# Probability of Intercept

## My Background

I have no classified work experience in this area so what you see here is just my thoughts.

## Time to Intercept Example

Suppose that an emergency service frequency is used infrequently, say once every 15 minutes, but not exactly 15 minutes.  When someone speaks they talk for about 5 seconds and typically after a 1 second pause someone else replies for 5 seconds.  Now suppose that a radio is tuned to the frequency where these communications are taking place.  Whenever anyone transmits on the frequency there is a 100% probability of receiving the transmission.

Now suppose that the frequency is unknown, only that it is in the 130 to 170 MHz band and the band can be divided into 5 kHz channels.  So there are 8,000 possible frequencies where this transmission can be taking place.  Further suppose that a scanning receiver can check 10 channels per second, i.e. it takes 13 minutes and 20 seconds to make one scan of the band.  But the probability that the station will be transmitting is only (10 sec / 15*60 = ) 0.0111 so there's about a 1% chance of hearing the transmission.  The inverse of 0.01111 (1/0.1111=) is 90, so after 90 sweeps you would expect the scanner to hear the transmission, or the Time To Intercept (TTI) is (13:20 * 90 =) 20 hours.

An equation for TTI might look like:

TTI = [(length of period) / (transmit time per period)] * [(# of channels to scan) / (channels per second)]
where all time units are in seconds
TTI = [(900 seconds) / (10 seconds)] * [(8,000 channels) / (10 Channels per second)] = 20 hours

## Probability of Intercept Example

Suppose that in the example above a scanner could scan all 8,000 channels in just under 5 seconds.  The probability of intercept would be 100%.  So one strategy would be:
Only scan a limited range of channels where the total scan time is less than the expected transmission time.  Wait for the period between transmissions then move the band being scanned up a notch repeat untill the full band has been covered.
Now suppose that all the possible channels can not be scanned in a time less than the length of a typical transmission.  Then there are two factors: first is the probability that the scanner will be on the correct frequency that could be expressed as:
P(on freq) = (# of channels scanned in one transmit time) / (total # of channels to scan),
second is the chance that someone will be talking when the correct frequency is tuned which might be expressed as:
P(talk) = (talk time in a period) / (period length).
So the total Probability Of Intercept is:

POI = P(on freq) * P(talk)
POI =  [(# of channels scanned in one transmit time) / (total # of channels to scan)] *[ (talk time in a period) / (period length)]
For the example above:
POI = [100 / 8,000] * [10 / 900] = 0.000139

## Another Meaning for Probability of Intercept

Someone who did not want their signal to be intercepted might design the modulation in such a way as to minimize the chance that someone would hear it using conventional receiving equipment.

GPS is an example.  If you connect a spectrum analyzer to an antenna designed to receive the GPS frequencies and use a very low noise figure amplifier at the antenna then connect the amplifier output to a spectrum analyzer, you will NOT see any signal.  This is because the GPS signal is spread using a pseudo random code and until a correlator despreads the signal it has less power per Hertz than the background noise.

The Black Box transmitter uses a spread signal that can not be heard on a standard VHF FM receiver even when tuned to the center frequency.

## Spectrum Analyzer

A spectrum analyzer can scan a given frequency range much faster than a scanner radio, but you don't get any audio out.  By using the "data hold max" function of the Agilent 4395A spectrum analyzer the trace remembers the maximum peaks for as long as it has been running.  Typically in 24 hours the trace will change from no signals to a dozen in a functional band.

118 - 136 MHz Aircraft AM band - After a dozen traces you might see one signal which will disapear on the next sweep
136 - 138 MHz Satellite down link band
138 - 144 Mil tactictal aircraft
150 - 154 MHz spectrum
153 - 157 MHz  spectrum max hold plot where a school buss a few hundred feet away was captured.  When the span / (# of points) = 5 kHz, as in this case, when a radio is tuned to the SA peak frequency, it is the correct frequency.  This is not the case if the distance between display points exceeds the channel spacing.

Many years ago while working with the HP 8566B spectrum analyzer on a mixer test automated system, I had the SA scanning with a piece of wire on it's input.  A similar signal showed up (maybe 50 dB above everything else like in this case).  I went to the front door and found that a police car was sitting in our driveway waiting for speeders.  He must have keyed his radio.

At an HP equipment show held at the Santa Clara facility (near Lawrence and 280) there was a demo running based on the 8566B.  It was doing a waterfall display over a narrow band that included the ham 2 meter range (144 - 148 MHz).  In a waterfall display the x axis is just like a standard spectrum display, i.e. frequency, but the y axis is time with the top of the screen current and older information as you go down the screen.  Signal strength is either gray scale or color.  Black is no signal.  The interesting thing is that repeater pairings are very obvious as well as which is the input and which is the output frequency.  The waterfall software may have been running inside the 8566B as an Instrument Basic program.

Note that the time required for a spectrum to scan a band of frequencies is much shorter than for a scanner radio.  Also there are two types of spectrum analyzers:

Classical - The first spectrum analyzers worked by actually sweeping the Local Oscillator.  The Resolution Bandwidth needs to be wide enough to allow the signal to settle, so as the RBW is narrowed the sweep speed also needs to be slowed down.

DSP - Modern spectrum analyzers, like the 4395A, can analyze a band of frequencies without changing the LO.  The frequency display is obtained by doing a transformation on the sampled input so all the band is being covered on a 100% basis.  Agilent makes some VXI cards that are samplers with deep memory and DSP capability that make high performance spectrum monitors.

WJ App Note:  EW Acquisition Systems, Probability of Intercept and Intercept Time -
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IEEE web page with 3D Java app -

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