# Precoder and Decoder Co-Designs for Radar and Communication Spectrum Sharing +
### Brief Overview of Related Work  
Various contributions have been presented in the radar and communication spectrum sharing literature. In general, these works can be classified into three main classes [22; 23; 24; 25]: codesign, cooperation and coexistence. This paper belongs to the third category. * **Co-design**: When hardware modification is possible, radar and communication systems can be jointly designed to maximize joint performance [4; 26; 27]. One example is a joint Orthogonal Frequency Division Multiplexing (OFDM) radar-communication system: information transmission and target localization tasks can be irrelevantly and simultaneously accomplished by a jointly designed system based on an OFDM signal [28; 29]. Furthermore, the works in [30; 31; 32; 33] show that communication information could be embedded into the sidelobe of the radar waveform to develop a co-designed dual-function system. * **Cooperation**: Limited information can be shared between radar and communication systems to effectively mitigate interference rather than isolate systems. [PERSON] et al. presented cooperative joint radar-communications inner bounds in [34; 35; 36] and extended this concept to MIMO systems [37]. Radar waveforms can be embedded as a pilot signal of communication systems in a doubly selective channel for detection and channel state estimation [38]. * **Coexistence**: When radar and communication systems coexist, interference management is the key issue. Practically, if the interfering energy is weak or the signal structure is unknown, an interfering signal may be treated as interference, e.g., interference from a Wi-Fi transmitter to a radar receiver. Furthermore, physical separation was introduced in [39; 40] to reduce the interfering energy below the noise level. Most of the prior radar-communication spectrum sharing approaches address interference management by exploiting orthogonality [17; 18; 19; 41; 42; 43] or designing radar and communication signals while guaranteeing acceptable performance [6; 7; 44; 45]. A robust precoder that minimizes power is proposed for coexistence between MIMO radar and downlink multiuser MIMO communication systems in [46]. The works in [22; 35] explore information-theoretic bounds for a single joint radar-communication user. The theoretical foundation of joint radar-communication research is established in these studies. However, the channel capacity of a multiuser radar-communication interference channel [47; 48; 49] is still an open problem. An inspiring study [50] showed that the IA scheme could achieve the total DoF upper bound as \(\frac{K}{2}\) for a \(K\)-user interference channel. The key idea of IA is a linear precoding and decoding technique to design the signal space and orthogonal interference space for each user. Essentially, the IA is a trade-off between DoFs and interference in a multiuser interference channel. The definition of DoF is clear in the communication literature but is rarely studied in the radar literature. In general, radar extracts information from targets [51]. The number of frequency-domain DoFs of radar equals the rank of the target response matrix, implying the capability of resolving targets [7]. Maximizing the DoF upper bound corresponds to maximizing the achievable capability of resolving targets. When the independent random variables follow an exponential distribution and the Neyman-Pearson detection strategy is applied, maximizing the frequency DoFs corresponds to maximizing the diversity gain because the diversity gain for each independent variable in the exponential family is 1 [52]. Although there is a large amount of results in the radar-communication coexistence category, the problem of interference management has not been thoroughly studied in multiuser communication scenarios considering mutual interference and DoF exploitation simultaneously.