Signal Processing for Communication Systems
In a given communication system, we always want to send data that represent real world data representing some physical quantity (be it speech, temperature, etc..,) .The real world physical quantity exist in analog domain and it becomes imperative to convert it to digital domain if we want to send it via a digital communication system. … Read more
What is Probability? Probability is a branch of mathematics that deals with uncertainty. The term “probability” is used to quantify the degree of belief or confidence that something is true (or false). It gives us the likelihood of occurrence of a given event. It is expressed as a number that could take any value in … Read more
When simulating digital modulations in Matlab, it is useful to verify the simulated BER performance curves against theoretical BER curves.Matlab has an inbuilt visualization tool, ‘BERTOOL’, for this purpose. Matlab’s BERTOOL supports 6 types of digital modulations over 3 types of channel for plotting theoretical BER. The six supported modulations are PSK,DPSK,OQPSK,PAM,QAM,FSK and the three … Read more
Log-distance / log-normal shadowing path loss: formula beyond Friis, path-loss exponent by environment, shadowing χ, and how it extends free-space models.
Friis transmission equation and free-space path loss: $latex (4\pi d/\lambda)^2$, dB form, assumptions, and when to move to log-distance or two-ray models.
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The medium between the transmitting antenna and the receiving antenna is generally termed as “channel”. In wireless transmission, the characteristics of the signal changes as it travels from the transmitter to the receiver. The signal characteristics are due to several phenomena: 1) existence of line of sight path between the antennas, 2) reflection, refraction and … Read more
Let’s review indexing techniques in Matlab: Indexing one dimensional array, two dimensional array, logical indexing, reversiong a vector – are covered. Consider a sample vector in Matlab. Index with single value Index with range of values Select a range of elements using ‘:’ operator. Example: Select elements with index ranging from 1 to 5. Making … Read more
Cholesky decomposition is an efficient method for inversion of symmetric positive-definite matrices. Let’s demonstrate the method in Python and Matlab. Cholesky factor Any $n \times n$ symmetric positive definite matrix $A $ can be factored as $$A=LL^T $$ where $L$ is $n \times n$ lower triangular matrix. The lower triangular matrix $L$ is often called … Read more
It is often required to check if a given matrix is positive definite or not. Three methods to check the positive definiteness of a matrix were discussed in a previous article . I will utilize the test method 2 to implement a small matlab code to check if a matrix is positive definite.The test method … Read more