  Integrated sensing and communication (ISAC) is widely recognized as a
fundamental enabler for future wireless communications. In this paper, we
present a joint communication and radar beamforming framework for maximizing a
sum spectral efficiency (SE) while guaranteeing desired radar performance with
imperfect channel state information (CSI) in multi-user and multi-target ISAC
systems. To this end, we adopt either a radar transmit beam mean square error
(MSE) or receive signal-to-clutter-plus-noise ratio (SCNR) as a radar
performance constraint of a sum SE maximization problem. To resolve inherent
challenges such as non-convexity and imperfect CSI, we reformulate the problems
and identify first-order optimality conditions for the joint radar and
communication beamformer. Turning the condition to a nonlinear eigenvalue
problem with eigenvector dependency (NEPv), we develop an alternating method
which finds the joint beamformer through power iteration and a Lagrangian
multiplier through binary search. The proposed framework encompasses both the
radar metrics and is robust to channel estimation error with low complexity.
Simulations validate the proposed methods. In particular, we observe that the
MSE and SCNR constraints exhibit complementary performance depending on the
operating environment, which manifests the importance of the proposed
comprehensive and robust optimization framework.
