# Polynomial Cancellation Coded DFT-s-OFDM for Low-PAPR Uplink Signaling
## 1 Introduction
Furthermore, since the sidelink used for proximity services (ProSe) in device-to-device (D2D) communication has been defined as a subset of the uplink resources [18], the issue of D2D power control critically challenges system performance [16; 19]. This is because the D2D network dynamically connects various types of user equipment (i.e., various qualities of PA) to support different scenarios of ProSe. DFT-s-OFDM signaling is expected to be a more robust waveform for uplink through adjustable PAPR reduction schemes. Hence, several data-independent schemes such as spectral shaping (SS) [20], which use extra subcarriers to further reduce PAPR, have been investigated to overcome the need for a flexible countermeasure to the PAPR problem [16; 21]. Although the results in [16] successfully achieved 2-3 dB PAPR reduction compared with conventional DFT-s-OFDM with 10%-20% spectral efficiency loss, further spectral efficiency loss does not improve the PAPR performance more, and instead degrades it. In addition, a long-established OFDM-based waveform, polynomial cancellation coding (PCC)-OFDM [22], is developed for reducing the out-of-band (OOB) interference between users. The PCC applied in PCC-OFDM is treated as a frequency coding technique for OFDM that maps the data onto weighted groups of subcarriers. With this simple preprocessing, the differential operation in the time domain benefits PCC-OFDM on the performance of frequency localization, and the immunity of frequency offset and Doppler spread, making it one of the waveform candidates for 5G and beyond [23]. As taking PCC in the data domain can shape the components in the transformed domain, this inspires us to exploit PCC as a novel SS scheme to reduce the PAPR of DFT-s-OFDM signals. The goal of this paper is to further the idea of applying PCC on DFT-s-OFDM, i.e., PCC-DFT-s-OFDM, for improving the PAPR performance in a more flexible manner by making the following contributions:* Time-domain transform and the SS function of PCC-DFT-s-OFDM are proposed for the PAPR reduction. By using the designed parameter to perform different orders of PCC, a wide range of trade-offs between spectral efficiency and energy efficiency performance can be achieved. * The computational complexity of PCC-mapped DFT precoding matrix is analyzed. Comparing most of significant PAPR reduction techniques, e.g., selected mapping (SLM) [24] and partial transmit sequence (PTS) [25], the PCC increases complexity negligibly (add a simple subtractor circuit only) based on DFT-s-OFDM, which has been widely used in the uplink for existing LTE/NR systems. * A comprehensive numerical simulation of the PCC-DFT-s-OFDM transceiver for a single user and multiple users in terms of PAPR, power spectral density (PSD) and bit error rate (BER) performances are provided. It shows that the PAPR of DFT-s-OFDM signals can be significantly reduced using the proposed method, thereby enhancing the PSD and BER, particularly when PA nonlinearity and inter-user interference are considered. The rest of this paper is organized as follows. In Section 2, the system and signal model of the DFT-s-OFDM is described. In Section 3, we present the proposed PCC-DFT-s-OFDM with its principle of PAPR reduction from the viewpoints of both the time and frequency domains. An in-depth discussion of the properties of the proposed method and the results of simulations are provided in Section 4, which is followed by the concluding remarks.