QPSK Waveform for MIMO Radar with Spectrum Sharing Constraints

Multiple-input multiple-output (MIMO) radar is a relatively new concept in the field of radar signal processing. Many novel MIMO radar waveforms have been developed by considering various performance metrics and constraints. In this paper, we show that finite alphabet constant-envelope (FACE) quadrature-pulse shift keying (QPSK) waveforms can be designed to realize a given covariance matrix by transforming a constrained nonlinear optimization problem into an unconstrained nonlinear optimization problem. In addition, we design QPSK waveforms in a way that they don't cause interference to a cellular system, by steering nulls towards a selected base station (BS). The BS is selected according to our algorithm which guarantees minimum degradation in radar performance due to null space projection (NSP) of radar waveforms. We design QPSK waveforms with spectrum sharing constraints for a stationary and moving radar platform. We show that the waveform designed for stationary MIMO radar matches the desired beampattern closely, when the number of BS antennas $N^{\text{BS}}$ is considerably less than the number of radar antennas $M$, due to quasi-static interference channel. However, for moving radar the difference between designed and desired waveforms is larger than stationary radar, due to rapidly changing channel.