# Integrated Radar and Communications Waveform Design Based on Multi-Symbol OFDM
## 1 Introduction
Among these state-of-the-art techniques, the TR technique is an attractive and widely used PMEPR reduction technique since it does not require the transmission of additional side information [10]. The basic idea of TR is that some of all subcarriers are used for data transmission and the remaining subcarriers are reserved for PMEPR reduction, it was first introduced in [19] and the TR ratio (TRR) is defined as the ratio of the number of reserved subcarriers to the number of all subcarriers. Since TRR determines the data transmission efficiency, its value generally takes 5-15% for OFDM systems in order to achieve good communication performance [21]. Many radar systems require waveforms with PMEPR below 3 dB [24]. However, this may be difficult to achieve for OFDM systems, even with some conventional PMEPR reduction techniques [10]. Therefore, a new PMEPR reduction method for IRC waveforms is urgently needed. In principle, to obtain excellent radar detection performance, such as good range resolution, the bandwidth allocated to radar systems may be much larger than that of traditional communication systems [6]. In view of the different bandwidth requirements between radar and communications, it is feasible to design the IRC waveform structure based on TR, a method with ultra-flexible bandwidth allocation. In other words, some subcarriers allocated in the IRC waveform structure are used for data transmission, and all contiguous subcarriers (including the allocated ones) constitute the entire detection bandwidth for radar detection. It is worth mentioning that the large TRR in this waveform structure is also beneficial to further reduce the PMEPR [22; 23]. Therefore, in this paper, the TR-based PMEPR reduction for IRC waveforms is investigated. Range sidelobes are a very important performance metric for radar [4]. High-range sidelobes are undesirable. They can severely interfere with targets in nearby range cells, and may even obscure targets with a small radar cross section or that are far away. Subcarrier complex weighting and phase coding methods are two popular waveform design methods and can be used not only to reduce PMEPR, but also to suppress sidelobes [16; 25; 26; 27]. However, a lower PMEPR and better sidelobe suppression cannot be achieved simultaneously. The PSLL performance of the IRC waveform is improved by using direct spread spectrum sequence in [27] and a method is investigated to keep the channel capacity of the IRC waveform from degrading while suppressing the radar range sidelobe in [28], however, neither of them consider the PMEPR problem. In the existing literature, in addition to the waveform design method, sidelobe suppression can also be achieved by signal processing at the radar receiver, for instance, the authors of [2] proposed a signal processing method based on the \"modulation symbol\" domain (MSD), which eliminated the range sidelobe fluctuation caused by the randomness of the transmitted signal, ref. [29] proposed a sidelobe suppression method with low signal-to-noise ratio (SNR) loss based on the MSD method, and the authors of [30] proposed a joint weighted optimization method to design the filters for IRC waveforms, where the range sidelobe modulation, SNR loss, and sidelobe level of the filters are jointly minimized. All the above-cited studies attempt to either reduce PMEPR or reduce sidelobes. However, little attention has been paid to jointly solving these two problems, especially given the randomness of the communication data. In [31], the optimal ambiguity function for OFDM radar signal is studied, and a method to improve PMEPR and PSLL is proposed. Although there is a certain effect, the effect is not very significant. In [6], the authors propose a new waveform design algorithm based on the majorization-minimization method for reducing the PMEPR of OFDM-based IRC waveforms, where, although the integrated sidelobe level improvement is involved, the actual PSLL is still poor, since oversampling is generally required in practical digital signal processing.