  This paper proposes highly accurate closed-form approximations to channel
distributions of two different reconfigurable intelligent surface (RIS)-based
wireless system setups, namely, dual-hop RIS-aided (RIS-DH) scheme and
RIS-aided transmit (RIS-T) scheme. Differently from previous works, the
proposed approximations reveal to be very tight for arbitrary number $N$ of
reflecting metasurface's elements. Our findings are then applied to the
performance analysis of the considered systems, in which the outage
probability, bit error rate, and average channel capacity are derived. Results
show that the achievable diversity orders $G_d$ for RIS-DH and RIS-T schemes
are $N-1<G_d<N$ and $N$, respectively. Furthermore, it is revealed that both
schemes can not provide the multiplexing gain and only diversity gains are
achieved. For the RIS-DH scheme, the channels are similar to the keyhole
multiple-input multiple-output (MIMO) channels with only one degree of freedom,
while the RIS-T scheme is like the transmit diversity structure.
