A QPSK modulated signal from an additive white Gaussian noise (AWGN) channel is received with an dB at the input of a coherent QPSK demodulator. A maximum-likelihood reception method is used in the demodulator.
Assume the complimentary error function .
Which is the nearest bit error rate (BER) at the output of the demodulator?
ANSWER
The nearest bit error rate is , option (B).
Official answer: BSource: Official answer key, GATE 2026 EC (IIT Guwahati)
Convert the SNR to a ratio: .
Coherent QPSK with Gray mapping and ML detection has the same bit error rate as BPSK, because the two quadrature bits are detected independently, each with energy per bit: .
Set , so .
Apply the given approximation . Here and .
.
. This is nearest to , so the answer is option (B).
KEY IDEA
Coherent QPSK with Gray mapping has the same BER as BPSK at the same : . Convert dB to a ratio first, then use the given erfc approximation.
WATCH OUT FOR
Using inside the erfc argument without the matching change, or forgetting the factor in front of erfc. Forgetting the gives , which is still nearest to . Using as the erfc argument gives a far smaller value near , which matches no option.
From the GATE 2026 EC paper. Every question of this paper · Download the full paper · All 15 Digital communication questions, with notes
