# A Reliable Uplink Control Channel Design with Complementary Sequences

## TL;DR

This paper introduces two novel uplink control channel schemes using non-contiguous complementary sequences that achieve low PAPR and enable flexible resource allocation, improving performance over existing sequences like Zadoff-Chu.

## Contribution

It extends Golay's methods to design sequences with low PAPR for non-contiguous resources, enabling flexible allocation and coherent detection in uplink control channels.

## Key findings

- Significantly reduces PAPR and cubic metric compared to 3GPP NR sequences.
- Enables flexible non-contiguous resource allocation in frequency.
- Provides schemes for both interference minimization and coherent detection.

## Abstract

In this study, we propose two schemes for uplink control channels based on non-contiguous complementary sequences (CSs) where the peak-to-average-power ratio (PAPR) of the resulting orthogonal frequency division multiplexing (OFDM) signal is always less than or equal to 3 dB. To obtain the proposed schemes, we extend Golay's concatenation and interleaving methods by considering extra upsampling and shifting parameters. The proposed schemes enable a flexible non-contiguous resource allocation in frequency, e.g., an arbitrary number of null symbols between the occupied resource blocks (RBs). The first scheme separates the PAPR minimization and the inter-cell interference minimization problems. While the former is solved by spreading the sequences in a Golay complementary pair (GCP) with the sequences in another GCP, the latter is managed by designing a set of GCPs with low cross-correlation. The second scheme generates reference symbols (RSs) and data symbols on each RB as parts of an encoded CS. Therefore, it enables coherent detection at the receiver side. The numerical results show that the proposed schemes offer significantly improved PAPR and cubic metric (CM) results in case of non-contiguous resource allocation as compared to the sequences defined in 3GPP New Radio (NR) and Zadoff-Chu (ZC) sequences.