2 Characterization of Propagation Channels a ysis of any neoosaadndomspeoadosp coya r() N Figure 2.1 A wireless communication system consisting of three parts
2 Characterization of Propagation Channels In general, any wireless communication systems include three parts, i.e., transmitter (Tx), receiver (Rx), and wireless channel in between to connect them, as shown in FIGURE 3.1. Unlike the Tx and Rx, which can be designed to make the system present better tradeoff between reliability and efficiency, the wireless channel cannot be engineered. However, reliable knowledge of the propagation channel serves as the enabling foundation for the design and analysis of any wireless communication system. Various concepts and definitions of the wireless channel usually make the beginner get lost. This chapter will manage to provide a unified and conceptually simple explanation of a morass of concepts for wireless channels. This is a Book Title Name of the Author/Editor c XXXX John Wiley & Sons, Ltd Figure 2.1 A wireless communication system consisting of three parts
22 Characterization of Propagation Channels 2.1 Three Phenomena in Wireless Channels is what wireless channels ding can path oss and Path loss,P,and shadowing,S,belong to large scale fading since they are dominant when the mobile station moves over distance al tens of wavelengths wavelengths.Shadowingis the slow variations of the received signal power over distances of several ten or hundred of the T and Rx.and are observed over distance of the order of the wavelength g=P.S.h (2.1) where P is path loss,s is shadowing,and h is multipath fading.It must be noted that throughout this book,we
22 Characterization of Propagation Channels 2.1 Three Phenomena in Wireless Channels Wireless channels are the real environments, in which the Tx and Rx are operating. Fading is what wireless channels bring to us. Fading refers to the time variation of the received signal power induced by changes in the transmission medium or path. Generally speaking, fading can be categorized as large-scale fading, consisting of path loss and shadowing, and small-scale fading. Therefore, in total we have three phenomena in wireless channels. Path loss, P, and shadowing, S, belong to large-scale fading since they are dominant when the mobile station moves over distances of several tens of wavelengths. As shown in FIGURE 3.2, path lose P means the attenuation in the transmitted signal while propagating from the Tx to Rx and is observed over distance of several hundred or thousand wavelengths. Shadowing S is the slow variations of the received signal power over distances of several ten or hundred wavelengths due to large terrain features such as buildings and hills. Large-scale fading is very important for the system design at the network level. For example, the cell coverage area, outage, and handoffs are influenced by these effects. On the other hand, small-scale fading appears due to the multipath propagation. As shown in FIGURE 3.2, multipath fading, h, refers to fast variations of the received signal power due to the constructive and destructive interference of the multiple signal paths between the Tx and Rx, and are observed over distance of the order of the wavelength. Small-scale fading plays an important role in determining the link level performance according to bit error rates, average fade durations, etc. Therefore, as shown in FIGURE 3.1, to completely characterize wireless channels, we can use the following expression g = P · S · h (2.1) where P is path loss, S is shadowing, and h is multipath fading. It must be noted that throughout this book, we constrain our interests in the investigation and modeling of small-scale fading for different types of channels, e.g., F2M channels, V2V channels, cooperative MIMO channels, etc
Characterization of Propagation Channels 23 Mutipath fading Path loss Shadowing Distance between the Tx and Rx Path Loss,PShedowisg,.合Mtipsth Fading,工+g=P.S.h Large Sehle Fading Small Schle Fading Figure 2.2 Three phenomena in wireless channels
Characterization of Propagation Channels 23 Figure 2.2 Three phenomena in wireless channels
24 Characterization of Propagation Channels 2.2 Path loss and shadowing Path loss is the attenuation in the transmitted sign al while pr ation ie cauced PR-PrG1GRD 入2 2.2) e the smit and re elv A is the A.Shorter the wavelength,higher the path loss. e p path loss in different propagation environments such as urban,rural,and indoor areas.Experiments show that the pootieaearohn8etmghieheatrgnuaioathanfie-pacepropagaioncondions.A ving can be modeled as a log-normal random variable,which is consistent with shown shadowing is due to the pow wer loss blocked by big objects,e.g high bu 1n8 e know tha the shad wing fulfills norm al distribution,ie.,Gaussian distribution,in the log domain,and thus the (2.3 206 can befod of the sh wing.Typic 2.3 Multipath fading agation mechanism manifested when the transmitted signal reaches the Rx by two ns and buildings,ofter path 0) obstructsa direct waves must pr ays.The muliple waves combine vectorially at the receiver antenna s mentioned above.the presence of local scatterers gives rise to NLoS scenarios,where Rayleigh distribution is the most popular distribution used to describe the Input delay-spread function (channel impulse response)) Output doppler-spread function)
24 Characterization of Propagation Channels 2.2 Path loss and shadowing Path loss is the attenuation in the transmitted signal while propagating from the Tx and Rx. This attenuation is caused by the effects such as free-space loss, refraction, diffraction, and reflection. Significant variations in the path loss are observed over distance of several hundred or thousand wavelengths. The simplest path loss model corresponds to a propagation in free space, i.e., line-of-sight (LoS) link between the Tx and Rx. In this case, the received signal power can be expressed as ? PR = PT GTGR λ 2 4πD2 (2.2) where PT is the transmitted power, GT and GR are the transmit and receive antenna gains, respectively, λ is the carrier wavelength, and D is the distance between the Tx and Rx. Note that the path loss exponents (i.e., the power of the distance dependence D) are 2 for free-space propagation. Therefore, the received power decreases with a factor of distance-squared under free-space propagation. (2.2) also shows the path loss dependency on the carrier wavelength λ. Shorter the wavelength, higher the path loss. However, in a real environment, the wireless signals seldom experience the free-space propagation. Therefore, several different models such as the Okumura-Hata ??, Lee ?, Walfish-Ikegami ?, etc., have been proposed to model path loss in different propagation environments such as urban, rural, and indoor areas. Experiments show that the actual path loss exponents are around 3–8, suggesting higher attenuation than free-space propagation conditions. A detailed description of different path loss models can be found in ?. The aforementioned path loss models assume that the path loss is constant at a given distance. However, the presence of obstacles, e.g., buildings and trees, leads to random variations of the received power at a given distance. This effects is termed shadowing (shadow fading). Experiments illustrate that shadowing can be modeled as a log-normal random variable, which is consistent with our intuition. As shown in FIGURE 3.2, shadowing is due to the power loss blocked by big objects, e.g., high buildings. Therefore, the total power loss, i.e., shadowing, can be calculated by multiplying every power loss caused by big objects. In log domain, the multiplication becomes the addition of every power loss. Based on the central limit theory ?, we know that the shadowing fulfills normal distribution, i.e., Gaussian distribution, in the log domain, and thus the shadowing can be modeled as a log-normal distribution. Therefore, the shadowing distribution is given by ? fΩp (x) = 10 xσΩp √ 2π ln 10 exp " − 10 log10 x − µΩp(dBm) 2 2σ 2 Ωp # (2.3) where Ωp denotes the mean squared envelope level, µΩp designates the area mean expressed in dBm, and σΩp is the standard deviation of the shadowing. Typical values of σΩp range from 5 to 10 dB. Detailed discussions of shadowing can be found in ?. 2.3 Multipath fading Multipath propagation is the propagation mechanism manifested when the transmitted signal reaches the Rx by two or more paths. The presence of local scatterers, e.g., mountains and buildings, often obstructs a direct wave path between the Tx and Rx (i.e., the LoS). Therefore, a non-LoS (NLoS) propagation path will appear between the Tx and Rx. Consequently, the waves must propagate through reflection, diffraction, and scattering. This results in the received waves from various directions with different delays. The multiple waves combine vectorially at the receiver antenna (a phenomenon called multipath fading) to produce a composite received signal. As mentioned above, the presence of local scatterers gives rise to NLoS scenarios, where Rayleigh distribution is the most popular distribution used to describe the fading envelope. Some types of scattering environments have a specular component, i.e., LoS or a strong reflected path. These scattering environments are called LoS scenarios, where Ricean distribution is used to describe the fading envelope. A non-directional channel can be characterised by one of the four system functions also termed as the first set of Bello’s functions ?. These four system functions of non-directional channel are the • Input delay-spread function (channel impulse response) h(t, τ′ ) • Output doppler-spread function H(fD, fc)
Characterization of Propagation Channels 25 h(t.r) G,) Figure 2.3 Fourier relationship between the system functions of non-directional channels. fodm(fp,,到 Fori Trasfomm G,到。t foog(f. Mt,,。 fH(p fe. Figure 2.4 Fourier relationship between the system functions of directional channels. Delay-Doppler-spread function(spread function)(fp.) .Time-variant transfer function G(t,f) Wheresfoeeight system functions?,which are extended from the traditional four system fnctionstbxineoporninganothertioimYdomansdirecion sPme.needConsndeinhthe system eaking.double-directional channel description)is ver ns here we gi dired onal channels and invite interested readers to refer to ??The eight system functions of
Characterization of Propagation Channels 25 Figure 2.3 Fourier relationship between the system functions of non-directional channels. Figure 2.4 Fourier relationship between the system functions of directional channels. • Delay-Doppler-spread function (spread function) g(fD, τ′ ) • Time-variant transfer function G(t, fc) where t denotes the time, τ ′ designates the time delay, fc is the carrier frequency, and fD is the Doppler shift. The Fourier relationship between the system functions is shown in FIGURE 3.3. Whereas for a directional channel, eight system functions ?, which are extended from the traditional four system functions by incorporating another two terms/domains (direction and space), can be used. Considering that the system functions of directional channels include those of non-directional channels as special cases and directional channel description (strictly speaking, double-directional channel description) is very useful for MIMO systems, here we give a brief overview of directional channels and invite interested readers to refer to ??. The eight system functions of directional channels are the