Statistical modeling of the LMS channel - Vehicular Technology, IEEE ...

IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 50, NO. 6, NOVEMBER 2001

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Statistical Modeling of the LMS Channel Fernando Pérez Fontán, Member, IEEE, Maryan Vázquez-Castro, Cristina Enjamio Cabado, Jorge Pita García, and Erwin Kubista

Abstract—In this paper, a statistical model for the land mobile satellite (LMS) channel is presented. The model is capable of describing both narrow- and wide-band conditions. Other relevant characteristic is that it can be used to study links with geostationary as well as nongeostationary satellites. The model is of the generative type, i.e., it is capable of producing time series of a large number of signal features: amplitudes, phases, instantaneous power-delay profiles, Doppler spectra, etc. Model parameters extracted from a comprehensive experimental data bank are also provided for a number of environments and elevation angles at L-, S-, and Ka-Bands. Index Terms—Land mobile satellite (LMS), propagation, statistical modeling.

I. INTRODUCTION

T

HIS paper presents the basic principles for the design and implementation of a land mobile satellite (LMS) channel simulator at various frequency bands. The simulator is based on a number of statistical assumptions (statistical model). The simulator and its associated statistical model can be used in the study of the performance and availability of different services including communications, broadcast, navigation, etc. Such systems may be based on geostationary (GEO) satellites or on low earth orbit (LEO) and other nongeostationary (non-GEO) satellites. For current LMS engineering applications, models solely providing cumulative distribution functions (cdfs) are not sufficient. New statistical models must be suitable for interfacing system studies including link-level and network-level simulations. This is the reason why a new generation of statistical models capable of producing “time-series” (generative models) is appearing on the scene of LMS channel models. Another feature that is very distinctive of the LMS channel when compared to the terrestrial mobile channel is that no longer a single distribution describes its behavior: very marked differences are observed for line-of-sight (LOS) and shadowed links. This explains why LMS models try to classify propaga-

Manuscript received February 17, 2000; revised February 1, 2001. This work was supported by ESA/ESTEC (European Space Agency) contract and in the framework of EuroCOST Project 255. F. Pérez Fontán and C. Enjamio Cabado are with the Department de Tecnologias de las Comunicaciones, E.T.S.I. Telecomunication, Universidad de Vigo, Campus Universitario, Vigo E-36200, Spain (e-mail: [email protected]). M. Vázquez-Castro is with the Department de Tecnologias de las Comunicaciones, Universidad Carlos III, Madrid 28911-Leganés, Spain (e-mail: [email protected]). J. Pita García is with ESA/ESTEC, XEP, Noordwijk NL-2200 AG, Netherlands (e-mail: [email protected]). E. Kubista is with Joanneum Research, Institute of Applied Systems Technology, Graz A-8010, Austria (e-mail: [email protected]). Publisher Item Identifier S 0018-9545(01)09167-8.

Fig. 1. Received signal amplitude at S-Band under narrow-band conditions.

tion events according to the degree of shadowing and quantify these events independently (“good” and “bad” states). LMS terminals may operate in some cases within cluttered areas where shadowing effects dominate (e.g., urban, tree-shadowed areas, etc.). System engineers, operators, and planners require reliable and comprehensive information related to the propagation effects that such systems face. This paper addresses the statistical modeling of shadowing and multipath effects in LMS applications for a wide range of environments with different clutter densities (from open to dense urban areas) and elevation angles (5 –90 ) at L-, S-, or Ka-Bands. A comprehensive experimental data bank has been used to extract the model parameters for the different bands, environments, and elevations. A basic feature of the channel model/simulator described in this paper is that it is able to generate time-series of any channel parameter whose study is required: signal envelope, phase, instantaneous power delay profiles, Doppler spectra, etc. As a second step, conventional statistics, e.g., cdfs, may be computed later from the generated series. To illustrate some of the features found in the LMS channel, two examples of measured time series are presented. In Fig. 1 [1] the signal amplitude variations received under narrow-band conditions are presented and in Fig. 2 [2] a measured series of instantaneous power delay profiles (PDP) (wide-band reception) is shown. In Fig. 1 it can be observed how the received signal is subject to very marked variations. It can also be observed, on the lower right corner, how the probability density function (pdf) is bimodal for this particular case. This is further illustrated in Fig. 3 where the cdf of the overall signal and the cdfs corresponding to the LOS and shadowed states are plotted. These observations clearly suggest that classical distributions used in radio propagation cannot be used directly to characterize the channel. Rather,

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Fig. 2. Measured instantaneous power delay profiles at L-Band. Wide-band conditions.

has been selected to accomplish the goals stated throughout this section. In the context of channel modeling, the terms “echo” or “ray” are widely used. They indicate the different components giving rise to the multipath phenomenon. The electromagnetic features involved are described in a simplified way using this concept of echo, which is able to model fairly well the fast variations and associated Doppler spread and the time dispersion in the channel. Fig. 2 shows that the channel not only causes signal amplitude variations but it also gives rise to time dispersion in the received signal, which, depending on the transmitted signal bandwidth, will cause distortion effects like frequency selectivity or intersymbol interference (ISI). These and other features of the LMS channel have to be accounted for in a suitable channel model/simulator. Finally, the LMS channel may present significant differences depending on the elevation angle and the environment where the mobile terminal is located. If GEO satellites are used, relatively low elevation angles are found, especially for the northern latitudes. Other orbits such as LEO or medium earth orbits (MEO) or highly elliptical orbits (HEO) provide higher elevation angles for satellite-to-mobile transmissions, thus making it possible to overcome, in part, the shadowing effects caused by man-made and/or natural features in the vicinity of the mobile. This elevation angle dependence has also to be accounted for in a suitable model. II. MODEL AND SIMULATOR BASICS

Fig. 3. Overall received signal cdfs and cdfs for the LOS state (S1) and the heavy shadowed state (S3).

a combination of distributions is required; the overall pdf follows the general expression given in (1) where probability that the link is in LOS conditions; pdf of the amplitude variations when in LOS conditions; probability of the link being under shadowed conditions; pdf of the signal variations when in shadowed conditions. The previous approach is valid for the study of link budgets in which standard link margins and availability levels are the wanted outcome. If, however, more detail is required, including duration of different shadowing events or the time dispersion caused by the channel and their influence on link and system performance, an approach capable of producing time-series is indicated. In this case, a model built around a Markov chain

The elements making up the signal received through the LMS channel are the direct ray and the multipath. Both the time and locations variability and the time dispersion introduced by the channel have to be accurately characterized. An important feature to be included in newer LMS models is the possibility to account for both mobile and satellite movement along their respective trajectories. The model presented in this paper is of the statistical type, this means that assumptions have to be made in which given statistical distributions are used to describe the various physical phenomena affecting the direct signal and the multipath. In this respect, a first-order Markov chain [3]–[5] is used here to describe the slow variations of the direct signal, basically due to shadowing/blockage effects. The overall signal variations due to shadowing and multipath effects within each individual Markov state are assumed to follow a Loo [6] distribution with different parameters for each shadowing condition (Markov state). Up to this point the model is of the narrow-band type since it does not account for time dispersion effects. These effects are introduced by using an exponential distribution to represent the excess delays of the different echoes [7]. Different operational situations have been identified depending on the type of satellite and mobile user. These different situations will involve slightly different simulator implementations. The following cases have been identified. Case 1) stationary satellite and stationary mobile; Case 2) stationary satellite and moving mobile; Case 3) moving satellite and stationary mobile;

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Both the direct ray and the different multipath echoes are shown as delta functions in the signal level-excess delay plane (Fig. 5). Below, the two main elements in the model, namely the direct signal and the multipath component, are discussed in more detail. A. The Direct Signal

Fig. 4. Modeling steps.

Case 4) moving satellite and moving mobile. There are situations where shadowing affecting two links from two different satellites with the same mobile terminal present nonnegligible correlation. This will mainly occur when the satellites are seen by the mobile with closely spaced angles. This condition has also to be accounted for in the model/simulator. A methodology that can be used to produce correlated Markov chains is the one presented by Lutz in [8]. The statistical model described here assumes ideal transmission conditions, i.e., no band-limiting effects due to transmit and receive filters are included. This means that the different paths are treated as ideal delta functions affected by attenuations, phase shifts and delays which are time varying as indicated by (2)

For the characterization of the direct signal a two-stage approach is proposed in which its variations are divided into very slow, which can be described by a state-based model (Markov), and slow, which can be represented by a log-normal distribution. A three-state model was selected to accommodate the high dynamic range in the received signal, especially due to the broad range of elevation angles considered. The following states were defined (Fig. 6): — S —LOS conditions; — S —moderate shadowing conditions; — S —deep shadowing conditions. A first-order Markov chain is a stochastic process [4], [5] that can take on a number of discrete states in such a way that the probability of being in a given state is only dependent on the previous state. Markov chain models can be used to describe the LMS propagation channel at a given time or route position by means of two matrices: — state probability matrix—[ ]; — state transition probability matrix—[ ]. represents the probability of Each element in matrix [ ], change from state- to state- . The overall probability for each , repstate is contained in matrix [ ] where each element, resents the total probability of being in state- . The matrix eleand can be defined analytically as follows: ments (3)

The consideration of real transmission system constraints (i.e., IF/RF, pulse-shaping filters, etc.) may be done later at postprocessor level or when performing link-level simulations. Fig. 4 illustrates the general organization of the model. It must be pointed out that there exists an intermediate step in which time series are produced prior to the generation of conventional statistics. In addition to this, the effects of antenna selectivity can be introduced later, at a different stage in the modeling. Fig. 4 also acknowledges the fact that the model can be used as the channel input to link-level (BER, FER studies) simulations. III. MODEL ELEMENTS The channel features to be modeled statistically and their corresponding model elements are now discussed. In Fig. 5, the main model elements are graphically illustrated as follows: — direct signal; — diffuse multipath due to the direct signal illuminating nearby scatterers; — specularly reflected rays (in case they exist); — diffuse multipath associated to the specular rays (in case they exist).

is the number of state frames (i.e., minimum state where length: this concept is explained below) corresponding to stateand is the total number of state frames and (4) is the number of transitions from state- to statewhere and is the number of state frames corresponding to state- . For the computation of matrices [ ] and [ ] a sufficiently large number of states and transitions is required in the experimental data set used. Three properties of Markov chains will be highlighted here: — the sum of all elements in every [ ] row must be equal to one; — the sum of all elements in matrix [ ] must be equal to one; — the asymptotic behavior (convergence property) of the Markov chain is defined by the equation (5) The number of states in the model, three for each environment, was selected by trading off complexity and received

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Fig. 5.

IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 50, NO. 6, NOVEMBER 2001

Main model elements.

Fig. 6. Three-state model used to describe the dynamics of the direct signal. Fig. 7. Different rates of change of the various received signal components.

signal dynamic range for every environment and elevation angle, taking into account that the model has to describe very different situations ranging from very cluttered areas at low elevations to open areas at very high elevation angles. Typically, each state will last a few meters along the traveled route. In [9] a minimum state length or state frame of 3–5 m was observed in the analysis of a large experimental S-Band data set [1]. The definition of a minimum state length affects the generation of direct signal series: a new state will be drawn randomly every time the mobile travels a distance meters. The triggering of the Markov engine (or enof gines) is discussed later in more detail. The model makes the simplifying assumption of the existence of three basic rates of change (very slow, slow and fast) in the received signal corresponding to the different behaviors of its components. States represent different gross shadowing conditions, e.g., if the mobile goes from being behind a tree or a building to being in the clear LOS of the transmitter. These situations correspond to different states. The marked signal variations due to state changes are considered as the very slow variations of the direct signal and, consequently, of the overall signal. As for the slow variations, they represent small-scale changes in the shadowing attenuation produced as the mobile travels in the shadow of the same obstacle: shadowing variations behind a group of trees due to different leaf and branch

densities or shadowing variations behind a single building or group of buildings. In the LOS state, slow variations may be due to different reasons: nonuniform receive antenna patterns and/or changes in mobile orientation with respect to the satellite. An element in the modeling of the slow variations lacking suf, (Fig. 7). ficient reported data is the correlation distance, This parameter describes how fast the log-normally distributed values in the order of 1–3 m have been obvariations are served [9]. The autocorrelation properties of the very slow variations are implicitly present in the Markov chain (transition matrices) and in the state frame concept. B. The Multipath Component Multipath contributions can be broken down into two classes: those originating from the direct ray (i.e., those echoes generated by the direct signal’s illumination of scatterers in the vicinity of the mobile terminal) and those due to specular rays, if they exist. Few strong, far-echo events (existence of specular rays) have been recorded in the experimental data sets analyzed, as indicated later in Section V. Under narrow-band conditions, i.e., when multipath echoes are not significantly spread in time, for the modeling of the diffuse contributions, the most commonly used parameter is

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Fig. 8. Measured narrow-band time-series in a tree-shadowed area at S-Band and 40 elevation.

Fig. 9. Simulated narrow-band time-series in a tree-shadowed area at S-Band and 40 elevation.

the average multipath power, or, alternatively, the car. To jointly model the berier-to-multipath ratio, havior of the direct signal and the multipath component within each state (not for the overall received signal) the Loo distribution is widely used and it is proposed in this model [6]. The Loo distribution is a very versatile one that comprises the Gaussian, the Rice and the Rayleigh distributions as extreme cases. This property makes it valid for a very wide range of situations including LOS through to very shadowed conditions. The Loo distribution considers that the received signal originates from the sum of two components: the direct signal and the diffuse multipath. The direct signal is assumed to be log-normally distributed with mean (decibel relative to LOS) and standard deviation (dB), while the multipath component follows a Rayleigh distribution characterized by its average (decibel relative to LOS). The Loo probability power, density function is given by Fig. 10. Measured and model fitted averaged power delay profile for an open area for 80 elevation at L-Band [2].

(6) where

and

are related to

and

as follows:

(7) Fig. 7 illustrates the different components intervening in the narrow-band model and their different rates of variation. As an example of the joint application of a three-state Markov chain and the Loo distribution for narrow-band LMS channel modeling, Figs. 8 and 9 show measured and simulated time series at S-Band for a tree shadowed scenario. There is a fairly good agreement between the measured and the simulated series. In the case of the figures, the same state series have been used to facilitate the comparison. As for the superposed fast variations, the differences observed are due to the fact that the Loo model parameters used in the modeled series are average values. To calculate these average values a large number of individual series belonging to each state-elevation pair were analyzed by

calculating their individual cdfs. Then each measured cdfs was and fitted to the Loo distribution, thus obtaining sets of values. The values of the parameters finally used in the model, and given tabulated form later, are the average values of each of those sets. More details are given in Section V. The previously presented narrow-band model does not describe all channel effects encountered, more specifically, time and angle of arrival dispersion. In this respect, experimental data was available where time-dispersion effects could be observed. Examples of measured power delay profiles (PDPs) are shown in Figs. 10 and 11 corresponding to L-Band in open and lightly wooded scenarios. In the figures the noise floor is, in one case, approximately 30 dB relative to the direct signal and, in the other, about 25 dB. Echoes close to these values may be actual multipath features or artifacts caused by the channel sounder (Section V). For this reason such echoes have not been considered for model parameter extraction. Unfortunately, no angle of arrival measurements were available for study and, thus, standard, widely accepted assumptions have been used in this model.

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Fig. 13. Proposed linear multipath decay profile and multipath power normalization process. Fig. 11. Measured averaged power delay profile with a far echo for a lightly wooded scenario and 45 elevation at L-Band [2].

Fig. 14. Model output: samples of the amplitudes of the direct signal and of the multipath echoes classified according to their excess delays and angles of arrival. Fig. 12. Introduction in the Markov multipath component.

+ Loo model of the time-spreading of the

So far, multipath has been introduced in terms of its average and this approach is valid when time-dispersion is power not significant. However, to include wide-band effects, the time dispersion caused by the channel must be included in the modeling. That is, it must be acknowledged that echoes arrive at the receiver with different excess delays with respect to the direct signal (shadowed or not). An overview of the model is graphically illustrated in Figs. 5 and 12. Two distributions are typically assumed to model the number of occurrences and the times of arrival of multipath echoes [7], these are the Poisson and the exponential distributions respectively. In the proposed model, a fixed and sufficiently large number ) is assumed, thus eliminating the need to use of rays ( a Poisson distribution and, in this way, simplifying the model. The criterion followed for the selection of the number of rays, , was to generate smooth continuous Doppler spectra. Smaller

values of can be used for most applications, in this way helping speed up simulation times. multipath echoes an expoAs for the excess delays of the , representing nential distribution is used with parameter the average of the distribution

(8) where is the excess delay of the th echo. For this wide-band part of the model, several other parameters are required, namely, the multipath power decay profile, which represents the rate at which the multipath contributions weaken as their excess delays increase. Here, the use of a linear (dB/ s), is proposed as decay rate quantified by a slope, shown in Fig. 13. One consideration to be made, ratified by the experimental data in Section V, is that the time dispersion of the LMS channel is much smaller than that of the terrestrial cellular channel.

PÉREZ FONTÁN et al.: STATISTICAL MODELING OF THE LMS CHANNEL

Fig. 15.

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Generation of synthetic scenarios consisting of point scatterers belonging to two consecutive scattering functions like the one in Fig. 14.

As indicated in Fig. 13, the total average power of the mul(average multitipath rays (power sum) must be equal to path power) dB

(9)

where is the amplitude of the th multipath echo. The previous expression allows for the appropriate normalization of the relative powers of the direct and multipath components. The convention throughout is that LOS conditions imply a direct signal ]. amplitude of 1 or 0 dB [ parameter It should be clarified at this point that the describes the diffuse multipath power generated by the direct signal illuminating the environment in the vicinity of the mobile values extracted from experimental data are (near echoes). tabulated in Section V. Far echoes, in case they exist, must be introduced separately in the model and, hence, they do not affect . As indicated later in Section V the number of the value of events in which far echoes were recorded is not large enough to extract significant model parameters out of the available experimental data sets. This statistical model has to be complemented with one further element, namely, the distribution of angles of arrival of the multipath echoes. Due to lack of experimental data it is proposed that a uniform azimuth distribution be employed for near echoes. This assumption is realistic and widely used in other models. IV. MODEL OUTPUTS The model output consists of two elements: 1) a series of direct signal (amplitude and phase) variations meters; sampled every 2) for multipath echoes, a series of point scattering func(stored channel file), sampled in the tions, meters mobile traveled distance domain every

[or time domain for cases 1) and 3), Section II, when the mobile is stationary and the satellite is moving]. These functions contain the complex amplitudes of the multipath echoes classified according to their excess delays and angles of arrival ( ). has to be chosen so as to fulfill the wideThe value of sense stationary (WSS) assumption. Values of a few meters are widely reported in the literature. Fig. 14 schematically illustrates one entry to the stored channel file produced at this stage in the modeling. In an subsequent step (Fig. 4), from of these outputs, synthetic scenarios are created geometrically as illustrated in Fig. 15. These scenarios are made up of point isotropic scatterers giving rise to multipath echoes whose amplitudes, delays and angles of arrival have already been generated with the aid of the statistical distributions outlined earlier and contained in the functions previously generated. The main purpose of generating synthetic scenarios is to reproduce the ray interference effects due to path changes (and associated phase changes) as the mobile and the satellite move by keeping track of the varying distances from the satellite to the scatterers and from the scatterers to the mobile. This modeling approach, although statistical, introduces a geometrical component which is very intuitive and helps to reproduce phase effects due to path length changes caused by the mobile and satellite dynamics. It also has the advantage of the possible reuse of simulation runs for different receiver antenna patterns (flow diagram in Fig. 4). To clarify the use of the synthetic scenario approach, two postprocessing tasks, namely, the procedures for the generation of narrow-band received signal time series and the generation of Doppler shift time series are presented below. A. Generation of Narrow-Band Time-Series To show how the model outputs [direct signal series and series , and their of multipath point scattering functions,

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Fig. 16.

Combination of rays belonging to consecutive synthetic scenarios to generate complex-envelope time series.

Fig. 17.

Satellite-to-mobile geometry and reference coordinate system.

Fig. 18.

Example of generated signal amplitude series.

Fig. 19. Example of generated phase series corresponding to the same simulation as Fig. 18.

Fig. 20.

associated synthetic scenarios] may be processed to produce meaningful information, the generation process of narrow-band amplitude series is explained with the aid of Figs. 15 and 16 for case 2) (stationary satellite and moving mobile).

Phase change/Doppler generation geometry.

In the figures, for two neighboring points along the mobile ) synthetic scenarios corresponding to two route ( and and consecutive scattering functions, are created as a first step. In Fig. 16 two scatare shown. terers, and , generated for route points and

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Fig. 21.

Mobile velocity Doppler spread and combined Doppler spread and satellite originated Doppler shift.

Fig. 22.

Time variation of Doppler shift for a link with a LEO satellite.

Scatterers and belong to scattering functions and , respectively. For the generation of the narrow-band amplitude series, the coherent sum of all rays arriving at every route sampling point – is sufficient) is computed. (typically a separation of In this way, a complex (amplitude and phase) time series is produced that represents the received signal: voltage or field strength (not power). Also phase information is available if needed. In order to maintain continuity in the signal series (amplitude and phase) generated, two neighboring scattering functions and ) are used when performing the coherent sum ( of rays. A linear weighting algorithm is employed to allow smooth transitions in the amplitudes and phases generated. At the same time, samples of the direct signal produced meters apart have to go through a rate conversion process (inter– m, the same as in polation) to yield a sample every the multipath case, while preserving its slower rate of change. Also, the direct signal phase is kept track of by computing and updating the satellite-to-mobile distance. Fig. 17 illustrates the satellite-to-mobile geometry together with a reference coordinate system. By following this approach, when a change in Markov State takes place, it will give rise to smooth transitions in the direct signal amplitude while maintaining phase continuity.

Fig. 23. Availability analysis for multisatellite systems with uncorrelated shadowing.

Fig. 24.

Markov engine(s) triggering events.

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Fig. 25.

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A change in Markov engine due to a 10 change in elevation is assumed to be accompanied by a new random state draw. TABLE I AVAILABLE DATABASES AND THEIR CHARACTERISTICS

The overall received complex envelope variations can be is the linear represented by the expression below where weighing function corresponding to route sampling point

where ray amplitudes in two neighboring scattering matrices and are called and , respectively, while denotes the direct signal and denotes the different multipath echoes. Figs. 18 and 19 show generated amplitude and phase series respectively. In the figures, it is clearly shown how the received phase continuity is preserved through state transitions. Also it can be observed that phase linearity is lost for deep shadowing events as expected. B. Doppler Spectra

(10)

All received signal contributions (direct ray and multipath echoes) are subject to Doppler shifts. In Fig. 20 an illustration

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TABLE II MARKOV CHAIN MATRICES [P ] AND [W ] FOR VARIOUS ELEVATIONS. URBAN AREA (UNIVERSITY OF BRADFORD, S-BAND)

TABLE III MARKOV CHAIN MATRICES [P ] AND [W ] FOR VARIOUS ELEVATIONS. SUBURBAN AREA (UNIVERSITY OF BRADFORD, S-BAND)

TABLE IV MARKOV CHAIN MATRICES [P ] AND [W ] FOR VARIOUS ELEVATIONS. OPEN AREA (UNIVERSITY OF BRADFORD, S-BAND)

of this is presented. The direct signal shift may be calculated by keeping track of the path increments for each route sampling – ). Similarly, for the diffuse scatterers, the situpoint ( ation may be modeled by taking into consideration that the total phase of each contribution can be split into a phase change due to the movement of the satellite (or path change from the satellite to the scatterer) and a phase change due to the movement of the mobile terminal (or path change from the scatterer to the mobile) as indicated in (11) A reasonable simplification is to consider that the total instantaneous Doppler spectrum is made up of two independent

elements: the mobile movement contribution Doppler spread that can be several hundred Hertz wide and the satellite movement contributions Doppler shift that can be in the order of several tens of kiloHertz. A simplified representation of the received Doppler spectra can be achieved by shifting the mobile movement induced Doppler spectrum by the satellite generated Doppler shift, as illustrated in Fig. 21. In this figure, it is shown how the Doppler shift affecting the received signal is made up of two modulation-like effects, one due to the mobile movement and the other due to the satellite movement. This last effect shifts the mobile movement induced Doppler spectrum up and down in frequency at a rather slow pace even for LEO satellites as

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TABLE V MARKOV CHAIN MATRICES [P ] AND [W ] FOR VARIOUS ELEVATIONS. INTERMEDIATE TREE SHADOWED AREA (UNIVERSITY OF BRADFORD, S-BAND)

TABLE VI MARKOV CHAIN MATRICES [P ] AND [W ] FOR VARIOUS ELEVATIONS. HEAVY TREE SHADOWED AREA (UNIVERSITY OF BRADFORD, S-BAND)

TABLE VII AVERAGE LOO MODEL PARAMETERS FOR DIFFERENT ELEVATIONS AND DIFFERENT STATES (UNIVERSITY OF BRADFORD, S-BAND)

shown in Fig. 22, where an example for a polar orbit LEO satellite is presented. V. SIMULATOR IMPLEMENTATION ISSUES In previous sections, the basic model elements have been described, now the adequate sequencing of all these elements into

a channel simulator is presented. As indicated in the Introduction (Section I) the approach followed is to generate time-series of the different elements in the received signal—direct ray and multipath—and combine them suitably at the receiver taking into consideration their distributions and their relative rates of change, i.e., slow and fast variations. A postprocessor is required to produce the relevant received signal statistics from the

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TABLE VIII MARKOV CHAIN MATRICES [P ] AND [W ] FOR VARIOUS ELEVATIONS. NARROW-BAND, URBAN AREA, VEHICLE MOUNTED ANTENNA (DLR, L-BAND)

AVERAGE LOO MODEL PARAMETERS

FOR

TABLE IX DIFFERENT ELEVATIONS AND DIFFERENT STATES. NARROW-BAND, URBAN AREA, VEHICLE MOUNTED ANTENNA (DLR, L-BAND)

TABLE X MARKOV CHAIN MATRICES [P ] AND [W ] FOR VARIOUS ELEVATIONS. NARROW-BAND, SUBURBAN AREA, VEHICLE MOUNTED ANTENNA (DLR, L-BAND)

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AVERAGE LOO MODEL PARAMETERS

FOR

TABLE XI DIFFERENT ELEVATIONS AND DIFFERENT STATES. NARROW-BAND, SUBURBAN AREA, VEHICLE MOUNTED ANTENNA (DLR, L-BAND)

TABLE XII MARKOV CHAIN MATRICES [P ] AND [W ] FOR VARIOUS ELEVATIONS. NARROW-BAND, URBAN AREA, HAND-HELD ANTENNA (DLR, L-BAND)

generated time series, both for narrow- and wide-band conditions. When investigating the combined behavior of a network consisting of a constellation of several satellites, the model must be run as many times as satellites in the constellation under study. The variations (very slow, slow, and fast) of the received signals from the different satellites are considered to be uncorrelated (Fig. 23). Only when the degree of shadowing correlation is high enough (for small angle separations between two satellites) the combined production of correlated time series is required. This special case will occur with a small likelihood. One possible way to model situations where shadowing correlation is not negligible is to use the methodology formulated by Lutz [8] for the generation of correlated Markov chains. The implementation of the described model into a practical channel simulator presents additional complexities not found in the terrestrial mobile case. These are due to the fact that not only the mobile is capable of changing its position with time but also that the satellites may move at high speeds, e.g., LEO satellites. There even exists the case in which it is only the satellite

that moves while the mobile is stationary. The special case in which both the satellite and the mobile are stationary must also be addressed. This is the reason why, in the model/simulator, special attention must be paid to a preprocessing task in which the positions along the mobile route and the satellite trajectory as well as the instants when a state change event may occur are identified. Different triggering events must be considered for the different phenomena accounted for in this model. Below, the implications involving each of the model elements are analyzed. The direct signal is assumed to undergo very slow variations along the route. These variations are modeled by means of a Markov chain model. In a first, narrow-band version of this model [5] a minimum state length called Frame was already meters along the mobile considered. Thus, for every route a draw of a random number has to be made to trigger the current Markov chain engine. This is valid for the case where the satellite is stationary (GEO) and the mobile is moving. However, the situation in which the satellite is moving while the mobile is stationary must also be accounted for. For such situations, additional triggering events must be considered (Fig. 24).

PÉREZ FONTÁN et al.: STATISTICAL MODELING OF THE LMS CHANNEL

AVERAGE LOO MODEL PARAMETERS

FOR

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TABLE XIII DIFFERENT ELEVATIONS AND DIFFERENT STATES. NARROW-BAND, URBAN AREA, HAND-HELD ANTENNA (DLR, L-BAND)

TABLE XIV MARKOV CHAIN MATRICES [P ] AND [W ] FOR VARIOUS ELEVATIONS. NARROW-BAND, SUBURBAN AREA, HAND-HELD ANTENNA (DLR, L-BAND)

AVERAGE LOO MODEL PARAMETERS

FOR

TABLE XV DIFFERENT ELEVATIONS AND DIFFERENT STATES. NARROW-BAND, SUBURBAN AREA, HAND-HELD ANTENNA (DLR, L-BAND)

Few measured data are available to quantify this. However, it is clear that state changes can be triggered by changes in the satellite elevation and/or azimuth with respect to a stationary/moving terminal. Here it is assumed that state changes , in addition to may be triggered by changes in elevation, (every meters). changes in the mobile position, , the Markov model is As for the changes in elevation, structured around engines valid for elevation ranges of 10 , i.e., the Markov model uses different matrices [ ] and [ ] for dif, 40 , 50 , 60 . ferent elevations: 10 Whenever a change in Markov engine occurs, for example, from that of 40 to that of 50 , a new draw of a random number

has to be made to decide whether a change in state in addition to a change in Markov engine has occurred. This is illustrated with the aid of Fig. 25. Both direct signal and multipath conditions (model parameters [ ], [ ], ) will change for different Markov engines (different elevations) and for different states. VI. MODEL PARAMETERS In this section, the parameters for the model/simulator described in the previous sections are presented. These parameters have been extracted from part of the ESA/ESTEC (Euro-

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TABLE XVI AVERAGE LOO MODEL PARAMETERS FOR DIFFERENT ORIENTATIONS AND SIDES OF THE ROAD (IAS, GRAZ, Ka-BAND)

pean Space Agency) LMS measurement database. Table I summarizes the main features of the measurement campaigns and available experimental data.

TABLE XVII MARKOV CHAIN MATRICES [P ] AND [W ] FOR VARIOUS ELEVATIONS. FRANCE, LEAF TREES, 30 ELEVATION (IAS, GRAZ, Ka-BAND)



A. Narrow-Band Model Parameters The data from the University of Bradford, U.K., was obtained under narrow-band conditions at S-Band [1]. The data consists of a comprehensive set for several environments: open, suburban, urban, tree-shadowed, and elevations: 40 , 60 , 70 and 80 . Flights were parallel to the road. Radio paths were, thus, orthogonal to the route (orientation 90 ). Measurements were carried out with a carrier frequency of 2618 MHz. The parameters extracted from the data set are summarized in Tables II–VII. The DLR (Germany) data set is narrow-band and was obtained at L-band (1820 MHz) both for hand-held and car-roof antennas and both for stationary as well as moving vehicle conditions [10]. The airplane carrying the transmitter flew in circles around the receiver. The model parameters extracted from this data set are summarized in Tables VIII–XV. The IAS (Austria) data was obtained at Ka-Band using the Italsat satellite for a fixed elevation of 30 –35 and orientations of approximately 0 , 45 , and 90 [11]. Satellite side (Sat) and opposite side (Opp) of the road runs were available for analysis. Since a directive antenna was used, only direct signal variations (and little multipath) were available for analysis. The extracted model parameters form this data set are summarized in Tables XVI–XXI. The extraction of model parameters in the above cases was made by plotting the cdfs of individual sections of the measured series (corresponding to specific states) and finding the Loo cdf that more closely fitted the measured cdf. After this process a ) were large number of Loo distribution parameters ( available for each environment, elevation, and state. The parameters shown in Tables XVI–XXI are averaged values. B. Wide-Band Model Parameters Wide-band data obtained from measurements using a sliding correlator channel sounder were analyzed. Two data sets from the university of Surrey, U.K., (L- and S-Bands) were studied. From the measured data (series of instantaneous power delay profiles, PDPs) corresponding to shadowed conditions (States 2 and 3) it was observed that due to sounder power limitations, the dynamic range available was too small to “see” most delayed echoes. It was thus decided to carry out the wide-band study (model parameter fitting) only for LOS (State-1) paths. This decision does not dramatically affect the possible use of this model for system performance and availability studies.

LMS systems are typically implemented with small fade margins; this means that, once the received signal is below a given threshold, i.e., when in states 2 and 3, system outage will occur regardless of channel-time dispersion. As for LOS paths (State-1), potential situations of unavailability will only occur when the channel time dispersion is significant compared to the inverse of the symbol rate. The parameter fitting procedure is illustrated with the aid of Fig. 26. In order to compare measured and simulated PDPs the internal signal processing in the channel sounder was emulated. Ideal instantaneous channel impulse responses (made up of delta functions) resulting from the channel model/simulator were passed through a filter representing the behavior and characteristics of the channel sounder. A first step before performing profile fitting was to compute the average of various neighboring measured PDPs in order to remove instantaneous multipath cancellation and enhancement effects (averaged power delay profiles, APDPs). A similar process was carried out for the simulated instantaneous PDPs. Model parameter extraction, in this case, was also carried out by comparing measured and modeled APDPs: their shapes, their average delays, and delay spreads. An example of model fitted APDP is shown in Fig. 10. Model parameters for homogeneous sections of the measured PDPs corresponding to different environments and elevations were obtained. Finally, all the parameters obtained for a given environment and elevation were av-

PÉREZ FONTÁN et al.: STATISTICAL MODELING OF THE LMS CHANNEL

TABLE XVIII MARKOV CHAIN MATRICES [P ] AND [W ] FOR VARIOUS ELEVATIONS. GERMANY NEEDLE TREES, 30 ELEVATION (IAS, GRAZ, Ka-BAND)



MARKOV CHAIN MATRICES AUSTRIA, TREE ALLEY,

TABLE XIX [P ] AND [W ] FOR VARIOUS ELEVATIONS. 30 ELEVATION (IAS, GRAZ, Ka-BAND)



eraged to provide a single value for each case considered (Tables XXII and XXIII). LOS power delay profiles were classified into the following three categories: — —

—

type 1.A—representing those APDPs with no features other than in the first delay bin; type 1.B—representing those APDPs with additional (i.e., with time disfeatures in delay bins 2, 3, 4, persion); type 2—those APDPs where long delays were observed (far echoes).

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TABLE XX MARKOV CHAIN MATRICES [P ] AND [W ] FOR VARIOUS ELEVATIONS. GERMANY/AUSTRIA, SUBURBAN, 30 ELEVATION (IAS, GRAZ, Ka-BAND)



TABLE XXI MARKOV CHAIN MATRICES [P ] AND [W ] FOR VARIOUS ELEVATIONS. GERMANY, URBAN, 30 ELEVATION (IAS, GRAZ, Ka-BAND)



In the extraction of model parameters from these three profile types, the criteria presented below were followed. —

—

For 1.A profiles, no wide-band model fitting was possible. The channel in this case may be considered to be narrow-band with respect to the characteristics of the channel sounder employed. For this case, model parameters obtained in narrow-band measurement campaigns can used (Tables II–XXI). For 1.B profiles, wide-band model fittings were performed and model parameters extracted. Also the occurrence probabilities of profiles 1.A and 1.B have been recorded (Tables XXII and XXIII).

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Fig. 26.

IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 50, NO. 6, NOVEMBER 2001

Simulation of the channel sounder. TABLE XXII L-BAND SURREY. PDP TYPE OCCURRENCE PROBABILITIES

—

Type 2 profiles occurred very seldom and its study is left out of this paper pending further analysis. The proposed APDP classification in types 1.A and 1.B (type 2 may be, in a first approach, disregarded given its very low occurrence probability) suggest a possible way of extending the narrow-band three-state Markov model to study wide-band conditions. In this enhanced model, only for the LOS state, the Markov chain is modified to include a split state-1: S-1 nondepressive and S-1 depressive. The Markov engine bounces back and forth from the nondepressive to the depressive states as illustrated in Fig. 27. For this wide-band model only occurrence probabilities have been obtained form measurements but no reliable transition probabilities are yet available. As indicated earlier, wide-band data from the University of Surrey, U.K., at L- and S-Band was analyzed. Radio-paths

were orthogonal with respect to the mobile route [2]. A channel sounder chip rate of 10 Mc/s was used with two different code and ). Extracted parameters from this lengths ( data set are listed in Tables XXII and XXIII. VII. CONCLUSION In this paper, a geometric-statistical model/simulator has been presented and described. The model is based on the assumption of the existence on three different rates of change in the main propagation channel elements: the direct signal that may undergo shadowing/blockage effects and the multipath (specular and diffuse). These three rates of variation are described by means of a three-state Markov chain, a log-normal distribution and the coherent sum of the direct ray and the multipath echoes, respectively. The model has been extended to

PÉREZ FONTÁN et al.: STATISTICAL MODELING OF THE LMS CHANNEL

TABLE XXIII L-BAND, SURREY. CLASS 1B PROFILES. FIT PARAMETERS ASSUMING Sp (DECAY SLOPE) 10 dB/s

=

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REFERENCES [1] H. Smith, S. K. Barton, J. G. Gardiner, and M. Sforza, “Characterization of the land mobile-satellite (LMS) channel at L and S bands: Narrowband measurements,”, Bradford, ESA AOPs 104 433/114 473, 1992. [2] B. G. Evans, G. Butt, M. J. Willis, and M. A. N. Parks, “Land mobile satellite wideband measurement experiment at L- and S-bands,” University of Surrey, ESA ESTEC Contract no. 10 528/93/NL/MB(SC), Final Rep., 1996. [3] E. Lutz et al., “The land mobile satellite communication channel-recording, statistics, and channel model,” IEEE Trans. Veh. Technol., vol. 30, pp. 375–386, May 1991. [4] B. Vucetic and J. Du, “Channel modeling and simulation in satellite mobile communication systems,” IEEE J. Select. Areas Commun., vol. 10, pp. 1209–1217, 1992. [5] F. P. Fontan, J. Pereda, M. J. Sedes, M. A. V. Castro, S. Buonomo, and P. Baptista, “Complex envelope three-state Markov chain simulator for the LMS channel,” Int. J. Satellite Commun., pp. 1–15, Jan. 1997. [6] C. Loo, “A statistical model for land mobile satellite link,” IEEE Trans. Veh. Technol., vol. VT-34, pp. 122–127, Aug. 1985. [7] A. Jahn, H. Bischl, and G. Heis, “Channel characterization of spread spectrum satellite communications,” in Proc. IEEE 4th Int. Symp. Spread Spectrum Techniques and Applications (ISSSTA’96), Mainz, Germany, Sept. 1996, pp. 1221–1226. [8] E. Lutz, “A Markov model for correlated land mobile satellite channels,” Int. J. Satellite Commun., vol. 13, pp. 333–339, 1996. [9] F. P. fontan, M. A. V. Castro, S. Buonomo, P. Baptista, and B. ArbesserRastburg, “S-band LMS propagation channel behavior for different environments, degrees of shadowing and elevation angles,” IEEE Trans. Broadcasting, vol. 44, pp. 40–76, Mar. 1998. [10] A. Jahn and E. Lutz, “Propagation Data and channel model for LMS systems,”, Final Rep. ESA PO 141 742. DLR, 1995. [11] F. Murr, S. Kastner-Puschl, B. Bolzano, and E. Kubista, “Land Mobile Satellite narrowband propagation measurement campaign at Ka-Band,”, ESTEC Contract 9949/92/NL, Final Rep., 1995. Fernando Pérez Fontán (M’96) was born in Vilagarcia de Arousa, Spain. He received the Diploma (telecommunications engineering) and Ph.D.degrees from the Polytechnic University of Madrid, Spain, in 1982 and 1992, respectively. He is a Senior Lecturer with the Telecommunications Engineering School, University of Vigo, Spain, where he teaches a graduate course on mobile communications. His main research interests are in the field of mobile propagation channel modeling, especially mobile satellite, and in link- and network-level performance evaluation of terrestrial and satellite mobile and broadcast networks. Maryan Vázquez-Castro was born in Vigo, Spain. She received the M.S. degree in telecommunications engineering in 1994 and the Ph.D. degree (cum laude) in 1998, both from the University of Vigo. Since 1998, she has been an Assistant Professor with the Theory of Signal and Communications Department, Carlos III University of Madrid, Spain. Her research interests are in the area of satellite channel modeling and spread spectrum communication systems.

Fig. 27.

Wide-band model.

describe both narrow- and wide-band conditions by assuming that individual multipath ray excess delays are exponentially distributed. Model parameters have been extracted from a comprehensive measurement campaign at L-, S-, and Ka-Bands for a number of elevations and environments. A fairly good agreement between measurements and model outputs has been observed in all cases. Specific areas of further work have been identified mainly in the modeling of highly depressive conditions in which a dual Markov model has been proposed for LOS situations.

Cristina Enjamio Cabado received the Diploma degree in telecommunications engineering from the University of Vigo, Spain, in 1999. She is currently working toward the Ph.D. degree at the same university. She is a part-time Research Student at the University of Portsmouth, U.K. Her main research interests are in the field of broad-band wireless access and propagation in millimeter wavelengths. Jorge Pita García was born in Madrid, Spain, in 1974. He received the Diploma degree in telecommunications engineering from the University of Vigo, Spain, in 1998. He is currently working toward the Ph.D. degree at the same university. Since 2000, he has been with the Wave Interaction and Propagation Section, European Space Agency (ESA), Noordwijk, The Netherlands. Erwin Kubista received the Dipl. Ing. degree in telecommunications and electronic engineering from the Technical University of Graz, Austria, in 1985. From 1985 to 1989, his was a Research Assistant in the Department of Communications and Wave Propagation, Technical University of Graz, responsible for radiometer diversity data analysis and processing under the European Space Agency (ESA) and European Union (EU) contracts.