1. Digital Modems Lecture 1 Fall 2008

2. Course “mechanics”

3. Schedule & names for this semester Every Tuesday, 12 pm-2:15 pm Lecturers  Andreas Polydoros  Costas Aidinis  Stelios Stefanatos {polydoros}, {caidinis}, {sstefanatos}@phys.uoa.gr Offices: Building V, Second floor.

4. Course Outline Fundamentals of detection theory  Detection problem formulation  Cost functions  Likelihood ratio  Optimal detection rules (Bayes/Neyman-Pearosn)  Handling of nuisance parameters Discrete representation of stochastic processes  Signal space/basis  Orthonormal/Karhunen-Loeve expansion  Likelihood functionals Application in communications  Binary/M-ary systems  Coherent/Non-coherent detection in AWGN  Error probability

5. Recommended Reading Course text-book  H. L. Van Trees, Detection, Estimation, and modulation theory Additional references  J. G. Proakis, Digital Communications  S. M. Kay, Fundamentals of statistical signal processing: Detection theory

6. A Systems View

7. ISO-OSI Protocol stack

8. Terminology The 'Open Systems Interconnection Basic Reference Model' (OSI Reference Model or OSI Model) is an abstract description for layered communications and computer network protocol design.network protocol It was developed as part of the Open Systems Interconnection (OSI) initiative[1].Open Systems Interconnection[1] In its most basic form, it divides network architecture into seven layers which, from top to bottom, are the Application, Presentation, Session, Transport, Network, Data-Link, and Physical Layers. It is therefore often referred to as the OSI Seven Layer Model. The Physical Layer defines the electrical and physical specifications for devices.Physical Layer In particular, it defines the relationship between a device and a physical medium. To understand the function of the Physical Layer in contrast to the functions of the Data Link Layer, think of the Physical Layer as concerned primarily with the interaction of a single device with a medium, where the Data Link Layer is concerned more with the interactions of multiple devices (i.e., at least two) with a shared medium. The Physical Layer will tell one device how to transmit to the medium, and another device how to receive from it (in most cases it does not tell the device how to connect to the medium). Obsolescent Physical Layer standards such as RS-232 do use physical wires to control access to the medium.RS-232 The major functions and services performed by the Physical Layer are: Establishment and termination of a connection to a communications medium.connectioncommunicationsmedium Participation in the process whereby the communication resources are effectively shared among multiple users. For example, contention resolution and flow control.contentionflow control ModulationModulation, or conversion between the representation of digital data in user equipment and the corresponding signalsdigital data transmitted over a communications channel. These are signals operating over the physical cablingchannel (such as copper and optical fiber) or over a radio link.optical fiberradio link Source: http://en.wikipedia.org/wiki/OSI_model

9. Three-part PHY-layer system model Tx: Transmitter Rx: Receiver Channel: Models the physical distortion Noise: Thermal noise, interference, …

10. Block-Diagram Functions of Tx Source  Discrete or analog Source coding  Redundancy removal (entropy coding)  Data compression (introducing distortion) Channel coding  Introduces redundancy to compensate for channel/noise Data format  Mapping bits to symbols, create packets, frames, e.t.c. Modulator  Convert the discrete-time input to the continuous-time transmitted waveform Receiver performs the inverse operations

11. Tx-Rx diagram for different AI’s

12. Scrambler PuncturingInterleaver Reed- Solomon Convolutional Encoder Turbo EncoderPuncturing Constellation Encoder Pilot Generator Pilot & Data Multiplexer ST Encoder (TSD) Mapping IFFT Cyclic Prefix Insertion PAPR Scaling Output Logic Adaptivity Control From Rx Preambles Generator Output Logic PAPR Scaling Cyclic Prefix Insertion Input Logic Data Command A modern Tx: MIMO/OFDM

13. A modern Rx: MIMO/OFDM

14. Theory

15. Physical Channel Distortion-less (LOS) channel: Two-ray channel: : channel gain : delay

16. Physical Channel The two-ray channel is the simplest example of a multipath fading channel Question: Under what circumstances is the two-ray channel distortion-less Answer: It depends on the pulse shape  If the channel is (approximately) distortion-less  If the channel inevitably introduces severe distortion

17. Inference in general Inference is the task of learning (e.g., making estimations/decisions) based on given data Examples of inference:  Estimate the path loss introduced by a fading channel  Estimate the range of an enemy aircraft  Predict the stock market’s gain/loss  Decide on which product is best  Decide on which model best fits the observations In this course we concentrate on a single sub-topic of inference theory: Hypothesis testing (Detection theory) Emphasis will be given on how the theory is applied to design optimal receiver structures

18. Decision criteria A cost function must be defined in order to obtain a detection rule This function quantifies the cost of taking erroneous decisions  What is the cost of “detecting” an aircraft when it is actually not there?  What is the cost of missing the presence of the aircraft? After construction of the cost function an optimal decision rule can be obtained that results in minimum cost The appropriate cost function depends upon the context of the specific problem and is not unique

19. Hypothesis testing @ Rx side Problem formulation:  We are given a set of data (observations)  This set could have been generated as the outcome of one of M possible hypothesis  Given the data, and any other statistical information, we want to decide on the correct hypothesis Examples:  Decide if the data provided by a radar indicate the presence of an aircraft  From a noisy received signal, decide on the transmitted digital sequence

20. Rx Problem formulation Radar example: Binary transmission example: : observed signal : signal generated by the aircraft (if present) : AWGN of power

21. Rx Problem formulation In this class, only distortion-less channels will be considered, including AWGN The observed signals are of the form: In case the observation is discrete we have : Observation interval where now we use vectors instead of continuous-time functions