Optimal Radix-2 FFT Compatible Filters for GFDM

TL;DR

This paper introduces a novel filter design for GFDM that ensures non-singular modulation matrices with an optimal condition number, enabling efficient radix-2 FFT implementation and improving signal quality.

Contribution

It presents an analytical method to compute the modulation matrix condition number and proposes a new filter design for GFDM with optimal properties not achievable before.

Findings

The new filter design yields non-singular matrices for even subcarriers and subsymbols.

The optimal filter minimizes the condition number of the modulation matrix.

Numerical results show improved SIR and NEF for the proposed design.

Abstract

For a linear waveform, a finite condition number of the corresponding modulation matrix is necessary for the waveform to convey the message without ambiguity. Based on the Zak transform, this letter presents an analytical approach to compute the condition number of the modulation matrix for the multi-carrier waveform generalized frequency division multiplexing (GFDM). On top, we further propose a filter design that yields non-singular modulation matrices for an even number of subcarriers and subsymbols, which is not achievable for any previous work. Such new design has significant impact on implementation complexity, as the radix-2 FFT operations for conventional multicarrier waveforms can readily be employed for GFDM. Additionally, we analytically derive the optimal filter that minimizes the condition number.We further numerically evaluate the signal-to-interference ratio (SIR) and noise-enhancement factor (NEF) for matched filter (MF) and zero-forcing (ZF) GFDM receivers for such design, respectively.