API for wired transmission of OFDM/OFDMA GroupDelay Analysis in Java

Purpose

As coax or wired systems are aging and have not been updated, operators are continuously increasing their data rates by both increasing the QAM order and/or widening channel bandwidth using OFDM. One of the considerations is placing an OFDM near a cable roll-off. The immediate effect is a lowering of attenuation, which can result in a lower signal-to-noise (SNR) or MER. Additionally, there is also a secondary effect called the Group Delay (GD) of the signal.

At the time I wrote this API it was used to take the OFDM/OFDMA channel estimation and derive the GD which is based on the OFDM probe pilot data. Since OFDM/OFDMA is a common transport protocol using in WIFI, DOCSIS, MoCA, Home Plug, and others, this API is generic enough to be used for calculating GD for an OFDM signal.

This API is based on a paper written by CHRISTOPHER J. STRUCK titled Group Delay

Group Delay Process

The following example was generated using GroupDelay_OFDM

Convert IQ or Complex to Radians "Remember your highSchool trigonometry class"

Get Phase/Radian from Complex Number Howto

Unwrap Phase Information

Wrapped Radians/Phase

Unwrapped Radians/Phase

Calculate Group Delay

API Usage

Create a list of IQ or Complex samples that MUST include the Center Frequency to properly calculate the group delay.

Code Example 1

Input Values

FREQ			REAL(Q)			Imaginary(I)
729700000		-1.050292969		0.223144531
729750000		-0.984375		0.439697266
729800000		-0.874755859		0.635986328
729850000		-0.726806641		0.806274414

Group Delay Output

Frequency(hertz): 729750000 - GroupDelay(seconds): 0.000000670807
Frequency(hertz): 729800000 - GroupDelay(seconds): 0.000000663868
Frequency(hertz): 729850000 - GroupDelay(seconds): 0.000000663804