Signal Processing for Communication Systems
Key focus: Euclidean & Hamming distances are used to measure similarity or dissimilarity between two sequences. Used in Soft & Hard decision decoding. Distance is a measure that indicates either similarity or dissimilarity between two words. Given a pair of words a=(a0,a1, … ,an-1) and b=(b0,b1,…,bn-1) , there are variety of ways one can characterize … Read more
Fading & Diversity — 6 lessons (same on every page in this path) 1. Rayleigh BER → 2. Clarke’s model (you are here) → 3. Young’s model → 4. SIMO models → 5. Selection combining → 6. MRC Tools: BER vs Eb/N0 · 3GPP TDL · CDL / Doppler Optional branch from Fading & Diversity. … Read more
Simulate BPSK bit-error rate in Python and Matlab, compare Monte Carlo curves to the Q-function formula, and open the same points on the BER calculator.
Markov chains are useful in computing the probability of events that are observable. However, in many real world applications, the events that we are interested in are usually hidden, that is we don’t observe them directly. These hidden events need to be inferred. For example, given a sentence in a natural language we only observe the … Read more
MRC weights each diversity branch by its channel gain to maximize post-combiner SNR — formula, intuition, and comparison to selection combining.
MIMO — Diversity path 1. Intro → 2. Diversity vs mux → 3. SIMO → 4. Selection combining → 5. MRC Tools: Diversity & multiplexing demo Introduction Selection combining is the diversity scheme you can explain at a whiteboard in one minute: measure the SNR on each antenna, keep the best, ignore the rest. The … Read more
MIMO — Diversity path 1. Intro → 2. Diversity vs mux → 3. SIMO → 4. Selection combining → 5. MRC Tools: Diversity & multiplexing demo Introduction Turn off every transmit antenna but one, and keep several receive antennas. That SIMO setup is the cleanest way into spatial diversity in class: no space-time code to … Read more
Key focus: Learn how to generate color noise using auto regressive (AR) model. Apply Yule Walker equations for generating power law noises: pink noise, Brownian noise. Auto-Regressive (AR) model An uncorrelated Gaussian random sequence \(x[n]\) can be transformed into a correlated Gaussian random sequence \(y[n]\) using an AR time-series model. If a time series random … Read more
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