Question

Can use some assistance with a question from someone familiar with (and using) MATLab. This has to do with understanding Raleigh Channels (Wireless Networking and communications)

Use MatLab’s Communications toolbox to model Flat and Frequency Selective Rayleigh channels, and to simulate and analyze the effects of these channels on transmitted signals.

Question: Obtain a Rayleigh fading envelope plot. Generating a plot for fd=30, discuss in detail what the plot indicates.

Answer 1

18.2 The Challenge of a Fading Channel In the study of communication systems, the classical (ideal) additive-white-Gaussian-noise (AWGN) channel, with statistically independent Gaussian noise samples corrupting data samples free of inter- symbol interference (ISI), is the usual starting point for understanding basic performance relation- ships. The primary source of performance degradation is thermal noise generated in the receiver Often, external interference received by the antenna is more significant than the thermal noise. This external interference can sometimes be characterized as having a broadband spectrum and quantified by a parameter called antenna temperature [1]. The thermal noise usually has a flat power spectral density over the signal band and a zero-mean Gaussian voltage probability density function (pdf) When modeling practical systems, the next step is the introduction of bandlimiting filters. The filter in the transmitter usually serves to satisfy some regulatory requirement on spectral containment. The filter in the receiver often serves the purpose of a classical "matched filter" [2] to the signal bandwidth. Due to the bandlimiting and phase-distortion properties of filters, special signal design and equalization techniques may be required to mitigate the filter-induced ISI. If a radio channel's propagating characteristics are not specified, one usually infers that the signal The model of free space treats the region between the transmit and receive antennas as being free of all objects that might absorb or reflect radio frequency (RF) energy. It also assumes that, within this region, the atmosphere behaves as a perfectly uniform and nonabsorbing medium. Furthermore, the earth is treated as being infinitely far away from the propagating signal (or, equivalently, as having a reflection coefficient that is negligible). Basically, in this idealized free-space model, the attenuation of RF energy between the transmitter and receiver behaves according to an inverse-square law. The received power expressed in terms of transmitted power is attenuated by a factor, L, (d), where this factor is called path loss or attenuation vs. distance behaves as if propagation takes place over ideal free space.

In Eq. (18. l), d is the distance between the transmitter and the receiver, and λ is the wavelength of the propagating signal. For this case of idealized propagation, received signal power is very predictable For most practical channels, where signal propagation takes place in the atmosphere and near the ground, the free-space propagation model is inadequate to describe the channel and predict system performance. In a wireless mobile communication system, a signal can travel from transmitter to receiver over multiple reflective paths; this phenomenon is referred to as multipath propagation. The effect can cause fluctuations in the received signal's amplitude, phase, and angle of arrival, giving rise to the terminology multipath fading. Another name, scintillation, having originated in radio astronomy, is used to describe the multipath fading caused by physical changes in the propagating medium, such as variations in the density of ions in the ionospheric layers that reflect high frequency (HF) radio signals. Both names, fading and scintillation, refer to a signal's random fluctuations or fading due to multipath propagation. The main difference is that scintillation involves mechanisms (e.g. ions) that are much smaller than a wavelength. The end-to-end modeling and design of systems that mitigate the effects of fading are usually more challenging than those whose sole source of performance degradation is AWGN 18.3 Mobile-Radio Propagation: Large-Scale Fading and Small- Figure 18.1 represents an overview of fading channel manifestations. It starts with two types of fading effects that characterize mobile communications: I Large-scale fading represents the average signal power attenuation or the path loss due to motion over large areas. In Fig. 18.1, the large-scale fading manifestation is shown in blocks 1, 2, and 3. This phenomenon is affected by prominent terrain contours (e.g., hills, forests, billboards, clumps of buildings, etc.) between the transmitter and receiver. The receiver is often represented as being "shadowed" by such prominences. The statistics of large-scale fading provide a way of computing an estimate of path loss as a function of distance. This is described in terms of a mean-path loss (nth-power law) and a log-normally distributed variation about the mean. Small-scale fading refers to the dramatic changes in signal amplitude and phase that can be experienced as a result of small changes (as small as a half-wavelength) in the spatial separation between a receiver and transmitter. As indicated in Fig. 18.1, blocks 4, 5, and 6, small-scale fading manifests itself in two mechanisms, namely. time-spreading of the signal (or signal dispersion) and time-variant behavior of the channel. For mobile-radio applications, the channel is time-variant because motion between the transmitter and receiver results in propagation path changes. The rate of change of these propagation conditions le fading and small-scale fading

FADING CHANNEL MANIFESTATIONS LARGE-SCALE FADING DUE TO MOTION OVER LARGE AREAS SMALL SCALE FADING DUE TO SMALL CHANGES IN POSITION MEAN SIGNAL- ATTENUATION VS DISTANCE VARIATIONS ABOUT THE MEAN TIME SPREADING OF THE SIGNAL TIME VARIANCE OF THE CHANNEL 10 13 16 TIME-DELAY DOMAIN DESCRIPTION DOPPLER-SHIFT TIME DOMAIN DESCRIPTION Fourier Transforms -Transforms FourierDOMAIN FREQUENCY DESCRIPTION DESCRIPTION Duals 17 18 FREQUENCY SELECTIVE FADING FLAT FADING FAST FADING SLOW FADING 12 14 15 FREQUENCY SELECTIVE FADING FLAT FADING FAST FADING SLOW FADING

. Reflection occurs when a propagating electromagnetic wave impinges upon a smooth surface with very large dimensions compared to the RF signal wavelength (a) Diffraction occurs when the radio path between the transmitter and receiver is obstructed by a dense body with large dimensions compared to , causing secondary waves to be formed behind the obstructing body. Diffraction is a phenomenon that accounts for RF energy travelling from transmitter to receiver without a line-of-sight path between the two. It is often termed shadowing because the diffracted field can reach the receiver even . when shadowed by an impenetrable obstruction. Scattering occurs when a radio wave impinges on either a large rough surface or any surface whose dimensions are on the order of a or less, causing the reflected energy to spread out (scatter) in all directions. In an urban environment, typical signal obstructions that yield scattering are lampposts, street signs, and foliage Figure 18.1 may serve as a table of contents for the sections that follow. We will examine the two manifestations of small-scale fading: signal time-spreading (signal dispersion) and the time-variant nature of the channel. These examinations will take place in two domains: time and frequency. as indicated in Fig. 18.1, blocks 7, 10, 13, and 16. For signal dispersion, we categorize the fading degradation types as being frequency-selective or frequency-nonselective (flat), as listed in blocks 8, 9, 11, and 12. For the time-variant manifestation, we categorize the fading degradation types as fast fading or slow-fading, as listed in blocks 14, 15, 17, and 18. The labels indicating Fourier transforms and duals will be explained later. Figure 18.2 illustrates the various contributions that must be considered when estimating path loss for a link budget analysis in a cellular application [4]. These contributions are: . Mean path loss as a function of distance, due to large-scale fading Near-worst-case variations about the mean path loss (typically 6-10 dB) or large-scale fading margin Near-worst-case Rayleigh or small-scale fading margin (typically 20-30 dB) In Fig. 18.2, the annotations* ะ 1-2% "indicate a suggested area (probability) under the tail ofeach to provide adequate received n goal. H lence, the amount of margin indicated is intended signal power for approximately 98-99% of each type of fading variation (large-and small-scale) A received signal, is generally described in terms of a transmitted signal s(t) convolved with the impulse response of the channel he). Neglecting the degradation due to noise, we write: r(t)()he(t) (18.2)

In Fig. 18.2, the annotations* ะ 1-2% "indicate a suggested area (probability) under the tail ofeach pdf as a design goal. Hence, the amount of margin indicated is intended to provide adequate received signal power for approximately 98-99% of each type of fading variation (large-and small-scale) A received signal, is generally described in terms of a transmitted signal s(t) convolved with the impulse response of the channel he). Neglecting the degradation due to noise, we write: r(t)()he(t) (18.2) where * denotes convolution. In the case of mobile radios, r(t) can be partitioned in terms of two component random variables, as follows [5] r(t) = m(t) ro(1) (18.3) where m(t) is called the large-scale-fading component, and ro(t) is called the small-scale-fading component. m(t) is sometimes referred to as the local mean or log-normal fading because the magnitude of m(t) is described by a log-normal pdf (or, equivalently, the magnitude measured in decibels has a Gaussian pdf). ro(t) is sometimes referred to as multipath or Rayleigh fading. Figure 18.3 illustrates the relationship between large-scale and small-scale fading. In Fig. 18.3(a) received signal power r() vs. antenna displacement (typically in units of wavelength) is plotted for the case of a mobile radio. Small-scale fading superimposed on large-scale fading can be readily

BASE STATION MOBILE STATION DISTANCE POWER TRANSMITTED MEAN PATH LOSS LOG-NORMAL LARGE-SCALE FADING LARGE-SCALE FADING MARGIN # 1-2% RAYLEIGH SMALL-SCALE FADING SMALL-SCALE FADING MARGIN POWER RECEIVED # 1-2% FIGURE 18.2: Link-budget considerations for a fading channel. identified. The typical antenna displacement between the small-scale signal nulls is approximately a half wavelength. In Fig. 18.3(b), the large-scale fading or local mean, m(t), has been removed in order to view the small-scale fading. ro(t), about some average constant power In the sections that follow, weenumerate some of the details regarding the statistics and mechanisms of large-scale and small-scale fading.

Signal Power (dB)t r(t) m(t) Antenna Signal Power (d B) Fo (t) Antenna Displacemert FIGURE 18.3: Large-scale fading and small scale fading.