  Recently, the rapid development of metasurface facilitates the growth of
extremely large-scale antenna arrays, making the ultra-massive MIMO possible.
In this paper, we study the codebook design and beam training for an
intelligent omni-surface (IOS) aided multi-user system, where the IOS is a
novel metasurface enabling simultaneous signal reflection and refraction. To
deal with the near field expansion caused by the large-dimension of IOS, we
design a near-far field codebook to serve users both in the near and far fields
without prior knowledge of user distribution. Moreover, to fully exploit the
dual functionality of the IOS, the coupling between the reflective and
refractive signals is analyzed theoretically and utilized in the codebook
design, thereby reducing the training overhead. On this basis, the multi-user
beam training is adopted where each codeword covers multiple areas to enable
all users to be trained simultaneously. Simulation results verify our
theoretical analysis on the reflective-refractive coupling. Compared to the
state-of-the-art schemes, the proposed scheme can improve the sum rate and
throughput.
