72988 - Digital Receiver Design And Optimization M

Learning outcomes

Fundamentals of decision and estimation theory. General approach to the design and optimization of digital receivers through Decision and Estimation theories; application to carrier recovery and synchronization, design of digital receivers in memory-less channels and in channels with memory; BCJR and Viterbi algorithms for detection and equalization. Detailed contents: universal approach to digital modulation, decision theory and estimation theory, estimation of carrier and clock parameters, digital detection in memory-less channels, digital detection in channels with memory; equalization.

Course contents

First module:

Introduction

Parametric description of a digital signal

 

1) Digital Modulation

Generalized approach to digital modulation. Signal space. Digital constellations. Waveforms. Orthonormality and Nyquist criterion. Matched filtering. Multi-carrier modulation (OFDM).

 

2) Decision Theory and Estimation Theory

Introduction and definitions. Classification of decision and estimation problems.

Decision theory . Binary decisions. Bayes risk and Bayes criterion. Maximum A Posteriori (MAP) criterion. Maximum Likelihood (ML) criterion. Minimax criterion. Neyman-Pearson criterion. Examples. Sufficient statistics. Receiver Operating Characteristics (ROC). Problems.

Estimation theory . Estimation of random parameters. Bayes risk and Bayes criterion. Minimum Mean Sqaure Error (MMSE), ABS, and MAP estimation. Examples. MMSE optimality. Estimation of unknown deterministic parameters. Unbiased estimation. ML estimation. Cramer-Rao bound (CRB). Efficient estimation. Modified CRB. Problems.

 

3) Estimation in digital receivers

Average Likelihood Ratio Test (ALRT) and Generalized Likelihood Ratio Test (GLRT). Pragmatic approach: Data Aided (DA), Decision Feedback (DF), Non-Data Aided (NDA) estimation. Phase uncertainty. Non coherent receiver. Differential demodulator. ML phase estimation: DA, DF, NDA. Ad hoc phase estimators. ML Symbol timing estimation: DF, NDA. ML Frequency estimation.

Second module:

4) Digital detection in memoryless channels

Additive White Gaussian Noise (AWGN) channel. Sufficient statistics. MAP and ML detection in AWGN. Performance. Union bound. Problems

 

5) Digital detection of correlated sequences

Coding and finite state machines (FSM). Trellis and state diagrams. Maximum Likelihood Sequence Detection (MLSD). Viterbi Algorithm (VA). MAP decoding: BCJR algorithm. Channels with distortion. Intersymbol interference. Equivalent channel models. Viterbi equalizer. Linear equalization.

 

Appendix) Elements of signal theory

Deterministic signals. Energy, power, correlation. Spectrum, Wiener-Kintchine theorem. Orthonormal representations. Fourier Series. Sampling theorem.

Random signals. Classification. Probability density and distribution functions. Bayes theorem. Stationarity. Statistical correlation. Gaussian processes. Error and Q functions. AWGN.

Readings/Bibliography

Lecture notes.
Van Trees, "Detection, Estimation, and Modulation Theory", Wiley and Sons, New York.

Teaching methods

Lectures and practical examples.

Assessment methods

The final exam includes a written test and and oral verification.
The written test consists of exercises from the two modules. Examples are provided in the course. The duration is set to 1h 40 min.
The oral part covers theoretical questions related to the two modules.

Office hours

See the website of Giovanni Emanuele Corazza

See the website of Alessandro Vanelli Coralli