Signal Processing for Communication Systems
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MIMO — Capacity path 1. Intro → 2. Channel model → 3. SISO capacity → 4. Ergodic SISO → 5. MIMO capacity Tools: Shannon calculator Introduction Shannon’s formula \(C=\log_2(1+\mathrm{SNR})\) shows up in every communications course. On a fading channel the SNR itself is random, so capacity becomes a random variable. What does that mean in … Read more
MIMO — Capacity path 1. Intro → 2. Channel model → 3. SISO capacity → 4. Ergodic SISO → 5. MIMO capacity Tools: Shannon calculator Introduction Capacity formulas and diversity analyses assume you already have a channel model. Skip that step, jump straight to \(\log\det\), and it is hard to see why correlated antennas multiplex … Read more
MIMO — Diversity path 1. Intro → 2. Diversity vs mux → 3. SIMO → 4. Selection combining → 5. MRC Tools: Diversity & multiplexing demo Introduction We already wrote \(\mathbf{y}=\mathbf{Hx}+\mathbf{n}\) and noted that space can buy reliability or rate. Can you maximise both at once? In general, no: you can have some of each, … Read more
MIMO — Diversity path 1. Intro → 2. Diversity vs mux → 3. SIMO → 4. Selection combining → 5. MRC Tools: Diversity & multiplexing demo MIMO — Capacity path 1. Intro → 2. Channel model → 3. SISO capacity → 4. Ergodic SISO → 5. MIMO capacity Tools: Shannon calculator Introduction If you have … Read more
Generate linear chirps, view their evolving frequency, and compute FFT/PSD in Matlab and Python — with links to basic FFT plotting posts.
Generate a Gaussian pulse, compute its FFT/PSD, and see why a Gaussian time pulse has a Gaussian spectrum.
Numerous texts are available to explain the basics of Discrete Fourier Transform and its very efficient implementation – Fast Fourier Transform (FFT). Often we are confronted with the need to generate simple, standard signals (sine, cosine, Gaussian pulse, square wave, isolated rectangular pulse, exponential decay, chirp signal) for simulation purpose. I intend to show (in a series of articles) … Read more
Generate a square wave, take its FFT/PSD, and recognize the odd-harmonic 1/n envelope predicted by Fourier series.
Matlab walk-through: sample a sinusoid, take FFT, build the frequency axis, and read peak locations — with Python twin link and FFT tool.
In the previous post, a method for generating two sequences of correlated random variables was discussed. Generation of multiple sequences of correlated random variables, given a correlation matrix is discussed here. Correlation Matrix Correlation matrix defines correlation among N variables. It is a symmetric $latex N \times N $ matrix with the $latex (ij)^{th} $ … Read more