The applet allows three of the commonest Amplitude Comparison DF algorithms to be compared under realistic conditions. Example patterns are included, but there is a facility for the user to input own antenna patterns for evaluation.

Here two adjacent ports containing the largest responses from a signal are selected for ratio measurement; then

(3.2.3)

r(θ) depends directly on the antenna pattern and is incorporated as a built-in system function.

3.2.2.2 Quadratic Fit DF

Here, the mth port containing the largest signal is identified. Adjacent port pairs are compared and weighted (Reference 1) to provide a linear estimator assuming Gaussian-shaped antennas.

(3.2.4)

Functions f_L(x), are now log-video.

This case minimises discontinuities at antenna boresights, optimises sensitivity, and features good immunity to antenna beamwidth variations and channel tracking errors.

r(θ) is a linear function when antenna patterns are essentially Gaussian and followed by log video amplification.

In this case, all port signals in Equation 3.2.1 are weighted vectorially before comparison in the manner:

(3.2.5)

r(θ) is now less dependent upon antenna pattern and it is usual to use the approximation

(3.2.6)

The effect of small uncertainty in the values of x(θ) and y(θ) on the indicated angle in Equation 3.2.2 can be determined by differentiating r(θ) with respect to θ, denoted r'(θ).

Let

     ,    where R = r(θ),     X = x(θ),  and   Y = y(θ)

Then

     ,   where ,  , ,    and    

Combining these equations and inverting, we get

(3.2.7)

For the particular case of amplitude comparison system considered, Equation 3.2.7 can be used to model the system to determine the effect of system noise or channel tracking on DF performance achievable.

In wideband ESM applications, the receiving channels following array antennas employ RF amplification prior to square-law detection. Assuming rectangular RF and video passbands, the signal-to-noise ratio at the detector output may be shown to be

(3.2.8)

Channel noise voltages can be substituted in dX and dY to calculate angle noise error from Equation 3.2.7. Since the noise sources between channels are completely uncorrelated, video noise adds power-wise and total angle noise is given by

(3.2.9)

where

(3.2.11)

Factory calibration techniques can be used to give a moderate improvement in DF accuracy by compensating for parametrically stable error sources. These include antenna pattern and squint, RF channel gain, and log video/detector tracking differences. Closed-loop calibration can provide somewhat better compensation by using either the signal or a tunable oscillator to correct for amplitude and phase errors as a function of signal amplitude.

In general, the DF performance of an amplitude comparison DF system improves with the number of antenna channels. The optimum arrangement is when the antenna 3dB beamwidth matches the antenna angular spacing in the array.

An alternative configuration uses an N-channel amplitude comparison DF receiver that is switched between two concentric squinted N-port antenna arrays. Sets of DF measurements made alternately on the two arrays are combined to produce an improved bearing estimate. This approach maintains 100% single pulse intercept probability and allows the system to become sensitive to all signal polarisations by the use of cross-polarised antenna sets. Cross-polarised signals at either N-port array will not produce valid DF measurements and this can be sensed by inspecting adjacent channel signal amplitudes; the best DF accuracy possible in this situation is just that of the other copolarised array. Inverting elements in the arrays helps to compensate for antenna element pattern squint and switching to elements at opposite sides of the array compensates for channel unbalance. This technique can provide better than double the DF accuracy of a single antenna set.

A 2N-port amplitude comparison DF system can be configured as N or 2N interferometer pairs; one pair is shown in Figure 3.2.2. Signal amplitudes from each of the 2N channels is used to produce a coarse DF estimate, which is used to resolve the relevant interferometer ambiguities.

Figure 3.2.2 Squinted Antenna Interferometer Pair

Phase comparator output signals are

(3.2.12)

(3.2.13)

where, P_s is the signal power, θ is the source direction angle from the interferometer boresight, and f(θ) is the antenna power response.

An N-interferometer arrangement puts a difficult differential amplitude constraint on the phase discriminator because of the wider coverage required, but leads to a simpler overall system design. Figure 3.2.3 shows the required interferometer coverage for the N-pair configuration, which defines the limits on source angle for calculating ambiguity tolerance to amplitude comparison DF errors. For the 2N interferometer configuration, the required interferometer maximum field of view is just from –α to α relative to each interferometer pair boresight.