Multicast Capacity of Wireless Ad Hoc Networks Under Gaussian Channel Model

We study the multicast capacity of large-scale random extended multihop wireless networks, where a number of wireless nodes are randomly located in a square region with side length
a
= √
n
, by use of Poisson distribution with density 1. All nodes transmit at a constant power
P
, and the power decays with attenuation exponent
α > 2
. The data rate of a transmission is determined by the
SINR
as
B
log(1+ SINR), where
B
is the bandwidth. There are
ns
randomly and independently chosen multicast sessions. Each multicast session has
k
randomly chosen terminals. We show that when
k
≤ θ
₁
[(
n
)/((log
n
)
^{2α+ 6}
)] and
ns
≥ θ
₂
n
^1/2+β
, the capacity that each multicast session can achieve, with high probability, is at least
c
₈
[(√
n
)/(
ns
√
k
)], where
θ
₁
,
θ
₂
, and
c
₈
are some special constants and
β > 0
is any positive real number. We also show that for
k
=
O
( [(
n
)/(log
²
n
)]) , the per-flow multicast capacity under Gaussian channel is at most
O
([(√
n
)/(
ns
√
k
)]) when we have at least
ns
= Ω(log
n
) random multicast flows. Our result generalizes the unicast capacity for random networks using percolation theory.