# Polynomial Cancellation Coded DFT-s-OFDM for Low-PAPR Uplink Signaling
## 1 Introduction  
Orthogonal frequency division multiplexing (OFDM) underlies modern wireless communication systems such as IEEE 802.11 a/g/n/ac wireless local area networks (WLANs), digital audio broadcasting (DAB), digital video broadcasting (DVB), fourth-generation (4G) cellular networks (e.g., long-term evolution/LTE and worldwide interoperability for microwave access/WiMAX), and the 5G new radio (NR) [1; 2; 3]. However, the high peak-to-average power ratio (PAPR) problem [4] of OFDM remains a long-standing implementation issue [5; 6; 7; 8]. Many studies have considered how to operate the transmit power amplifier (PA) in its linear region with less input backoff (IBO). That is, to be more power-efficient. Although reducing the PAPR of the signal is an issue both at the uplink and downlink, it is more critical for the uplink, owing to the limited cost and power-budget of user equipment. As PAs are one of the most energy-hungry components of a user equipment transceiver, the energy efficiency can be improved by efficient PA conversion, which can extend the battery life of the user equipment. Alternatively, it can significantly boost the transmission power to increase the number of cell-edge users and the signal-to-noise ratio (SNR) at the same IBO [9]. Therefore, PAPR has been regarded as one of the requirements of waveform design for 5G and beyond [10; 11; 12]. Nevertheless, the Third GenerationPartnership Project (3 GPP) still uses the cyclic prefix (CP)-OFDM and discrete Fourier transform-spread OFDM (DFT-s-OFDM) as the waveforms of 5G NR [3]. This postpones many waveform candidates such as filter-bank multicarrier (FBMC), generalized frequency division multiplexing (GFDM), universal filtered multicarrier (UFMC), windowed-OFDM (W-OFDM), and filtered-OFDM (F-OFDM) [12; 13], mainly owing to their high-PAPR essence and low LTE compatibility. The importance of backward compatibility can be also reflected in PAPR reduction schemes for 3 GPP standards. Various PAPR reduction methods are described in the literature [5; 6; 7; 8]. However, only two have been agreed upon as standard solutions for 4G LTE and 5G NR uplink signaling [2; 3]. The first standard solution, DFT-s-OFDM, which is also known as single-carrier frequency-division multiple access (SC-FDMA), appeared in 2006 [14]. It was used to conduct relatively low-PAPR signaling by only reusing the chip-built-in DFT module in user equipment. The second solution is rotated modulation, including \(\pi/2\)-binary phase shift keying (\(\pi/2\)-BPSK) and \(\pi/4\)-quadrature PSK (\(\pi/4\)-QPSK), which were originally adopted for narrow-band internet of things (NB-IoT) mono-tone transmissions since Rel-13 [15]. Apart from the QPSK and quadrature amplitude modulations (QAMs), \(\pi/2\)-BPSK has been a part of the available modulations of the DFT-s-OFDM uplink since Rel-15 [3]. The \(\pi/2\)-BPSK and \(\pi/4\)-QPSK perform identically in terms of errors to BPSK and QPSK, but reduce the PAPR without any increase in computational complexity, making it highly compatible with the current waveforms. However, the PAPR performance of the current standard solution is fixed and cannot be further improved if the communication scenario values the PAPR than other performances. Therefore, it is important to establish a mechanism to adjust a signal's PAPR in a flexible manner that ensures a sufficient trade-off between spectral efficiency and energy efficiency (in PAPR aspect) in 5G [16]. The device capabilities for each 5G use case, including enhanced mobile broadband (eMBB), ultra-reliable and low latency communications (URLLC), and massive machine type communications (mMTC) are quite different [17]. For example, reducing the PAPR of a signal can directly increase the reliability for URLLC owing to the increased SNR, but can lower the signal nonlinearity and power consumption for mMTC devices, which are usually only equipped with basic PA. Nonlinear uplink signals bring severe interferences between users, particularly those with narrowband transmissions.