Due to the different applications of radar and communication systems, they have significant differences in working methods, function implementation, and signal characteristics. From the perspective of system principles, radar and communication technologies are both related to the transmission and reception of electromagnetic waves in space. From the perspective of system structure, both hardware systems include modules such as antennas, transmitters, receivers, and signal processors. The functions of radar implemented by traditional hardware devices are being replaced by digital signal processing. At the same time, the carrier frequency of the communication system is also moved to the microwave and millimetre wave range, which is on the same order of magnitude as the frequency used by traditional radar systems. Therefore, radar systems and communication systems are converging in terms of both hardware structure implementation and software algorithm processing.

Recently, with the development of mathematical theory, compressed sensing and tensor techniques have been applied in the field of radar and communication systems to mitigate the effect of environmental noise, multipath propagation, channel inconsistency of receivers, and various interferences. These methods can achieve high target detection performance, suppress background noise, and deal with multipath effects, as well as handle multi-dimensional signals, however, they suffer from high computational complexity and model mismatch. Thus, new mathematical theories and tools based on compressed sensing and tensor are needed to improve their performance.

The aim of this Special Issue is to provide a platform for research into the development of these new mathematical theories and tools for the improvement of communication and radar systems, based on compressed sensing and tensors. We welcome both original research and review articles.

Potential topics include but are not limited to the following:

• Compressed sensing-based methods for channel estimation
• Compressed sensing-based methods for radar application
• Tensor-based methods for wireless communication
• Target detection and tracking based on compressed sensing
• Super-resolution for unmanned aerial vehicle (UAV) swarms based on compressed sensing and tensors
• Compressed sensing and tensor-based methods for polarisation sensitive arrays
• Quaternion-based modelling and processing for communication and radar systems
• Compressed sensing and tensors for radar and communication coexistence
• Advanced mathematical theories for waveform design in radar and communication systems
• Tensor-based methods for high dimensional parameter estimation
• Compressed sensing and tensor for 6G communication
• The application of convex and nonconvex optimisation for radar and communication systems
• Hardware implementation of compressed sensing and tensor
• New technologies and research trends for radar and communication systems