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GATE 2026 EC – Question 44

Communications · Digital Communications · 2 marks · Multiple choice

A QPSK modulated signal from an additive white Gaussian noise (AWGN) channel is received with an $E_b/N_o=8.4$ dB at the input of a coherent QPSK demodulator. A maximum-likelihood reception method is used in the demodulator. Assume the complimentary error function $\mathrm{erfc}(u)\cong[1/(u\sqrt\pi)]\exp(-u^2)$. Which is the nearest bit error rate (BER) at the output of the demodulator?

  1. $10^{-3}$
  2. $10^{-4}$
  3. $10^{-5}$
  4. $10^{-6}$

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Correct answer: (B) $10^{-4}$

Explanation

$\mathrm{BER}=\tfrac12\mathrm{erfc}(\sqrt{E_b/N_0})$ with $E_b/N_0=10^{0.84}=6.92$, so $u=2.63$. Then $\mathrm{erfc}\approx e^{-6.92}/(2.63\sqrt\pi)\approx2.1\times10^{-4}$ and BER $\approx1.06\times10^{-4}\approx10^{-4}$.