Direction finding

In the United Kingdom a radio direction finding service is available on 121.5 MHz and 243.0 MHz to aircraft pilots who are in distress or are experiencing difficulties. The service is based on a number of radio DF units located at civil and military airports and certain HM Coastguard stations.[11] These stations can obtain a "fix" of the aircraft and transmit it by radio to the pilot.

Maritime and aircraft navigation

R-5/ARN7 radio compass components, with the radio control box (left), indicator (center), and radio compass unit (right)

Radio transmitters for air and sea navigation are known as beacons and are the radio equivalent to a

RDF was once the primary form of aircraft and marine navigation. Strings of beacons formed "airways" from airport to airport, while marine NDBs and commercial AM broadcast stations provided navigational assistance to small watercraft approaching a landfall. In the United States, commercial AM radio stations were required to broadcast their station identifier once per hour for use by pilots and mariners as an aid to navigation. In the 1950s, aviation NDBs were augmented by the VOR system, in which the direction to the beacon can be extracted from the signal itself, hence the distinction with non-directional beacons. Use of marine NDBs was largely supplanted in North America by the development of LORAN in the 1970s.

Today many NDBs have been decommissioned in favor of faster and far more accurate

Location of illegal, secret or hostile transmitters – SIGINT

In World War II considerable effort was expended on identifying secret transmitters in the United Kingdom (UK) by direction finding. The work was undertaken by the

A comprehensive reference on World War II wireless direction finding was written by Roland Keen, who was head of the engineering department of RSS at Hanslope Park. The DF systems mentioned here are described in detail in his 1947 book Wireless Direction Finding.[13]

At the end of World War II a number of RSS DF stations continued to operate into the Cold War under the control of GCHQ the British SIGINT organisation.

Most direction finding effort within the UK now (2009) is directed towards locating unauthorised "pirate" FM broadcast radio transmissions. A network of remotely operated VHF direction finders are used mainly located around the major cities. The transmissions from mobile telephone handsets are also located by a form of direction finding using the comparative signal strength at the surrounding local "cell" receivers. This technique is often offered as evidence in UK criminal prosecutions and, almost certainly, for SIGINT purposes.^[14]

Emergency aid

Avalanche transceivers operate on a standard 457 kHz, and are designed to help locate people and equipment buried by avalanches. Since the power of the beacon is so low the directionality of the radio signal is dominated by small scale field effects^[15] and can be quite complicated to locate.

Wildlife tracking

Location of radio-tagged animals by

Reconnaissance

Phased arrays and other advanced antenna techniques are utilized to track launches of rocket systems and their resulting trajectories. These systems can be used for defensive purposes and also to gain intelligence on operation of missiles belonging to other nations. These same techniques are used for detection and tracking of conventional aircraft.

Astronomy

Earth-based receivers can detect radio signals emanating from distant stars or regions of ionized gas. Receivers in radio telescopes can detect the general direction of such naturally-occurring radio sources, sometimes correlating their location with objects visible with optical telescopes. Accurate measurement of the arrival time of radio impulses by two radio telescopes at different places on Earth, or the same telescope at different times in Earth's orbit around the Sun, may also allow estimation of the distance to a radio object.

Sport

Events hosted by groups and organizations that involve the use of radio direction finding skills to locate transmitters at unknown locations have been popular since the end of World War II.

Selection radio direction-finding stations

• 
  RDF lorry
  (British Post Office, 1927)
• 
  RDF antennas
  (Galeta Island)
• 
  B-17F RDF antenna (in the prominent teardrop housing under the nose)
• 
  ILS Localizer (providing horizontal guidance)
• 
  VORTAC (providing azimuth

  guidance)
• 
  RDF on 121.5 MHz (Aircraft emergency frequency)
• 
  Aereal 121.5/156.8

  MHz

  (Emergency location beacon aircraft)
• 
  RDF station 410

  kHz
• 
  Maritime RDF station (GT-302)
• 
  Maritime RDF station (Pelengator)

Direction finding at microwave frequencies

DF techniques for microwave frequencies were developed in the 1940s, in response to the growing numbers of transmitters operating at these higher frequencies. This required the design of new antennas and receivers for the DF systems.

In Naval systems, the DF capability became part of the

Over time, it became necessary to improve the performance of microwave DF systems in order to counter the evasive tactics being employed by some operators, such as low-probability-of-intercept radars and covert Data links.

Brief history of microwave development

Earlier in the century,

Intensive research work was carried out in the 1930s in order to develop transmitting tubes specifically for the microwave band which included, in particular, the

Typically, the boresight gain of an antenna is related to the beam width.[26]^: 257 For a rectangular horn, Gain ≈ 30000/BW_h.BW_v, where BW_h and BW_v are the horizontal and vertical antenna beamwidths, respectively, in degrees. For a circular aperture, with beamwidth BW_c, it is Gain ≈ 30000/BW_c².

Two antenna types, popular for DF, are cavity-backed spirals and horn antennas.

• 
  Antenna polar plot
• 
  Antenna log plot
• 
  Cavity backed spiral
• 
  Pyramidal horn

Spiral antennas are capable of very wide bandwidths ^{[26]: 252 [27]} and have a nominal half-power beamwidth of about 70deg, making them very suitable for antenna arrays containing 4, 5 or 6 antennas.^[18]: 41

For larger arrays, needing narrower

Early microwave receivers were usually simple "crystal-video" receivers,[31]^{: 169 [18]: 172 [32]} which use a crystal detector followed by a video amplifier with a compressive characteristic to extend the dynamic range. Such a receiver was wideband but not very sensitive. However, this lack of sensitivity could be tolerated because of the "range advantage" enjoyed by the DF receiver (see below).

Klystron and TWT preamplifiers

The klystron and TWT are linear devices and so, in principle, could be used as receiver preamplifiers. However, the klystron was quite unsuitable as it was a narrow-band device and extremely noisy^[21]: 392 and the TWT, although potentially more suitable,^[21]: 548 has poor matching characteristics and large bulk, which made it unsuitable for multi-channel systems using a preamplifier per antenna. However, a system has been demonstrated, in which a single TWT preamplifier selectively selects signals from an antenna array.^[33]

Transistor preamplifiers

Transistors suitable for microwave frequencies became available towards the end of the 1950s. The first of these was the

Range advantage

Source:^[34]

The DF receiver enjoys a detection range advantage

Amplitude comparison has been popular as a method for DF because systems are relatively simple to implement, have good sensitivity and, very importantly, a high probability of signal detection.[43]^{: 97 [18]: 207} Typically, an array of four, or more, squinted directional antennas is used to give 360 degree coverage.^{[44]: 155 [18]: 101 [45]: 5–8.7 [43]: 97 [46]} DF by phase comparison methods can give better bearing accuracy,^{[45]: 5–8.9} but the processing is more complex. Systems using a single rotating dish antenna are more sensitive, small and relatively easy to implement, but have poor PoI.^[42]

Usually, the signal amplitudes in two adjacent channels of the array are compared, to obtain the bearing of an incoming wavefront but, sometimes, three adjacent channels are used to give improved accuracy. Although the gains of the antennas and their amplifying chains have to be closely matched, careful design and construction and effective calibration procedures can compensate for shortfalls in the hardware. Overall bearing accuracies of 2° to 10° (rms) have been reported ^[45][47] using the method.

Two-channel DF

Two-channel DF, using two adjacent antennas of a circular array, is achieved by comparing the signal power of the largest signal with that of the second largest signal. The direction of an incoming signal, within the arc described by two antennas with a squint angle of Φ, may be obtained by comparing the relative powers of the signals received. When the signal is on the boresight of one of the antennas, the signal at the other antenna will be about 12 dB lower. When the signal direction is halfway between the two antennas, signal levels will be equal and approximately 3 dB lower than the boresight value. At other bearing angles, φ, some intermediate ratio of the signal levels will give the direction.

If the antenna main lobe patterns have a Gaussian characteristic, and the signal powers are described in logarithmic terms (e.g.

To give 360° coverage, antennas of a circular array are chosen, in pairs, according to the signal levels received at each antenna. If there are N antennas in the array, at angular spacing (squint angle) Φ, then Φ = 2π/N radians (= 360/N degrees).

Basic equations for two-port DF

If the main lobes of the antennas have a Gausian characteristic, then the output P₁(φ), as a function of bearing angle φ, is given by^[18]: 238

${\displaystyle P_{1}(\phi )=G_{0}.\exp {\Bigr [}-A.{\Big (}{\frac {\phi }{\Psi _{0}}}{\Big )}^{2}{\Bigr ]}}$

where

G₀ is the antenna boresight gain (i.e. when ø = 0),

Ψ₀ is one half the half-power

beamwidth

A = -\ln(0.5), so that P₁(ø)/P1₀ = 0.5 when ø = Ψ₀

and angles are in radians.

The second antenna, squinted at Phi and with the same boresight gain G₀ gives an output

${\displaystyle P_{2}=G_{0}.\exp {\Bigr [}-A.{\Big (}{\frac {\Phi -\phi }{\Psi _{0}}}{\Big )}^{2}{\Bigr ]}}$

Comparing signal levels,

${\displaystyle {\frac {P_{1}}{P_{2}}}={\frac {\exp {\big [}-A.(\phi /\Psi _{0})^{2}{\big ]}}{\exp {\Big [}-A{\big [}(\Phi -\phi )/\Psi _{0}{\big ]}^{2}{\Big ]}}}=\exp {\Big [}{\frac {A}{\Psi _{0}^{2}}}.(\Phi ^{2}-2\Phi \phi ){\Big ]}}$

The natural logarithm of the ratio is

${\displaystyle \ln {\Big (}{\frac {P_{1}}{P_{2}}}{\Big )}=\ln(P_{1})-\ln(P_{2})={\frac {A}{\Psi _{0}^{2}}}.(\Phi ^{2}-2\Phi \phi )}$

Rearranging

${\displaystyle \phi ={\frac {\Psi _{0}^{2}}{2A.\Phi }}.{\big [}\ln(P_{2})-\ln(P_{1}){\big ]}+{\frac {\Phi }{2}}}$

This shows the linear relationship between the output level difference, expressed logarithmically, and the bearing angle ø.

Natural logarithms can be converted to

${\displaystyle \phi ={\frac {\Psi _{0}^{2}}{6.0202\Phi }}.{\big [}P_{2}(dB)-P_{1}(dB){\big ]}+{\frac {\Phi }{2}}}$

Three-channel DF

Improvements in bearing accuracy may be achieved if amplitude data from a third antenna are included in the bearing processing.^{[48][44]: 157}

For three-channel DF, with three antennas squinted at angles Φ, the direction of the incoming signal is obtained by comparing the signal power of the channel containing the largest signal with the signal powers of the two adjacent channels, situated at each side of it.

For the antennas in a circular array, three antennas are selected according to the signal levels received, with the largest signal present at the central channel.

When the signal is on the boresight of Antenna 1 (φ = 0), the signal from the other two antennas will equal and about 12 dB lower. When the signal direction is halfway between two antennas (φ = 30°), their signal levels will be equal and approximately 3 dB lower than the boresight value, with the third signal now about 24 dB lower. At other bearing angles, ø, some intermediate ratios of the signal levels will give the direction.

Basic equations for three-port DF

For a signal incoming at a bearing ø, taken here to be to the right of boresight of Antenna 1:

Channel 1 output is

${\displaystyle P_{1}=G_{T}.\exp {\Bigr [}-A.{\Big (}{\frac {\phi }{\Psi _{0}}}{\Big )}^{2}{\Bigr ]}}$

Channel 2 output is

${\displaystyle P_{2}=G_{T}.\exp {\Bigr [}-A.{\Big (}{\frac {\Phi -\phi }{\Psi _{0}}}{\Big )}^{2}{\Bigr ]}}$

Channel 3 output is

${\displaystyle P_{3}=G_{T}.\exp {\Bigr [}-A.{\Big (}{\frac {\Phi +\phi }{\Psi _{0}}}{\Big )}^{2}{\Bigr ]}}$

where G_T is the overall gain of each channel, including antenna boresight gain, and is assumed to be the same in all three channels. As before, in these equations, angles are in radians, Φ = 360/N degrees = 2 π/N radians and A = -ln(0.5).

As earlier, these can be expanded and combined to give:

${\displaystyle \ln(P_{1})-\ln(P_{2})={\frac {A}{\Psi _{0}^{2}}}.(\Phi ^{2}-2\Phi \phi )}$

${\displaystyle \ln(P_{1})-\ln(P_{3})={\frac {A}{\Psi _{0}^{2}}}.(\Phi ^{2}+2\Phi \phi )}$

Eliminating A/Ψ₀² and rearranging

${\displaystyle \phi ={\frac {\Delta _{1,2}-\Delta _{1,3}}{\Delta _{1,2}+\Delta _{1,3}}}.{\frac {\Phi }{2}}={\frac {\Delta _{2,3}}{\Delta _{1,2}+\Delta _{1,3}}}.{\frac {\Phi }{2}}}$

where Δ_1,3 = \ln(P₁) - ln(P₃), Δ_1,2 = \ln(P₁) - \ln(P₂) and Δ_2,3 = \ln(P₂) - \ln(P₃),

The difference values here are in

The bearing value, obtained using this equation, is independent of the antenna beamwidth (= 2.Ψ0), so this value does not have to be known for accurate bearing results to be obtained. Also, there is a smoothing affect, for bearing values near to the boresight of the middle antenna, so there is no discontinuity in bearing values there, as an incoming signals moves from left to right (or vice versa) through boresight, as can occur with 2-channel processing.

Bearing uncertainty due to noise

Many of the causes of bearing error, such as mechanical imperfections in the antenna structure, poor gain matching of receiver gains, or non-ideal antenna gain patterns may be compensated by calibration procedures and corrective look-up tables, but

In general, a guide to bearing uncertainty is given by [45]^[51]>^{: 82  [31]: 91 [52]: 244}

${\displaystyle \Delta \phi _{RMS}=0.724{\frac {2.\Psi _{0}}{\sqrt {SNR_{0}}}}}$ degrees

for a signal at crossover, but where SNR₀ is the signal-to-noise ratio that would apply at boresight.

To obtain more precise predictions at a given bearing, the actual S:N ratios of the signals of interest are used. (The results may be derived assuming that noise induced errors are approximated by relating differentials to uncorrelated noise).

For adjacent processing using, say, Channel 1 and Channel 2, the bearing uncertainty (angle noise), Δø (rms), is given below.^{[18][31]: 91 [53]} In these results, square-law detection is assumed and the SNR figures are for signals at video (baseband), for the bearing angle φ.

${\displaystyle \Delta \phi _{RMS}={\frac {\Phi }{2}}.{\frac {\Psi _{0}^{2}}{-ln(0.5).\Phi }}.{\sqrt {{\frac {1}{SNR_{1}}}+{\frac {1}{SNR_{2}}}}}}$ rads

where SNR₁ and SNR₂ are the video (base-band) signal-to-noise values for the channels for Antenna 1 and Antenna 2, when square-law detection is used.

In the case of 3-channel processing, an expression which is applicable when the S:N ratios in all three channels exceeds unity (when ln(1 + 1/SNR) ≈ 1/SNR is true in all three channels), is

${\displaystyle \Delta \phi _{rms}={\frac {1}{-2.ln(0.5)}}.{\frac {\Psi _{0}^{2}}{\Phi ^{2}}}.{\sqrt {{\bigg (}\phi +{\frac {\Phi }{2}}{\bigg )}^{2}.{\frac {1}{SNR_{2}}}+{\frac {4.\phi ^{2}}{SNR_{1}}}+{\bigg (}\phi -{\frac {\Phi }{2}}{\bigg )}^{2}.{\frac {1}{SNR_{3}}}}}}$

where SNR₁, SNR₂ and SNR₃ are the video signal-to-noise values for Channel 1, Channel 2, and Channel 3 respectively, for the bearing angle φ.

A typical DF system with six antennas

A schematic of a possible DF system,^[18]: 101 employing six antennas,^[54][55] is shown in the figure.

The signals received by the antennas are first amplified by a low-noise preamplifier before detection by detector-log-video-amplifiers (DLVAs).^[56][57][58] The signal levels from the DLVAs are compared to determine the angle of arrival. By considering the signal levels on a logarithmic scale, as provided by the DLVAs, a large dynamic range is achieved ^[56]: 33 and, in addition, the direction finding calculations are simplified when the main lobes of antenna patterns have a Gaussian characteristic, as shown earlier.

A necessary part of the DF analysis is to identify the channel which contains the largest signal and this is achieved by means of a fast comparator circuit.^[44] In addition to the DF process, other properties of the signal may be investigated, such as pulse duration, frequency, pulse repetition frequency (PRF) and modulation characteristics.^[45] The comparator operation usually includes hysteresis, to avoid jitter in the selection process when the bearing of the incoming signal is such that two adjacent channels contain signals of similar amplitude.

Often, the wideband amplifiers are protected from local high power sources (as on a ship) by input limiters and/or filters. Similarly the amplifiers might contain notch filters to remove known, but unwanted, signals which could impairs the system's ability to process weaker signals. Some of these issues are covered in RF chain.

See also

• Amplitude monopulse
• AN/FLR-9, a cold war US Air Force HF direction finding system.
• AN/FRD-10, a cold war US Navy HF direction finding system.
• Battle of the Beams
• Electric beacon
• Geolocation
• Indoor positioning system
• MUSIC (algorithm)
• Phase interferometry
• Position fixing
• Radio determination
• Radio fix
• Radio location
• Real-time locating system
• TDOA
• VOR/DME
• Wullenweber

References