Classification of Fading
We consider three types of channels to place bounds on radio system performance:
• Gaussian channel
• Rayleigh channel
• Rician channel
10.4.2.1 The Gaussian Channel. The Gaussian channel can be considered the ideal channel, and it is only impaired by additive white Gaussian noise (AWGN) developed internally by the receiver. We hope to achieve a BER typical of a Gaussian channel when we have done everything we can to mitigate fading and its results. These efforts could be diversity, equalization, and FEC coding with interleaving. The ideal Gaussian channel is very difficult to achieve in the mobile radio environment.
10.4.2.2 The Rayleigh Channel. The Rayleigh channel is at the other end of the line, often referred to as a worst-case channel. Remember, in Chapter 2, we treated fading on LOS microwave as Rayleigh fading, which gave us the very worst-case fading scenario. Figure 10.7 shows a channel approaching Rayleigh fading characteristics. Of course, we are dealing with multipath here. We showed that in the mobile radio scenario, multipath reception commonly had many components. Thus, if each multipath component is independent, the PDF (power distribution function) of its envelope is Rayleigh.
10.4.2.3 The Rician Channel. The characteristics of a Rician channel are in-between those of a Gaussian channel and those of a Rayleigh channel. The channels can be characterized by a function K (not to be confused with the K-factor in Chapter 2). K is defined as follows:
power in the dominant path
power in the scattered paths
As cells get smaller, the LOS component becomes more and more dominant. There are many cases, in fact nearly all cases where there is no full shadowing, in which there is a LOS component and scattered components. This is a typical multipath scenario. Turning now to equation (10.9), when
- Figure 10.7. Typical Rayleigh fading envelope and phase in a mobile scenario. Vehicle speed is about 30 mph; frequency is 900 MHz. (From Figure 1.1, Ref. 3.)
K = 0, the channel is Rayleigh (i.e., the numerator is 0 and all the received energy derives from scattered paths). When K = the channel is Gaussian and the denominator is zero. Figure 10.8 gives BER values for some typical values of K. It shows that those intermediate values of K provide a superior BER than for the Rayleigh channel where K = 0. For a microcell mobile scenario, values of K vary from 5 to 30 (Ref. 3). Larger cells tend more toward low values of K.
There is also an advantage for Rician fading with higher values of K regarding co-channel interference performance for a desired BER. The smaller the cell, the more fading becomes Rician, approaching the higher values of K.
- Figure 10.8. BER versus channel SNR for various values of K; noncoherent FSK. (From Figure 1.7, Ref. 3.)
10.4.3 Diversity—A Technique to Mitigate the Effects of Fading and Dispersion
10.4.3.1 Scope. We discuss diversity to reduce the effects of fading and to mitigate dispersion. Diversity was briefly covered in Chapter 2 where we dealt with LOS microwave radio system. In that chapter we discussed frequency and space diversity. There is a third diversity scheme called time diversity, which can be applied to digital cellular radio systems.
In principle, such techniques can be employed at the base station and/or at the mobile unit, although different problems have to be solved for each. The basic concept behind diversity is that when two or more radio paths carrying the same information are relatively uncorrelated, and when one path is in a fading condition, often the other path is not undergoing a fade. These separate paths can be developed by having two channels, separated in frequency. The two paths can also be separated in space, as well as in time.
When the two (or more) paths are separated in frequency, we call this frequency diversity. However, there must be at least some 2% or greater frequency separation for the paths to be comparatively uncorrelated. Because, in the cellular situation, we are so short of spectrum, using frequency diversity (i.e., using a separate frequency with redundant information) is essentially out of the question and will not be discussed further except for its implicit use in code division multiple access (CDMA).
10.4.3.2 Space Diversity.. Space diversity is commonly employed at cell sites, and two separate receive antennas are required, separated in either the horizontal or vertical plane. Separation of the two antennas vertically can be impractical for cellular receiving systems. Horizontal separation, however, is quite practical. The space diversity concept is illustrated in Figure 10.9.
One of the most important factors in space diversity design is antenna separation. There are a set of rules for the cell site and another for the mobile unit.
Space diversity antenna separation, shown as distance D in Figure 10.9, varies not only as a function of the correlation coefficient but also as a function of antenna height, h. The wider the antennas are separated, the lower the correlation coefficient is and the more uncorrelated the diversity paths are. Sometimes we find that, by lowering the antennas as well as adjusting the distance between the antennas, we can achieve a very low correlation coefficient. However, we might lose some of the height-gain factor.
Lee (Ref. 9) proposes a new parameter, t, where antenna height h
antenna separation d
In Figure 10.10 we relate the correlation coefficient (p) with t The orientation of the antenna regarding the incoming signal from the mobile unit is a. Lee recommends a value of p = 0.7. Lower values are unnecessary because of the law of diminishing returns. There is much more fading advantage achieved from p = 1.0 to p = 0.7 than from p = 0.7 to p = 0.1.
Based on p = 0.7 and t = 11, from Figure 10.10, we can calculate antenna separation values (for 850-MHz operation). For example, if h = 50 ft (15 m), we can calculate d using formula (10.10):
For an antenna 120 ft (36.9 m) high, we find that d = 120/11 = 10.9 ft or 3.35 m (from Ref. 9).
Figure 10.9. The space-diversity concept.
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