  Terahertz (THz) cell-free massive multiple-input-multiple-output (mMIMO)
networks have been envisioned as a prospective technology for achieving higher
system capacity, improved performance, and ultra-high reliability in 6G
networks. However, due to severe attenuation and limited scattering in THz
transmission, as well as high power consumption for increased number of access
points (APs), further improvement of network capacity becomes challenging.
Reconfigurable intelligent surface (RIS) has been introduced as a low-cost
solution to reduce AP deployment and assist in data transmission. However, due
to the ultra-wide bandwidth and frequency-dependent characteristics of RISs,
beam split effect has become an unavoidable obstacle. To compensate the severe
performance degradation caused by beam split effect, we introduce additional
time delay (TD) layers at both access points (APs) and RISs. Accordingly, we
propose a joint precoding framework at APs and RISs to fully unleash the
potential of the considered network. Specifically, we first formulate the joint
precoding as a non-convex optimization problem. Then, given the location of
unchanged RISs, we adjust the time delays (TDs) of APs to align the generated
beams towards RISs. After that, with knowledge of the optimal TDs of APs, we
decouple the optimization problem into three subproblems of optimizing the
baseband beamformers, RISs and TDs of RISs, respectively. Exploiting
multidimensional complex quadratic transform, we transform the subproblems into
convex forms and solve them under alternate optimizing framework. Numerical
results verify that the proposed method can effectively mitigate beam split
effect and significantly improve the achievable rate compared with conventional
cell-free mMIMO networks.
