GATE EC 2019 Set 1 — Question 44
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MCQ+2 / -0.67MediumError ProbabilityDigital Modulation & DetectionCommunications
Communications → Digital Modulation & Detection → Error Probability
Last updated
Question
A single bit, equally likely to be 0 and 1, is to be sent across an additive white Gaussian noise (AWGN) channel with power spectral density . Binary signaling, with and , is used for the transmission, along with an optimal receiver that minimizes the bit-error probability.
Let form an orthonormal signal set.
If we choose and , we would obtain a certain bit-error probability .
If we keep , but take , for what value of would we obtain the same bit-error probability ?
Let form an orthonormal signal set.
If we choose and , we would obtain a certain bit-error probability .
If we keep , but take , for what value of would we obtain the same bit-error probability ?
Correct answer
(D) 3
Solution
The bit-error probability for binary signaling in AWGN is determined by the Euclidean distance between the two signal points: .
The squared distance is .
The squared distance is .For the bit-error probability to be the same, the distances must be equal:
.
1.Case 1 (Antipodal Signaling):
The squared distance is .
2.Case 2 (Orthogonal Signaling):
The squared distance is .For the bit-error probability to be the same, the distances must be equal:
.
Continue learning with Success Tracker
A step still unclear? Work through it with support
Use Success Tracker to ask about the reasoning, then try another GATE EC question to check your understanding.
AI-powered practice· Unlimited practice on eligible plans
- PYQs with solutions
- Attempt available previous-year questions, then compare your reasoning with the worked solution. Coverage varies by stream.
- Practice that adapts
- Choose a topic, work on weaker areas and bookmark questions to revisit. Your attempts feed your progress tracking.
- AI doubt support
- Ask follow-up questions about a step or concept while practising, instead of stopping at the final answer.
Unlimited practice is available on eligible plans. Free practice and AI usage have limits; check the current plan allowances before choosing.
This page stays readable without an account. AI responses can be wrong; check them against the solution and source material.
More questions on Digital Modulation & Detection
2026 Set 1 Q22Consider a discrete memoryless source with an alphabet of four source symbols. is a…2026 Set 1 Q32A wireless digital transmission scheme is using -QAM over an additive white Gaussian noise…2026 Set 1 Q44A QPSK modulated signal from an additive white Gaussian noise (AWGN) channel is received with an…2026 Set 1 Q55Let the relevant bandwidth () of a digital communication system be and…2026 Set 1 Q57Consider a real, narrowband signal where the maximum…