## Aircraft Scatter – Much Power, Little Glory

I was asked to give a short overview of how to calculate the *received power*, scattered by an aircraft on HF. The answer is easy if we focus on AM DX signals from broadcasting stations, illuminating an aircraft. In this case the spectrogram, *Figure 1*, shows the carrier as well as the scattered signal – the latter being the Doppler trace. We also can easily measure both signal strength and calculate their difference. This has been done for the maximum values of carrier and Doppler in *Figure 2 *below:

Mean value of the carrier in the analyzed 10-minute’s part of the whole observation is -32.7dBm at a standard deviation of 4.98 – see *Figure 3* below.

**Broadcaster’s Footprint**

Backbone of all calculations is the well-established Radar Equation. Let’s think of it as a reliable, but Black Box. Critical points are in this case:

- illuminating power
- distance aircraft -> receiver
- reflectivity of the aircraft at the specific frequency (radar cross section, or RCS)

I took a strong broadcaster, namely Kashi, running 500kW AM (250kW carrier) on 17’650kHz on a curtain array antenna with a gain of ca. 20dB towards Central Europe. Effective Radiated Power (ERP) of the carrier is 104dBm. An approximate calculation (free-space loss, the prevailing attenuating factor with propagation) over this distance of 5’109km and at 17’650kHz via Matlab’s *fspl *function yields an attenuation of 131.5dB, resulting in a signal of -27.5dBm. As 2-hop ionospheric HF propagation is not exactly free-space propagation,so a VOAAREA HF propagation simulation had been done, giving the transmitter’s footprint in dB**W** (add 30dB to get dB**m**):

**Scattering Power**

The illuminating power, a proxy for transmitter power within the -65dBW footprint in *Figure *4, measures -32dBm. The minimum slant distance between the aircraft and my location measures 1000m. The RCS of this aircraft is given at 10 … 100, let’s generously take 100, because the wingspan of the given aircraft (35m) almost exactly measures 2*wavelength (17m) in this case providing strong forward and backward scatter.

What value can be *caclulated *from as scattered signal which me *measured *-63dBm at highest? According to the equation #6 given in OTH-B Radar System: System Summary of the University of Massachusetts Lowell, we land at a level of -62.1dBm, given the mean value of the carrier with -32.7dBm. This almost exactly matches the measured value of -63dBm.

Now some people claim to “see” and even identify aircraft not over a few tens of kilometers, but over many thousands of kilometers. Let’s check this. *Figure 5 *shows the development of reception levels over distance, sticking to the Kashi example as above. You see the signal peaking to slightly above -20dBm at about 1’800km distance from the transmitter. And you see the separation from one-hop to two-hop propagation at a distance of 3’000km from the transmitter.

Please keep in mind that this is only a rough calculation, not taking into account several factors, among them:

- fading of the carrier (see
*Figure 3*) - pearlstring effect of the Doppler
- change of effective RCS due to different horizontal and vertical illuminations angles

**That’s a powerhouse – but what about WSPR?**

In praxi, I observed Doppler traces only from aircrafts at a distance not more than a very few ten kilometres from my location – given that they are illuminated by a multi-hop DX signal from a strong broadcaster.

In contrast, some people claim to have not only observed, but even identified aircraft

- over thousands of kilometres,
- illuminated by a
*5W*transmitter

Let’s take a look on this, same conditions as with the Kashi case above. First, we do the VOAAREA simulation. I took extraordinary benevolent conditions, taking a *50W* transmitter (WSPR mainly runs between 1 and 10W) at an isotrope antenna of 10dBi gain. The system loss mounts to about -50dB over the Kashi case. The VOAAREA simulation (*Figure 6* below) largely reflects this situation, delivering a signal of about -115dBW/Hz [WSPR] over -65dBW/Hz [Radio China International].

**How far will the scattered signals reach?**

Now for the crucial question: How far will scattering from both signals (-65dBW from the broadcaster, -115dBW from WSPR) reach? You will find an answer in *Figure 7*, below:

From *Figure 7* we see scatter from the strong broadcaster sinking into the noise from a distance aircraft-receiver of 200km. WSPR from DX is good only for distances up to 10km.

This calculation has been done under *unusually generous conditions*, among them:

- RCS has been set to 100, where 10 … 50 would be the regular case, resulting in a much reduced performance
- forward/backward scatter have been applied to the calculation as well as to the measurements. This seems justified where the aircraft heading was 295° and Kashi->DK8OK was 302°, resulting in backward scatter from the wings and, thus, the strongest signal
- the wings of this Airbus A320 do perform like a dipole of two wavelengths
- only the strongest signals have been taken into account
- neither fading of the illuminating station, nor the pearlstring-effect of the aircraft – due to phase changes under moving – have been taken into account

In praxi, such a strong DX signal never showed Doppler traces at distances of more than, say, 60km. I owe this observation also to the physicist Dr. Victor Iannello, who kindly examined many of my spectrograms with a Python program written specifically for this purpose and determined the distances of even the faintest Doppler traces, as seen at .1Hz bandwidth (+10dB system gain).

Caveat: Please keep in mind that this case is valid only for DX (i.e., multi-hop) signals illuminating the aircraft. If aircraft is illuminated by a transmitter’s backscatter signal (at a distance of ca. 100 – 1’000km from the receiver), other mechanisms take place resulting in Doppler traces from aircraft at an height, which “sees” both transmitter and receiver – see for “radio horizon”. This speical case is not covered here, and plays no role either in the texts of the WSPR/MH370 proponents.