Infocommunication Theory I.

1. week
The general description of the modulated signals. Description of the modulated signals in the vector space.  The generalized Fourier series, Gram–Schmidt orthogonalization. The description of the white Gaussian noise in the vector space. The autocorrelation function of the white Gaussian noise. The joint probability density function of the noise vector.
2. week
Examples for the description of the modulated signals in the vector space. QPSK signal, FSK signal, analysis of some special cases (MSK, FFSK). Further analysis of the MSK signal (MSK signal with non continuous phase, MSK signal with continuous phase, the phasor diagram of the continuous phase MSK signal and its phase tree). Example: technical parameters of a MSK type baseband modem. Advantages of the continuous phase systems.
3. week
The optimum demodulation rule: criterion of the minimization of the probability of error. Theoretical background of the Bayesian decision, notion of decision regions in the case of white Gaussian noisy channels. Calculation of the decision regions.
 4. week
Examples for the calculation of the decision regions (QPSK type signals (N = 2, M = 4) with uniform energies, but different a priori probabilities, QPSK type signals (N = 2, M = 4) with uniform energies and a with uniform a priori probabilities). The structure of the optimum coherent receiver, alternative variances.
 5. week
Calculation of the probability of error in optimum coherent receiver. Union bounding technique, notion of the pair wise probability of error. Analysis of the argument of Q(x) function and study of the features of the function, approximate calculations, asymptotic behavior.  
6. week
Examples for the calculation of probability of error (BPSK signal, QPSK signal, MSK signal). Approximate calculations of the probability of error, the role of the minimum Euclidean distance. Further characteristics of the Q(x) function.
7. week
Generalized characterization of the coherent modulation systems. Examples for the generalized characterization of the coherent modulation systems (modulation system with general elementary signals, continuous phase MSK modulation system, Ungerboeck code in the case of 4PSK, calculation of the minimum Euclidean distance with 8 inner states).
8. week
Structure and the probability of error of the optimum non coherent receiver. Description of the non coherent signals in the vector space. Calculation of the probability density functions necessary for the optimum receiving (for Bayesian decision). Use of the theory of sufficient statistics. Defining of the necessary decision parameters for the optimum non coherent receiving.
9. week
Structures of non coherent receivers (baseband quadrature correlation receiver, baseband quadrature matched filter receiver, bandpass non coherent matched filter receiver, simplified bandpass detector). Illustrative comparison of the optimum non coherent receivers. (signals of the quadrature correlation receiver and the  baseband quadrature matched filter receiver, illustration of the signals of  bandpass non coherent matched filter receiver).
10. week
Probability of error in non coherent receivers. Optimum decision based on Rice- and Rayleigh-distributions. Example for calculation of probability of error in non coherent receivers. Comparison of coherent and non coherent systems (asymptotic behavior of coherent and non coherent channels).
 
11. week


Extension of the vector space for band limited signals. The L2 space of the square integrable functions. General definition of vector space. Description of baseband band limited signals in the vector space. Description of band pass band limited signals in the vector space. The description of the white Gaussian noise in the generalized vector space. The orthogonal PAM and QAM modulations. Performance of uncoded systems compared with the Shannon capacity. Performance analysis of M-PAM and (MxM)-QAM systems.
12. week
Performance of small vector spaces. Signal constellations in the case of white Gaussian noise. Performance analysis in power limited region. Performance analysis in band limited region.  Introduction into the binary codes. Binary signal constellations. The binary linear block codes, as binary vector spaces. The binary linear codes in the Euclidean space.
13. week
Reed-Muller codes. Decoding of the binary block codes. Analysis of the power spectrum of the modulated signals.  Characteristics of the cyclic stationary signals. Power spectrum density function of the sinusoidal signal with random phase. The power spectrum density function of bandpass PAM signals. Illustrative examples for spectral analysis of PAM signals.
14. week
Analysis of the general optimum PAM system. Partial response PAM type systems. Examples for the spectral analysis of the partial response PAM type systems. Spectral analysis of general modulation systems. The power spectrum of the continuous phase FM signals.