  Integrated sensing and communications (ISAC) is envisioned as a key
technology for future wireless communications. In this paper, we consider a
downlink monostatic ISAC system wherein the base station serves multiple
communications users and sensing targets at the same time in the presence of
clutter. We aim at both guaranteeing fairness among the communications users
while simultaneously balancing the performances of communications and sensing
functionalities. Therefore, we optimize the transmit and receive beamformers to
maximize the weighted minimum signal-to-interference and clutter-plus-noise
ratios. The design problem is highly challenging due to the non-smooth and
non-convex objective function and strongly coupled variables. We propose two
efficient methods to solve the problem. First, we rely on fractional
programming and transform the original problem into convex sub-problems, which
can be solved with standard convex optimization tools. To further reduce the
complexity and dependence on numerical tools, we develop a novel approach to
address the inherent non-smoothness of the formulated problem. Finally, the
efficiencies of the proposed designs are demonstrated by numerical results.
