As a consequence of the growing interest in wireless communications systems, much effort is being devoted to the channel characterization and modelling. This is obvious since the performance depends fundamentally on the channels under consideration, so a communication system design must be preceded by the study of channel characteristics. This chapter considers the propagation environment in which a wireless system operates. In other words, we are primarily interested in the characterization of radio links between the transmitter and the receiver antenna that will be modelled by randomly time-variant linear systems. Wireless communication channels are usually described by considering three separable phenomena, namely, path loss, shadowing, and multipath fading. In the following, we briefly overview various efforts to characterize such aspects of wireless communication channels. Firstly, in this chapter we address the estimation of signal decay due to propagation loss which is very important in the determination of the necessary transmission power and the coverage area. Although propagation loss models are sometimes quite accurate, they generally fail to predict signal fluctuations due to the effect of the terrain near the antenna. Such a phenomenon of signal fluctuations is usually called shadowing. However, the effect of multipath fading is generally more complex because it does not only change in time but also varies over frequency. As a result, this topic will also be presented in enough depth and a number of statistical models will be studied. Moreover, the various categories of fading will be discussed. Finally, a novel small-scale model derived by the author is presented in order to give a recent application of the theory.
The mobile terminal operates in a dynamic, often hostile environment in which propagation conditions are constantly changing and have a significant impact on the achievable quality of service (QoS). The time-varying nature of the wireless mobile channel makes channel characterization and its analysis an important issue. In a mobile wireless scenario, the time-varying nature of the channel could be encountered in many different ways, e.g., a relative motion between the transmitter and the receiver, time variation in the structure of the medium, etc. All these scenarios make the channel characteristics random, and do not offer any easy analysis on the signals, transmitted through this channel. The strength of the received signal depends on the characteristics of the channel and on the distance between the transmitter and the receiver. In general, as an information signal propagates through the channel, the strength of this signal decreases as the distance between the transmitter and receiver increases.
In this chapter, at first we give mathematical representations of the transmitted and received signals. Then, the characterization of the variation in received signal power over distance due to path loss and shadowing follows. Path loss is caused by dissipation of the power radiated by the transmitter as well as effects of the propagation channel. Path loss models generally assume that path loss is the same at a given transmit-receive distance1. We present the simplest model for signal propagation: free space path loss. A signal propagating between two points with no attenuation or reflection follows the free space propagation law. We also describe empirical models with parameters based on measurements for both indoor and outdoor channels. Shadowing is caused by obstacles between the transmitter and receiver that attenuate the signal power through absorption, reflection, scattering, and diffraction. In modern wireless communications, the effect of shadowing is usually compensated in the network layer by power control and/or rate adjustment. For the evaluation of such technologies, statistical description of the shadowing loss by a log-normal distribution provides useful insights and effective analytical channel models. The log-normal model based on a large number of shadowing objects is also given. When the attenuation is very strong, the signal is blocked. Variation due to path loss occurs over very large distances (100-1000 meters), whereas variation due to shadowing occurs over distances proportional to the length of the obstructing object (10-100 meters in outdoor environments and less in indoor environments). Since variations due to path loss and shadowing occur over relatively large distances, this variation is sometimes referred to as large-scale propagation effects. Also, we deal with the variation due to the constructive and destructive addition of multipath signal components. Variation due to multipath occurs over very short distances, on the order of the signal wavelength, so these variations are sometimes referred to as small-scale propagation effects. When the number of multipath components is large, or the geometry and dielectric properties of the propagation environment are unknown, statistical models must be used. The autocorrelation, cross correlation, and power spectral density of a received narrowband signal are presented and studied in depth. The case of uniform scattering is investigated. A thorough review of the most accepted statistical models proposed in the scientific literature is presented, considering small-scale fading. The level crossing rate (LCR) and the average duration of fades (AFD) are defined and given for the most basic models. Moreover, the wideband fading is presented and characterized by the equivalent lowpass time-varying channel impulse response and using it we can describe the channel in terms of certain parameters and define categories of the fading occurred. Finally, a novel small-scale model derived by the author is presented in order to give a recent application of the theory. In Figure 1 is illustrated the ratio of the received-to-transmit power in dB versus log-distance for the combined effects of path loss, shadowing, and multipath fading. We can observe clearly the very rapid variations due to multipath fading which change on the order of half the signal wavelength.
Path loss, shadowing and multipath fading versus distance
Key Terms in this Chapter
QoS: Quality of Service
AFD: Average Fade Duration
CCDF: Complementary Contribution Distribution Function
WSS: Wide-Sense Stationary
LCR: Level Crossing Rate
JPDF: Joint Probability Density Function
GRLN: Generalized Rice–Lognormal
PSD: Power Spectral Density
BER: Bit Error Rate
ISI: Intersymbol Interference