A Hybrid PAPR Reduction Scheme in OFDM-IM Using Phase Rotation Factors and Dither Signals on Partial Sub-Carriers  
[PERSON]  
1 Key Laboratory of Modern Measurement and Control Technology, Ministry of Education, Beijing Information Science and Technology University, Beijing 100101, China 1+
Footnote †: This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license ([[https://creativecommons.org/licenses/py/4](https://creativecommons.org/licenses/py/4)]([https://creativecommons.org/licenses/py/4](https://creativecommons.org/licenses/py/4)). transmitted through two statuses, the constellation symbols and the indices of sub-carriers. An overview of this technique can be found from works [6; 7]. Compared with the conventional OFDM, OFDM-IM can achieve a trade-off between energy efficiency and system performance with an adjustment of the number of active sub-carriers in the system [8]. OFDM-IM has been applied in several scenarios, such as vehicle to vehicle (V2V) networks [9] and visible light communication systems (VLC) [10]. Therefore, OFDM-IM is a promising candidate for the next generation communication systems thanks to its fitness and flexibility for some business in beyond 5G (B5G) or 6G [11]. However, as a kind of multi-carrier modulation technique, OFDM-IM also has a significant weakness of high peak-to-average power ratio (PAPR), which is inherited from OFDM and general multi-carrier techniques. High PAPR may raise non-linear distortion and error performance degradation [12] when OFDM-IM signals pass through high power amplifiers (HPAs). Hence, if no PAPR reduction scheme is implemented, OFDM-IM signals can cause serious problems, including a severe power penalty at the transmitter, which is particularly not affordable in portable wireless devices. For conventional OFDM, there are several PAPR reduction schemes utilizing different domain resources, such as clipping, pre-coding [13], active constellation extension (ACE) [14], selective mapping (SLM) [15], partial transmit sequence (PTS) [16], tone reservation (TR), etc. These PAPR reduction schemes can be directly implemented in OFDM-IM systems and have been verified to achieve satisfying performance. However, the unique properties of OFDM-IM systems are not considered, which may limit the corresponding PAPR reduction performance of OFDM-IM. Compared with the conventional OFDM, OFDM-IM owns a number of idle (inactive) sub-carriers, which may be used for PAPR reduction. In order to take advantage of the idle sub-carriers of OFDM-IM systems, the author in [17] proposed an efficient PAPR reduction scheme by injecting some amplitude constraint dither signals, which are generated from convex programming, to the idle sub-carriers. This paper can be regarded as the first work utilizing the structure of OFDM-IM. According to this work, several schemes and algorithms are investigated and proposed to further explore idle sub-carriers for improving PAPR reduction performance [18; 19; 20] by utilizing multi-level or time-domain dither signals. However, all of the above works do not solve the problem of bit error rate (BER) degradation due to the introduction of dither signals. Moreover, these extra signals actually affect the energy efficiency of OFDM-IM, which compromises an irreplaceable advantage of OFDM-IM compared with OFDM. In this paper, to solve the problems of error performance and energy efficiency degradation in previous works of PAPR reduction based on dither signals, a hybrid PAPR reduction method that jointly utilizes dither signals and phase rotation factors is proposed. The proposed method injects dither signals to partial idle sub-carriers in order to make a trade-off between PAPR reduction performance and error performance. Simulation results and theoretical analyses show that utilizing partial sub-carriers is helpful for enhancing error performance and energy efficiency, but the PAPR reduction performance is compromised.