Signal Processing for Communication Systems
[ratings] 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 … Read more
[ratings] 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 … Read more
Log distance path loss model Log distance path loss model is an extension to the Friis free space model. It is used to predict the propagation loss for a wide range of environments, whereas, the Friis free space model is restricted to unobstructed clear path between the transmitter and the receiver. The model encompasses random … Read more
Friis free space propagation model is used to model the line-of-sight (LOS) path loss incurred in a free space environment, devoid of any objects that create absorption, diffraction, reflections, or any other characteristic-altering phenomenon to a radiated wave. It is valid only in the far field region of the transmitting antenna [1] and is based … Read more
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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 $latex n \times n$ symmetric positive definite matrix $latex A $ can be factored as $latex A=LL^T &s=2$ where $latex L$ is $latex n \times n$ lower triangular matrix. The lower triangular … Read more
[ratings] 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 … Read more
Key focus: Know the expressions to solve triangular matrix using forward and backward substituting techniques and the FLOPS required for solving it. Forward Substitution: Consider a set of equations in a matrix form $latex Ax=b $, where A is a lower triangular matrix with non-zero diagonal elements. The equation is re-written in full matrix form … Read more