Part 3-This series of four articles is a primer on some of the propagation-related basics of microwave path design. This month's installment explains the effect of path reflections on fading, how to derive a power budget and the fade margin.

In the first two parts of this series (MRT May and June), the microwave path design process was described in terms of: * determining whether a proposed path is "line-of-sight." * evaluating path clearances with regard to refractive effects. * evaluating path clearances with regard to Fresnel zones. This section covers path reflections and how to derive a power budget and fade margin. The concluding installment will examine path reliability.

Considering path reflections

A point of reflection will exist somewhere along the length of the path where (with regard to the reflecting plane and antennas at both ends) the angle of incidence equals the angle of reflection (see Figure 1 below). If antennas at each end of the path are at the same height above a flat, reflecting surface, the reflection point will be located halfway between the two. However, if antenna elevations are different, the reflection point will be closer to the lower antenna and will move along the length of the path, toward one endpoint or the other as K varies ("K" was defined in Part 1 of this series). If sufficient out-of-phase signal from the reflection point is received at the far-end receiver, catastrophic fading may occur.

In some cases the reflection point will be blocked naturally by terrain features. Manipulation of antenna heights is a method of moving the reflection point to a different spot along the length of the path so that it can be blocked by an obstruction or perhaps so that it may fall on a less reflective surface. Rough surfaces do not reflect as well as smooth, flat surfaces, such as water.

The magnitude of the reflection coefficient (amount of "reflectivity") also increases as the angle of incidence decreases. Because of this, short paths with endpoints at a considerable height above the reflecting surface will be affected less than those with endpoints barely higher than the reflective surface itself (a microwave link between two offshore oil platforms, for example). The magnitude of the reflection coefficient can vary from 0 to 21.0, the latter corresponding to 100% reflection. The negative sign refers to a 1808 phase reversal at the point of reflection.

There is an advantage to using vertical polarization when the grazing angle on a reflective surface is a couple of degrees or greater. The magnitude of the reflection coefficient with vertical polarization is much less than that of horizontal polarization. Less reflected signal will be present at the receive antenna on the other end of the path. In fact, with a grazing angle of 6.58, the magnitude of the reflection coefficient for a vertically polarized wave is only about 20.08 compared to about 21.0 for horizontal polarization. The magnitude rises as the grazing angle increases above 6.58 until it finally meets the same value of the horizontally polarized signal (at 908).

The phase change (or lag) at the point of reflection for a vertically polarized signal is also significantly affected at low grazing angles as compared to the practically uniform 1808 phase reversal for a horizontally polarized signal. As the angle increases from 18 to 308, the phase change of a vertically polarized signal drops quickly from about 1808 to 48. With only a 48 phase lag, the reflected signal that reaches the receive antenna on the other end of the path would have more of an additive, rather than canceling effect.

The distance to the reflection point can be calculated using the equation

d1 = nD [Eq. 1]

where (for K = [infinity] only):

n=(h[sub-one]/(h[sub-one] + h[sub-two])

and

h1 = the elevation of the lower antenna above the reflecting surface. h2 = the elevation of the higher antenna above the reflecting surface. d1 = the distance (mi.) to the reflection point from the h1 end. D = the total path length.

Because calculations for n, where K = 2/3 and K = 4/3, get a bit involved, estimated values can be obtained from graphs offered in R.F. White (see references).

As refractive conditions change, the degree of bowing that occurs on the wavefront will change. As the amount of bowing changes, the location of the reflection point will vary in relative distance between the two path endpoints. In designing a path, it is useful to analyze the overall range of movement (or distance of travel) that can occur for this reflection point. The design engineer must determine whether (in its range of movement) it may wander onto a highly reflective surface (such as a body of water) that lies between path endpoints. In such an undesirable situation, measures might be taken to move the reflection point elsewhere by changing antenna heights, or by attempting to block the reflection.

To determine the practical limits of travel for the reflection point, two values of K are typically used that would describe limits of refractive conditions. One limit is when refractive conditions correspond to a value of K 5 `. The other extreme limit will be the value of K that would bend the path downward to the point of grazing the ground. Beyond this grazing point, no reflection can exist because the path itself is being obstructed by the earth.

The value of K that corresponds to "grazing" can be calculated from the equation: K = 1/(1.5(x+y+z*(SQR)XY)) [Eq. 2]

where x=h{sub-one]/D^Z and Y=h[sub-two]/D^Z

(h1, h2 and D are already defined in Equation 1).

The distance to the grazing point is calculated from Equation 1, where:

n=1/(1+(SQR)Y/X)

Deriving a power budget

A path power budget is nothing but an itemized list of all system losses and gains (in decibels) from the transmitter on one end of the path to the receiver on the other end, and everything in between.

For example, if starting with the transmitter on one end of the path, one would note transmitter output power (1dBm), then subtract all the losses in subsequent connectors and circulators external to the radio assembly, along with waveguide losses (2dB) until the antenna is reached. The gain of the antenna would be added to that value (minus the loss in the radome, if used) to give the resultant effective radiated power (ERP.). This is the available RF signal that will be propagated through the atmosphere to the other end of the link. As the signal makes its way through the atmosphere to the receiving site, free space loss (2dB) (the formula for this was given in Part 2, MRT June), in addition to atmospheric losses (2dB), would then be subtracted from the ERP value.

The term atmospheric loss or "absorption" pertains to effects that atmospheric gases, primarily oxygen and water vapor, have on microwave propagation. These effects are calculated separately from free space losses. Attenuation figures are directly proportional to path length and increase with frequency (0.0002 dB/mi. at 2GHz, 0.002 dB/mi. at 8GHz and almost 0.2dB/mi. at 20GHz).

At the receiving end of the link, the considerations are the same as on the transmitter end, only in reverse order (radome loss; antenna gain, waveguide, connector and hybrid/coupler losses), with the remaining signal level being applied to the receiver (2dBm).

Fade margin The receiver manufacturer will offer a noise threshold specification (expressed in 2dBm) which, simply stated, is the sensitivity of the receiver. It is considered to be the lowest receive signal level at which the receiver will still be considered "unusable." There are variations in the definition of the term "unusable," which means the use of different standards in determining how a particular receiver threshold specification will be obtained. For example, on most industrial analog microwave systems the practical threshold of the receiver is considered the absolute RF signal level (2dBm) injected into the receiver that will establish a 30dB (flat) signal-to-noise ratio (58dBrnc0) as measured in a discriminated baseband noise slot. The telephone companies, however, have used a 33dB (flat) signal-to-noise ratio (55dBrnc0). (The baseband frequency of this noise slot will typically be specified by the equipment manufacturer and is dependent on the particular channel loading of that equipment. It is usually assigned somewhere above the highest occupied frequency slot on the baseband. Because noise effects are worst on the high end of the baseband, this slot would offer a worst case scenario for the signal-to-noise measurement.)

The threshold specification on digital microwave receivers makes reference to the bit-error rate (BER) of the recovered data rather than to a discriminated analog noise measurement. The old Bell standard for digital systems is the RF signal level injected into the receiver that will produce a BER that exceeds 1023. This is typically referred to as the "outage" threshold. Often, however, a BER of 1026 (referred to as the operating point threshold) is used because this is a more common T-1 level standard. (As a note, the difference between these two bit-error rates relates to a change in RF receive level of only 2dB-3dB. This is because BER performance on digital radios degrades rapidly after the 1026 point.) As long as the BER is defined along with the threshold specification, no confusion over terms should exist.

On analog microwave systems, the difference between the receiver threshold value (2dBm) and the receive signal level (RSL) being applied to the receiver (2dBm) under normal path conditions is referred to as the fade margin (expressed in dB). This is a "safety margin" of excess signal that the path can fade before the receiver becomes "unusable" due to noise. The same general definition could be used for digital microwave systems, although in this case it might be termed "flat" or thermal fade margin (TFM). Other terms applicable to digital systems are dispersive fade margin (DFM), adjacent channel interference fade margin (AIFM), and external interference fade margin (EIFM). Composite fade margin (CFM) is a term used to describe the composite affects of TFM, DFM, AIFM and EIFM. Typical receiver threshold levels for digital or analog commercial microwave receivers are usually in the ballpark area of 270dBm to 285dBm.

It should be noted that microwave receivers have a specified range of RF input signal level over which they should properly detect and decode modulated information. This means not only that there is a minimum signal level (receiver "threshold") but also a maximum signal level that can be applied to the receiver input without expecting distortion or data errors in the recovered signal. This restricts the path designer from creating a huge fade margin by applying excessively high RF levels to the receiver under normal path conditions. Additionally, a path phenomenon referred to as "up-fading" can occur (particularly around the end of a period of severe multipath activity) where the microwave link receivers realize an extreme increase in RF signal level (relative to normal RSL). Up-fading is thought to be the result of an anomalous "lens" effect in the atmosphere. For such reasons, the design engineer should leave a margin of at least 10dB between normal path RSL and the receiver's upper RF input limit. The typical design RSL for a microwave receiver is about 235dBm.

The next and final article in this four-part series will discuss microwave path reliability.

Read More:

Part 1: Microwave Path Design

Part 2: Microwave Path Design

Part 4: Microwave Path Design

References "Atmospheric Effects on Microwave," Technical Note TN-5.0, Digital Microwave, Aug. 1986. Hartmann, P.R., J.A. Crossett and E.W. Allen, "Propagation and Countermeasures in Line of Site Digital Transmission Systems," Rockwell International, Collins Transmission Systems Division, Technical Bulletin 523-0609099-011A3J. Laine, R.U., "Determining Antenna Heights for Coastal Areas," Lenkurt Electric, Monograph 197. Llanes, Cesar L., "6-Gigahertz Space-Diversity Digital Microwave Test Link," Los Angeles County Internal Services Department, ITS Engineering Study, Los Angeles, CA, Nov. 1989. "Microwave Transmission Engineering (Part One)," Demodulator, GTE-Lenkurt, July 1972. "Microwave Transmission Engineering (Part Two)," Demodulator, GTE-Lenkurt, Aug. 1972. "Multipath Fading," Demodulator, GTE-Lenkurt, Nov. 1967. White, R.F., Engineering Considerations for Microwave Communications Systems, 4th Ed., GTE-Lenkurt, San Carlos, CA, 1983.