# Precoder and Decoder Co-Designs for Radar and Communication Spectrum Sharing +
###### Abstract  
The coexistence of radar and communication systems is necessary to facilitate new wireless systems and services due to the shortage of the useful radio spectrum. Moreover, changes in spectrum regulation will be introduced in which the spectrum is allocated in larger chunks and different radio systems need to share the spectrum. For example, 5G NR, LTE and Wi-Fi systems have to share the spectrum with S-band radars. Managing interference is a key task in coexistence scenarios. Cognitive radio and radar technologies facilitate using the spectrum in a flexible manner and sharing channel awareness between the two subsystems. In this paper, we propose a nullspace-based joint precoder-decoder design for coexisting multicarrier radar and multiuser multicarrier communication systems. The maximizing signal interference noise ratio (max-SINR) criterion and interference alignment (IA) constraints are employed in finding the precoder and decoder. By taking advantage of IA theory, a maximum degree of freedom upper bound for the \(K+1\)-radar-communication-user interference channel can be achieved. Our simulation studies demonstrate that interference can be practically fully canceled in both communication and radar systems. This leads to improved detection performance in radar and a higher rate in communication subsystems. A significant performance gain over a nullspace-based precoder-only design is also obtained.  
communication-radar coexistence; spectrum sharing; integrated sensing and communications 20  
signal has already been widely accepted as a physical layer modulation solution both in communication systems [8; 9; 10] and in the radar field [11; 12; 13; 14].  
Furthermore, a communication signal that is scattered off the target is unitized to capture mutual-information-based radar waveform designs in [15; 16]. Currently, the interference signal can be projected into the nullspace of the channel matrix to avoid interference. The majority of recent projection-based radar-communication coexistence techniques, e.g., [17; 18; 19], project either radar or communication signals into the other system's nullspace. Indeed, in the studies of precoder-only projection-based design [17; 18; 19], a multiuser communication system is simplified to a single communication user with combined signal spaces of all communication users, ignoring the mutual interference.  
The radar subsystem searches for a nullspace or alternative nullspace of the communication subsystem to project a signal into it. However, the feasibility of the precoder-only design depends on the channel state matrix, which is determined by the propagation and the target environment. Furthermore, comparing with precoder-only projection-based design [17; 18; 19], this type of precoder design allows for avoiding interference on either subsystem but not on both.  
In the case that radar and communication systems are jointly designed and co-located, the sharing of channel knowledge and interference awareness can be conveniently arranged. Consequently, optimizing transmitted waveforms and receiver processing for radar and communication systems can be performed jointly. For example, precoders and decoders in radar and communication systems may be jointly designed to construct signal spaces and orthogonal interference spaces and to obtain more effective and flexible interference management.