The minimum detectable signal for a given range, or maximum range for a given signal power, is not as simple a question as one might think.
Here we will see how this answer is dependent on a number of mission-dependent factors. Since minimum detectable signal and maximum range are closely related problems, we will focus here on the example of minimum detectable signal.
Other signals in the frequency band of interest may interfere with our target signal. Depending on the extent of interference, detection may still be possible using signal processing techniques.
Many minimum detectable signal values assume ideal free space conditions. In real scenarios, one has to factor in obstacles such as buildings and mountains blocking, diffracting and reflecting signals such that signals may be lost entirely or subject to multipath effects. For large areas, earth curvature effects on signal propagation also come into play. Placing a receiver on a higher point (e.g. on top of a building or mounted on a pole) will help minimise the effects of obstacles including earth curvature.
Friis Transmission Loss
Friis transmission loss captures several factors affecting signal power between transmitter and receiver: distance, frequency and antenna gains. Signal power decreases with the square of distance from transmitter antenna to receiver antenna i.e. doubling the distance reduces the power by a factor of 4. Power also decreases with the square of frequency, since a higher frequency signal reduces the effective aperture of both receiver and transmitter antennas. Finally, directional antenna gains may be used to increase received signal power.
Antenna to receiver cabling will result in some signal attenuation primarily due to skin-effect and dielectric losses. This will depend on cable parameters such as length and material as well as signal frequency – losses will increase with both cable length and signal frequency.
The ability to detect a given signal power will depend on whether it can be distinguished from noise. The lower the noise floor, the easier a signal will be to detect. This noise will be primarily thermal which increases with temperature owing to increased agitation of charge carriers. Since thermal noise is approximately white (constant power with frequency), it will also increase with bandwidth – in this case bandwidth corresponds to receiver FFT bin width. Receiver noise figure, indicating the extent of noise amplification by the receiver, is the final variable affecting noise floor. Noise figure is usually stated on receiver datasheets; CRFS provides frequency responses to capture variation in noise figure with frequency.
Otherwise undetectable signals can be detected using advanced signal processing techniques. One can even detect signals below the noise floor using correlation between two receivers.
CRFS’s RFeye software includes a package of simulation tools to model the combined impact of these different factors. Rather than rely on a generic minimum detectable signal value, a mission-specific minimum detectable signal (or maximum detection range) can be obtained by simply inputting values such as cable loss and signal frequency.