  Reconfigurable intelligent surfaces (RISs) are widely considered to become an
integral part of future wireless communication systems. Various methodologies
exist to design such surfaces; however, most consider or require a very large
number of tunable components. This not only raises system complexity, but also
significantly increases power consumption. Sparse RISs (SRISs) consider using a
smaller or even minimal number of tunable components to improve overall
efficiency while maintaining sufficient RIS capability. The versatile
semidefinite relaxation-based optimization method previously applied to
transmit array antennas is adapted and applied accordingly, to evaluate the
potential of different SRIS configurations. Because the relaxation is tight in
all cases, the maximum possible performance is found reliably. Hence, with this
approach, the trade-off between performance and sparseness of SRIS can be
analyzed. Preliminary results show that even a much smaller number of
reconfigurable elements, e.g. only 50%, can still have a significant impact.
