If only the upper side band of an AM wave is transmitted an there is a facility for generating the carrier at the receiving end then is it possible to recover the modulating signal at the receiver station if a device is available for multiplying two signals ? Expalain.

Explanation

Yes.
Let the received signal be `A_1 cos (omega_(c) + omega_(m))t`
where, `(omega_(c) + omega_(m))` represents the upper band.
The carrier voltage at the receiving station will be `A_(c) cos omega_(c)t`.
On multiplying the two we get the product
`=A_(1)A_(c) cos (omega_(c)+ omega_(m))t cos omega_(c)t`
`= (A_(1)A_(c))/(2) [cos(2omega_(c) + omega_(m))t + cos omega_(m)t]`
If this is passed through a low filter, we can retrieve the modulating signal.
`m(t)= (A_(c)A_(c))/(2) cos omega_(m)t`.