Frequency-Domain Modeling of OFDM Transmission with Insufficient Cyclic Prefix using Toeplitz Matrices

TL;DR

This paper introduces a new mathematical framework using Toeplitz matrices to model ISI in OFDM systems with insufficient cyclic prefix, improving understanding and simulation efficiency of interference effects.

Contribution

It presents a novel formula for FFT of triangular Toeplitz matrices and demonstrates its application in modeling ISI and enhancing real-time channel simulation in OFDM systems.

Findings

Distortion from ISI is most significant for nearby subcarriers.

Knowledge of ISI coefficients near the diagonal improves error performance.

Framework is more efficient than traditional time domain models for high user counts.

Abstract

A novel mathematical framework is proposed to model Intersymbol Interference (ISI) phenomenon in wireless communication systems based on Orthogonal Frequency Division Multiplexing (OFDM) with or without cyclic prefix. The framework is based on a new formula to calculate the Fast Fourier Transform (FFT) of a triangular Toeplitz matrix, which is derived and proven in this paper. It is shown that distortion inducted by the ISI from a given subcarrier is the most significant for the closest subcarriers and the contribution decays as the distance between subcarriers grows. According to numerical experiments, knowledge of ISI coefficients concentrated around the diagonal of Channel Frequency Response (CFR) matrix improves the receiver's error floor significantly. The potential use of the framework for real-time frequency domain channel simulation was also investigated and demonstrated to be more efficient than conventional time domain Tapped Delay Line (TDL) model when a number of simulated users is high.