Signal Processing for Communication Systems
The aim of this article is to demonstrate the application of spectral factorization method in generating colored noise having Jakes power spectral density. Before continuing, I urge the reader to go through this post: Introduction to generating correlated Gaussian sequences. In spectral factorization method, a filter is designed using the desired frequency domain characteristics (like … Read more
Key focus: Colored noise sequence (a.k.a correlated Gaussian sequence), is a non-white random sequence, with non-constant power spectral density across frequencies. Introduction Speaking of Gaussian random sequences such as Gaussian noise, we generally think that the power spectral density (PSD) of such Gaussian sequences is flat.We should understand that the PSD of a Gausssian sequence … Read more
What’s the need for GMSK Minimum shift keying (MSK) is a special case of binary CPFSK with modulation index $latex h=0.5$. It has features such as constant envelope, compact spectrum and good error rate performance. The fundamental problem with MSK is that the spectrum is not compact enough to satisfy the stringent requirements with respect … Read more
Introduction An exponential random variable (RV) is a continuous random variable that has applications in modeling a Poisson process. Poisson processes find extensive applications in tele-traffic modeling and queuing theory. They are used to model random points in time or space, such as the times when call requests arriving at an exchange, the times when … Read more
Binomial random variable, a discrete random variable, models the number of successes in $latex n$ mutually independent Bernoulli trials, each with success probability $latex p$. The term Bernoulli trial implies that each trial is a random experiment with exactly two possible outcomes: success and failure. It can be used to model the total number of … Read more
Bernoulli random variable is a discrete random variable with two outcomes – success and failure, with probabilities p and (1-p). It is a good model for binary data generators and also for modeling bit error patterns in the received binary data when a communication channel introduces random errors. To generate a Bernoulli random variable X, … Read more
An important consideration for propagation models are the existence of objects within what is called the first Fresnel zone. Fresnel zones, referenced in Figure 1 are ellipsoids with the foci at the transmitter and the receiver, where the path length between the direct path and the alternative paths are multiples of half-wavelength ($latex \lambda/2$). Rays … Read more
Modeling diffraction loss Propagation environments may have obstacles that hinder the radio transmission path between the transmitter and the receiver. Idealized models for estimating the signal loss associated with diffraction by such obstacles are available. The shape of the obstacles considered in these model are too idealized for real-life applications, nevertheless, these models can serve … Read more
Friis propagation model considers the line-of-sight (LOS) path between the transmitter and the receiver. The expression for the received power becomes complicated if the effect of reflections from the earth surface has to be incorporated in the modeling. In addition to the line-of-sight path, a single reflected path is added in the two ray ground … Read more
Outdoor propagation models involve estimation of propagation loss over irregular terrains such as mountainous regions, simple curved earth profile, etc., with obstacles like trees and buildings. All such models predict the received signal strength at a particular distance or on a small sector. These models vary in approach, accuracy and complexity. Hata Okumura model is … Read more