  This paper investigates the utilization of triple polarization (TP) for
multi-user (MU) holographic multiple-input multi-output surface (HMIMOS)
wireless communication systems, targeting capacity boosting and diversity
exploitation without enlarging the antenna array sizes. We specifically
consider that both the transmitter and receiver are both equipped with an
HMIMOS consisting of compact sub-wavelength TP patch antennas within the
near-field (NF) regime. To characterize TP MU-HMIMOS systems, a TP NF channel
model is constructed using the dyadic Green's function, whose characteristics
are leveraged to design two precoding schemes for mitigating the
cross-polarization and inter-user interference contributions. Specifically, a
user-cluster-based precoding scheme assigns different users to one of three
polarizations at the expense of the system's diversity, and a two-layer
precoding scheme removes interference using the Gaussian elimination method at
a high computational cost. The theoretical correlation analysis for HMIMOS in
the NF region is also investigated, revealing that both the spacing of transmit
patch antennas and user distance impact transmit correlation factors. Our
numerical results show that the users far from transmitting HMIMOS experience
higher correlation than those closer within the NF regime, resulting in a lower
channel capacity. Meanwhile, in terms of channel capacity, TP HMIMOS can almost
achieve 1.25 times gain compared with dual-polarized HMIMOS, and 3 times
compared with conventional HMIMOS. In addition, the proposed two-layer
precoding scheme combined with two-layer power allocation realizes a higher
spectral efficiency than other schemes without sacrificing diversity.
