If carrier is suppressed then what is the use of carrier in modulation?

Answer 1

If the carrier is suppressed, then the carrier is only needed at the modulation stage, in order to generate the sideband(s), and it needs to be regenerated at the demodulation stage, in order the recover the original signal.

The purpose of suppressing the carrier is to increase the power to the signal-carrying portion of the transmission, by eliminating the "wasted" power in the carrier. This is done at the expense of complexity in the transmitter and receiver.

More insight:

Actually the added complexity is mainly at the receiver side.

The two common methods for the carrier recovery of its receivers are:

1) squaring the DSB-SC signal then dividing by two.

2) the "Costas Loop".

The third method, not known by IEEE yet, is "Kerim Loop" that uses a conventional PLL (VCO, phase comparator and an RC filter). It is therefore very simple to be implemented since it doesn't require selective filters of any kind. And it can be integrated to produce low cost AM receivers that recover the baseband signal for any AM modulation index, up to infinity which is the case of no carrier (DSB-SC). These new AM receivers would therefore have also both the features of the synchronous demodulator and the Automatic Frequency Control (AFC) function.

Note: Since 30 years, to let "Kerim Loop" concept be known globally, I had to pay a good amount of money first! So, when necessary, I took advantage of it in my private links only.