  This paper explores the potential of near-field beamforming (NFBF) in
integrated sensing and communication (ISAC) systems with extremely large-scale
arrays (XL-arrays). The large-scale antenna arrays increase the possibility of
having communication users and targets of interest in the near field of the
base station (BS). The paper first establishes the models of electromagnetic
(EM) near-field spherical waves and far-field plane waves. With the models, we
analyze the near-field beam focusing ability and the far-field beam steering
ability by finding the gain-loss mathematical expression caused by the
far-field steering vector mismatch in the near-field case. We formulate the
NFBF design problem as minimizing the weighted summation of radar and the
communication beamforming errors under a total power constraint and solve this
quadratically constrained quadratic programming (QCQP) problem using the least
squares (LS) method. Moreover, the Cram\'er-Rao bound (CRB) for target
parameter estimation is derived to verify the performance of NFBF. Furthermore,
we also perform power minimization using convex optimization while ensuring the
required communication and sensing quality-of-service (QoS). The simulation
results show the influence of model mismatch on near-field ISAC and the
performance gain of transmit beamforming from the additional distance dimension
of near-field.
