Lec 31: Performance of Orthogonal Signalling

Lec 31: Performance of Orthogonal Signalling

by Prof. Ribhu

Formal & Physical Sciences Engineering & Technology TJKCommunications engineering
🎙 Prof. Ribhu 👥 226K 📅 August 6, 2026 ⏱ 12 min 👁 2 📄 tutorial 🧭 2026-08-06
Available in: English (current) Français

Keywords

orthogonal signallingprobability of errorunion boundcorrelation receiverGaussian noise

Summary

This lecture, part of the NPTEL course ‘Analog and Digital Communications II’, focuses on the performance analysis of orthogonal signalling schemes. The instructor, Prof. Ribhu, begins by recalling the union bound method previously applied to PSK and QAM. He then introduces an M-dimensional orthogonal signalling scheme where transmitted signals are scaled columns of the identity matrix, ensuring equal energy and equal probability. The optimal receiver for this scheme is identified as the correlation receiver. The derivation of the probability of error proceeds by analyzing the received signal vector, which is the transmitted signal plus Gaussian noise. The error probability conditioned on transmitting a particular symbol is expressed in terms of the Q-function, yielding a result independent of the number of constellation points M. The union bound is then computed, showing that it increases with M, while the actual error probability remains constant due to the orthogonality of the constellation. The lecture concludes by noting that this property will be exploited in future link budget analyses comparing different modulation schemes, and announces the next topic: non-coherent detection.

176 words

Critical Evaluation

The lecture provides a clear and rigorous derivation of the probability of error for orthogonal signalling, a fundamental topic in digital communications. The instructor methodically builds the analysis, starting from the signal model and receiver structure, then deriving the error probability and comparing it with the union bound. The mathematical steps are well-explained, and the key insight—that the actual error probability is independent of the number of constellation points due to orthogonality—is highlighted effectively. The use of the Q-function and Gaussian noise properties is standard and correct. The presentation is typical of a formal academic lecture, with a focus on theoretical derivation rather than practical examples. The lack of visual aids or simulations may make it less accessible, but the content is solid. The sources are limited to the course page and playlist, which is appropriate for a lecture. The title accurately reflects the content. Overall, this is a high-quality educational resource for students of digital communications, though it assumes prior knowledge of modulation and probability concepts.

167 words

Title / Content Match

The title accurately reflects the content: the lecture analyzes the performance (probability of error) of orthogonal signalling, including the union bound.

Quality & Reliability

8/10

Lecture by an IIT professor, part of a formal NPTEL course. The derivation is mathematically rigorous and follows standard communication theory. The video is a tutorial with clear step-by-step reasoning, though it lacks references to external sources.

Key Moments

Markers derived by PSI from the transcript: the creator did not define chapters.

Cited Sources

Concurring Sources

Contribution & Novelties

The lecture provides a clear derivation of the probability of error for orthogonal signalling, emphasizing the role of orthogonality in making the error probability independent of the number of signals. This is a key theoretical result in digital communications.

Pour aller plus loin :

  • Union bound — The union bound is a fundamental tool in probability theory used to bound the probability of a union of events.
  • Q-function — The Q-function is the tail distribution function of the standard normal distribution, widely used in communication theory.
  • Correlation receiver — The correlation receiver is an optimal receiver for equally likely signals in AWGN, as discussed in the lecture.

107 words

Radar Profile

The radar profile shows high scores in quality of information, technical level, and reliability, with a slightly lower score in quantity of information due to the short duration and focused scope. This indicates a dense, technically rigorous lecture with limited breadth.

Reliability 8/10