This research deals with different aspects of channel modeling in land mobile satellite communications (LMS). Land Mobile Satellite Communications (LMSC) is part of Global Mobile Satellite Communications (GMSC), which provides global communications services to end users from a GEO (Geostationary Earth Orbit) or non-GEO satellite.
Issues in LMS Channel Modeling
However, to calculate the power spectral density and autocorrelation function of the received signal, the autocorrelation expression of the envelope with a certain statistical distribution must be related to the expression formulated in some analytical model. One popular example is [16], where the autocovariance of the Nakagami-m distributed envelope was related to the same envelope of the received signal formulated in [17–19].
Relevant Works in LMS Channel Modeling
Broadband effects are usually studied via delay profile of multipaths or impulse response of the channel. The effect of the channel impulse response is generally represented by a tapped delay line structure.
Motivation of the Present Work
Thesis Contribution
Organization of the Thesis
Satellite Unavailability: A single satellite may not be sufficient to maintain the minimum received signal power necessary for reliable communications. Fluctuation in signal amplitude and phase: While shadowing from large obstacles is responsible for low received power, scattered reflection from objects in the immediate vicinity of the receiver causes the reception of numerous electromagnetic waves attenuated and phase-shifted to an uncertain amount.
Propagation Effects in Land Mobile Satellite Channel
Propagation Characteristics of Land Mobile Satellite (LMS) Channel
Faraday rotation is defined as the rotation of the polarization axis of a non-circularly polarized wave caused by the ionosphere. The loss due to polarization rotation can be eliminated by using circular polarization of the carriers.
Modeling Approaches for Land Mobile Satellite Channel
Impulse Response Model of Wireless Multipath Channel
However, if the symbol period is so small that only one multipath signal arrives during the symbol period, then small-scale fading does not occur because the multipath can be resolved. In the case of narrowband transmission, almost all multipaths cannot be resolved and arrive within the symbol period.
Narrowband modeling
- Empirical models
- Analytical models
- Statistical models
Another quantity called the coherence time is used to represent the time-varying nature of the impulse response of the channel. The Doppler PSD can be evaluated by the Fourier transform of the autocovariance function and it is shown in [1] that it does not have a discontinuity like the Doppler PSD calculated in [19]. Instead, statistical distributions are assigned for the envelope and phase of the received signal with the goal of adequately matching the statistics of measured data collected at one or more locations.
As can be seen from the table, some models consider the connection of the two processes as additive [22, 23] or multiplicative [24]. Different propagation conditions due to frequent changes in satellite elevation angle cannot be modeled by a single distribution as the mobile receiver travels from one propagation scenario to another (eg urban to rural). The envelope and phase of this additional scattered component are independent of R, which includes the LOS and another part of the scattered components.
Wideband Modeling
For statistical analysis, all dominant and non-dominant components of the received signal are combined into a random complex envelope process with a single mixture distribution to describe all types of fading experienced by the different components. The relative power and delays of distinguishable groups of received multipaths are described by the impulse response of the channel. In other words, if the narrowband model is already proven to be useful in a particular propagation scenario, the path distribution in the channel impulse response (CIR) can be obtained by simply dividing the narrowband complex envelope process into distinguishable groups of dominant and nondominant components and arranging the corresponding simpler distribution.
The Doppler power spectral density (PSD), another important quantity in narrowband modeling, of the non-dominant scattered components is usually kept the same for trajectories that represent distinguishable groups of non-dominant components in the CIR. Most researchers wanted to propose the distribution of branch gain, delay and Doppler spectrum of each branch [29–31]. The excess delay and power of the taps and the number of multipaths in case of near and far echo are modeled with different statistics.
Summary
Flat areas with low clustering density
Non-flat or tree-covered area
High clustering density with LOS blocked
Open area with few obstacles
Effect of Circular Polarization in Small-Scale Fading of Received Electric Field
Effect of Antenna Directivity in Three-dimensional Scattering Model
In the direction of one of the motives of this thesis, we also provide a rationale for using the additive or multiplicative interaction of the small-scale fading process and the shadow fading process in connection with actual propagation phenomena. One of the main goals of this thesis is to present the effects of propagation in different types of propagation situations. In other words, the mathematical expression for the complex envelope should provide insight into the effect of actual propagation phenomena in a given propagation scenario.
Thus, the small-scale fading of the scattered components can be represented by a complex constant-power envelope process, while a separate random process describes the shadow-faded LOS. In areas where the LOS path is unblocked (eg rural areas, farmland, coasts), there must be a constant in the complex envelope along with the in-phase and quadrature components of the scattered components. Thus, keeping the EoA pdf the same as [1], it turns out to be the normalized autocovariance or autocorrelation function rρ(τ) of the zero-mean complex Gaussian envelope of scattered multipath components.
Summary
First Order Statistics
Now, with the transformation from Cartesian to polar coordinates, we get the total conditional pdf pR,Θ(r, θ|Y =y) as [60]. Under certain conditions, if there is no shadow fading, the total envelope phase distribution in equation (4.4) indicates a new distribution.
Second Order Statistics
- LCR and AFD
- Normalization with respect to Maximum Doppler Frequency Using
Results and Discussions
We, thus, present a comparison of the LCR derived from our proposed model with the same data in [22,23] along with the same parameters and show this result in Figure 4.2(a) and 4.2(b ). As can be observed from Figure 4.2 (a) and 4.2 (b), the LCR curves obtained from our proposed model have only good correlation with the existing additive Rayleigh-lognormal models [22,23]. In Figure 4.3, the analytically calculated LCR is compared with the LCR curve of peripheral measurement data reproduced from [20].
Like Figures 4.1(a) and 4.1(b), similar grouping is also possible here, depicting the dominance of small-scale blurring for R¿S0 and of shadow blurring in the reverse case. In accordance with Figure 4.2(a) and 4.2(b), AFD curves obtained from the proposed model are consistent with the curves of existing additional Rayleigh lognormal model [22] when meq = 1 and which higher fading duration for meq < 1 tone , thus reflecting the ability of the proposed model to depict more severe fading conditions. It is shown in Figure 4.5 that the AFD curve of our model is in good agreement with suburban measurement curve of AFD reproduced from [20] and also outperforms other related models [22,23].
Special Cases
Absence of LOS: Nakagami-q envelope process
Absence of Shadow Fading: Extended Nakagami-q Distribution
- Relation with Nakagami-m, Rician and Rayleigh Distribution
Summary
First and Second Order Statistics
Since both ˙X and ˙Z are zero-mean processes, the intervariance functions in the covariance matrix K are replaced by the corresponding cross-correlation functions. To calculate second-order statistics such as LCR and AFD, the moment of observation time for all processes must be the same, implying that τ = 0 must be set for all correlation functions in K. By integrating forzand ˙ z, we obtain the expression for the coupling pdfpRR˙(r,r) of the signal envelope˙ (R) and its time derivative (˙R) as.
Effect of 3D Scattering Model on the Derived Statistics
Analysis of Results
Since the expressions of LCR were not given in [10, 24], we derive them for the sake of comparison.
Summary
First and Second-Order Statistics in Wideband LMS Channel Model
Initial Considerations
We hereby consider four different propagation scenarios discussed in Section 3.1 for broadband LMS channel modeling.
Calculation of CDF, LCR and AFD
- Propagation scenario – flat areas with low clustering density
- Propagation scenario – non-flat or tree-covered area
- Propagation scenario – High clustering density with LOS blocked . 73
The statistical distribution for lag bin 0 is the same as that of first dominant path - lognormal in this case. The expression of the pdf at a specific delay bin (other than 0th bin) is (equation 4.6). The expression of LCR at a specific delay bin (other than 0th bin) is (equation 4.15) LCRRth|∆τi = Rth.
The expression of LCR, as given in section 5.2 and repeated here, for a specific delay bin, . whereσi2in a particular delay bin is the cumulative sum of allσ2 up to that particular bin, i.e. LCR calculated for different multipath arrival rate λ is shown in Fig. 6.2 plotted, LCR curves do not move up as multipath arrival rate is increased. The expression of LCR, given in [59] and repeated here, for a specific delay bin, . 6.14) LCR calculated for different multipath arrival rates is shown in Fig.
Calculation of Statistics in a State-based Model
Summary
In this chapter we endeavor to calculate the capacity of the channels presented in earlier chapters, both in ergodic and non-ergodic condition. Calculation of ergodic capacity for frequency-selective fading channel usually involves the random channel matrix with the fading coefficients of the channel impulse response as its elements. Simplification has been attempted by researchers mostly by avoiding direct involvement of the channel matrix.
The productFG stands for Fourier transform of the diagonal coefficients (Gi) and GandFx indicates the Fourier transform of the transmitted symbols. With the assumption of unavailability of LOS or other dominant path and shadow blurring, if the fading envelope of the multipaths or Hare's elements is represented with a complex equal-variance Gaussian distribution (i.e., the absolute values are Rayleigh), then Gi is a series of also complex Gaussian variables. Thus, the expression for channel capacity is given by (assuming the channel.
Capacity versus outage
An example of calculating capacity in state-based channel model
Summary
In this thesis, we propose several narrowband and wideband channel models based on a newly identified complex envelope process and a modified 3D scattering model for LMS communication. In this section, we briefly summarize and discuss our contributions and findings during this thesis work. Then we proposed mathematical expressions for the complex envelope that should give an insight into the effect of the actual propagation phenomena in a particular propagation scenario.
We formulated the effect of circular polarization on the received electric field and found that it has no additional effect on the attributes of the received signal in an LMS system. Finally, we incorporated the directional effect of LMS antenna systems, in general, into the 3D scattering models available in the literature and formulated the autocovariance function. We proposed two narrowband models using the complex additive and multiplicative convolution process with a Doppler PSD generated from the 3D scattering model introduced earlier.
Suggestions for Future Work
Harles, “Measurement and modeling of the Ku-band land mobile satellite channel,” IEEE Trans. Matt, “Propagation measurements for land mobile satellite services,” in 33rd IEEE Vehicular Technology Conference, vol. Laue, “Study of a Land Mobile Satellite Channel Model with Asymmetric Doppler Power Spectrum and Logarithmically Distributed Field-of-View Component,” IEEE Trans.
Vatalaro, “A statistical model for land mobile satellite channels and its application to non-geostationary orbit systems,” IEEE Trans. Ernst, “Comparison of statistical properties of a land mobile satellite channel in the Ku, Ka and EHF bands,” in IEEE Veh. 43] ——, “Fade statistics of a mobile satellite system for shading and multipath from roadside trees at UHF and L-band,” IEEE Trans.
Comparison of Single Distribution LMS Channel Models
Comparison of State-oriented LMS Channel Models
List of Channel Models Available in Literature
List of State-oriented Models available in Literature
Parameters for the analytical models
