RDF Analysis, Appendices
Ruling out ships on 3120 kHz as sources of signals heard at the DF sites.

This appendix describes the test used to rule out the 12 ships capable of A3 transmissions on 3120 kHz as potential sources of signals heard at the DF sites. The test is general and can be applied to any source in the high frequency band.

Ruling out a potential signal source requires showing that a signal from the source could not produce the required output SNR in a receiver tuned to 3105 kHz. As stated in the main text, a 40 dB SNR in a 1 Hertz band, at the input of a receiver with a 6 kHz bandwidth, is required for a 1 dB audio output SNR, the level needed to detect the presence of an A3 signal carrier.

The required input SNR is

(Equation 1):  SNR = P + Gt + Gr -Lfs -La -N -Rsel, dB


P = transmitter output power, dBw
Gt = transmitter antenna gain, dB
Gr = receiver antenna gain, dB
Lfs = free-space component of skywave path loss, dB
La = ionospheric absorption component of skywave path loss, dB
N = noise power at the receiver input, dBw
Rsel = signal attenuation due to receiver selectivity, 103 dB at 3120 kHz

Given the assumption of isotropic antennas stated in the main text, Gt and Ga are zero in this analysis, and equation (1) can be simplified to:

(Equation 2):  SNR = P - Lfs - La - N - Rsel, dB

Skywave path loss has two components, free-space loss and ionospheric absorption loss. The free-space component depends only on frequency and path length. The ionospheric absorption component is a variable function of multiple factors. The theoretical minimum possible path loss would exist if the absorption component was zero. This condition, although extremely unlikely, is assumed for this test.

Receiver input noise power is a complex combination of galactic, atmospheric, and manmade noise. Galactic noise originates outside the solar system and its intensity at a given location is subject to variable conditions in the ionosphere. Atmospheric noise is caused by lightning discharges, propagates long distances via the ionosphere, and varies randomly. Manmade noise is generated by electrical equipment and can be considered constant at a given location. Therefore, the quietest condition at a DF site would exist if the galactic and atmospheric noise components were zero, although this too would be extremely unlikely. The lowest value of manmade noise specified in ITU-R P.372-8 is -163.6 dBw at 3.1 Mhz, and is adopted for this test.

Incorporating these path loss and noise assumptions, equation (2) can be simplified to:

(Equation 3):  SNR = P - Lfs - Nm - Rsel, dB

where: Nm = manmade noise, -163.6 dBw

This statement of SNR establishes the theoretical best case signal environment for the potential source being tested, and thus provides a conservative basis for deciding whether the source can be ruled out. If the source signal could not produce the required receiver output SNR given the ideal conditions of equation (3), then it could not do so given non-zero absorption loss, non-zero galactic noise, and non-zero atmospheric noise.

Free-space loss is

(Equation 4):  L(fs) = 20 log(F) + 20 log(D) + 37.79, dB

F = frequency in Megahertz,
D = distance in nautical miles,
37.79 = a constant associated with the frequency and distance terms.

Substituting the right hand side of equation (4) for Lfs in equation (3), inserting the values of Nm and Rsel, and expressing P in terms of Pt, transmitted power in watts,

(Equation 5):  SNR = 10log(Pt) -20 log(F) -20 log(D) -37.79 + 163.6 -103, dB

Combining terms,

(Equation 6):  SNR = 10log(Pt) -20 log(F) -20log (D) + 22.81 dB

The test procedure is to compute the SNR using equation (6) and compare the result to the required SNR.

If the computed value is less than the required value, the source is ruled out.

If the source under consideration is a fixed land-based transmitter, the value of D is the transmitter’s actual distance from the receiver.

If the source is a mobile transmitter, such as on a ship, the actual distance would be unknown. In that case, the maximum distance D from which the ship’s signal could produce the required SNR can be found directly by rearranging the terms in equation (6), giving

(Equation 7):  D = antilog{(17.78 -9.88 -40.0 + 22.81)/20}

Eleven of the 12 ships with A3 capability on 3120 kHz were Soviet. Five of those ships had 50-watt transmitters, and the other 6 had 60-watt transmitters. Assuming a 60-watt transmitter on each of the 11 ships simplifies the computation and yields conservative results without loss of rigor.

The maximum distance at which a ship transmitting at 60 watts on 3120 kHz could produce the required 40 dB receiver output SNR is:

D = antilog{(17.78 -9.88 -40.0 + 22.81)/20} = 0.343 nmi.

A ship that close to any of the DF sites would be easily seen and would be in imminent danger of running aground. The fact that no such ship sightings were reported suggests that none of the Soviet ships on 3120 kHz were close enough be heard at any of the DF sites.

The twelfth ship capable of A3 transmission on 3120 kHz was a U.S. ship, with a 500-watt transmitter, working on U.S. inland waterways – at least 3000 miles from the nearest DF site. Applying the equation (6) test to this ship for a distance of 3000 miles:

SNR = 26.99 -9.88 db -69.5 dB + 22.81 = -29.58 dB

This SNR is 69.58 dB below the reception threshold, so there was no possibility this ship could be heard at any of the DF sites.

In view of the results shown above, all 12 ships capable of A3 transmission on 3120 kHz can be ruled out as sources of signals heard on receivers tuned to 3105 kHz at the DF sites.

Ruling out the Magnitogorsk

The Soviet ship Magnitogorsk was listed in the March 1938 edition of the ITU List of Coast Stations and Ship Stations as having a 50-watt transmitter capable of A1 (CW) or A3 (voice) emission, and was authorized to use 3105 kHz, 4140 kHz, 6180 kHz, and 6210 kHz. But merely having A3 capability does not mean that it was used on all assigned frequencies.

The Magnitogorsk was the only non-U.S. ship listed as authorized to operate on 3105 kHz. Numerous U.S. ships and coast stations were authorized to operate on 3105 kHz, but not in A3 mode. Consequently, there were no known ships or coast stations with which the Magnitogorsk could communicate on 3105 kHz in A3 mode, and the Magnitogorsk can be ruled out as a possible source of voice signals on 3105 kHz.

A search of the ITU list for shore stations with frequencies matching those of the Magnitogorsk found that only 2 Soviet coast stations, Jilaia Kosa and Donbas, used 6180 kHz. Both stations were on the Caspian Sea.

Jilaia Kosa, with a 70-watt transmitter (A1 only) was assigned 3105, 4140, 4170, and 6180 , and was the only Soviet coast station operating on 3105. Donbas, with a 50-watt transmitter (A1 and A3) was assigned 4170 and 6180, but not 3105.

The fact that two of the Magnitogorsk’s four frequencies, 3105 and 6180, were used only by Jilaia Kosa and Donbas suggests that the Magnitogorsk operated in the Caspian Sea. The ship also apparently operated on other inland seas and on inland waterways, as indicated by the fact that the other two frequencies assigned to the Magnitogorsk, 4140 and 6210 kHz, were used only by coast stations in those areas. Specifically:

  1. The Astrakhan station on the Caspian Sea at the Volga River delta: 4140 kHz (A1 & A3);
  2. The Rostov-Don station at the Don-Volga canal junction with the Sea of Azov: 4140 and 6210 (A1);
  3. The Kerch station at the passage from the Sea of Azov to the Black Sea: 4140 and 6210 (A1 & A3);
  4. The Yalta station on the Black Sea: 4140, 5625, 6210, and 6290 (A1 & A3).xwx
  5. The Sevastopol station on the Black Sea: 4140 and 6210 (A1 & A3);
  6. The Novorossiisk station on the Black Sea: 4140 and 6210 (A1 & A3).

Since Jilaia Kosa was the only station with which the Magnitogorsk could communicate on 3105 kHz, and since Jilaia Kosa could only operate in A1 mode, the Magnitogorsk could not have been a source of A3 signals heard on 3105 kHz.

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