Adcock/WatsonWatt Radio Direction Finding
"It has for some time been recognized that the wireless operator employed at a D/F station must be regarded as a specialist, and experience has shown the necessity for specialized training of those who are to undertake this work."
W.E. Crook. D/F Handbook for wireless operators. 1942.
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Abstract:
Technical description of the radio direction finding systems type Adcock/WatsonWatt, based on the employ of four monopololes with an additional sense monopole to avoid ambiguities. Those systems are commonly used in military environments (SIGINT), radio navigation and radio direction finding during emergencies, in the MF, HF, VHF and UHF radio bands. The theoretical explanation is backed by radiation patterns made with 4Nec2 and the analysis of the demodulated signals using a function plotting software.
Table of Contents.
1. The Adcock array and the WatsonWatt system.
2. Computation of the angle of arrival.
3. Implementation of the method.
4. How to solve the ambiguity problem.
5. Referencies and bibliography.
1. The Adcock array and the WatsonWatt system.
During the Second World War, one of the most common techniques of radio direction finding employed in the “Y” stations for signals intelligence^{1} (SIGINT) was based in the use of arrays of 4 monopoles or dipoles arranged in an ortogonal pattern^{2}. By means of rotating the array and combining the signals received in a proper way, a bidirectional radiation pattern is achieved, allowing to determine the direction of arrival of a radio signal of interest, especially through the nulls of the radiation pattern^{3}. This technique was patented by the Lieutenant Engineer Frank Adcock, No.3 Army Wireless Observation Group, in 1919^{4}. This is therefore a method of amplitude comparison to determine the direction of arrival of radio signals (DF, Direction Finding)^{5}.
In an Adcock array, the four antennas are grouped in pairs, laying each pair along a reference axis. Let’s suppose, i.e. that one of the pairs lays in the NorthSouth axis (Y) and the other lays in the EastWest axis (X), as shown in the fig.1.
Fig.1. Adcock 4monopole array simulated in 4Nec2
In 192526, Sir Robert WatsonWatt (one of the pioneers of the implementation of radar as an early warning system during the WWII) improved the system proposed by Adcock by means of using a fifth antenna to avoid the ambiguities and using a cathode ray oscilloscope to plot the angle of arrival^{3}, allowing to operate the antenna array in static configuration.
The precision of an Adcock/WatsonWatt radio direction finding system in the computation of angles of arrival is estimated to be around 23 degrees^{6}. On the other hand, the system is not adequate for high frequency radio direction finding (HF/DF) for NVIS signals, due to the fact that the radiation patterns of the monopoles or dipoles employed have low gain for high takeoff angles^{7}.
In order to back the explanation of the Adcock/WatsonWatt radio direction finding technique from a theoretical point of view, I will use several simulations made with the 4Nec2 software.
In the examples, the aim will be focused on the determination of the direction of arrival (DOA) of a radio signal of interest which may be in the range between 2 MHz and 10 MHz (MFHF). A specific example for a 5 MHz signal will be shown.
In order to simulate the Adcock array with 4Nec2, I will consider 1/4 wavelength monopoles for a working frequency of 5 MHz. That is, each monopole will have a length of 15 metres. In order to simplify the analysis, the part relative to the antenna coupling in all the working band will be obviated, although in fact it is not necessary for the antennas to be resonant in the frequency of the signal of interest^{8}.
The antenna separation or line of base is another important point and must be half the wavelength of the maximum working frequency^{9,10} at the most, ideally around 1/8 or 1/10 of the working wavelength^{5,7}. If the separation is higher that half the wavelength, a risk of having ambiguities in the measurements exists. That’s the reason why, if the bandwith to be watched is high, it may be appropriate to have different lines of base for each frequency range.
In our examples this limit is 10 MHz, with a wavelenght of 30 metres, so we will lay each pair of antennas with a separation of 15 metres.
A model of perfect ground will be used, in such a way that it should not be necessary to configure a network of radials to simulate the ground plane of each monopole, according to the NEC2 algorithm rules of design.
Below you will find the contents of the simulation file. Please note that in the 4Nec2 simulations I will analyze only one of the pairs of monopoles, specifically the NS pair.
CM 4monopole Adcock array optimized for 5 MHz CM by EA4FSI CM CE SY monlen=15 'Monopole length SY monsep=15 'Monopole separation GW 1 128 0 monsep/2 0.001 0 monsep/2 monlen 2mm 'North Monopole GW 2 128 0 monsep/2 0.001 0 monsep/2 monlen 2mm 'South Monopole GW 3 128 monsep/2 0 0.001 monsep/2 0 monlen 2mm 'West Monopole GW 4 128 monsep/2 0 0.001 monsep/2 0 monlen 2mm 'East Monopole GE 1 GN 1 EK EX 0 1 1 0 1 0 0 'Generator at North Monopole EX 0 2 1 0 1 1.22e16 0 'Generator at South Monopole FR 0 0 0 0 5 0 EN 
2. Computation of the angle of arrival.
Once the array is configured with each pair of antennas lying along the NS and EW axis, let’s suppose that we start to receive a signal of interest (SOI) whose wavefront arrives at the array with an unknown direction of arrival (DOA), which we need to determine.
Let “Phi” be the angle formed by the direction of propagation of the wavefront of the signal of interest and the EW axis (the X axis in our reference system). That is, “Phi” is the DOA which we need to compute.
The wavefront will arrive at different time instants at each of the antennas of the array because the travel distance is different, as shown in the fig. 2. This implies that each antenna will receive the signal of interest with some phase shift.
Fig.2. Wavefront arrival at the Adcock array
In order to make the computations easier, we will consider the origin of the coordinate system as the phase reference and we will be focused on the first quadrant (N and E monopoles). Each monopole is placed at a distance R from the origin of the coordinate system.
According to the sketch shown in the fig.2, the wavefront arriving at the N monopole travels a distance d1 lower than the distance to the phase reference, whereas the wavefront arriving at the E monopole travels a distance d1+d2 lower. Being those distances known, we will be able to determine the phase shift of the wavefront in both monopoles
Using trigonometry, we can compute the distance d1+d2 as follows [1]:
[1] 
In a similar way, we compute the distance d1 [2]:
[2] 
Due to the fact that our array is symmetric and having the phase reference at the origin of coordinates, in the S monopole we will have the same phase shift as in the N monopole, buth with negative value. The same way, in the W monopole we will have the same phase shift as in the E monopole, with negative value.
Therefore, the wavefront will induce the following voltages in each of the monopoles [3]:
[3] 
Being m(t) the modulated signal of interest received in the array and K the wave number for the working frequency [4]:
[4] 
This wave will have a linear polarization which won’t probably be neither vertical nor horizontal with respect to the ground plane, due to the effects of the ionospheric propagation. Due to the fact that the monopoles of our array are vertical (perpendicular to the ground plane), only the vertical polarization component of the incident wave is considered. The horizontal polarization component, whose energy may cause errors in the determination of the angle of arrival^{3,6,8}, is eliminated in this way.
At this point, the technique described by Adcock to determine the DOA lies in substracting the signals received in the monopoles of each pair. First of all, let’s consider the subtraction of the signals from the monopoles N and S [5]:
[5] 
Now, we may use the following identity [6]:
[6] 
The development of the subtraction [5] follows in this way [7]:
[7] 
On the other hand, we may consider that the wave number K has a very low value for the frequencies in our working band, so finally we can make the following approximation [8]:
[8] 
Let’s now consider the subtraction of the signals received at the monopoles E and W [9]:
[9] 
Using the identity [6] again, results in [10]:
[10] 
The same way, taking into account the small value of the wave number K, we make the following approximation [11]:
[11] 
In order to determine the DOA, it suffices to calculate the arctangent of the quotient of both subtractions [8, 11], in the following way [12]:
[12] 
3. Implementation of the method.
In the first implementations of the method described before, cathode ray tubes (CRT) of the oscilloscope type were employed^{3,8}. In this type of CRT, the signals plotting in the screen are controlled horizontally by means of applying an electrical field in the plates located in the right and left parts of the device, and vertically by means of another pair of plates placed above and below the screen.
The signals are demodulated in the different receivers or in a single multichannel receiver. Then, the demodulated signals from the North and South monopoles are applied to the vertical plates and the signals from the East and West monopoles are applied to the horizontal plates, as shown in the fig.3.
.
Fig.3. Implementation of the method using a CRT
This way, when detecting a signal of interest arriving at the array with a direction of arrival “Phi”, a straight line would be plotted in the CRT, as shown in the fig.4. If the channels NS and EW are not well balanced, there will be errors in the DOA computation and an ellipse will be plotted in the CRT, instead of a straight line. It is important to have a correct synchronisation between the local oscillators of the different channels or, even better, to have a common local oscillator^{8}.
Fig.4. DOA plotted in a CRT
Knowing the geographical location of several Adcock arrays, the exact position of a transmitter of interest (PF, Position Fixing) may be computed in a collaborative way among several stations, using triangulation.
4. How to solve the ambiguity problem.
The radiation pattern resulting from the subtraction of the voltages induced in two monopoles has an eight shape^{3,5,6,8,11}, as shown in the fig.5, obtained from simulations using 4Nec2.
As indicated before, to make the simulations of the diagram with 4Nec2, a source connected to the N monopole and another source connected to the S monopole, with a 180 degree phase shift, have been considered. This way, the simulation of the subtraction of the signals is achieved.
Fig.5. Radiation pattern of a pair of Adcock monopoles
The problem of ambiguity, following the previous example, results from a signal arriving at the array with the same angle but from the third quadrant (from the SW) instead of from the first quadrant (from the NE), which may generate the same straight line in the CRT. The same ambiguity will exist between signals arriving with the same angle through the second and fourth quadrants.
There are several methods to solve the problem of ambiguity. The most common of them is adding a fifth antenna, which will be named sense monopole, just in the center point of the Adcock array^{11}. The signal received by this additional antenna can be used to modulate the intensity channel of the CRT, by means of plotting the half straight line corresponding to the quadrant where the signal of interest is arriving through. The array layout will be the one shown in the fig.6.
Fig.6. Four element Adcock array with sense antenna
This new sense monopole is placed exactly in the phase reference used in our analysis (see fig.2). In order to explain how the system works, we will consider as an example the two following signals of interest arriving at the array:
1) Sinusoidal signal of 5 MHz arriving through the NE quadrant with DOA = 60º (Azimuth = 30º).
2) Sinusoidal signal of 5 MHz arriving through the SW quadrant with DOA = 240º (Azimuth = 210º).
Being in both cases the wavelength equal to 60 m and the wave number [13]:
[13] 
Those two signals would produce exactly the same straight line in the CRT using a system of four monopoles only, that is, a case of ambiguity would occur.
Let’s see what happens when adding the sense monopole.
According to [2], we compute the distance d1 [14]. Remind that the monopoles of the example have a separation of 15 metres between them, so R = 7,5 m:
[14] 
Knowing this distance, the phase shift in the N monopole is [15]:
[15] 
The same way and according to [1], the phase shift in the S monopole will be 0,679631 rad.
Let’s consider now the subtraction of the signals of the monopoles NS, as described in [5]. If the wavefront is arriving through the first quadrant (NE), after the process of demodulation we will have the signals shown in the fig.7.
Fig.7. Subtraction of the signals NS and signal in the sense monopole (DOA=60º)
Now, we will shift 90 degrees the phase of the signal received in the sense monopole, as shown in the fig.8. Note that, with this modification, the zerocrossings occur just at the same time instants.
Fig.8. Subtraction of signals NS and signal in the sense monopole with 90º phase shift (DOA=60º)
Let’s consider now another signal arriving in the opposite direction, through the third quadrant (SW). Using the signal of the sense monopole phase shifted 90 degrees, we will have the signals shown in the fig.9.
Fig.9. Subtraction of signals NS and signal in the sense monopole with 90º phase shift (DOA=240º)
The results would be similar if we compare signals arriving with equal angles through the quadrants NW and SE.
Analyzing both results (figs. 8 and 9), we conclude that we may use the signal of the sense monopole phase shifted 90 degrees in order to control the plotting of the straight line in the CRT. If we use the positive semicicles (positive voltage) to enable the plotting in the CRT and the negative semicicles (negative voltage) to stop it, we will have the two following cases:

If the signal arrives through the NE or the NW quadrants, the voltage applied to the Y axis of the CRT will be always positive and thus only the Y > 0 part of the straight line will be plotted.

If the signal arrives through the SE or the SW quadrants, the voltage applied to the Y axis of the CRT will be always negative and thus only the Y < 0 part of the straight line will be plotted.
Therefore, using this method the ambiguity is solved and only an angle of arrival is determined.
The complete system has the block diagram shown in the fig.10.
Fig.10. Block diagram of an Adcock/WatsonWatt radio direction finder with sense antenna
At present, the systems are implemented with digital technology. The signals coming from the receivers are digitized and processed in the time and frequency domains to compute the phase shift, allowing to work out the angle of arrival. Besides, using automatic antenna switches, the number of necessary receivers can be reduced.
5. References and bibliography.

PIDGEON G. "Bletchley Park  Admiral Sinclair's War Station".The Secret Wireless War. The Story of MI6 Communications 19391945. Arundel Books, 2008. p.4854.

GETHING P.J.D. "Review of DF Techniques". Radio Direction Finding and Superresolution. IEE Electromagnetic Waves Series 33. 2nd Edition. Peter Peregrinus Ltd., 1991. p.79.

JOHNSON R. et al. “Direction Finding Antennas and Systems”. Antenna Engineering Handbook. 3rd Edition. McGrawHill, 1993. Chapter 39.

GB patent 130490, Frank Adcock, "Improvements in Means for Determining the Direction of a Distant Source of Electromagnetic Radiation", granted 19190807. Enlace.

VOLAKIS J. et al. “Direction Finding Antennas and Systems”. Antenna Engineering Handbook. 4th Edition. McGrawHill, 2007. Chapter 47.

LAPORT E.A. Radio Antenna Engineering. McGrawHill, 1952. p.6067, 214215.

REMBOVSKY A. et al. "Direction Finding of Radio Emission Sources". Radio Monitoring. Problems, Methods and Equipment. Springer, 2009. p.237316.

CARR J.J. “Antennas for Radio Direction Finding (RDF)”. Practical Antenna Handbook. 4th Edition. McGrawHill, 2001. p.439456.

US Army Intelligence Center. Introduction to Radio Direction Finding. Subcourse Number IT0302. Edition C. 1999.

KEAVENY J.J. "Analysis and Implementation of a Novel Single Channel Direction Finding Algorithm on a Software Radio Platform". Virginia Polytechnic Institute and State University, 2005. Enlace.

TETLEY L., CALCUTT D. "Radio Direction Finding". Electronic Navigation Systems. 3rd Edition. ButterworthHeinemann, 2001. p.346368.
Ismael Pellejero  EA4FSI 