# On Single-Antenna Rayleigh Block-Fading Channels at Finite Blocklength

## TL;DR

This paper derives a high-SNR approximation for the maximum coding rate in noncoherent single-antenna Rayleigh block-fading channels, valid at large SNR and multiple coherence intervals, aiding in understanding finite blocklength communication limits.

## Contribution

It introduces a high-SNR normal approximation for the maximum coding rate in noncoherent Rayleigh block-fading channels, valid as SNR and coherence intervals grow large.

## Key findings

- Approximation is accurate at SNR above 15dB.
- Approximation is reliable when the number of coherence intervals exceeds 10.
- Numerical results confirm the approximation's effectiveness in practical scenarios.

## Abstract

This paper concerns the maximum coding rate at which data can be transmitted over a noncoherent, single-antenna, Rayleigh block-fading channel using an error-correcting code of a given blocklength with a block-error probability not exceeding a given value. A high-SNR normal approximation of the maximum coding rate is presented that becomes accurate as the signal-to-noise ratio (SNR) and the number of coherence intervals $L$ over which we code tend to infinity. Numerical analyses suggest that the approximation is accurate at SNR values above 15dB and when the number of coherence intervals is 10 or more.