Long delayed echo
Long delayed echoes (LDEs) are radio echoes which return to the sender several seconds after a radio transmission has occurred. Delays of longer than 2.7 seconds are considered LDEs. LDEs have a number of proposed scientific origins.
These echoes were first observed in 1927 by civil engineer Jørgen Hals from his home near Oslo, Norway. Hals had repeatedly observed an unexpected second radio echo with a significant time delay after the primary radio echo ended. Unable to account for this strange phenomenon, he wrote a letter to Norwegian physicist Carl Størmer, explaining the event:
At the end of the summer of 1927 I repeatedly heard signals from the Dutch short-wave transmitting station PCJJ at Eindhoven. At the same time as I heard these I also heard echoes. I heard the usual echo which goes round the Earth with an interval of about 1/7 of a second as well as a weaker echo about three seconds after the principal echo had gone. When the principal signal was especially strong, I suppose the amplitude for the last echo three seconds later, lay between 1/10 and 1/20 of the principal signal in strength. From where this echo comes I cannot say for the present, I can only confirm that I really heard it.
Physicist Balthasar van der Pol helped Hals and Stormer investigate the echoes, but due to the sporadic nature of the echo events and variations in time-delay, did not find a suitable explanation.
Long delayed echoes have been heard sporadically from the first observations in 1927 and up to our time.
Five hypotheses 
Shlionskiy lists 15 possible natural explanations in two groups: reflections in outer space, and reflections within the Earth's magnetosphere. Vidmar and Crawford suggest five of them are the most likely. Sverre Holm, professor of signal processing at the Centre for Imaging, University of Oslo, details those five; in summary,
- Ducting in the Earth's magnetosphere and ionosphere at low HF frequencies (1–4 MHz). Some similarities with Whistlers.
- Signals may pass the ionosphere and then be ducted in the magnetosphere out to a distance of several earth radii over to the opposite hemisphere where they will be reflected on top of the ionosphere. The round-trip time varies with the geomagnetic latitude of the transmitter and is typically in the 140–300 ms range. The further North the station, the larger the delay. Due to the short delay, this cannot be considered to be a real long-delayed echo. For completeness it is still included here.
- Travel many times around the world. Signals can travel around the Earth seven times in one second. Such signals are also not uncommon.
- "Goodacre  reports that he pointed his antenna towards the horizon and received his own 28 MHz signal delayed by up to about 9 seconds.... His measurement implies travel up to 65 rounds around the earth." Probably the upper frequency limit for such effects.
- The most popular current theory is that the radio signals are trapped between two ionized layers in the atmosphere and then are guided around the world many times over until they fall out of a gap in the bottom layer. (Ducting propagation between air layers in the lower atmosphere is a well-understood phenonemon. See Radio propagation.)
- Mode conversion: Signals couple to plasma waves in the upper ionosphere.
- Investigated experimentally by Crawford et. al.; they recorded echoes with delays up to 40 seconds at 5–12 MHz.
- Reflection from distant plasma clouds coming originally from the sun.
- Freyman  did experiments at 9.9 MHz and detected several thousand echoes of delay up to 16 seconds at times when solar plasma probably entered the magnetosphere.
- Non-linearity in addition to mode conversion. Two transmitted signals combine to generate a difference frequency, which travels with a plasma wave, then is converted back.
- Could explain amateur VHF/UHF echoes. Hans Rasmussen found echoes delayed by 4.6 seconds at 1296 MHz, Yurek recorded a 5.75 second delay at 432 MHz.
None of these hypotheses can explain everything. Only the first mechanism is well established, and none of the other four are well-established enough to deserve the term "theory". The phenomena are often fleeting and non-repeatable. Our understanding of how the magnetosphere interacts with the solar wind is still evolving.
Alternative hypotheses 
Still others believe that LDEs are double EME (EMEME) reflections, i.e. the signal is reflected by the moon and that reflected signal is reflected by the Earth back to the moon and reflected again by the moon back to the earth.
Duncan Lunan proposed the radio echoes observed by Størmer and Van der Pol in 1928 might have been transmissions from a Bracewell probe, an artifact of aliens trying to communicate with us by bouncing back our own signals. This concept is also addressed by Holm.
Volker Grassmann writing in VHF Communications noted the possibility of individuals hoaxing LDEs, saying, "Attempts at deception can in no case be ruled out, and it is to be feared that less serious radio amateurs contribute to deliberate falsification.... Short transmissions using different frequencies are a relatively simple procedure for excluding potential troublemakers."
See also 
-  ARRL: Stan Horzepa, Radio Ghosts
- ARRL: Stan Horzepa,Long-Delayed Echoes Again
- Carl Stormer, "Short Wave Echoes and the Aurora Borealis," Nature, 122, 681, (1928)
- Balthus van der Pol, "Short Wave Echoes and the Aurora Borealis," Nature, 122, 878-879 (1928)
-  V. Grassmann, Long-delayed radio echoes, Observations and interpretations, VHF Communications vol 2, pp. 109-116, 1993.
- Holm summary, Shlionskiy's 15 possible explanations for Long Delayed Echoes
- A. G. Shlionskiy, "Radio echos with multisecond delays," Telecomm. and Radio Eng., Vol 44, No. 12, pp. 48–51, Dec. 1989.
- R. J. Vidmar and F. W. Crawford, "Long-delayed radio echoes: Mechanisms and observations," Journ. Geophys. Res., vol. 90, no. A2, pp. 1523–1530, Feb. 1985.
- Sverre Holm, The Five Most Likely Explanations for Long Delayed Echoes
- Sverre Holm, Unusual HF Propagation Phenomena - MDE
- A. K. Goodacre (VE3HX), "Observations of long-delayed echoes on 28 MHz," QST, March 1980, pp. 14–16.
- A. K. Goodacre (VE3HX), "Some observations of long-delay wireless echoes on the 28-MHz amateur band," Journ. Geophys. Res., Vol. 85, No. A5, pp. 2329–2334, May 1980
- F. W. Crawford, D. M. Sears, R. L. Bruce, "Possible observations and mechanism of very long delayed radio echoes," Journ. Geophys. Res., Space Physics, vol. 75, no. 34, pp. 7326–7332, Dec. 1970.
- R. W. Freyman, "Measurements of long delayed radio echoes in the auroral zone," Geophys. Res. Letters, Vol. 8, No. 4, pp. 385–388, April 1981.
- H. L. Rasmussen (OZ9CR), "Ghost echoes on the Earth-Moon path," Nature, Vol. 257, p 36, Sept. 4, 1975.
- J. Yurek (K3PGP), “Echoes: An amateur observation and a professional reply,” QST, 62, pp. 35–36, May 1978.
- J. H. Dellinger, "Observations on Long-Delay Radio Echoes," ST, 8, 42, 88 (1934).
- K. C. Budden, C. C. Yates, "A Search for Radio Echoes of Long Delay," Journal of Atmospheric and Terrestrial Physics, 2, 272-281 1952).
- O. G. Villard, Jr., A. F. Fraser-Smith, R. T. Cassan, "LDE's, Hoaxes, and the Cosmic Repeater Hypothesis,,' ST, 55, 54-58 (1971)
- A. T. Lawton, S. J. Newton, "Long Delayed Echoes: The Search for a Solution," Spaceflight, 16, 181-187, 195 (1974).
- George Sassoon, "A Correlation of Long-Delay Radio Echoes and the Moon's Orbit," Spaceflight, 16, 258-264 (1974).
- O. G. Villard (W6QYT), D. B. Muldrew, and F. W. Waxham (K7DS), "The magnetospheric echo box - A type of long-delayed echo explained," QST, Oct. 1980, pp. 11–14.
- G. T. Goldstone and G. R. A. Ellis, "Observations of 1.91 MHz echoes from the magnetic conjugate point after propagation through a magneto-ionic duct," Proceedings of the Astronomical Society of Australia, vol. 6, no. 3, 1986, p. 333-335
- Ellis, G. R. A. and G. T. Goldstone, "Observations of long delayed echoes", Journal of Atmospheric and Terrestrial Physics, v49 #10 (1987) pp 999 – 1005.
- P. Martinez (G3PLX), "Long Delayed Echoes, A Study of Magnetospheric Duct Echoes 1997-2007," Radcom, Oct 2007, pp. 60–63.
- Duncan A. Lunan, "Space Probe from Epsilon Boötis" Spaceflight, 16:122-31 (April 1973)