  Reconfigurable intelligent surfaces (RIS) have been actively researched as a
potential technique for future wireless communications, which intelligently
ameliorate the signal propagation environment. In the conventional design, each
RIS element configures and reflects its received signal independently of all
other RIS elements, which results in a diagonal phase shift matrix. By
contrast, we propose a novel RIS architecture, where the incident signal
impinging on one element can be reflected from another element after an
appropriate phase shift adjustment, which increases the flexibility in the
design of RIS phase shifts, hence, potentially improving the system
performance. The resultant RIS phase shift matrix also has off-diagonal
elements, as opposed to the pure diagonal structure of the conventional design.
Compared to the state-of-art fully-connected/group-connected RIS structures,
our proposed RIS architecture has lower complexity, while attaining a higher
channel gain than the group-connected RIS structure, and approaching that of
the fully-connected RIS structure. We formulate and solve the problem of
maximizing the achievable rate of our proposed RIS architecture by jointly
optimizing the transmit beamforming and the non-diagonal phase shift matrix
based on alternating optimization and semi-define relaxation (SDR) methods.
Moreover, the closed-form expressions of the channel gain, the outage
probability and bit error ratio (BER) are derived. Simulation results
demonstrate that our proposed RIS architecture results in an improved
performance in terms of the achievable rate compared to the conventional
architecture, both in single-user as well as in multi-user scenarios.
