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Does the modulation scheme, whether OOK, SSB, AM, FM, a digital mode, etc, affect the propagation of a signal?

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It depends on what you mean by propagation. If you mean, does the modulation scheme affect the physical means by which EM energy gets from point A to point B?, then the answer is no. Mostly, EM propagation is linear, so the differences in modulation have little effect on how the wave propagate.

However, if you expand propagation to include the intelligibility of the signal at the other end, modulation can make a very big difference. Though propagation can practically be considered linear, it is not time-invariant. On VHF and UHF it's common for the transmitter or receiver to be moving. At HF, the ionosphere constantly changes, significantly altering propagation. Across all the amateur frequencies, there are properties about the radio channel that vary with time.

Different modulation schemes may be more or less robust against the disruptions encountered in practical RF channels. For example, the frequency division multiplexing used in FreeDV provides good robustness against comb filtering caused by multipath propagation. It also provides forward error correction for additional robustness. This is why FreeDV can transmit a 1275 bit/s voice codec with better reliability and less bandwidth than 300 baud FSK.

The differences among analog modulation schemes are less complex, but they still exist. CW works well for communication under adverse conditions because all of the transmitter power is focused in a very narrow carrier. On the other hand, AM spreads this same transmitter power over a wider bandwidth, and in that same bandwidth there is more noise the transmitter must overcome. Thus the principal advantage of SSB: it eliminates power wasted in the carrier and the 2nd sideband which carry no information. Furthermore, the wetware that decodes the baseband signal in analog modulation schemes is much better at detecting the pure tone of CW vs. the complex sound of a human voice in AM or SSB.

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Usually, the answer is no. While modulation may affect the acceptable Signal to Noise ratio, allowing a given signal to be received from further away or in worse conditions than a different modulation, that happens at the receiver, the propagation is the same. The only factors of a radio wave that affect propagation, once it's in the air, are the field strength, frequency, and polarization.

The only slight wrinkle in this that I can think of has to do with multipath distortion. Multipath distortion happens when signals are reflected by multiple surfaces and take more than one path from transmitter to receiever, of different lengths. Radio waves move at about $3*10^8 m/s$, so if one path is $35cm$ longer than another, and the radio wave is at $440MHz$ (with a $70cm$ wavelength), then they will arrive and cancel out perfectly. The modulation can affect this somewhat - but not by very much - simply because a CW signal has a much tighter bandwidth and is affected much more uniformly by multipath distortion than a very wide band (or even frequency-hopping) signal would.

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I agree with the other answers. And that it comes down to the definition of propagation...

I can yell in a large empty room and be heard on the other side. But if you fill that room with noise sources and I yell at the same volume, my voice is still propagating the same power levels across the room, but gets lost in the noise.

So I suggest a brief substitution of "propagation" to instead be "the distance to which a message can be delivered"

With that substitution I would mention that CW signals can very often reach places where SSB cannot. Narrow bandwidth filters are a great help for the receiver as it cuts out most of the noise, for instance.

CW has proven to be very capable of getting the message through in adverse conditions.

I believe that the answer to your post is a qualified no.

Just because I can propagate my voice all the way across the room whether I am singing (FM) or yelling (AM) does not determine whether it is able to be heard.

The qualifier is that CW is an exception to the rule because of the active filtering and tuning of the receiver to receive a narrow-band single frequency while cutting out the extraneous noise..

Add in frequency hopping at a "unit" rate and it gets even better.

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