Access Mechanism for Multihop Cellular Networks
G. Kannan, S. N. Merchant and U. B. Desai
SPANN Laboratory, Department of Electrical Engineering, IIT Bombay, India
Email: {gkannan, merchant, ubdesai}@ee.iitb.ac.in
Abstract— We propose a CDMA-OFDM access mechanism for
Multihop Cellular Networks (MCN). We construct groups within
the MCN, where each group comprises of a source node, a
destination node, their intermediate relay nodes and assign a
correlated PN sequence to each such group. Within a particular
group, a single carrier is assigned to each intermediate hop.
The sub carriers assigned to the intermediate hops in a given
group are mutually orthogonal. Hence the proposed OFDM is
FDMA in nature. The sub carriers and transmit power levels to
the relay nodes are assigned in such a way as to maximize the
end-to-end throughput. The end-to-end throughput is formulated
by assuming a Rayleigh flat fading channel between nodes. We
present a method to reuse the PN codes assigned to the groups in
a particular cell. We also introduce a novel architecture for MCN.
Simulation results show that the proposed access mechanism
achieves better end-to-end throughput and bit error rate (BER)
performance as compared to standard access mechanisms like
CDMA and OFDM-FDMA. Furthermore the proposed access
mechanism has considerably higher BER performance in the
presence of multiple transmit sources.
Control messages
Base station
Mobile station
Multihop Voice/
Data messages
Fig. 1.
Proposed System Architecture
I. I NTRODUCTION
Multihop cellular network is the integration of cellular
network and adhoc network. Consequently, nodes in MCN
can communicate with each other or access the base station
through multiple hops. Such an architecture promises the advantages of increase in coverage and improvement in throughput for cellular communications. Though MCN leads to performance enhancement, there are a number of issues that have
to be addressed to make MCN an effective technology. We
address one such important issue, namely access mechanism.
The primary objectives of the MCN access mechanism are
efficient bandwidth utilization, low implementation complexity
and higher data rates. To achieve these objectives, the two
primary contending technologies are
• Orthogonal Frequency-Division Multiplexing (OFDM),
which has higher spectral efficiency and very low implementation complexity.
• Code Division Multiple Access (CDMA), which promises
higher data rate.
The combination of CDMA and OFDM is a promising candidate for MCN. We will derive the mechanisms for using
OFDM-CDMA in MCN in the subsequent sections of this
paper.
The main contributions of this paper are as follows:
1) We propose a strategy to use CDMA-OFDM access
mechanism in MCN. Our proposed OFDM is FDMA
This work was supported by Microsoft Corporation and Microsoft Research
India under the Microsoft Research India PhD Fellowship Award.
in nature. We propose a sub carrier and transmit power
allocation scheme to the intermediate hops such that the
end-to-end throughput is maximized with the constraint
that the interference is maintained below a threshold.
2) We formulate the end-to-end throughput by assuming an
i.i.d Rayleigh flat fading propagation channel between
nodes instead of the commonly encountered distancedecay law in literature.
3) We propose a code allocation scheme and a method of
reusing the PN code and OFDM spectrum in MCN.
4) We also present a novel architecture for MCN.
II. R ELATED WORK
There is a significant amount of research work going on
in access mechanism design for MCN. MC-CDMA access
mechanism is proposed for MCN in [1]; however the system
model assumes fixed relays and the proposed algorithm is only
for downlink communication. Sub carrier allocation scheme
to maximize the information theoretic capacity of an OFDM
based multihop network is proposed in [2]. An OFDM relaying
scheme by taking into account the propagation channel is
proposed in [3]. Optimal number of subcarriers into which the
bandwidth should be split in order to maximize the throughput
of the OFDM based MCN is analyzed in [4]. Fair amount of
work has also been done on CDMA based MCN [5], [6],
[7]. However to the best of authors’ knowledge, there is no
literature available on CDMA-OFDM for MCN with generic
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279
OFDM
Sub Carrier 3
OFDM
Sub Carrier 1
OFDM
Sub Carrier 1
Group 1,
Spreading code c 1
Group n,
Spreading code c n
Group 2,
Spreading code c 2
OFDM
Sub Carrier 2
OFDM
Sub Carrier 1
Fig. 2.
Proposed Access Mechanism
system model and Rayleigh fading channel to maximize the
end-to-end throughput.
III. P ROPOSED A RCHITECTURE
We consider a single cell with a base station at the center
and mobile nodes distributed according to a two dimensional
Poisson point process, as shown in Fig. 1. The communication
is assumed to be in the form of packets. We assume that
nodes do not transmit and receive in the same time slot to
avoid primary collision at nodes [8]. We also assume that
the propagation channel between the mobile nodes follows
an i.i.d Rayleigh distribution. The logical channel is divided
into Control Channels (CCH) and a Traffic Channels (TCH).
Note that the logical channel is different from the propagation
channel. CCH handles only signaling, while TCH carries
speech and data traffic. Control messages containing the source
ID and the destination ID, will be exchanged between the
nodes and base station using CCH. Control messages follow
Dijkstra shortest path routing as they are very short and occur,
only at the time of call initialization. TCH follow multihop
communication. Fig. 1 shows such a routing strategy with
dashed lines for control messages and continuous lines for
voice/data communications. We follow the unified routing
strategy proposed in [9] to determine the routing path from
source to destination. Whenever a node wants to initiate a
communication, it will send a call initiation request to the
base station through CCH. Base station will find the route by
using the algorithm proposed in [9] and will convey the route
information to source and destination through CCH. Hereafter
we assume that definite path exists for TCH and CCH from
source to destination.
be many such groups in a cell. Each group is assigned a
single PN spreading sequence. The PN sequences assigned to
different groups are correlated. In a particular group each node
uses a single OFDM sub carrier to forward the call. Hence
the proposed OFDM is FDMA in nature. Moreover, FDMA
based OFDM has higher throughput than TDMA based OFDM
[2]. To reduce the receiver complexity a simple matched
filter receiver is considered. The message packets are CDMA
spreaded and OFDM modulated at the source node. The relay
nodes are assumed to be of demodulate and forward type; i.e.,
relay nodes demodulate the OFDM packet and modulate them
again with a different OFDM carrier and forward it to the next
node in the path. Note that CDMA spreading/despreading will
be done only at the source node and/or destination node (end
nodes) not at relay nodes (intermediate nodes).
B. System Model
We consider a CDMA-OFDM system with G groups transmitting at a given instant. Assume Binary Phase Shift Keying
(BPSK) constellation for generating the input bits with equal
probability for symbols +1 and -1. Let us consider a group g
consisting of a source node u, a destination node d and a set of
intermediate relay nodes. Assume that the group g is assigned
a spreading waveform cg (.) whose support is [0, Tbit ] and
sg = [sg0 , sg1 , . . . , sgN −1 ] denotes the corresponding spreading sequence with spreading gain N . Then,
cg (t) =
A. Proposed Access Mechanism
The underlying system model is shown in Fig. 2. Let us
construct a group with source node, destination node and
intermediate relay nodes as shown in Fig. 2. There could
sgn rect[t − nTc ]
n=0
where rect(t) is a rectangular waveform with unit amplitude
in [0, Tc ] and Tc is the chip period. Let us assume bg (i) is
the transmitted bit in group g. The kth relay node in group
g transmits bit bg (i) with amplitude Akg in ith bit interval
and the length of signaling interval for each user is Tbit . The
baseband signal of the kth transmitting node in gth group can
now be expressed as
j2πkt
cg (t − iTbit ),
xkg (t) = Akg bg (i)exp
Tbit
iTbit ≤ t < (i + 1)Tbit
1) Processing at relay nodes: Assume perfect synchronization at the relay nodes in the underlying CDMA-OFDM
model. The received signal at any relay node l from any other
node k in group g at any instant t is given by
ŷkl (t) = Akg bg (i)cg (t − iTbit ) +
G
AνG bG (i)cG (t − iTbit )
G=1
G=g
where
IV. P ROPOSED ACCESS M ECHANISM AND S YSTEM M ODEL
N
−1
G=1 (.)
G=g
+ η(t)
is the signal received at node l from some
node ν of group G which uses same carrier as that of node
k and η(t) is zero mean Additive White Gaussian Noise
(AWGN). Once the OFDM demodulation is complete the
signals are again OFDM modulated with a different carrier
and transmitted to the next relay node.
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2) Processing at end nodes: The processing at the end node
consists of OFDM demodulation and CDMA despreading. Let
us assume that the end node d receives signal from node m.
The OFDM demodulated signal ŷmd (t) at node d can also be
derived in a similar fashion as ŷkl (t). After matched filtering
and despreading of ŷmd (t), the received symbol yd [i] in bit
interval i at node d can be written as,
yd [i] = Amg bg (i) +
G
h AνG bG (i)ρGg + ηh
ν=1 G=1
G=g
(1)
Tbit
where ρGg = t=0
cG (t−iTbit )cg (t−iTbit )dt is the correlation
factor between group g and group G, h is the number of
hops and ηh is the noise added to the symbol over one
bit interval at all nodes. Note that Amg will be sufficiently
h G
higher than
G=1 (.) and ηh due to the power and
ν=1
G=g
envelope still follows Rayleigh distribution [10]. Using the fact
that if Y is Rayleigh distributed and X=Y2 , then X will follow
exponential distribution, we can conclude that rlm follows
exponential distribution as given below
lm
1 −r
e Rlm
P(rlm ) =
(2)
Rlm
where Rlm denotes the average received power Rlm = dplm
γ ,
lm
plm is the transmitted power from node l to node m, dlm is
the distance between node l and node m and γ is the path
loss coefficient [11]. Let χm = {1, 2, 3, . . . , h} be the path
selected to relay the communication from source node 1 to
the destination node h in group g, with h − 1 number of
hops. The probability P(C1h ) that the message is successfully
transmitted from source 1 to destination h is given by
h−1
P(C1h ) = P(
bandwidth allocation strategy as will be explained in the
following section.
h−1
Cii+1 ) = 1 − P(
i=1
≥1−
V. A LLOCATION OF R ESOURCES
A. Sub carrier and power allocation
We allocate the sub carriers and transmit powers to the
intermediate nodes such that the end-to-end throughput is
maximized with the condition that the interference caused
to other nodes is bounded. We define end-to-end throughput
as probability of successful transmission of packets from
source to destination. Successful transmission from source to
destination involves successful transmission at each and every
intermediate node. The successful single hop transmission
from node l to its neighbor node m occurs when the received
power at node m from node l (rlm ) is stronger than interference plus noise power by a factor of β (i.e SIN R ≥ β). The
probability of successful transmission from node l to node m
is
rlm
≥ β)
P(Clm ) = P(SIN Rlm ≥ β) = P(
(Ilm + φ)
= P(rlm ≥ β.(Ilm + φ))
where Ilm is the interference at node m from other communicating nodes, SIN Rlm is the signal to interference plus noise
ratio at the link between l and m and φ is the noise power.
Let rGm , G = 1, . . . , G (G = g) be the received power at
node m from the interferer in group G. The total interference
at node m from the interferers in all G − 1 groups which use
the same carrier as that of the hop between l and m is given
by
Ilm
1
=
N
G
ρ2Gg rGm
G=1,G=g
Erroneous detection occurs when SIN Rlm < β, and this
probability P(Elm ) is given by
P(Elm ) = P(rlm < β.(Ilm + φ))
The propagation channel between mobile to mobile is different
from the conventional wireless channel. However channel
Eii+1 )
i=1
h−1
(3)
P(Eii+1 )
i=1
where the last inequality is obtained by using the union bound.
Note that P(Cii+1 ) is dependent on correct detection of all its
previous nodes. Let us consider the communication between
node i and i + 1 in group g.
P(Eii+1 ) = P(SIN Rii+1 < β) = P(rii+1 < β.(Iii+1 + φ))
β.(Iii+1 +φ)
r
1
− ii+1
=
(e Rii+1 )drii+1
Rii+1 0
= 1 − (e
−β(Iii+1 +φ)
Rii+1
)
where Iii+1 itself is a random variable, therefore, by analyzing
along similar lines of [11], P(Eii+1 ) can be written as
G
β 1
ρ2
rGi+1 +φ
Gg
N
G=1
P(Eii+1 ) =
∞
∞
...
0
0
G=g
−
1− e
Rii+1
×
G
P (rGm )drGm
G=1
G=g
By substituting P(rGi+1 ) from (2) and by invoking independence of P(rGi+1 ) the above equation can be written as
−
βφ
G
−γ
1
P(Eii+1 ) = 1 − e pii+1 dii+1 .
2
β ρGi+1 pGi+1 dii+1 γ
( dGi+1 )
G=1 1 + N
pii+1
G=g
(4)
Using (3) and (4), the end-to-end throughput can be written
as
−
βφ
h−1
−γ
1 − e pii+1 dii+1 .
P(C1h ) ≥ 1 −
i=1
.
G
G=1,G=g
1
1+
2
β ρGi+1 pGi+1 dii+1 γ
( dGi+1 )
N
pii+1
(5)
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0
10
CDMA
OFDM−FDMA
−1
CDMA−OFDM
10
−2
BER
10
Rc
Rc
−3
10
Node i
Node j
−4
10
Ri
Ri
−5
10
Fig. 3.
Proposed code reuse scheme
Now the sub carriers (ci , ∀i ∈ χm − {h}) and transmit power
levels are obtained from
f (c1 , c2 , . . . , ch−1 , p12 , p23 , . . . , ph−1h ) = M ax Pl (c1h )
(6)
such that Iij < Imax ∀i, j ∈ χm , where Pl (C1h ) is the lower
bound of P(C1h ).
B. PN code and bandwidth scheduling
We propose CDMA PN code and OFDM sub carrier reuse
in this subsection. Consider communication between node i
and node j as shown in Fig. 3. We draw two types of circles
i.e., a communication circle with radius Rc and an interference
circle with radius Ri around each node. The radius Rc is equal
to the distance between node i and node j (dij ). Let us assume
βI to be the tolerable interference level at any node from any
other node. To avoid secondary collision ([8]) the radius Ri
is chosen as
1
2
ρij pij γ
Ri =
and Ri > Rc
βI
Now the OFDM carrier of the hop between i and j can be
reused at any node beyond the interference circles of both node
i and node j. PN code is reused in some other group which
is beyond the interference circle of all nodes in the group.
VI. S IMULATION AND R ESULTS
We simulate a single cell system with the simulation parameters presented in table below:
Parameters
Cell radius
Number of nodes in the cell
Propagation loss exponent (γ)
SINR threshold (β)
Interference threshold (Imax )
Correlation coefficient
between spreading codes (ρGg )
Spreading factor (N )
Thermal noise at receiver
Antenna Gain in MT
Value
1 Km
1000
4
3 dB
-80 dB
0.1
32
-90 dB
0 dB (Omni directional)
0
2
4
Fig. 4.
6
8
10
12
SNR in dB
14
16
18
20
BER performance comparison
To validate the performance of the proposed model, a MonteCarlo simulation was carried out by randomly selecting the
source and destination nodes, and the results were averaged
over at least 100 realizations of the nodes distribution. We
employ genetic algorithm (GA) to solve the constrained optimization of (6) [12]. Chromosome values of GA are generated
from a uniformly distributed random number generator. Maximum transmit power (maximum value of chromosomes) from
any node is assumed to be 1 watt. We use 0.95 as Pl (c1h )
threshold. The square of the error between the value of Pl (c1h )
(obtained by substituting chromosomes’ values of GA) and
0.95 is taken as the fitness function. Cross over probability is
assumed to be 0.5 while mutation probability is 0.01.
A. BER performance
BER performances of various access mechanisms is compared in Fig. 4. For comparison purpose we consider a CDMA
access mechanism which has similar PN correlation coefficient
as that of our proposed CDMA-OFDM mechanism. We also
consider an OFDM-FDMA access mechanism proposed in [2].
We allow 50 randomly placed groups to transmit at the same
time. We examine a single group communication and assume
a matched filter receiver at the end node as explained in (1).
From Fig. 4 we can infer that the proposed CDMA-OFDM
access mechanism has better BER performance as compared
to CDMA and OFDM-FDMA algorithms.
B. Multiple access interference analysis
The effect of increasing the number of active groups (transmitting groups) in the system for SNR of 20 dB at each node
is shown in Fig. 5. It is evident that more the number of active
groups, more the interference in the system. Therefore as the
number of active groups increases the BER performances of
the access mechanisms reduce as shown in Fig. 5. However in
the proposed algorithm due to the interference constraint and
reuse scheme, interference at the nodes will be at tolerable
levels. Hence the performance is significantly better in the
proposed algorithm compared to CDMA and OFDM-FDMA
algorithms.
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−1
10
CDMA
OFDM−FDMA
CDMA−OFDM
Mean square error in 100 realizations
1.4
−2
BER
10
−3
10
−4
10
1.2
1
0.8
0.6
0.4
0.2
20
40
60
80
100
Number of active groups
120
140
5
Fig. 5. BER performance against number of active groups for a fixed SNR
of 20 dB
15
20
25
30
Number of generations
35
40
45
50
Fig. 7. Convergence of Genetic algorithm in power and subcarrier allocations
constrained optimization of power and sub carrier allocation.
Our proposed algorithm is simple in implementation and has
better BER and throughput performance compared to the
CDMA and OFDM-FDMA. Analytical study of spatial reuse
of the proposed algorithm has been taken up as future work.
0.96
Lower bound on end−to−end throughput
10
0.94
0.92
0.9
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0.88
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0.86
CDMA−OFDM
OFDM−FDMA
CDMA
0.84
0.82
0
Fig. 6.
50
100
Number of active groups
150
End-to-end throughput versus number of active groups
C. End-to-end throughput analysis
We have plotted lower bound on end-to-end throughput by
varying the number of active groups in Fig. 6. From (5) it is
clear that the end-to-end throughput is a function of transmit
powers of nodes (pii+1 ). In the proposed algorithm the power
levels are optimized such that the end-to-end throughput is
maximized. Therefore the minimum guaranteed throughput in
the case of proposed algorithm is considerably higher compared to other algorithms as shown in Fig. 6. Moreover as the
number of active group increases the end-to-end throughput
reduces for the reason stated in Section VI. B.
D. Convergence analysis
The mean square convergence of GA in power and sub
carrier optimization of (6) is shown in Fig. 7. We can deduce
that the GA converges to a mean square error of about 10−3
within 50 generations.
VII. C ONCLUSION
We have proposed a novel CDMA-OFDM access mechanism for MCN. We used a simple genetic algorithm for the
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