# Channel Shortening by Large Multiantenna Precoding in OFDM

## TL;DR

This paper proposes a novel frequency-domain precoding method called TF-precoding that leverages large multi-antenna systems to effectively shorten channels in OFDM, reducing interference and improving high-SNR performance.

## Contribution

It introduces TF-precoding, a new channel shortening technique exploiting large antenna arrays, which outperforms traditional time-reversal filtering in finite-size systems.

## Key findings

- TF-precoding asymptotically cancels ISI/ICI with infinite antennas.
- Finite-size analysis shows faster convergence of TF-precoding to its rate.
- TF-precoding outperforms TR-filtering in high-SNR regimes with fewer antennas.

## Abstract

A channel delay spread larger than the cyclic prefix (CP) creates inter-carrier/symbol interference (ISI/ICI) in orthogonal frequency-division multiplexing (OFDM). Recent interests in low-latency applications have motivated the usage of shorter OFDM symbols where one can either downscale the CP at the cost of interference, or maintain it but with larger overhead. Alternatively, this paper studies channel shortening methods exploiting the properties of large multi-antenna precoding in order to steer the transmitted signal energy toward channel paths inside an insufficient CP. It is shown that ISI/ICI can asymptotically be canceled by conventional subcarrier-based precoding with an infinite number of antennas. This is achieved by introducing time-delay selectivity inside frequency-selective precoders in order to remove undesired delayed signals, providing a trade-off between interference mitigation and multi-path combining gains, and leading to subsequent gains in high SNR. This frequency-domain precoding method, coined time-frequency (TF) precoding, is compared to time-reversal (TR) filtering whose asymptotic rate is optimal but introduces post-modulation processing with channel-dependent signal distortion. In addition to maintain the legacy precoded multi-antenna OFDM structure, finite-size analysis shows that TF-precoding converges faster to its asymptotic rate than TR-filtering, so that TF-precoding can outperform TRfiltering in the high-SNR regime with not-so-many antennas.