Wireless Communication Systems
Est. read time: 2 minutes | Last updated: April 09, 2024 by John Gentile
Contents
Overview
I & Q Data
Given the trigonometric identity: $$ \cos(\alpha)\cos(\beta) = \cos(\alpha)\cos(\beta) - \sin(\alpha)\sin(\beta) $$
We can describe a sinusoidal signal in component parts as: $$ A\cos(2\pi f t + \phi) = A\cos(2\pi f t)\cos(\phi) - A\sin(2\pi f t)\sin(\phi) $$
Setting I (the amplitude of the In-Phase carrier) and Q (the amplitude of the Quadrature-phase carrier) allows us to describe the magnitude and phase (polar coordinate) of a sinusoid by the simple amplitudes: $$ I = A\cos(\phi) $$ $$ Q = A\sin(\phi) $$ $$ A\cos(2\pi f t + \phi) = I\cos(2\pi ft) - Q\sin(2\pi ft)$$
From the Euler identity of a sinusoidal signal , we can see the relationship between the polar coordinate phasor notation of a signal vector (e.g. a signal described by its amplitude and phase) and its cartesian coordinate equivalent when described in the complex 2D plane, which shows the I/Q data format is the real and imaginary parts, respectively, of a given sinusiod:
The benefit of I/Q data, and why its a popular data representation when working with RF systems (e.x. communications devices), is that it makes phase modulated signals easier to work with; because a sine wave with a -90 degree phase offset is equal to a cosine wave, the above I/Q relationships mean that the same carrier can be used for both I & Q (just simply phase shifted for Q) and that phase modulation can be achieved by simply modulating the amplitude of I & Q. This is much simpler (e.g. cost effective & performant) in real, digital implementations than direct phase modulation of a signal. For instance, a simple and common way to transform I/Q to RF can be shown in the following block diagram:
I/Q data can also be represented by a Constellation Diagram which provides an intuitive mapping between a set of digital bits and I/Q symbols for a given modulation scheme, for example 16-ary Quadtrature Amplitude Modulation (QAM):
Software Defined Radio (SDR)
RTL-SDR
RTL-SDR Installation
- RTL-SDR Quick Start Guide: general guides to RTL-SDR features and dipole antenna usage.
- RTL-SDR for Linux Quick Start Guide: installation instructions for necessary drivers and libraries to get up and running.
References
- Learn SDR with Prof Jason - YouTube Playlist
- veeresht/CommPy
- Wireless Pi
- MathWorks Communications, SATCOM and Wireless HDL Toolboxes