definitions

basics

contents

  1. Signal Representations for Communication Systems
    1. Review of signals and digital transmission systems.
    2. Complex envelope representation of real band-pass signals and its energy relationships.
    3. Signal space representation.
  2. Random Variables and Processes for Communication Systems
    1. Review of a single RV and related operations (expected value, moments, central moments).
    2. Pairs of RVs: Joint distributions, conditional distributions, covariance and correlation. Multivariate Gaussian distribution.
    3. Introduction to random processes, statistical characterization and classification. Spectral characteristics.
    4. Random processes through LTI systems. Gaussian processes and AWGN. Capacity of the AWGN channel.
  3. Baseband Digital Transmission Over Band-Limited Channels
    1. Inter-symbol interference (ISI), Nyquist's criterion, partial response signalling, data detection for controlled ISI. Eye diagrams.
    2. Applications to practical baseband systems.
  4. Passband Digital Transmission
    1. Linear digital modulation techniques: ASK, PSK, and QAM. Constellation diagrams.
    2. Nonlinear modulation techniques: FSK. Spectra of modulated signals, spectral and power efficiencies.
    3. Optimum receivers: MAP and ML principles, receiver implementation, matched filter and correlation realizations, error performance.
    4. Comparison of different modulation schemes.
    5. Applications to practical passband systems.

AWGN case ⇒ non distortive channel. only additive noise is present

v(t) = P epsilon uk p (t -kt - tou) t n(t)

attenuation is compensated using an amplifier and propagation delay can be corrected using timing recovery circuits

we can assume there is no additive noise but still there can be errors due to … due to inter symbol interference, so we have to select $P(t)$ carefully

apply inverse function, and sample at T intervals should give us u(t), the $k^{th}$ sample will give $\color{#DFA7F7}u_k$

nyquist criteria for ISI (Inter symbol Interference) free communications

Errors Errors Errors

Pulse Shaping- remove ISI

Equalization - channel distortion

Noise

Pulse Overlaps