# Distance-measuring and interferometric techniques.

Continuing with our review of emitter-location techniques, this month we'll consider two ways to measure the distance from a receiving system to an emitter. Then we'll cover interferometric direction finding.

Distance Measurement

If both the transmitted and received power levels are known, it is possible to calculate the distance over which a signal has been transmitted, as shown in Figure 1. Since this technique is used only in EW systems, which do not require high-accuracy distance measurement, it is common practice to ignore all factors except for the spreading (or space) loss. The spreading loss is given by the following formula:

[L.sub.S] = 32.4 + 20 log(F) + 20 log(d)

Where:

[L.sub.S] is the spreading loss in dB

F is the transmitted frequency in MHz

d is the transmission path length in km

This equation can be solved for d.

d = antilog{[[L.sub.S] - 32.4 - 20 log(F)]/20}

antilog(fn) is actually [10.sup.fn]

For example, if a radar operating at 10 GHz is known to have an effective radiated power of +100 dBm and arrives at the receiving antenna at -50 dBm, the spreading loss is 150 dB. Plugging the values into the equation yields a distance of approximately 76 km.

[FIGURE 1 OMITTED]

In practical systems, particularly on aircraft, the accuracy of this measurement may be no better than 25% of the measured range.

A much more accurate technique involves measuring propagation time Signals travel at very close to the speed of light (3 X [10.sup.8] m/sec). This is very close to 1 ft./nanosecond. Thus, if the time a signal leaves the transmit antenna and the time it arrives at the receiving antenna are known, the exact propagation distance can be determined from the following formula:

d = tc

Where:

d = the propagation distance in meters

t = the transmission time in seconds

c = the speed of light (3 X [10.sup.8] m/sec)

For example, if the transmission time is 1 msec, the distance is 300 km. This is the way the radars measure distance--easy, because the transmitter and receiver are typically collocated. However, it is much more difficult in one-way communication. The problem is the accurate determination of the time of transmission and the time of arrival. The time-of-arrival problem has been largely solved by use of very accurate GPS-based clocks, but the time of transmission can only be determined in cooperative systems (such as GPS).

As will be discussed next month, one of the important precision emitter-location techniques (for hostile emitters) is based on measurement of the difference between the times of arrival of a signal at two receiving stations.

Interferometric Direction Finding

When a direction-finding system is specified at about 1[degrees] RMS accuracy, it usually uses the interferometric technique. This technique measures the phase of a received signal at each of two antennas and derives the direction of arrival of the signal from the difference between those two phase values. The basis of the interferometric direction-finding technique is best explained in terms of the interferometric triangle in Figure 2.

The two antennas form a baseline. It is assumed that the system knows the locations of these two antennas, so their separation and orientation can be accurately calculated. Now consider the "wave front" of the arriving signal. The wave front does not exist in nature, but it is a useful concept. This is a line perpendicular to the direction from which the signal arrives at the location of the receiving system.

Consider that a transmitted signal is sinusoidal and that it propagates at the speed of light. The length of a full cycle of the signal (the wavelength) includes 360[degrees] of phase. The observed phase of the signal would be the same at any point along the wave front. The relationship between wavelength and frequency is given by the following formula:

c = [lambda] F

Where:

c = the speed of light (3 X 108 m/sec)

[lambda] = the wavelength in meters

F = the signal frequency in Hz

In the interferometric triangle, the wave front touches one of the antennas and is a distance, D, from the other antenna. By construction, this is a right triangle formed by the baseline, the wave front, and D. The ratio of D to the wavelength is the same as the number of cycles of phase divided by 360. The phase difference between the signal received at the two antennas, thus, is the ratio of D to a wavelength (which can, of course, be calculated from the measured frequency of the received signal).

The ratio of D to the baseline length is the sine of the angle A, and angle A is equal to angle B. Since the perpendicular to the baseline is considered the "zero" angle of an interferometer, angle B is the measured angle of arrival. The angle of arrival at the site also includes the orientation of the baseline.

In most interferometer systems, the baseline is between 0.1 and 0.5[lambda]. A baseline less than 0.1[lambda] does not provide adequate accuracy, and if over 0.5[lambda], it produces ambiguous answers.

There is also the so-called "front-back ambiguity" if the antennas have 360[degrees] coverage. A signal arriving from the mirror-image direction would cause the same phase difference between the antennas. This is resolved by use of antennas with high front-to-back ratios or by use of multiple baselines. Figure 3 shows a four-dipole array used in many interferometer systems. From the top view, you can see there are six pairs of antennas (i.e., six baselines) in this array. The correct angle of arrival will correlate between data from different baselines.

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

What's Next

Next month, we'll review precision emitter-location techniques. For your comments and suggestions. Dave Adamy can be reached at dave@lynxpub.com.

This installment of "EW101" originally appeared in the November 2002 issue of JED.
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