(a)
A channel has a bandwidth of 5 kHz and a signal-to-noise power ratio of 63. (i) Determine the bandwidth needed if the S/N power ratio is reduced to 31.
(ii) What will be the signal power required if the channel bandwidth is reduced to 3 kHz?
(b)
Let C(x) = 1/2 log(1 + x) denote the channel capacity of a Gaussian channel with signal-to-noise ratio x.
Show:
C(P1/N) + C(P2/(P1 + N)) = C((P1 + P2)/N)
This suggests that 2 independent users can send information as well as if they had pooled their power.