Follow the signal from the users to the antenna and the order is forced : multiplex, modulate, amplify at IF, up-convert — (ii), (i), (iv), (iii), option 3.

Why multiplexing must come first. There is no point modulating each user's channel separately when one carrier is to be transmitted — combining first means one modulator serves them all. Reverse the two and the system would need a modulator per channel and a way to combine modulated carriers, which is a different architecture entirely.

Why modulation happens at IF rather than directly at RF. This is the key insight of the question. Modulators, filters and amplifiers are far easier to build well at a fixed intermediate frequency — commonly 70 MHz in satellite practice — than at several gigahertz. Working at IF gives sharper filters, better linearity, and equipment that can be reused across different RF channels. The final translation to the transmit frequency is then a single mixing operation:

\(f_{RF}=f_{IF}+f_{LO}\)

and the transmit channel is changed simply by retuning the local oscillator, leaving everything before it untouched.

Why the IF amplifier precedes the up converter. A mixer needs a healthy input level to work at reasonable conversion loss and to keep the noise contribution of the following stages small; and amplification is cheaper and cleaner at IF than at RF. The high-power amplification that remains is done after the up converter by the HPA feeding the antenna.

The receiver is the mirror image : low-noise amplifier, down converter, IF amplifier, demodulator, demultiplexer — the same chain traversed in reverse, which is a useful check on any answer of this kind.

Hence, the correct sequence is (ii), (i), (iv), (iii).