  We propose a novel approach to enable the coexistence between
Multi-Input-Multi-Output (MIMO) radar and downlink multi-user
Multi-Input-Single-Output (MU-MISO) communication system. By exploiting the
constructive multi-user interference (MUI), the proposed approach trades-off
useful MUI power for reducing the transmit power, to obtain a power efficient
transmission. This paper focuses on two optimization problems: a) Transmit
power minimization at the base station (BS) while guaranteeing the receive
signal-to-interference-plus-noise ratio (SINR) level of downlink users and the
interference-to-noise ratio (INR) level to radar; b) Minimization of the
interference from BS to radar for a given requirement of downlink SINR and
transmit power budget. To reduce the computational overhead of the proposed
scheme in practice, an algorithm based on gradient projection is designed to
solve the power minimization problem. In addition, we investigate the trade-off
between the performance of radar and communication, and analytically derive the
key metrics for MIMO radar in the presence of the interference from the BS.
Finally, a robust power minimization problem is formulated to ensure the
effectiveness of the proposed method in the case of imperfect Channel State
Information (CSI). Numerical results show that the proposed method achieves a
significant power saving compared to conventional approaches, while obtaining a
favorable performance-complexity trade-off.
