Study of a Multi-hop Communication in a Virtual Cellular System
Eisuke KUDOH and Fumiyuki ADACHI
Dept. of Electrical and Communication Engineering, Graduate School of Engineering, Tohoku University
05 Aza-Aoba, Aramaki, Aoba-ku, Sendai, 980-8579 Japan
E-mail: kudoh@mobile.ecei.tohoku.ac.jp, adachi@ecei.tohoku.ac.jp

Abstract: A virtual cellular system, which wasproposed recently to significantly reduce the transmit
power of a mobile terminal while increasing frequency
efficiency, consists of a central port and many
distributed wireless ports. In this paper, wirelessmulti-hop communication is applied between central
port and wireless ports and the cumulative distributionfunctions (cdfs) of the number of hops and the transmit
power of each wireless port are evaluated when themaximum number N of allowable hops is limited. It isfound that multi-hop communication can reduce thetransmit power of wireless port considerably while
avoiding unnecessary large time delay.
keywords: virtual cellular system, multi-hop network,
adhoc network, routing, transmit power efficiency
1. Introduction
Major services provided by cellular mobile
communications systems are shifting from voice
conversations to data communications. There is a strong
demand for higher speed data transmissions. However,there will be a serious problem; as data transmission
rate becomes higher, the peak transmit power becomeslarger [1], [2]. To decrease the peak transmit power
while increasing the data transmission rate, weproposed a virtual cellular system to significantly
reduce the transmit power of a mobile terminal while
improving the frequency efficiency [3].
Fig. 1 illustrates the conceptual diagram of thevirtual cellular system [3]. The virtual cellular system
consists of a central port, which is a gateway to thenetwork, and many distributed wireless ports. A mobile
terminal communicates simultaneously with thedistributed wireless ports. For the uplink, the signals
transmitted from a mobile terminal and received atwireless ports need to be relayed to the central wirelessport, while for the downlink, the signal to the mobile
terminal can be multicast from the central wireless port
to distributed wireless ports. Therefore, the routing
algorithm is an important technical issue. Routing
algorithms proposed for wireless multi-hop networks or
adhoc networks can be applied [4]~[6].
In Ref.[4], a routing algorithm that minimizes thenumber of hops is presented. Decreasing the number ofhops reduces the transmission time delay; however, thetotal transmit power may increase since a distantwireless port may be selected to relay. In Ref.[5] arouting algorithm using the link distance information isproposed. However, this algorithm does not necessarilychoose the wireless ports that minimize the propagation
path-loss due to the existence of shadowing. In the data
relay of virtual cellular system, the frequency reuse isalso applied to efficiently utilize the limited frequency
bandwidth as in present cellular systems. The frequency
reuse distance can be reduced by decreasing the totaltransmit power of wireless ports for data relay. In
Ref.[6], a routing algorithm to minimize the totaltransmit power of wireless ports for data relay isproposed and the total transmit power is only evaluatedfor the case of the maximum number of allowable hops
being limited to 2, a path-loss exponent of 3.5 and ashadowing loss standard deviation of 8dB.
In this paper, to utilize the frequency efficiently,
we apply the routing algorithm which minimizes thetotal uplink transmit power for data relay among
wireless ports in the virtual cell while limiting thenumber of hops. It was shown by computer simulation[7] that as the maximum number of allowable hops
becomes larger the total transmit power can be reduced
while limiting the number of hops under various
parameters (i.e. distance dependent path-loss andshadowing loss.) However, as the maximum number ofallowable hops becomes larger, the time delay of themulti-hop network becomes longer. Therefore, in thispaper, we evaluate the cumulative distribution function(cdf) of the number of hops and the transmit power of
each wireless port for various parameters, i.e., limited
number of hops, path-loss exponent and standard
deviation of shadowing loss, in the multi-hop virtual
cellular network.
The reminder of this paper is organized as follows.
Sect. 2 introduces a multi-hop system. Sect.3 evaluates
cdfs of the number of hops and the transmit power of
each wireless port by computer simulation. Sect.4 gives
some conclusions.

NetworkControl station
Wireless port

Fig. 1path-loss exponent α of 3.5 and the log-normally
distributed shadowing loss with standard deviation σof 7dB are assumed. Fig. 4(a) shows that the central
port needs to transmit/receive the uplink/downlink
signals via only one wireless port. This suggests thatthe downlink transmit power of central port can bereduced considerably. Of course, this does notalways happen. Sometimes, the central port needs tohave multiple connections with surrounding wirelessports.

Central port
Virtual cellular system.

2. Multi-hop System
If all wireless ports communicate with the central
port directly, the transmit powers of some wirelessports may become very large due to path-loss,
shadowing loss, and multipath fading. To avoid this,multi-hop wireless system is applied. In this paper,
the virtual cell control layer that is inserted between
the data link layer and the network layer isintroduced as illustrated in Fig. 2 [4]. The signaltransmitted from a mobile terminal is received by all
wireless ports. Since each wireless port can act as asite diversity branch, the transmit power of a mobile
terminal can be significantly reduced compared tothe present cellular systems [3]. The virtual cell
control layer manages the construction of multi-hop
routes between each wireless port and the centralport.
Network

Wireless port
Central port(a)Wireless port
Central port

Control station

Central port

Network layer
Mobile terminal

Wireless port
Virtual cell
control layer

Data link layer

Fig. 2Layer structure.

3. Computer Simulation
To reduce the interference power and increase thefrequency efficiency, the routing algorithm based on
the minimum total transmit power is considered [4].
Signal-to-noise power ratio (SNR)-based slow
transmit power control is assumed. Wireless ports are
randomly located in an entire virtual cell.
3.1. Constructed Multi-hop Routes
Fig. 3 shows some examples of constructed routes
for K=20 and N=5, where K is the number ofwireless ports and N is the maximum number ofallowable hops, respectively [4]. The propagation(b)Fig.3 Some examples of constructed routes.
3.2. Cdf of Transmit PowerFig.4 plots the cdf of wireless port transmit power
normalized by the average transmit power for the single
hop case (N=1) with the maximum number N ofallowable hops as a parameter. It can be seen thatmulti-hop communication can reduce the transmit
power of each wireless port considerably. When N ≥ 5,
at the probability of 80%, the transmit power can besmaller than that of the N=1 case by about -20dB.
However, the cdf of normalized transmit power isalmost identical for N ≥ 5. This suggests that themaximum number of allowable hops can be limited to 5in order to avoid unnecessary large time delay withallowing negligible increase of transmit power. In thefollowing, we show that this can also be true

irrespective of the values of the path-loss exponent α
and the standard deviation σ of log-normally distributed
shadowing loss.
10.8

105Fig. 6 plots cdf of normalized transmit power of eachwireless port as a function of the maximum number Nof allowable hops with the shadowing loss standard
deviation σ as a parameter for K=20 and α=3.5. As σbecomes larger, the medium value of normalized totaltransmit power reduces. This is because the route
diversity effect increases as the variation in thepropagation loss between wireless ports becomes larger.

70.6

12

N=1
N=2
N=3
N=5
N=7
N=100.4
N =10.2

K=20
α=3.5
σ=7

σ=80.80.6cdf

cdf

3N=3
N=5
N=7
N=10

σ=60.40-25-20-15-10-50Fig. 4 Cdf of normalized transmit power of eachwireless port with the maximum number N ofallowable hops as a parameter.
Fig. 5 plots the cdf of normalized transmit power of
each wireless port with α as a parameter for K=20 and
σ=7dB. It can be seen from the figure that as α
becomes larger, the medium value of normalized
transmit power reduces. This is because multi-hop canshorten link distance between transmitting andreceiving wireless ports significantly.

0.8
α=4.0

cdf

0.6
N=3
N=5
N=7
N=10

α=2.0
0.2

K=20
σ=70-30-25-20-150-30-25-20-15-10Normalized transmit power(dB)

Fig. 6 Cdf of normalized transmit power of eachwireless port with the standard deviation σ ofshadowing loss as a parameter.

3.3. Cdf of the Number of Hops
Fig.7 plots the cdf of the number of hops with themaximum number N of allowable hops as a parameterfor α=3.5 and σ=7dB. Fig.8 plots the cdf of the numberof hops with the propagation path-loss exponent α as aparameter for K=20 and σ=7dB. Fig.9 plots the cdf ofthe number of hops with the standard deviation σ of
log-normally distributed shadowing loss as a parameter
for K=20 and α=3.5. If an infinite number of hops isallowed, about 20% of constructed routes require morethan 5 hops. This suggests that about 20% ofconstructed routes with N=5 are not power minimum
routes and hence, the transmit power may increase.
However, it can be seen from Fig.4 that even if N=5 isneeded, the increase in the transmit power is negligible
irrespective of α and σ.

10.4

K=20
α=3.5

0.2

Normalized transmit power(dB)-10

Normalized transmit power(dB)

Fig. 5 Cdf of normalized transmit power of eachwireless port with the propagation path-lossexponent α as a parameter.

13N=240.8

N=2N=3N=4N=5N=6N=7N=8N=9N=10cdf

0.60.4

K =20α=3.5
σ=70.2

N=3N=5N=7N=10N=3N=5N=7N=100.6cdf

0.8

1650.4σ=6σ=8K =20α=3.50.2

0002468100246810

Number of hops

Number of hops

Fig.7 Cdf of number of hops with the maximum
number N of allowable hops as a parameter.

Fig.9 Cdf of the number of hops with the standard
deviation σ of the log-normally distributed
shadowing loss as a parameter.

4. Conclusions

1Multi-hop wireless communication was applied tothe virtual cellular system. Applying the routing
algorithm based on the minimum total uplink transmit
power, the cdfs of the wireless port transmit power andthe number of hops were evaluated by computer
simulation. It is found that the cdf curves are almost
identical, when the maximum number N of allowable
hops is larger than 5, irrespective of the path-loss
exponent α and shadowing loss standard deviation σ. It
suggests that multi-hop communication can reduce thetransmit power of wireless port considerably while
avoiding unnecessary large time delay.

0.8
N=3
N=5
N=7
N=10
N=3
N=5N=7N=10α=2.00.6
cdf

α=4.00.4

α=2.0

α=4.0

K =20
σ=70.2002468

10

Number of hops

Fig.8 Cdf of the number of hops with the propagation
path-loss exponent α as a parameter.

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