Showing papers on "Fading distribution published in 2001"

The impact of frequency-flat fading on the spectral efficiency of CDMA

Abstract: The capacity of the randomly spread synchronous code-division multiple-access (CDMA) channel subject to frequency-flat fading is studied in the wide-band limit of large number of users. We find the spectral efficiency as a function of the number of users per chip, the distribution of the flat fading, and the signal-to-noise ratio (SNR), for the optimum receiver as well as linear receivers (single-user matched filter, decorrelator, and minimum mean-square error (MMSE)). The potential improvements due to both decentralized transmitter power control and multi-antenna receivers are also analyzed.

Design, analysis, and performance evaluation for BICM-ID with square QAM constellations in Rayleigh fading channels

Abstract: We consider bit-interleaved coded modulation with iterative decoding (BICM-ID) for bandwidth-efficient transmission over Rayleigh fading channels. We propose the design criteria that utilize a large Hamming distance inherited in a low-rate code and a new labeling technique designed specifically for fading channels. This results in a large coding gain over noniterative coded modulation and performance close to that of "turbo" coded modulation with less complexity. We also show that BICM-ID designed for fading channels usually has a very good performance over the additive white Gaussian noise (AWGN) channel while the converse is difficult to achieve. When combined with signal space diversity, diversity order can be improved to twice the diversity order of conventional BICM-ID; therefore, the code complexity can further be reduced while maintaining the same level of performance. Specifically, with the bandwidth efficiency of 2 bits/s/Hz over Rayleigh fading channels, a bit error rate (BER) of 10/sup -6/ can be achieved with 16-QAM, a four-state rate 1/2 code at E/sub b//N/sub 0/ of about seven dB. We also derive performance bounds for BICM-ID with and without signal space diversity over Rayleigh fading channels, which can be easily extended for other types of fading channels.

Single-carrier frequency-domain equalization for space-time block-coded transmissions over frequency-selective fading channels

Abstract: We propose an Alamouti-like scheme for combining space-time block-coding with single-carrier frequency-domain equalization. With two transmit antennas, the scheme is shown to achieve significant diversity gains at low complexity over frequency-selective fading channels.

On the estimation of the K parameter for the Rice fading distribution

Abstract: We study the statistical performance of two moment-based estimators for the K parameter of Rice fading distribution, as less complex alternatives to the maximum-likelihood estimator. Our asymptotic analysis reveals that both estimators are nearly asymptotically efficient, and that there is a compromise between the computational simplicity and the statistical efficiency of these two estimators. We also show, by Monte Carlo simulation, that the fading correlation among the envelope samples deteriorates the performance of both estimators. However, the simpler estimator, which employs the second and the fourth moments of the signal envelope, appears to be more suitable for real-world applications.

Asymptotic analysis of proportional fair algorithm

Abstract: It was previously shown (under simplifying assumptions) that the proportional fair algorithm gives equal power and time to users who only differ in their distance from the BS, their fading characteristics being the same (see Holtzman, J.M., Proc. VTC2000-Spring, p.1663-7, 2000). We give here a more general result for two classes of users with different fading characteristics. All other things being equal, the user class with more fading variability gets more throughput with a lower (but not much lower) fraction of time transmitting. We also demonstrate a separability property-the effects of variability and distance from the base station are separable.

Limitations of sum-of-sinusoids fading channel simulators

Abstract: Rayleigh signal fading due to multipath propagation in wireless channels is widely modeled using sum-of-sinusoids simulators. In particular, Jakes' (1994) simulator and derivatives of Jakes' simulator have gained widespread acceptance. Despite this, few in-depth studies of the simulators' statistical behavior have been reported in the literature. Here, the extent to which Jakes' simulator adequately models the multipath Rayleigh fading propagation environment is examined. The results show that Jakes' simulator does not reproduce some important properties of the physical fading channel. Some possible improvements to Jakes' simulator are examined. The significances of the number and the symmetries of the Doppler frequency shifts on the validity of the simulator's reproduction of the physical fading channel are elucidated.

Error rates for Nakagami-m fading multichannel reception of binary and M-ary signals

Abstract: This paper derives new closed-form formulas for the error probabilities of single and multichannel communications in Rayleigh and Nakagami-m (1960) fading. Closed-form solutions to three generic trigonometric integrals are presented as part of the main result, providing a unified method for the derivation of exact closed-form average symbol-error probability expressions for binary and M-ary signals with L independent channel diversity reception. Both selection-diversity and maximal-ratio combining (MRC) techniques are considered. The results are generally applicable for arbitrary two-dimensional signal constellations that have polygonal decision regions operating in a slow Nakagami-m fading environments with positive integer fading severity index. MRC with generically correlated fading is also considered. The new expressions are applicable in many cases of practical interest. The closed-form expressions derived for a single channel reception case can be extended to provide an approximation for the error rates of binary and M-ary signals that employ an equal-gain combining diversity receiver.

Joint iterative channel estimation and decoding in flat correlated Rayleigh fading

Abstract: This paper addresses the design and performance evaluation with respect to capacity of M-PSK turbo-coded systems operating in frequency-flat time-selective Rayleigh fading. The receiver jointly performs channel estimation and turbo decoding, allowing the two processes to benefit from each other. To this end, we introduce a suitable Markov model with a finite number of states, designed to approximate both the values and the statistical properties of the correlated flat fading channel phase, which poses a more severe challenge to PSK transmission than amplitude hiding. Then, the forward-backward algorithm determines both the maximum a posteriori probability (MAP) value for each symbol in the data sequence and the MAP channel phase in each iteration. Simulations show good performance in standard correlated Rayleigh fading channels. A sequence of progressively tighter upper bounds to the capacity of a simplified Markov-phase channel is derived, and performance of a turbo code with joint iterative channel estimation and decoding is demonstrated to approach these capacity bounds.

On performance analysis for signaling on correlated fading channels

Abstract: A general approach is presented for analyzing the performance of digital signaling with multichannel reception on correlated fading channels. The approach is based on: (i) exploiting the complex Gaussian model for the joint distribution of the fading on the multiple channels; and (ii) applying recent results on the unified performance analysis of digital signaling on fading channels using alternative representations of the Q(/spl middot/) and related functions. Numerical results that illustrate the effect of correlation on the diversity gain from multichannel reception are also presented.

Double differential space-time block coding for time-selective fading channels

Abstract: Most existing space-time coding schemes assume time-invariant fading channels and offer antenna diversity gains relying on accurate channel estimates at the receiver. Other single differential space-time block coding schemes forego channel estimation but are less effective in rapidly fading environments. Based on a diagonal unitary matrix group, a novel double differential space-time block coding approach is derived in this paper for time-selective fading channels. Without estimating the channels at the receiver, information symbols are recovered with antenna diversity gains regardless of frequency offsets. The resulting transceiver has very low complexity and is applicable to an arbitrary number of transmit and receive antennas. Approximately optimal space-time codes are also designed to minimize bit error rate. System performance is evaluated both analytically and with simulations.

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

Abstract: We derive the capacity and optimal power allocation scheme for a multiuser 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 superposition coding can achieve the capacity of such channels and explicitly characterize the boundary of the capacity region. The optimal power allocation scheme is a two-step process: we first allocate the minimum power required to achieve the minimum rates in all fading states, and we then optimally allocate the excess power to maximize the ergodic rates averaged over all fading states in excess of the minimum rate requirements. The optimal allocation of the excess power is a multi-level water-filling relative to effective noise that incorporates the minimum rate constraints. Numerical results are provided for different fading broadcast channel models.

Analysis of an up/down power control algorithm for the CDMA reverse link under fading

Abstract: We analyze the performance of a code division multiple access (CDMA) reverse link a with an up/down power control algorithm in the presence of fading. We derive a stochastic nonlinear feedback control system model for the power controlled reverse link, and study the power control performance based on the nonlinear model using the technique of statistical linearization. We provide a general analysis framework that allows us to study the effect of mobile speed, power control step size, and fading channel parameters such as correlation coefficient and rate of fading on power control errors. Numerical results show excellent accuracy of our analysis, which can be used to design and optimize the system parameters without going through lengthy simulations. For example, in the presence of shadow fading, it is seen that a power control step size in the range of 0.5-1.3 dB is sufficient to keep power control errors near a minimum. In the case of Rayleigh fading, the standard deviation of power control errors grows quickly even at moderate mobile speeds.

Performance of generalized selection combining over Weibull fading channels

Abstract: The literature is relatively sparse in performance analyses of diversity combining schemes over Weibull fading channels, despite the fact that the Weibull distribution is often found to be a suitable fit to empirical fading channel measurements. 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 type of channels. The mathematical equations are validated and illustrated by some numerical examples for scenarios of practical interest.

Efficient use of fading correlations in MIMO systems

Abstract: We investigate the effects of both fading correlations and transmitter channel knowledge in multiple element antenna (MEA) communication systems. While, for independent and identically distributed fades between receive and transmit antennas, pioneering work showed that a huge increase in capacity is possible for MEA compared to a single antenna system, recent contributions warn that fading correlations destroy most of this advantage. While this is true for zero transmitter channel knowledge, we show however that long-term average channel state information enables the transmitter to efficiently use the fading correlations to its advantage and offers the potential to even increase capacity beyond the one possible for independent fading. A conceived transmit technique is presented that efficiently makes use of fading correlations, and also provides optimum choice of digital modulation schemes that carry the information.

A space-time block-coded OFDM scheme for unknown frequency-selective fading channels

Abstract: We introduce a space-time block-coded orthogonal frequency-division multiplexing (STBC-OFDM) selective fading channels which does not require channel knowledge either at the transmitter or at the receiver. The decoding algorithm is based on generalized maximum-likelihood sequence estimation. We investigate the performance of the proposed scheme over two-tap Rayleigh fading channels. Simulation results show the performance to be near optimum.

Noncoherent receivers for differential space-time modulation

Abstract: In this paper, noncoherent receivers for differential space-time modulation (DSTM) are investigated. It is shown that the performance of the previously proposed conventional differential detection (DD) receiver is satisfactory only for very slow flat fading channels. However, conventional DD suffers from a considerable loss in performance even for moderately fast fading. In order to overcome this problem, multiple-symbol detection (MSD) and low-complexity decision-feedback differential detection (DF-DD) receivers are derived.

Performance of adaptive linear interference suppression in the presence of dynamic fading

Abstract: Adaptive linear interference suppression for direct-sequence (DS) code-division multiple access (CDMA) is studied in the presence of time- and frequency-selective fading. Interference suppression is achieved with an adaptive digital filter which spans a single symbol interval. Both decision-directed and blind adaptive algorithms, which do not require a training sequence, are considered. Modifications to least squares adaptive algorithms are presented which are compatible with differential coding and detection. For frequency-selective fading, adaptive algorithms are presented based upon different assumptions concerning knowledge of the desired user's channel. Specifically, the cases considered are as follows: (1) perfect knowledge of the desired channel; (2) knowledge of only the relative path delays; and (3) knowledge of only one delay corresponding to the strongest path. Computer simulation results are presented which compare the performance of these algorithms with the analogous RAKE receivers. These results show that for case (3), even slow fading can cause a significant degradation in performance. Effective use of channel parameters in the adaptive algorithm reduces the sensitivity to fade rate, although moderate to fast fading can significantly compromise the associated performance gain relative to the RAKE receiver.

Minimum duration outages in Rayleigh fading channels

Abstract: Minimum duration outages have been introduced for lognormal shadow fading where the durations of signal fades were considered in evaluating outages. We develop and analyze such minimum duration outages for channels susceptible to Rayleigh fading. The results show that under typical Doppler frequencies the outages due to Rayleigh fading are more likely to cause frame or packet errors rather than call dropping due to the short time scales in effect.

Effect of spatial fading correlation on performance of space-time codes

Abstract: The performance of space-time codes is investigated over Rayleigh fading channels with spatially correlated fading between transmit antennas. An exact pairwise error probability is derived based on which an analytical estimate for bit error probability is computed. The analytical results are verified through computer simulation.

A simple alternative to the lognormal model of shadow fading in terrestrial and satellite channels

Abstract: The distribution of the local average power at the land mobile is widely accepted to be lognormal in both terrestrial and satellite channels. However, the mathematical form of the lognormal distribution is not convenient for analytic calculations. We show the utility of the gamma distribution for shadow fading, in both terrestrial and satellite channels, using empirical data. Furthermore, we show that the application of the gamma model of shadow fading, in place of the lognormal model, results in closed-form and mathematically-tractable solutions for key system performance measures such as the average symbol error rate of different modulations with a variety of diversity combining techniques.

SNR estimation in generalized fading channels and its application to turbo decoding

Abstract: We propose an online SNR estimation scheme for generalized fading channels. We derive the SNR estimate based on a statistical ratio of observables over a block of data, when the channel undergoes Nakagami fading. An online SNR estimator for AWGN channels has been derived by Summers and Wilson (see IEEE Trans. Commun., vol.46, no.4, p.421-23, 1998). Our SNR estimation scheme in this paper is for a general Nakagami fading channel, where the SNR estimates in Rayleigh fading and AWGN can be obtained as special cases corresponding to the Nakagami parameter m=1 and m=/spl infin/, respectively. As an example, we use our SNR estimate in the iterative decoding of turbo codes on both i.i.d and correlated Rayleigh fading channels. We show that the turbo decoder performance on Rayleigh fading channels using our SNR estimate is close to the performance using perfect knowledge of the fade amplitudes and the SNR.

Shadow fading cross correlation between basestations

Abstract: Macroscopic diversity improves radio link performance by combating shadow fading. Signals from paths between a mobile and different base stations are combined to mitigate log normal shadow fading. Link improvement is a function of cross correlation of shadow fading on paths between mobile and base stations. The lower the positive cross correlation, the higher the gain from macroscopic diversity. Negative cross correlation provides even higher gain. Signal level data were collected from a 1900 MHz GSM system in rural and suburban areas. The shadow fading cross correlation for several different base stations and a mobile traveling in an area ranged from -0.34 to +0. 43. Standard deviations for different paths ranged from 2 dB to 10 dB, and decorrelation lengths ranged from 50 m to 500 m. The angle between paths from the mobile to the base stations was calculated.

An efficient procedure for Nakagami-m fading simulation

Abstract: An efficient method for generating correlated Nakagami-m fading envelope samples is presented. The new method is compared to other methods used to generate Nakagami-m random variates. An accurate approximation to the inverse Nakagami-m cumulative distribution function, valid for all values of m, is derived. Uncertainties regarding the phase distribution and the autocorrelation of the Nakagami-m fading process are discussed. The fading envelope autocorrelation is determined by simulation and asymptotic analysis.

Optimum selection diversity for BPSK signals in Rayleigh fading channels

Abstract: We propose a new selection diversity scheme, called |ar|-selection diversity, that selects the branch providing the largest magnitude of log-likelihood ratio (LLR). The LLR for BPSK signals in fading channels is found to be proportional to the product of the fading amplitude and the matched filter output after phase compensation. The proposed |ar|-selection diversity scheme is shown to be optimal in the sense of minimizing the bit error rate (BER), and outperform existing selection diversity schemes. We also propose a suboptimal selection diversity scheme, called |aw|-selection diversity, that does not require a phase compensation in the selection process, thereby significantly reducing implementation complexity. We show that the proposed |ar|-selection and |aw|-selection diversity schemes exhibit significant power gains over existing selection diversity schemes in Rayleigh fading channels.

Wavelet modulation performance in Gaussian and Rayleigh fading channels

Abstract: Wavelet modulation simultaneously sends data at multiple rates through an unknown channel. Previous research has demonstrated that wavelet modulation bit error rate performance in the additive white Gaussian noise channel is comparable to theoretical binary phase shift keying. We extend the investigation to the performance of wavelet modulation in several time varying channels: Rayleigh, flat, slow fading channels and frequency selective, slow fading channels.

Impact of ultra wide band transmissions on a generic receiver

Abstract: The noise floor rise in a generic receiver as a basis for the determination of interference levels to a victim receiver is applied to assess interference to systems that are designed to operate in multipath fading environments. The interference levels might be over estimated by as much a 20 dB if fading is not properly taken into account. The impact of potentially interfering sources such as UWB emissions must be treated as an effect on the overall system reliability. Results here show that low power UWB systems operating at the same levels as unintended radiators can comfortably coexist with conventional users of the radio spectrum without significant impact on the performance of those radio services.

Timing phase estimator overcoming Rayleigh fading for OFDM systems

Abstract: A timing offset estimator robust to a Rayleigh fading channel and a fast Fourier transform (FFT) window selection algorithm that can remove inter symbol interference (ISI) are proposed for an orthogonal frequency division multiplexing (OFDM) system. Conventional algorithms using the scattered pilots for timing offset estimation only use phase information, whereas the proposed algorithm utilizes both phase and amplitude information. The use of amplitude information in the proposed algorithm means that the influence of distorted pilots due to fading becomes insignificant when estimating a timing offset. As a result, the proposed algorithm is robust to multipath fading channels and produces a superior performance with less computational complexity compared to conventional algorithms. The proposed FFT window selection algorithm based on the cyclic extension property of the OFDM structure can remove the ISI problems caused by multipath fading channels, thereby significantly improving the receiver performance without any additional computational requirements. The paper uses the DVB-T standard to evaluate the algorithms.

Matched filter bounds for wireless communication over Rayleigh fading dispersive channels

Abstract: This letter extends the theory of the matched filter bound for fading dispersive channels. We generalize to arbitrary fading, as well as delay, properties of the channel. The channel model is a standard time varying linear filter and the calculation of the matched filter bound is based on a Karhunen-Loeve expansion of the received pulse spectrum when an isolated pulse is transmitted. Results are presented illustrating the various diversity effects. We conclude that in addition to the effect on probability of bit error of implicit delay diversity there is the less well known effect of implicit Doppler diversity in fast fading. The effect on probability of bit error of pulse shaping and explicit diversity is also illustrated.

Shadow fading correlation between uplink and downlink

Abstract: Selection diversity among base stations can be employed to combat shadow fading in mobile telephony Selection of the strongest uplink received signal from a mobile at several base stations is straightforward However, determining the base station from which to transmit to the mobile for downlink diversity often relies on the assumption that shadow fading on the uplink is highly correlated with the shadow fading on the downlink Signal level data were collected from a GSM system in rural and suburban propagation environments at 1900 MHz After averaging out the small scale multipath fading, the correlation between uplink and downlink shadow fading ranged between 066 and 092 The experiment, environment and results are described

GPS Signal Degradation Modeling

Abstract: This paper attempts to provide some insight into the fading properties of GPS signals. When a GPS signal gets to an antenna, it suffers from masking and blocking effects from surrounding objects. With respect to these effects, GPS signals can be divided into clear LOS signals, shadowed signals, and blocked signals. A statistic model, Urban Three-State Fade Model (UTSFM), is discussed in this paper. Experimental results show that this model can describe the fading distribution of GPS signals very well. After model fitting, the model parameters can indicate the composition of the incoming signals in terms of the relative magnitude of the three signal types.