# Joint Radar and Communications Waveform Design Based on Complementary Sequence Sets
## 1 Introduction  
In recent years, with the development of automotive radar and communications technologies, more and more radar and communications systems have been deployed in vehicles [1; 2]. For example, in an intelligent transportation system (ITS), both radar and communications devices are integrated in a vehicle [3]. In an ITS, the vehicle needs to convey information to other cars or communications base stations via a communications device and detects targets including other vehicles, pedestrians, and roadblocks via a radar device. However, with the development of the fifth-generation (5G) communications technology and the millimeter-wave radar technology, radar and communications systems tend to use the same frequency bands, which will result in mutual interference between these two systems [4]. Since the space in a vehicle is limited, radar and communications devices have to be deployed close together, which aggravates the interference between radar and communications systems in vehicles [5]. Moreover, with the increasing demand for spectral resources for both radar and communications systems, the shortage of spectral resources becomes more and more serious [6]. To solve these problems, joint radar and communications (JRC) systems are proposed, which can alleviate the interference between radar and communications and improve the efficiency of spectral resources [7]. Usually, JRC systems can be divided into two types [8]. One type is called the coexistence JRC system, wherein radar and communications are regarded as two individuals. The co-existence JRC system aims at minimizing the mutual interference between radar and communications subsystems [9]. The other type is termed the co-use JRC system, in which the transmit waveforms are optimized to simultaneously carry out both radar and communications functions [10] to avoid mutual interference between radar and communications. In the co-existence JRC system, radar and communications occupy different resources in some domains, such as the time domain, frequency domain [11], spatial domain [12], and so on [5]. For example, in the co-existence JRC system, radar and communications can work in different time slots [13]. The main defect of this approach is that radar and communications cannot operate at the same time. In [14; 15], a spectral notching JRC system is proposed with the assumption that the bandwidth of radar is much greater than that of communications. In this system, radar and communications operate in different frequencies, although they can work at the same time. In [16], a JRC system that performs radar and communications functions in different directions is investigated. In this system, the transmit waveforms of each element of the array are optimized to synthesize specific radar or communications waveforms in the desired radar and communications directions. To design a co-use JRC system, the main challenge is how to make an optimal trade-off between radar and communications functions [13; 17; 18]. In order to perform the radar function in the mainlobe of the array and convey the communications information in the sidelobe simultaneously, various methods are proposed in [19; 20]. In [19], the sidelobe of the transmit beam is devised to transmit communications information at different pulse repetition intervals (PRIs), and the mainlobe of the transmit beam is designed to remain unchanged to guarantee radar performance. As an extension, the method in [19] is used for multi-user scenarios in [20]. The main shortcoming of this kind of JRC system is the low communications rate since only one communication symbol is conveyed in each PRI [19; 20]. To increase the communications rate, the traditional communications waveforms are modified to perform both radar and communications functions in [21]. The key to this type of method is to modify the traditional communications waveforms to satisfy radar demands [22].