The GATE Grind

GATE 2026 EC – Question 55

Communications · Information Theory · 2 marks · Multiple select

Let the relevant bandwidth ($B$) of a digital communication system be 1 MHz and $kT=-174$ dBm/Hz, where $k$ is Boltzmann’s constant and ‘$T$’ is equivalent noise temperature of the receiver. The power ($S$) of signal received through an additive Gaussian channel is $-80$ dBm. Which of the following options is/are TRUE about Shannon capacity ($C$) of the channel?

  1. $C=B$
  2. $C=2B$
  3. $C>3B$
  4. $C<B$

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Correct answer: (C) $C>3B$

Explanation

Noise power $=-174+60=-114$ dBm, so SNR $=34$ dB $\approx2512$. Then $C=B\log_2(1+2512)\approx11.3B>3B$.