C
no SIC
¼ max log
2
ð1 þ qg
1;3
Þ; log
2
ð1 þ qg
2;3
Þ
: ð2Þ
A receiver can simultaneously receive two transmissions
when SIC is utilized. Suppose g
23
[ g
13
, then node x
3
can
first decode the stronger signal from x
2
, treating the weaker
signal from x
1
as interference. Thus, the highest feasible
bandwidth-normalized rate for x
2
is R
2;3
,onlyifx
1
trans-
mits below a certain rate R
1;3
. Note that if x
1
transmits at a
rate higher than R
1;3
, the signal from x
2
can not be decoded
successfully, and consequently the decoding for x
1
will fail
either. Otherwise, after perfectly subtracting
2
the stronger
one from the composite received signal, the signal from
node x
1
can now be decoded and the best feasible rate is
R
1;3
. Hence, the corresponding capac ity is derived as
R
2;3
¼ log
2
1 þ
Pg
2;3
Pg
1;3
þ rB
R
1;3
¼ log
2
1 þ
Pg
1;3
rB
C
SIC
¼ R
2;3
þ R
1;3
¼ log
2
ð1 þ qðg
1;3
þ g
2;3
ÞÞ:
ð3Þ
The key observation from the above computation is that
the aggregate capacity of two transmitters with SIC can
always outperform the individual capacities, i.e.,
C
SIC
[ C
no SIC
. In order to achieve the maximum SE, each
node should transmit at its maximum allowable rate as
described in (3). Furthermore, it can be seen from [20 ] that
it is more beneficial to apply SIC in many-to-one (i.e., all
transmitters send to the same receiver) transmissions than
interfering one-to-one (i.e., different transmitters send to
different receivers) transmissions. Therefore, we focus on
exploring similar ideal gains by taking advantage of the
location diversities of nodes along a route to realize the
benefits of SIC.
4 Problem formulation for multihop transmission
with SIC
In this section, we first introduce the traditional transmis-
sion scheme without SIC. Then, a novel transmission
strategy applying one-level SIC is proposed. Based on this
proposed strategy, we formulate a cross-layer optimization
problem to explore the best joint routing and scheduling.
4.1 Transmission without SIC
We first determine the SE performance if SIC is not
allowed, that is, only one node is transmitting at any time
as proposed in [3]. We also consider the direct transmission
between the source and the destination, as shown in Fig. 1,
as a reference scheme. In single-hop context, the SE for a
band-limited AWGN channel is
gðLÞ
sh
¼ log
2
ð1 þ qÞ: ð4Þ
When there are N hops in the end-to-end transmission,
given optimum transmission time allocation among links
(i.e., optimal bandwidth sharing), [6] shows that the max-
imum SE along a route L is
gðLÞ
mh
¼
1
P
l
i;j
2E
L
1
log
2
ð1þc
i;j
Þ
:
ð5Þ
Since the denominator of (5) is additive, we can use the
Bellman–Ford or Dijkstra’s algorithm with a link metric of
1= log
2
ð1 þ c
i;j
Þ (i.e., 1=R
i;j
) to find the route that maxi-
mizes the SE by minimizing
P
l
i;j
2E
L
ð1= log
2
ð1 þ c
i;j
ÞÞ.
Such routing algorithm is referred to as ORBO [6]. Notice
that (5) applies when SIC is not considered. In what fol-
lows, the characteristics of SIC are captured to obta in a
more superior route in terms of SE.
4.2 Multihop transmission strategy with SIC
In this subsection, we describe the proposed multihop
transmission strategy with SIC. A novel approach that
applies SIC technique to the nodes along a certain selected
route and explores more simultaneous transmissions will be
introduced, so that the performance of the route can be
significantly improved.
For a path L 2L (L is the set of all possible paths
connecting a given source-destination pair), without loss of
generality, the nodes in V
L
are labeled as x
0
; x
1
; ...; x
jLj
according to their relay orders, where node x
0
is the source
and node x
jLj
is the destination. In addition, the transm is-
sion progress with respect to path L contains |L| stages. It
should be emphasized that jLj2 in the context of
multihop.
Under the traditional transmission model, the source and
all relays take up the channel alone one by one, and thus
only one node can transmit in a given stage. However,
when SIC is available, the multiple relaying progress can
be divided into two phases: source phase and relay phase.
The source phase consists of the first stage, while the relay
phase is composed of the other stages. In the source phase,
Fig. 2 Topology to explain the
gains of SIC
2
Perfect interference cancellation technique is considered, thus there
is no residual interference for the cancelled nodes. However, the
effect of imperfect SIC can also be captured utilizing a parameter
1 2½0; 1, which indicates that the interference is reduced by a factor
of 1 (see [9]).
Wireless Netw
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