On the Distribution of the Sum of Double-Nakagami-m Random Vectors and Application in Randomly Reconfigurable Surfaces

Meta-surfaces intend to improve the performance
of future wireless networks significantly by controlling the
wireless propagation and shaping the radio waves according
to the generalized Snell’s law. A recent application of metasurfaces
are reconfigurable intelligent surfaces that are mainly
proposed for the reflection and steering of the impinging signal.
In this paper, we introduce randomly reconfigurable surfaces
(RRSs) aiming to diffuse the incoming wave and characterize
the performance of an RRS-assisted communication network. To
facilitate the performance analysis of an RRS-assisted network,
first, we present novel closed-form expressions for the probability
density function, the cumulative distribution function, the
moments, and the characteristic function of the amplitude of the
distribution of the sum of double-Nakagami-m random vectors,
whose amplitudes follow the double-Nakagami-m distribution,
and phases following the circular uniform distribution. We
also consider a special case of this distribution, namely the
distribution of the sum of Rayleigh-Nakagami-m random vectors.
Then, we exploit the obtained expressions to investigate the RRSassisted
composite channel, assuming that the two links undergo
Nakagami-m fading. Specifically, closed-form expressions for the
outage probability, the average received signal-to-noise ratio, the
ergodic capacity, the bit error probability, the amount of fading,
and the channel quality estimation index are provided to evaluate
the performance of the considered system. Finally, these metrics
are also derived for the practical special case where one of the
two links undergoes Rayleigh fading, implying that this link is
non-line-of-sight.