Filter Design for Generalized Frequency-Division Multiplexing

TL;DR

This paper explores optimal filter design for GFDM to maximize data rate and minimize out-of-band emissions, demonstrating that tailored filters outperform standard Dirichlet filters, especially in channels with CFO.

Contribution

It formulates the GFDM filter optimization problems for rate and OOB emission minimization, providing solutions that adapt to channel conditions and improve performance.

Findings

Dirichlet filters are rate-optimal in AWGN channels without CFO.

Properly designed GFDM filters outperform Dirichlet filters in CFO-affected channels.

Joint filter and window design effectively balances rate maximization and OOB emission reduction.

Abstract

In this paper, optimal filter design for generalized frequency-division multiplexing (GFDM) is considered under two design criteria: rate maximization and out-of-band (OOB) emission minimization. First, the problem of GFDM filter optimization for rate maximization is formulated by expressing the transmission rate of GFDM as a function of GFDM filter coefficients. It is shown that Dirichlet filters are rate-optimal in additive white Gaussian noise (AWGN) channels with no carrier frequency offset (CFO) under linear zero-forcing (ZF) or minimum mean-square error (MMSE) receivers, but in general channels perturbed by CFO a properly designed nontrivial GFDM filter can yield better performance than Dirichlet filters by adjusting the subcarrier waveform to cope with the channel-induced CFO. Next, the problem of GFDM filter design for OOB emission minimization is formulated by expressing the power spectral density (PSD) of the GFDM transmit signal as a function of GFDM filter coefficients, and it is shown that the OOB emission can be reduced significantly by designing the GFDM filter properly. Finally, joint design of GFDM filter and window for the two design criteria is considered.