Constraint Waveform Design for Spectrum Sharing Under Coexistence of Radar and Communication Systems

Waveform design and spectrum sharing between Multiple Input Multiple Output (MIMO) radar and MIMO communication system is an optimization problem that has been typically addressed in literature with two-dimensional formalism involving radius and azimuth angles. In this paper, we address the problem and associated spectrum sharing constraints by the inclusion of an additional elevation angle. The design uses Finite Alphabet Constant Envelope (FACE) Binary Phase Shift Keying (BPSK) waveforms to formulate the covariance matrices. Through machine learning, a nonlinear optimization problem with constraints is converted to an optimization problem without constraints. The design criteria for the radar waveform does not interfere with the communication system. This is done by carefully selecting the base station (BS) and steering nulls towards it, which guarantees the least degradation in the radar's performance. We designed BPSK waveforms for spectral coexistence between MIMO radar and MIMO cellular communication system through different relaying protocols. Probability of detection and signal to noise ratio is formulated for different relaying protocols. The radar is capable of detecting a target in the air through azimuth as well as by elevation angle. We also showed that the desired covariance matrix is positive semi definite and radar can share the spectrum while detecting the target. We also showed a minimum square error for both angles based on the algorithm.