Overview
Module 2 presents the structure for the receiver, and develops a signal space analysis to quantify the receiver performance. In part A of Module 2, we optimize the performance of a linear sampling receiver by making appropriate choices for various receiver blocks. We introduce the optimization criteria MAP and ML, as well as the likelihood and the a priori probability. We define the matched filter. We introduce the signal space and we use the Gram-Schmidt process as an example to find a basis of the signal space.
Videos
- Linear sampling receiver
- Bayes Law, MAP and ML rules
- Binary Maximum Likelihood (ML) receiver
- Binary Maximum A Posteriori (MAP) receiver
- Matched Filter
Course notes
Objectives
- know the operating principles of a linear sampling receiver
- know how to exploit a test statistic for detection
- understand Bayes law and probability vocabulary: a priori, a posteriori and likelihood
- know the definition of a matched filter and its properties
- be able to find the matched filter for a system
- know vector space concepts (internal product, basis vectors, norms, dimension of a space, find coefficients for a given basis, etc.)
- be able to represent signals of M-ary systems into signal space
- be able to exploit the Gram-Schmidt process to create an orthonormal basis for signal space
Reading
- section 3.1 Signals and Noise
- section 3.2 Detection of Binary Signals in Gaussian Noise
- appendix B Fundamentals of Statistical Decision Theory
Overview
Module 2 presents the structure for the receiver, and develops a signal space analysis to quantify the receiver performance. In part B of Module 2, we quantify the bit error rate (BER) of a binary system by using the signal space analysis. We examine both BPSK and OOK. Then, we introduce the Nyquist pulses as a method to avoid ISI. We apply the raised cosine pulse in a virtual laboratory.
Videos
- Signal space analysis
- Equivalence of Matched Filter and Correlator
- Probability of error (binary case)
Course notes
Objectives
- understand noise statistics in signal space
- know ML and MAP receivers in signal space – choose the closest symbol to the received signal, or choose the closest symbol subject to a weighting
- know BPSK and OOK modulation and their signal space representation
- develop the error probability for the BPSK modulations
- know the error probability and interpret them in terms of the distance between symbols
- know the equivalence between the matched filter and the correlator
- know the definition of a Nyquist pulse and the ideal Nyquist pulse; know the importance of Nyquist pulses
- be able to de manipulate raised cosine pulses
- be able to interpret an eye diagram
Reading
- section 3.1 Signals and Noise
- section 3.2 Detection of Binary Signals in Gaussian Noise
- section 3.3 Intersymbol Interference
- section 3.4.1 Channel Characterization
- section 3.4.2 Eye Pattern
- appendix B Fundamentals of Statistical Decision Theory