# Detection, Estimation modulation theory part 1 - Vantress H.

ISBN 0-471-09517-6

**Download**(direct link)

**:**

**240**> 241 242 243 244 245 246 .. 254 >> Next

Comparison for infinite-bandwidth channel of

continuous modulation schemes with the bound

Bandlimited message and bandlimited channel

Comparison of optimum FM with bound

Comparison of simple companding schemes with

bound

Summary of analog message transmission and continuous

waveform estimation

664 Appendix: A Typical Course Outline

Chapter Ï-3 3.2.1

Lecture 26

Gaussian signals in Gaussian noise

Simple binary problem, white Gaussian noise on H0 and Hu additional colored Gaussian noise on Hx

Derivation of LRT using Karhunen-Loeve expansion

Various receiver realizations Estimator-correlator Filter-squarer

Structure with optimum realizable filter as component (this discussion is most effective when Lectures 20-22 are included; it should be mentioned, however, even if they were not studied) Computation of bias terms Performance bounds using fx(s) and tilted probability densities (at this point we must digress and develop the material in Section 2.7 of Chapter 1-2).

Interpretation of fi(s) in terms of realizable filtering errors

Example: Structure and performance bounds for the case in which additive colored noise has a one-pole spectrum

Lecture 27 665

Lecture 27

3.2.2 General binary problem

Derive LRT using whitening approach

Eliminate explicit dependence on white noise

Singularity

Derive fi(s) expression

Symmetric binary problems

Pr(e) expressions, relation to Bhattacharyya distance

Inadequacy of signal-to-noise criterion

666 Appendix: A Typical Course Outline

Lecture 28

Chapter Ï-3 Special cases of particular importance

3.2.3 Separable kernels

Time diversity

Frequency diversity

Eigenfunction diversity

Optimum diversity

3.2.4 Coherently undetectable case

Receiver structure

Show how fx(s) degenerates into an expression in

volving d2

3.2.5 Stationary processes, long observation times

Simplifications that occur in receiver structure

Use the results in Lecture 26 to show when these

approximations are valid

Asymptotic formulas for n(s)

Example: Do same example as in Lecture 26

Plot PD versus kT for various E/N0 ratios and

Pr s

Find the optimum kT product (this is continuous

version of the optimum diversity problem)

Assign remainder of Chapter II-3 (Sections 3.3-3.6) as reading

Lecture 29 667

Lecture 29

Chapter Ï-4 Radar-sonar problem

4.1 Representation of narrow-band signals and processes

Typical signals, quadrature representation, complex

signal representation. Derive properties: energy,

correlation, moments; narrow-band random pro

cesses; quadrature and complex waveform repre

sentation. Complex state variables

Possible target models; develop target hierarchy in Fig.

4.6

4.2 Slowly-fluctuating point targets

System model

Optimum receiver for estimating range and Doppler

Develop time-frequency autocorrelation function

and radar ambiguity function

Examples: Rectangular pulse

Ideal ambiguity function

Sequence of pulses

Simple Gaussian pulse

Effect of frequency modulation on the signal

ambiguity function

**240**> 241 242 243 244 245 246 .. 254 >> Next