Question

A digital communication system is operated at 30 dB SNR. Answer the following:

(a) If the required Shannon’s capacity for the communication system needs to be
maintained at 10 Mbps, determine the value of allocated bandwidth. [3]
(b) If the sufficient bandwidth calculated in 3a is not available, what needs to be done
so that same Shannon’s capacity is maintained.

Answer 1

(a) 1.003 MHz

(b) increase the signal-to-noise ratio

Step-by-step explanation:

The relationship between channel capacity, bandwidth, and signal-to-noise ratio was described by Claude Shannon in the 1940s, based on previous work by Harry Nyquist and Ralph Hartley. The relationship is given by the formula ...

C = Blog₂(1 +S/N)

where C is the channel capacity (bits per second), B is the bandwidth (Hz), and S/N is the signal to noise power ratio.

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(a)

You want to find B for C=10^7 and 10·log(S/N) = 30. Solving for B, we find ...

B = C/log₂(1 +S/N)

B = 10^7/log₂(1 +10^(30/10)) = 10^7/log₂(1001) ≈ 1.003 MHz

The allocated bandwidth must be at least 1.003 MHz.

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(b)

Shannon's relation tells us the alternative to increasing bandwidth is increasing signal-to-noise ratio. If "sufficient" bandwidth is not available, the signal-to-noise ratio must be increased.