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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?

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My question is, what compels us to transmit the frequency-shifted version of the negative frequency part?

Indeed, nothing compels us to do so. Transmitting the same (baseband) signal twice is inefficient, it unnecessarily doubles the use of frequency space.

why isn't this done for digital modulation methods like PSK, QAM or APSK?

What makes you think it is not done ? The modulation does not matter so you can add OFDM to the list.

Actually SSB is a bit "old hat". What is done with modern modulation techniques like OFDM, OFDMA is that a baseband signal is created using digital signal processing. This digital signal is then converted into an analog signal by an AD converter (ADC). OK, I lied, two of those actually. That gives us two analog signals. These are called quadrature signals. The essence of this signal (consisting of an I and a Q component) is that it has negative and positive frequencies !

Negative frequencies ? Huh, you must be joking !

No I'm not, a negative frequency simply relates to the phase of a signal. If you have only one signal, you cannot determine the phase because a phase is always relative. Now I hope you see why we need two signals because then I can "play" with the phase and make negative frequencies !

This quadrature signal can then be mixed (in a quadrature mixer !) with an RF carrier and transmitted.

If we would start with a baseband signal of 10 MHz wide it would exist between -5 MHz and + 5 MHz and after mixing it with a carrier of 1000 MHz it would occupy 995 MHz to 1005 MHz.

That's what is used in GSM, UMTS, CDMA, Wifi, nearly all modern digital communication standards use this.

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  • \$\begingroup\$ Thanks @Bimpelrekkie. I figured out almost as soon as I hit 'post' that there isn't any baseband signal which, when multiplied with a carrier sine-wave, will generate a PSK or QAM signal (except BPSK) -- so the comparison with AM is flawed from the start. We have to take two sine-waves 90 degrees out of phase, multiply each with two different baseband streams, an then add them -- that is just what you've so kindly pointed out. \$\endgroup\$ – Avijit Sep 12 '17 at 4:15
  • \$\begingroup\$ Negative frequencies merely rotate with opposite phasor. \$\endgroup\$ – analogsystemsrf Sep 12 '17 at 5:27

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