partition the received signal-to-noise ratio (SNR) into a finite number of states according to the time duration of each state. Each state corresponds to a different channel quality indicated by the bit-error rate (BER). The number of states and SNR partitions are determined by the fading speed of the channel. Computer simulations are performed to verify the accuracy of the model.

Optimum power control over fading channels

Abstract: We study optimal constant-rate coding schemes for a block-fading channel with strict transmission delay constraint, under the assumption that both the transmitter and the receiver have perfect channel-state information. We show that the information outage probability is minimized by concatenating a standard "Gaussian" code with an optimal power controller, which allocates the transmitted power dynamically to the transmitted symbols. We solve the minimum outage probability problem under different constraints on the transmitted power and we derive the corresponding power-allocation strategies. In addition, we propose an algorithm that approaches the optimal power allocation when the fading statistics are not known. Numerical examples for different fading channels are provided, and some applications discussed. In particular, we show that minimum outage probability and delay-limited capacity are closely related quantities, and we find a closed-form expression for the delay-limited capacity of the Rayleigh block-fading channel with transmission over two independent blocks. We also discuss repetition diversity and its relation with direct-sequence or multicarrier spread-spectrum transmission. The optimal power-allocation strategy in this case corresponds to selection diversity at the transmitter. From the single-user point of view considered in this paper, there exists an optimal repetition diversity order (or spreading factor) that minimizes the information outage probability for given rate, power, and fading statistics.

Analysis of hybrid selection/maximal-ratio combining in Rayleigh fading

Abstract: We use a novel virtual branch technique to succinctly derive the mean and variance of the combiner output signal-to-noise ratio for hybrid selection/maximal-ratio combining in a multipath-fading environment.

Effect of channel estimation error on M-QAM BER performance in Rayleigh fading

Abstract: We determine the bit-error rate (BER) of multilevel quadrature amplitude modulation (M-QAM) in flat Rayleigh fading with imperfect channel estimates, Despite its high spectral efficiency, M-QAM is not commonly used over fading channels because of the channel amplitude and phase variation. Since the decision regions of the demodulator depend on the channel fading, estimation error of the channel variation can severely degrade the demodulator performance. Among the various fading estimation techniques, pilot symbol assisted modulation (PSAM) proves to be an effective choice. We first characterize the distribution of the amplitude and phase estimates using PSAM. We then use this distribution to obtain the BER of M-QAM as a function of the PSAM and channel parameters. By using a change of variables, our exact BER expression has a particularly simple form that involves just a few finite-range integrals. This approach can be used to compute the BER for any value of M. We compute the BER for 16-QAM and 64-QAM numerically and verify our analytical results by computer simulation. We show that for these modulations, amplitude estimation error leads to a 1-dB degradation in average signal-to-noise ratio and combined amplitude-phase estimation error leads to 2.5-dB degradation for the parameters we consider.

Analysis of hybrid selection/maximal-ratio combining in Rayleigh fading

Abstract: The performance of a hybrid selection/maximal ratio combining (H-S/MRC) diversity system in a multipath-fading environment is analyzed. With H-S/MRC, L out of N diversity branches are selected and combined using maximal-ratio combining (MRC). This technique provides improved performance over L branch MRC when additional diversity is available, without requiring additional electronics and/or power. In particular, we consider independent Rayleigh fading on each diversity branch with equal signal-to-noise ratio averaged over the fading. We analyze this system using a "virtual branch" technique which results in a simple derivation and formula for the mean and the variance of the combiner output SNR for any L and N.

MRC performance for binary signals in Nakagami fading with general branch correlation

Abstract: Exact expressions are derived for the performance of predetection maximal ratio combiner diversity reception with L correlated branches in Nakagami fading. Bit error rates are evaluated for both coherent and noncoherent binary phase-shift-keying and frequency-shift-keying signals, starting from the L-variate moment generating function of the random input power vector. The new formulation presented for the bit error rate, in which the covariance matrix of the fading at the L branches explicitly appears, allows arbitrary branch correlation to be taken into account for any diversity order in the case of identical fading severity on the branches. Results are presented for evaluation of the outage probability, for integer values of fading severity, as well as for the effect of the presence of unbalanced channels with arbitrary correlation.

On the utility of gamma PDF in modeling shadow fading (slow fading)

Abstract: Shadow fading causes random fluctuations of the envelope mean at the mobile. The lognormal distribution is widely accepted for this phenomenon. In this paper we argue that, based on theoretical results and measured data, gamma distribution does the job as well. Then we show that by using the gamma distribution and in contrast with the use of the lognormal distribution, we can obtain easy-to-use and closed-form composite PDFs for fading channels, which in turn extremely simplify analytic calculations.

Analysis and optimization of the performance of OFDM on frequency-selective time-selective fading channels

Abstract: In mobile radio communication, the fading channels generally exhibit both time-selectivity and frequency-selectivity. Orthogonal frequency-division multiplexing has been proposed to combat the frequency-selectivity, but its performance is also affected by the time-selectivity. We investigate how various parameters, such as the number of carriers, the guard time length, and the sampling offset between receiver and transmitter, affect the system performance. Further, we determine the optimum values of the above parameters, which minimize the degradation of the signal to-noise ratio at the input of the decision device.

Effect of channel estimation error on M-QAM BER performance in Rayleigh fading

Abstract: We determine the bit error rate (BER) of multi-level quadrature amplitude modulation (M-QAM) in flat Rayleigh fading with imperfect channel estimates. Despite its high spectral efficiency, M-QAM is not commonly used over fading channels because of the channel amplitude and phase variation. Since the decision regions of the demodulator depend on the channel fading, the estimation error of the channel variation can severely degrade the demodulator performance. Among the various fading estimation techniques, pilot symbol assisted modulation (PSAM) proves to be an effective choice. We first characterize the distribution of the amplitude and phase estimates using PSAM. We then use this distribution to obtain the BER of M-QAM as a function of the PSAM and channel parameters. By using a change of variables our exact BER expression has a particularly simple form that involves just a few finite range integrals. This approach can be used to compute BER for any value of M. We compute the BER for 16-QAM and 64-QAM numerically and verify our analytical results by computer simulation. We show that for these modulations, amplitude estimation error leads to a 1 dB degradation in E/sub b//N/sub o/ and combined amplitude-phase estimation error leads to 2.5 dB degradation for the parameters we consider.

Exact evaluation of maximal-ratio and equal-gain diversity receivers for M-ary QAM on Nakagami fading channels

Abstract: Exact integral expressions are derived for calculating the symbol-error rate (SER) of multilevel quadrature amplitude modulation (MQAM) in conjunction with L-fold antenna diversity on arbitrary Nakagami fading channel. Both maximal-ratio combining (MRC) (in independent and correlated fading) and equal-gain combining (EGC) predetection (in independent fading) diversity techniques have been considered. Exact closed-form SER expressions for two restricted Nakagami fading cases (MRC reception) are also derived. An exact analysis of EGC for MQAM has not been reported previously, despite its practical interest. Remarkably, the exact SER integrals can also be replaced by a finite-series approximation formula. A useful procedure for computing the confluent hypergeometric series is also presented.

A unified performance analysis of digital communication with dual selective combining diversity over correlated Rayleigh and Nakagami-m fading channels

Abstract: Using a simple finite integral representation for the bivariate Rayleigh (1889) cumulative distribution function previously discovered by the authors, we present expressions for the outage probability and average error probability performances of a dual selective diversity system with correlated slow Rayleigh fading either in closed form (in particular for binary differential phase-shift keying) or in terms of a single integral with finite limits and an integrand composed of elementary (exponential and trigonometric) functions. Because of their simple form, these expressions readily allow numerical evaluation for cases of practical interest. The results are also extended to the case of slow Nakagami-m fading using an alternate representation of the generalized Marcum (1950) Q-function.

Signaling constellations for fading channels

Abstract: The performance of various coherent 8-ary and 16-ary modulations in additive white Gaussian noise (AWGN) and slowly fading channels are analyzed. New expressions for the exact symbol error rates (SER) in fading with diversity combining are derived for any two-dimensional signaling format having polygonal decision boundaries. Maximal ratio combining, equal gain combining, and selection combining are considered. The SER formulas obtained make it possible for the first time to optimize parameters of various constellations precisely and to determine,which constellation has the lowest probability of error. For example, a star constellation such as that specified in the CCITT V.29 standard can be improved by adjusting the amplitude ratios of the points in the constellation to save about 0.63 dB power in AWGN without sacrificing the phase error tolerance, while maintaining the same error rate. The sensitivity of each constellation to phase error is presented and comparisons are made. Six 8-ary signal sets and 11 16-ary signal sets are examined using the new symbol error probability formulas to determine best signal sets for fading channels.

Effects of time selective multipath fading on OFDM systems for broadband mobile applications

Abstract: The effects of time selective multipath fading are investigated for orthogonal frequency-division multiplexing (OFDM) systems in broadband mobile applications. Although in a multipath environment an OFDM system is very robust against frequency selective fading, it is very sensitive to time selective fading characteristics of the mobile channel, causing inter-carrier-interference and degrading system performance. To achieve a signal-to-interference ratio of 20 dB, the OFDM symbol duration must be less than 8% of the channel coherence time.

A new view of performance analysis techniques in correlated Rayleigh fading

Abstract: This paper provides a new formulation for the pair-wise error probability for any coherently demodulated system in flat Rayleigh fading. The novelty of the result is that the resulting error rate expression is a polynomial function of the eigenvalues of a 'signal' matrix. This view also enables a simple new asymptotically tight bound on the pair-wise error probability. Examples of single and multiple transmit antenna systems are considered.

Error probabilities of two-dimensional M-ary signaling in fading

Abstract: A new exact method for computing the average symbol error probability of two-dimensional M-ary signaling in slow fading is presented. The method is generally applicable to polygonal decision regions. The exact average symbol error rate of coherent 16-star-QAM is obtained and compared to that of 16-rectangular-QAM. New results for optimum ring ratios of 16-star-QAM in additive white Gaussian noise (AWGN) and in slow fading are also given.

Estimating local mean signal power level in a Rayleigh fading environment

Abstract: Good estimates of local mean signal power level are needed by wireless cellular systems for use in channel access, power control and handoff. Many systems today use weighted sample average estimators which are not optimal in Rayleigh fading environments. The optimal local mean signal level estimator for the Rayleigh fading environment is derived and compared with the sample average estimator.

Blind adaptive signal reception for MC-CDMA systems in Rayleigh fading channels

Abstract: We consider signal reception in multicarrier code-division multiple-access (MC-CDMA) systems. A blind adaptive algorithm is proposed to determine a weight vector which optimally combines the desired signal contributions from different carriers while suppressing noise and interference. No knowledge of the channel conditions (fading coefficients, signature sequences and timing of interferers, statistics of other noises, etc.) nor any training sequence is required. The performance is examined for Rayleigh fading channels. Results show that the proposed algorithm performs well and is robust to the near-far problem. Hence, the results show that MC-CDMA systems are attractive candidates for future CDMA systems.

An unified numerical approach for computing the outage probability for mobile radio systems

Abstract: A general finite-range integral for the probability of outage in mobile radio systems is derived. The method handles noninteger Nakagami-fading indices, unequal Rice factors, unequal shadowing spreads, and unequal transmitted powers as well as all the common fading distributions (Rayleigh, Rice, Nakagami-m, Nakagami-q, lognormal-Rice, Suzuki, and lognormal-Nakagami-m). The integral expression can also be approximated by a Gauss-Chebychev quadrature (GCQ) formula requiring knowledge of the moment generating function at only a small number of points. An estimate of the remainder term is also derived. This numerical technique allows computing the outage with arbitrary precision and it is extremely easy to program.

Outage capacities and optimal power allocation for fading multiple-access channels

Abstract: We derive the outage capacity regions of an M-user fading multiple-access channel under the assumption that both the transmitters and the receiver have perfect channel side information. We show that the outage capacity region is implicitly obtained by deriving the outage probability region for a given rate vector. Given the average power constraint and the required rate of each user, we find a successive decoding strategy and a power allocation policy that bound the outage probability region. Also discussed is a simpler minimum common outage probability problem under the assumption that the multiple-access channel is either not used at all when fading is severe or is used simultaneously by all users. Iterative algorithms are proposed for obtaining the optimal decoding order and power allocation in each fading state under the given power constraint of each user.

Outage and coverage considerations for microcellular mobile radio systems in a shadowed-Rician/shadowed-Nakagami environment

Abstract: This paper presents outage analysis and the associated reuse distance and service area estimations for microcellular mobile radio systems that operate in a shadowed-Rician/shadowed-Nakagami (1960) fading environment. Outages caused either by the minimum carrier-to-interference ratio (CIR) requirement alone or by the CIR plus the minimum signal strength [or, equivalently, carrier-to-noise ratio (CNR)] requirements are considered. The desired signal is assumed to suffer from Rician fading while the interference signals from cochannel cells experience Nakagami fading. The interferers may have identical or different statistics. In addition, the local mean strength of the desired and interference signals may fluctuate due to shadowing.

Random coding error exponents for two-dimensional flat fading channels with complete channel state information

Abstract: In this correspondence, we consider the random coding error exponent for nondispersive two-dimensional (2-D) (quadrature) fading channels for which the channel state information (CSI) is perfectly known at the receiver and the input to the transmitter is constrained in its average power. Also, the effect of space diversity on improving the performance is demonstrated. The results obtained in this correspondence shed light on the effect of fading on communications reliability as well as the amount of coding complexity required to achieve a certain decoding error rate. A treatment for the random coding error exponent for time-correlated flat fading channels with Rayleigh fading and Bessel function correlation (the Jake's model) is also provided.

Performance of MC-CDMA systems in non-independent Rayleigh fading

Abstract: In this paper, the average bit error probability of an uplink multi-carrier code division multiple access (MC-CDMA) system using maximal-ratio combiner (MRC) is derived for a frequency-selective slow fading channel. In contrast to a conventional multicarrier channel model in which the subcarriers experience independent subchannels, the subcarriers in MC-CDMA system undergo the correlated fading channel in a general tapped-delay line (TDL) model with variable channel parameters. Numerical results are shown based on the derived result, to show that conventional multicarrier channels tend to overemphasize the performance of an MC-CDMA system.

Impact of fading correlation and unequal branch gains on the capacity of diversity systems

Abstract: We investigate the effect of fading correlation and branch gain imbalance on the Shannon capacity of diversity systems in conjunction with adaptive transmission techniques. This capacity provides the theoretical upper bound for the spectral efficiency of adaptive transmission schemes. We obtain closed-form expressions for this capacity for Rayleigh fading channels under four adaptation policies: optimal power and rate adaptation (OPRA), optimal rate adaptation with constant power (ORA), truncated channel inversion with fixed rate (TIFR), and complete channel inversion with fixed rate (CIFR). We give numerical examples illustrating the main trends and offer comparisons on the behavior of OPRA, ERA, TIFR, and CIFR under variation of different parameters.

The union bound for turbo-coded modulation systems over fading channels

Abstract: We derive performance bounds for turbo-coded modulation systems over fading channels. We consider a Ricean fading channel model both with and without channel-state information (CSI). This model obviously includes Rayleigh fading channel as a special case. The bounds are extensions of similar bounds derived for additive white Gaussian noise channels. For the special case of a Rayleigh fading channel with CSI, we also derive a tighter version of the bound. We illustrate the use of the new bounds via some numerical examples.

Slow Fading Cross-Correlation Against Azimuth Separation of Base Stations

Abstract: A model is proposed to describe the cross-correlation of slow fading signals received from non-colocated base stations. The model summarises the results obtained from a bootstrap analysis of 900 MHz urban area propagation measurements.

Joint Data and Kalman Estimation for Rayleigh Fading Channels

Abstract: Channel estimation is an essential part of many detection techniques proposed for data transmission over fading channels. For the frequency selective Rayleigh fading channel an autoregressive moving average representation is proposed based on the fading model parameters. The parameters of this representation are determined based on the fading channel characteristics, making it possible to employ the Kalman filter as the best estimator for the channel impulse response. For IS-136 formatted data transmission the Kalman filter is employed with the Viterbi algorithm in a Per-Survivor Processing (PSP) fashion and the ove rall bit error rate performance is shown to be superior to that of detection techniques using the RLS and LMS estimators. To allow more than one channel estimation per symbol interval, Per-Branch Processing (PBP) method is introduced as a general case of PSP and its effect on performance is evaluated. The sensitivity of performance to parameters such as fading model order and vehicle speed is also studied.

Bit-error probability analysis of linear receivers for CDMA systems in frequency-selective fading channels

Abstract: The bit-error probability of a linear receiver for code-division multiple-access communications is analyzed. The analysis is presented for the additive white Gaussian noise and fading multipath channels also with data-aided channel estimation. Two ways to approximate the averaging over the interfering data symbol combinations are considered and compared. Numerical examples are presented to demonstrate the usefulness of the analysis methods.

Cochannel interference computation for arbitrary Nakagami fading

Abstract: A characteristic function method is used to calculate the probability that the signal-to-interference ratio (SIR) drops below some predefined threshold (probability of outage). The mobile unit receives a desired signal which has undergone Nakagami (1960) fading and multiple, cochannel, and independent Nakagami interferers. The development is based on a technique due to Bealieu (1990). The advantages of the method are twofold. First, it places no integral restriction upon the Nakagami fading parameter. Second, it avoids the evaluation of higher order derivatives (residues).

Canonical expressions for the error probability performance of M-ary modulation with hybrid selection/maximal-ratio combining in Rayleigh fading

Abstract: Hybrid selection/maximal-ratio combining (H-S/MRC) is a reduced-complexity diversity combining scheme, where L out of N diversity branches (with the largest signal-to-noise ratio (SNR) at each instant) are selected and combined using maximal-ratio combining (MRC). We derive closed-form expressions for the symbol error probability (SEP) of a H-S/MRC diversity system with arbitrary L and N. We consider coherent detection of M-ary phase-shift keying (MPSK) for the case of independent Rayleigh fading with equal SNR averaged over the fading.

Physical channel modeling, adaptive prediction and transmitter diversity for flat fading mobile channel

Abstract: Deterministic modeling of flat fading wireless channels using the method of images is presented. The models identify typical and worst-case channel parameter variation rates and yield datasets of channel strength vs. position, which are used to test a long-range adaptive prediction algorithm previously presented by the authors. Our physical insights and unique long-range prediction capability for the fast fading can be used in conjunction with space diversity-including novel transmitter diversity schemes for a single receiving antenna-or adaptive modulation to significantly reduce or eliminate the effects of deep fades in wireless communications.