I got this question while considering the Nyquist no-ISI criterion, the consequence of which is that if we send one baseband symbol every T (time) then unless the bandwidth B of the channel is at least 1/2T it is inevitable that there will be inter-symbol interference. That is to say, the highest possible ISI-free symbol-rate in a baseband channel of bandwidth B is 2B.
Then, if we multiply this baseband signal with a carrier frequency f, then the spectrum of the resulting signal is shifted right by f, but since the 'negative frequency' portion of the baseband signal also shifts right, it results in a signal that spans from f-B to f+B, and thus has a bandwidth of 2B. Which seems to indicate that in case of a bandpass channel of bandwidth B the highest possible ISI-free symbol rate is B.
My question is, what compels us to transmit the frequency-shifted version of the negative frequency part? In amplitude modulation we can have SSB (single sideband) transmission, where either the upper or the lower sideband is not transmitted: why isn't this done for digital modulation methods like PSK, QAM or APSK?
If it could be done, the maximum possible symbol rate in a bandpass channel of bandwidth B would have been 2B which is a good thing, so I assume there are sound mathematical reasons as to why suppressing either one of the sidebands would stop us from successfully demodulating the signal. Any pointers as to what they may be?