  Physical-layer key generation (PKG) based on wireless channels is a
lightweight technique to establish secure keys between legitimate communication
nodes. Recently, intelligent reflecting surfaces (IRSs) have been leveraged to
enhance the performance of PKG in terms of secret key rate (SKR), as it can
reconfigure the wireless propagation environment and introduce more channel
randomness. In this paper, we investigate an IRS-assisted PKG system, taking
into account the channel spatial correlation at both the base station (BS) and
the IRS. Based on the considered system model, the closed-form expression of
SKR is derived analytically considering correlated eavesdropping channels.
Aiming to maximise the SKR, a joint design problem of the BS precoding matrix
and the IRS phase shift vector is formulated. To address this high-dimensional
non-convex optimisation problem, we propose a novel unsupervised deep neural
network (DNN)-based algorithm with a simple structure. Different from most
previous works that adopt iterative optimisation to solve the problem, the
proposed DNN-based algorithm directly obtains the BS precoding and IRS phase
shifts as the output of the DNN. Simulation results reveal that the proposed
DNN-based algorithm outperforms the benchmark methods with regard to SKR.
