The September/October 2025 issue of ARRL’s QEX magazine features “Real and Complex Signal Basics” by Michelle Thompson W5NYV. The article provides a step-by-step mathematical explanation of how complex modulation works in digital radio systems.
The piece starts with simple single-carrier real signals and builds up to explain quadrature amplitude modulation (QAM). Using clear mathematical derivations, it shows how two real signals can be transmitted simultaneously using sine and cosine carriers that are 90 degrees out of phase, then separated at the receiver using trigonometric identities and integration.
Subjects covered include:
How real signals create symmetrical frequency domain images
The transition from 4-level amplitude modulation to 16QAM using I and Q coordinates
The mathematical basis for quadrature mixing at both transmitter and receiver
Why complex modulation eliminates unwanted frequency images
How this approach enables higher data rates without requiring finer amplitude resolution
The article emphasizes the practical advantages of complex modulation. You get increased spectral efficiency, easier filtering due to single-sided transmission, and the flexibility to implement any modulation scheme through software-defined radio techniques.
This mathematical foundation underlies much of ORI’s digital radio development work, including the Opulent Voice protocol and other broadband digital communications projects.
The full article is available to ARRL members through QEX magazine. Want to publish it in your club newsletter? Article is available on request from ARRL from qst@arrl.org
Looking to Learn more about IQ Modulation?
Basics of IQ Signals and IQ modulation & demodulation – A tutorial by W2AEW
https://www.youtube.com/watch?v=h_7d-m1ehoY
Software Defined Radio For Engineers (free PDF from Analog Devices)
https://www.analog.com/en/resources/technical-books/software-defined-radio-for-engineers.html
These resources will get you well on your way!