  Reconfigurable intelligent surface (RIS) is promising for future 6G wireless
communications. However, the increased number of RIS elements results in the
high overhead for channel acquisition and the non-negligible power consumption.
Therefore, how to improve the system capacity with limited RIS elements is
essential. Unlike the classical regular RIS whose elements are arranged on a
regular grid, in this paper, we propose an irregular RIS structure to improve
the system capacity. The key idea is to irregularly configure a given number of
RIS elements on an enlarged surface, which provides extra spatial degrees of
freedom compared with the regular RIS. In this way, the received signal power
can be enhanced, and thus the system capacity can be improved. Then, we
formulate a joint topology and precoding optimization problem to maximize the
capacity for irregular RIS-aided communication systems. Accordingly, a joint
optimization algorithm with low complexity is proposed to alternately optimize
the RIS topology and the precoding design. Particularly, a tabu search-based
method is used to design the irregular RIS topology, and a neighbor
extraction-based cross-entropy method is introduced to optimize the precoding
design. Simulation results demonstrate that, subject to the constraint of
limited RIS elements, the proposed irregular RIS can significantly enhance the
system capacity.
