Degrees of Freedom Region of a Class of Multisource Gaussian Relay Networks

We study a layered
K
-user
M
-hop Gaussian relay network consisting of
Km
nodes in the
m
^th
layer, where
M
≥ 2 and
K
=
K
₁
=
KM
+1. We observe that the time-varying nature of wireless channels or fading can be exploited to mitigate the interuser interference. The proposed amplify-and-forward relaying scheme exploits such channel variations and works for a wide class of channel distributions including Rayleigh fading. We show a general achievable degrees of freedom (DoF) region for this class of Gaussian relay networks. Specifically, the set of all (
d
₁
,...,
dK
) such that
di
≤ 1 for all
i
and Σ
i
=1
K di
≤
K
_Σ
is achievable, where
di
is the DoF of the
i
^th
source-destination pair and
K
_Σ
is the maximum integer such that
K
_Σ
≤ min
m
{
Km
} and
M
/
K
_Σ
is an integer. We show that surprisingly the achievable DoF region coincides with the cut-set outer bound if
M
/ min
m
{
Km
} is an integer; thus, interference-free communication is possible in terms of DoF. We further characterize an achievable DoF region assuming multi-antenna nodes and general message set, which again coincides with the cut-set outer bound for a certain class of networks.