The distribution of the local average power at a mobile is usually considered to be lognormal in terrestrial and satellite channels. However, the mathematical form of the lognormal distribution is not convenient for analytic calculations. In this paper, 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 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.

Estimation of the mobile speed, or equivalently, the maximum Doppler frequency, is of importance in a variety of applications in wireless mobile communications. In this paper, a unified framework for the performance analysis of several major speed estimation techniques is presented, which allows a fair comparison between all the methods, analytically. Interestingly, it is proved that all these methods are equivalent, asymptotically, i.e., for large observation intervals. In addition, we have derived closed-from expressions for the bias and variance of a recently proposed covariance-based method. We have also introduced a new estimator which relies on the average number of maxima of the inphase component, and have calculated its variance, analytically. Our extensive performance analysis, supported by Monte Carlo simulations, have revealed that depending on the channel condition and the observation interval, one needs to use a crossing- or a covariance-based technique, to achieve the desired estimation accuracy over a large range of mobile speeds.

The estimation of the mobile speed, or equivalently, the maximum Doppler frequency, is of importance in a variety of applications in wireless mobile communications. In this paper, a unified framework for the performance analysis of several major speed-estimation techniques is presented, which allows a fair comparison between all the methods, analytically. Interestingly, it is proved that all these methods are equivalent, asymptotically, i.e., for large observation intervals. In addition, we have derived closed-form expressions for the bias and variance of a recently proposed covariance-based method. We have also introduced a new estimator that relies on the average number of maxima of the inphase component, and have calculated its variance, analytically. Our extensive performance analysis, supported by Monte Carlo simulations, have revealed that depending on the channel condition and the observation interval, one needs to use a crossing- or a covariance-based technique, to achieve the desired estimation accuracy over a large range of mobile speeds.

In many engineering applications, specially in communication engineering, one encounters a bandpass non-Gaussian random process, with a slowly varying envelope. Among the available models for non-Gaussian random processes, spherically invariant random processes (SIRPs) play an important role. These processes are of interest mainly due to the fact that they allow one to relax the assumption of Gaussianity, while keeping many of its useful characteristics. In this paper, we have derived a simple and closed-form formula for the expected number of maxima of a SIRP envelope. Since Gaussian random processes are special cases of SIRPs, this formula holds for Gaussian random processes as well. In contrast with the available complicated expression for the expected number of maxima in the envelope of a Gaussian random process, our simple result holds for an arbitrary power spectrum. The key idea in deriving this result is the application of the characteristic function, rather than the probability density function, for calculating the expected level crossing rate of a random process.

We propose a new shadowed Rice (1948) model for land mobile satellite channels. In this model, the amplitude of the line-of-sight is characterized by the Nakagami distribution. The major advantage of the model is that it leads to closed-form and mathematically-tractable expressions for the fundamental channel statistics such as the envelope probability density function, moment generating function of the instantaneous power, and the level crossing rate. The model is very convenient for analytical and numerical performance prediction of complicated narrowband and wideband land mobile satellite systems, with different types of uncoded/coded modulations, with or without diversity. Comparison of the first- and the second-order statistics of the proposed model with different sets of published channel data demonstrates the flexibility of the new model in characterizing a variety of channel conditions and propagation mechanisms over satellite links. Interestingly, the proposed model provides a similar fit to the experimental data as the well-accepted Loo's (1985) model but with significantly less computational burden.

In wireless communications, the relative strength of the direct and scattered components of the received signal, as expressed by the Ricean K factor, provides an indication of link quality. Accordingly, efficient and accurate methods for estimating K are of considerable interest. In this paper, we propose a general class of moment-based estimators which use the signal envelope. This class of estimators unifies many of the previous estimators, and introduces new ones. We derive, for the first time, the asymptotic variance (AsV) of these estimators and compare them with the Cramer-Rao bound (CRB). We then tackle the problem of estimating K from the in-phase and quadrature-phase (I/Q) components of the received signal and illustrate the improvement in performance as compared with the envelope-based estimators. We derive the CRBs for the I/Q data model, which, unlike the envelope CRB, is tractable for correlated samples. Furthermore, we introduce a novel estimator that relies on the I/Q components, and derive its AsV even when the channel samples are correlated. We corroborate our analytical findings by simulations.

The recent surge in the application of antenna arrays for wireless cellular systems has opened up new problems in the area of array signal processing. One key issue is multipath propagation and local scattering, which requires the modification of the conventional point source model and the associated estimation techniques. In this paper we propose a parametric physical/statistical model for the distribution of angles of arrival of waves, originating from a far-field source through a scattering medium that is local to the source. Based on this model, we derive a compact and mathematically-tractable spatio-temporal cross-correlation function for the signal received by an antenna array. In the sequel we propose a simple yet asymptotically efficient technique for the estimation of the parameters of the spatially distributed source using an array of antennas. The computational complexity of the proposed method is much less than the other asymptotically efficient counterparts. Monte Carlo simulation results are presented to verify the theoretical predictions.

This paper relies on a characteristic function based approach to compute the level crossing rate and average outage duration of interference-limited wireless communication systems. The analytical results are quite general and are applicable to systems in which users are subject to nonidentically distributed Rician fading. These results are confirmed by Monte Carlo simulations and some numerical examples are discussed and interpreted.

Analysis and design of multielement antenna systems in mobile fading channels require a model for the space-time cross correlation among the links of the underlying multiple-input multiple-output (MIMO) channel. In this paper, we propose a general space-time cross-correlation function for mobile frequency nonselective Rice fading MIMO channels, in which various parameters of interest such as the angle spreads at the base station and the user, the distance between the base station and the user, mean directions of the signal arrivals, array configurations, and Doppler spread are all taken into account. The new space-time cross-correlation function includes all the relevant parameters of the MIMO fading channel in a clean compact form, suitable for both mathematical analysis and numerical calculations/simulations. It also covers many known correlation models as special cases. We demonstrate the utility of the new space-time correlation model by clarifying the limitations of a widely accepted correlation model for MIMO fading channels. As another application, we quantify the impact of nonisotropic scattering around the user, on the capacity of a MIMO fading channel.

The level crossing rate (LCR) of a random process conveys useful information about the underlying process, and is of interest in diverse engineering fields. In wireless communications, it is related to the system characteristics such as handoff, outage probability, fading rate, average duration of fades, velocity (or maximum Doppler shift) of the mobile, and the effect of diversity on fading. The LCR formula was originally derived by Rice in terms of the joint probability density function (pdf) of the underlying process and its time derivative. In this letter, we express the LCR in terms of the joint characteristic function (cf). This new formula is useful for many cases where the joint cf is simpler to derive than the associated joint pdf. As an application and for a direct-sequence code-division multiple-access system, the fading rate at the output of a RAKE receiver with either maximal ratio combiner or postdetection equal gain combiner, operating over a frequency-selective fading channel with different path statistics, is easily calculated using the new cf-based LCR formula.

For the analysis and design of multielement antenna systems in mobile fading channels, we need a model for the space-time cross correlation among the links of the multiple-input multiple-output (MIMO) channel. We propose a general space-time cross correlation function for narrowband Rayleigh fading MIMO channels, where various parameters of interest such as angle spreads at the base station and the user, the distance between the base station and the user, mean directions of the signal arrivals, array configurations, and Doppler spread are all taken into account. The new space-time cross correlation function includes all the relevant parameters of the MIMO narrowband Rayleigh fading channel in a clean compact form, suitable for both simulation and mathematical analysis. It also covers many known correlation models as special cases. We demonstrate the utility of the new space-time correlation model by clarifying the limitations of a widely-accepted correlation model for MIMO fading channels.

In mobile communications the strength of a line of sight component measured by the K factor of the Ricean received envelope distribution has significant impact on system performance analysis and link budget calculations. In this paper, we study the performance of moment-based estimators for the Ricean K-factor as less complex alternatives to the maximum likelihood estimator. Our asymptotic analysis reveals that the estimators that rely on lower-order moments have a better asymptotic performance for moderate/large values of K. We also illustrate, by Monte Carlo simulations, that the fading correlation among the envelope samples deteriorates the estimator performance. The simplest estimator, which can be expressed in closed form in terms of the second- and fourth-order sample moments offers a good compromise between statistical performance and computational simplicity.

In this paper we propose a new shadowed Rice model for land mobile satellite channels. In this model the amplitude of the line-of-sight is characterized by the Nakagami distribution. The model provides closed-form mathematically-tractable expressions for the fundamental channel statistics such as envelope probability density function and envelope-squared moment generating function. The model is very convenient for analytical and numerical performance prediction of complex narrowband and wideband land mobile satellite systems, with different types of uncoded/coded modulations, with or without diversity. Comparison of the new model with published channel data demonstrates the flexibility of the model in characterizing a variety of channel conditions and propagation mechanisms.

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.

A new simple model has been proposed for land mobile satellite channels. We study the second-order statistics of the new model. First we develop a characteristic function-based approach for calculating the level crossing rate of the new model in diversity systems, where the branches can have different fading statistics. Then we compare the level crossing rate and the average fade duration of the new model with measured data. Similar to the first-order statistics, our results show that the second-order statistics of the new model can be expressed in compact closed forms, convenient for both mathematical analysis and numerical calculations.

Antenna spacings, the angle spread and the Rice factor significantly affect the correlation of fading coefficients in a multi-antenna system. We study the effect of these parameters on the performance of different types of detection schemes in a BLAST architecture. We show that the detection method based on lattice decoding is more resistant to the correlated fading than other types of detection which are based on successive interference cancellation. We notice that highly correlated fades significantly degrade the performance of detection techniques based on successive interference cancellation whereas they slightly affect the lattice decoding algorithm. We also study the effects of correlated fades on some space-time block codes. We show that space-time block codes from orthogonal design are more resistant to correlation than other high rate linear space-time block codes.

Abstract Estimation of signal strength, a measure of channel quality, and Doppler spread which is proportional to the mobile speed, are important for handoff algorithms and optimal tuning of system parameters to changing channel conditions in adaptive transmission systems. This paper provides a survey of existing techniques for estimating the statistical parameters of the mobile channel. We discuss the current state of the art in estimation of the received signal strength, mobile velocity, and other related statistical channel parameters, illustrate their performance, and compare existing techniques. The sensitivity of these schemes to modeling error owing to the presence of line of sight, directional reception, and noise is characterized analytically and illustrated by simulations. Copyright © 2001 John Wiley & Sons, Ltd.

We propose the application of spherically invariant random processes for joint modeling of the fluctuations of the signal envelope and phase in narrowband wireless fading channels. In this model, the phase has a uniform distribution (which is very common in fading channels), while the envelope can be distributed according to an arbitrary distribution law (which includes Rayleigh as a special case). The great utility of the spherically invariant random processes, as a large family of non-Gaussian random processes, lies on their many Gaussian-like properties, which make them very flexible for multivariate statistical analysis, optimal estimation, simulation, and other signal processing issues. Empirical justifications are also given, which strongly support the acceptability of the model.

A "classical" probability density function (PDF)-based approach relying on the cumulative distribution function (CDF) of the combined output signal-to-noise ratio (SNR) as well as the joint PDF of the combined output SNR and its time derivative, is used to obtain exact closed form expressions for average outage duration (AOD) of maximal-ratio combiners (MRC) over independent and identically distributed (i.i.d.) Rayleigh and Rice fading channels. On the other hand, relying on numerical techniques for inverting Laplace transforms of CDFs and for the computation of the joint characteristic function (CF) of the combined output SNR random process and its time derivative, a CF-based approach is adopted to calculate the AOD of MRC over non-i.i.d. Rician diversity paths. The mathematical formalism is illustrated by presenting some numerical results/plots showing the impact of the power delay profile and the distribution of the angle of arrivals on the AOD of diversity systems operating over typical fading channels of practical interest.