Signal Processing for Communication Systems
This article discusses the method of generating two correlated random sequences using Matlab. If you are looking for the method on generating multiple sequences of correlated random numbers, I urge you to go here. Generating two vectors of correlated random numbers, given the correlation coefficient $latex \rho $, is implemented in two steps. The first … Read more
Generating a continuous signal and sampling it at a given rate is demonstrated here. In simulations, we may require to generate a continuous time signal and convert it to discrete domain by appropriate sampling. For baseband signal, the sampling is straight forward. By Nyquist Shannon sampling theorem, for faithful reproduction of a continuous signal in … Read more
What a power delay profile is, how it shows multipath taps vs excess delay, and how it connects to delay spread and wireless channel models.
Multipath & PDP (same on every page in this path) 1. Power delay profile → 2. Scattering function (you are here) → 3. TDL modeling Tools: PDP demo · 3GPP TDL Understand various characteristics of a wireless channel through multipath channel models. Discuss Wide Sense Stationary channel, uncorrelated scattering channel, wide sense stationary uncorrelated scattering … Read more
BLUE / Gauss–Markov: the best linear unbiased estimator is weighted least squares when noise covariance is known — intuition and formula.
Key focus: Understand step by step, the least squares estimator for parameter estimation. Hands-on example to fit a curve using least squares estimation Background: The various estimation concepts/techniques like Maximum Likelihood Estimation (MLE), Minimum Variance Unbiased Estimation (MVUE), Best Linear Unbiased Estimator (BLUE) – all falling under the umbrella of classical estimation – require assumptions/knowledge … Read more
The agenda for the subsequent series of articles is to introduce the idea of autocorrelation, AutoCorrelation Function (ACF), Partial AutoCorrelation Function (PACF) , using ACF and PACF in system identification. Introduction Given time series data (stock market data, sunspot numbers over a period of years, signal samples received over a communication channel etc.,), successive values … Read more
If a time series data is assumed to be following an Auto-Regressive (\(AR(N)\)) model of given form, the natural tendency is to estimate the model parameters \(a_1,a_2, \cdots, a_N\). Least squares method can be applied here to estimate the model parameters but the computations become cumbersome as the order \(N\) increases. Fortunately, the AR model … Read more
Key focus: “Why can’t I just use a matrix to solve ARMA?” The answer is right there in the shape of the surface—you can’t solve a “warped” landscape with a linear equation. Introduction In signal modeling, our goal is to find a set of coefficients (ak and bk) that best describe an observed signal. We … Read more
Key focus: AR, MA & ARMA models express the nature of transfer function of LTI system. Understand the basic idea behind those models & know their frequency responses. How do you describe a complex, random signal—like the sound of a human voice or the fluctuating power of a fading channel—using only a few numbers? The … Read more