Author: Peter Wittenberg

- Radar FSK ranging measurement accuracy

How can we produce a bound on FSK ranging accuracy? The basic approach is to start with the FSK ranging measurement equation, then determine the standard deviation of the measurement.

If two carrier frequencies are used, (f0 and f0+D f) the difference of the respective phases of the target signals is : D f =2p × 2 R0Df/c.

The measurement of D j . gives the unambiguous range R0 if D j <2p or D f<(c/2)/Rmax. where Rmax is the maximum target range.

As an example, if Rmax = 150 km unambiguous range is required, the maximal deviation frequency between the two carriers must lower than D f < 1kHz.

The range accuracy is related to the phase accuracy measurement, which depends on the signal to noise ratio and D f. Start with the equation

Df =2p × 2 R0Df/c

We set the phase such that the maximum range Rmax gives a phase difference of 2p. Thus

2p =2p × 2 RmaxDf/c     and     Rmax = c/(2Df)

Now we can rearrange the equations to solve for R0 as

R0 = c/(2Df) · (Df/2p)

Substituting Rmax,

R0 = Rmax · (Df/2p)

Now the range is just a function of one variable, the phase difference. Standard deviation can be determined as

sR0 = Rmax · (sDf/2p)

We have the formula for the bound on the standard deviation of the phase difference from an earlier problem as

Phase error is a function of SNR

We can now put this in the range error equation as

FSK ranging error is a function of SNR

In radar specifications, range error is often specified as a percentage of range. Sometimes it is specified as a function of maximum range and sometimes as a function of target range. For FSK ranging, it makes sense to specify error as a function of maximum range. We can rewrite the equation to show the fraction of maximum range as

FSK ranging error is a function of SNR

Problems

  1. A radar system is required to perform FSK ranging to a maximum of 150 km. What frequency difference Df is required to achieve this?
  2. For this specified system, what range accuracy is achievable for a single measurement of a 15 dB SNR target?
  3. The buyer decides that they need a 1 km range accuracy for that 15 dB SNR target, and they are willing to make multiple measurements to achieve this. How many measurements will need to be averaged?
  4. What are some of the practical problems involved in averaging multiple measurements?