[Paper Review] Overlap Frequency Domain Equalization for Faster-than-Nyquist Signaling

Hiroyuki Fukumoto, Kazunori Hayashi|arXiv (Cornell University)|Sep 2, 2015

PAPR reduction in OFDM12 references19 citations

TL;DR

This paper proposes overlap frequency domain equalization (FDE) for faster-than-Nyquist signaling (FTNS) to achieve higher spectral efficiency without guard intervals, using MMSE-based equalizer weights that account for colored noise from receive filters. The method enables 30% higher transmission rates than Nyquist rate with no BER performance degradation when using root raised cosine filters with 0.5 roll-off factor.

ABSTRACT

This letter proposes the Faster-than-Nyquist signaling (FTNS) using overlap frequency domain equalization (FDE), which compensates the inter-symbol interference (ISI) due to band limiting filters of the FTNS at the transmitter and the receiver as well as the frequency selective fading channel. Since overlap FDE does not require any guard interval (GI) at the transmitter such as cyclic prefix (CP), higher spectral efficiency can be achieved compared to FTNS scheme using the conventional FDE. In the proposed method, the equalizer weight is derived based on minimum mean square error (MMSE) criterion taking the colored noise due to the receiving filter into consideration. Moreover, we also give an approximated FDE weight in order to reduce the computational complexity. The performance of the proposed scheme is demonstrated via computer simulations.

Motivation & Objective

• To address the spectral efficiency loss caused by guard intervals (e.g., cyclic prefix) in conventional FDE-based FTNS receivers.
• To mitigate inter-symbol interference (ISI) from band-limiting transmit/receive filters and frequency-selective fading channels in FTNS systems.
• To explicitly account for colored noise due to receive filtering in FDE design, which is often neglected in prior work.
• To reduce computational complexity in FDE while maintaining performance through an approximated one-tap MMSE weight.
• To demonstrate that overlap FDE enables higher spectral efficiency than conventional FDE with CP, especially at high transmission rates.

Proposed method

• Employs overlap FDE to eliminate the need for guard intervals at the transmitter, improving spectral efficiency.
• Derives MMSE equalizer weights that explicitly consider colored noise from the receive filter, improving robustness.
• Introduces an approximated one-tap FDE weight to reduce computational complexity while preserving performance.
• Uses a block-processing approach with DFT size 512 and truncation of the pulse response with ν=10 to manage implementation complexity.
• Applies root raised cosine (RC) filters with roll-off factor 0.5 as transmit and receive filters to meet Nyquist criteria at higher symbol rates.
• Employs frequency-domain equalization with block-wise processing, where overlapping symbols are used to reduce edge distortion.

Experimental results

Research questions

• RQ1 Can overlap FDE eliminate the need for guard intervals in FTNS while maintaining or improving BER performance?
• RQ2 How does colored noise from the receive filter impact FDE performance in FTNS, and can it be effectively modeled and compensated?
• RQ3 What is the achievable spectral efficiency gain of overlap FDE over conventional FDE with cyclic prefix in FTNS systems?
• RQ4 Can a low-complexity approximated MMSE FDE weight achieve performance close to the full MMSE solution?
• RQ5 To what extent can the transmission rate exceed the Nyquist rate without BER degradation when using overlap FDE and proper filtering?

Key findings

• The proposed overlap FDE scheme achieves higher spectral efficiency than conventional FDE with cyclic prefix by eliminating guard intervals.
• Explicitly accounting for colored noise in the MMSE equalizer weight leads to significantly better BER performance than ignoring it, especially at higher transmission rates.
• The approximated one-tap FDE weight achieves performance comparable to the full MMSE weight, validating its use for complexity reduction.
• The proposed scheme achieves 30% higher transmission rate than the Nyquist rate without BER degradation when using root raised cosine filters with a roll-off factor of 0.5.
• In both AWGN and Rayleigh fading channels, the proposed scheme outperforms the conventional FDE with CP at the same effective data rate.
• The RMSE analysis shows that only a small portion of the FDE output (at block edges) needs to be discarded, confirming that the computational overhead of overlap FDE is limited.