By Bruce A. Fette
The following is excerpted from Chapter 5 of RF & Wireless Technologies by Bruce Fette. If you order a copy of this book before December 31, 2007 you can receive additional 20% off. Visit www.newnespress.com or call 1-800-545-2522 and use code 91137.
Part 1 introduces radio propagation.
We have seen that reflection of a signal from the ground has a significant effect on the strength of the received signal. The nature of short-range radio links, which are very often installed indoors and use omnidirectional antennas, makes them accessible to a multitude of reflected rays, from floors, ceilings, walls, and the various furnishings and people that are invariably present near the transmitter and receiver. Thus, the total signal strength at the receiver is the vector sum of not just two signals, but of many signals traveling over multiple paths.
In most cases indoors, there is no direct line-of-sight path, and all signals are the result of reflection, diffraction, and scattering. From the point of view of the receiver, there are several consequences of the multipath phenomena:
- Variation of signal strength. Phase cancellation and strengthening of the resultant received signal cause an uncertainty in signal strength as the range changes, and even at a fixed range when there are changes in furnishings or movement of people. The receiver must be able to handle the considerable variations in signal strength.
- Frequency distortion. If the bandwidth of the signal is wide enough so that its various frequency components have different phase shifts on the various signal paths, then the resultant signal amplitude and phase will be a function of sideband frequencies. This is called frequency selective fading.
- Time delay spread. The differences in the path lengths of the various reflected signals cause a time delay spread between the shortest path and the longest path. The resulting distortion can be significant if the delay spread time is of the order of magnitude of the minimum pulse width contained in the transmitted digital signal. There is a close connection between frequency selective fading and time-delay distortion, since the shorter the pulses, the wider the signal bandwidth. Measurements in factories and other buildings have shown multipath delays ranging from 40 to 800 ns.
- Fading. When the transmitter or receiver is in motion, or when the physical environment is changing (tree leaves fluttering in the wind, people moving around), there will be slow or rapid fading, which can contain amplitude and frequency distortion, and time delay fluctuations. The receiver AGC and demodulation circuits must deal properly with these effects.
Flat Fading
In many of the short-range radio applications covered in this chapter, the signal bandwidth is narrow and frequency distortion is negligible. The multipath effect in this case is classified as flat fading. In describing the variation of the resultant signal amplitude in a multipath environment, we distinguish two cases: (1) there is no line-of-sight path and the signal is the resultant of a large number of randomly distributed reflections; (2) the random reflections are superimposed on a signal over a dominant constant path, usually the line of sight.
Short-range radio systems that are installed indoors or outdoors in built-up areas are subject to multipath fading essentially of the first case. Our aim in this section is to determine the signal strength margin that is needed to ensure that reliable communication can take place at a given probability. While in many situations there will be a dominant signal path in addition to the multipath fading, restricting ourselves to an analysis of the case where all paths are the result of random reflections gives us an upper bound on the required margin.
Rayleigh Fading
The first case can be described by a received signal R (t), expressed as
where r and θ are random variables for the peak signal, or envelope, and phase. Their values may vary with time, when various reflecting objects are moving (people in a room, for example), or with changes in position of the transmitter or receiver that are small in respect to the distance between them. We are not dealing here with the large-scale path gain that is expressed in Eqs. (5.5) and (5.6). For simplicity, Eq. (5.7) shows a continuous wave (CW) signal as the modulation terms are not needed to describe the fading statistics. The envelope of the received signal, r, can be statistically described by the Rayleigh distribution whose probability density function is:
where σ2 represents the variance of R(t) in Eq. (5.7), which is the average received signal power. This function is plotted in Figure 5.6. We normalized the curve with σ equal to 1. In this plot, the average value of the signal envelope, shown by a dotted vertical line, is 1.253.
Note that it is not the most probable value, which is 1 (σ). The area of the curve between any two values of signal strength r represents the probability that the signal strength will be in that range. The average for the Rayleigh distribution, which is not symmetric, does not divide the curve area in half. The parameter that does this is the median, which in this case equals 1.1774. There is a 50% probability that a signal will be below the median and 50% that it will be above.
5.6. Rayleigh probability density function.
As stated previously, the Rayleigh distribution is used to determine the signal margin required to give a desired communication reliability over a fading channel with no line of sight. The curve labeled "1 Channel" in Figure 5.7 is a cumulative distribution function with logarithmic axes. For any point on the curve, the probability of fading below the margin indicated on the abscissa is given as the ordinate. The curve is scaled such that "0 dB" signal margin represents the point where the received signal equals the mean power of the fading signal, 2, making the assumption that the received signal power with no fading equals the average power with fading. Some similar curves in the literature use the median power, or the power corresponding to the average envelope signal level, ra, as the reference, "0 dB" value.
5.7.Fading Margins.
An example of using the curve is as follows. Say you require a communication reliability of 99%. Then the minimum usable signal level is that for which there is a 1% probability of fading below that level. On the curve, the margin corresponding to 1% is 20 dB. Thus, you need a signal strength 20 dB larger than the required signal if there was no fading.
Assume you calculated path loss and found that you need to transmit 4 mW to allow reception at the receiver’s sensitivity level. Then, to ensure that the signal will be received 99% of the time during fading, you’ll need 20 dB more power or 6 dBm (4 mW) plus 20 dB equals 26 dBm or 400 mW. If you don’t increase the power, you can expect loss of communication 63% of the time, corresponding to the "0 dB" margin point on the "1 Channel" curve of Figure 5.7.
The following table shows signal margins for different reliabilities.
Part 3 will cover Diversity Techniques
References
Gibson, J. D. (ed.), The Mobile Communications Handbook, CRC Press, Inc., 1996.
Rappaport, T. S., Wireless Communications, Principles and Practice, Prentice Hall, Upper Saddle River, NJ, 1996.
Spix, G. J., "Maxwell’s Electromagnetic Field Equations," unpublished tutorial, copyright 1995 http://www.connectos.com/spix/rd/gj/nme/maxwell.htm
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Copyright: Printed with permission from Newnes, a division of Elsevier. Copyright 2008. "RF & Wireless Technologies" by Bruce A. Fette. For more information about this title and other similar books, please visit www.newnespress.com.
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