Transmit Power Efficiency
of a Multi-hop 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 Japankudoh@mobile.ecei.tohoku.ac.jp, adachi@ecei.tohoku.ac.jp
Abstract—Recently, there is a strong demand for higher speed
data transmissions in cellular mobile communications systems.
However, there will be a serious problem; as data transmission
rate becomes higher, the peak transmit power becomes larger. To
decrease the peak transmit power while increasing the datatransmission rate, the cell size should be made significantly small.
We proposed a virtual cellular concept to efficiently realize picocell network and showed that the virtual cellular system cansignificantly reduce the transmit power of a mobile terminal
while increasing frequency efficiency. The virtual cell consists ofa central port, which is a gateway to the network, and many
distributed wireless ports. In the virtual cellular system, data
relay between the central port and wireless ports is necessary. In
this paper, multi-hop wireless system is applied for data relay.
The virtual cell control layer is introduced for the multi-hoptransmission. The routing algorithm that minimizes the total
uplink transmit power of wireless ports for data relay ispresented. The total transmit powers of uplink and downlink fordata relay are evaluated by computer simulation to show that themulti-hop system can reduce considerably the total transmit
powers, while avoiding unnecessary large time delay, irrespectiveof the values of path-loss exponent α and the shadowing loss
standard deviation σ.
Keywords: virtual cellular system, multi-hop network, adhoc
network, routing, transmit power efficiency

I.

INTRODUCTION
Major
services
providedbycellular
mobilecommunications systems are sifting 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 peaktransmit power becomes larger. To decrease the peak transmit
power while increasing the data transmission rate, the cell size
should be made significantly smaller, resulting in nano- or evenpico-cell network [1], [2]. However, if the cell size becomes
smaller, control signal traffic for handover and location
registration may increase. To avoid this problem, we proposeda virtual cellular concept [3]. Fig. 1 illustrates the virtual
cellular system. The virtual cell consists of a central port,
which is a gateway to the network, and many distributed
wireless ports. Since a group of distributed wireless ports acts
as one virtual base station, increase in the control traffic forhandover and location registration can be avoided.

A mobile terminal communicates simultaneously with
distributed wireless ports. We showed [3] that the virtual
cellular system can significantly reduce the transmit power of amobile terminal and wireless ports for communication betweena mobile terminal and wireless ports, and the frequency reusedistance from that of the present cellular system. However, inRef. [3], the transmit power and frequency efficiencies for data
relay among wireless ports in the virtual cell were notdiscussed.
The virtual cellular system requires the data relay between
the central wireless port and distributed wireless ports. For theuplink, the signals transmitted from a mobile terminal andreceived at wireless ports need to be relayed to the central
wireless port, while for the downlink, the signal to the mobileterminal can be multicast from the central wireless port to
distributed wireless ports. Therefore, routing among wirelessports is an important technical issue. Routing algorithms
proposed for wireless multi-hop network or adhoc network can
be applied [4]~[7]. In Ref.[6], a routing algorithm thatminimizes the number of hops is presented. Ref.[5] proposes arouting algorithm using the link distance information. In thedata relay of virtual cellular system, the frequency reuse is also
applied to efficiently utilize the limited frequency bandwidth asin present cellular systems. The frequency reuse distance canbe reduced by decreasing the total transmit power of wirelessports for data relay. In Ref.[7], a routing algorithm to minimize
the total transmit power of wireless ports for data relay isproposed and the total transmit power is evaluated for the caseof the maximum number of hops being limited to 2.
In this paper, multi-hop wireless system is applied for data
relay between the central port and wireless ports and the virtual
cell control layer is introduced. To avoid large transmission
delay, the number of hops should be limited. We present therouting algorithm which minimizes the total uplink transmit
power for data relay among wireless ports in the virtual cellwhile limiting the number of hops. The transmit power may besignificantly affected by propagation conditions (i.e. distancedependent path-loss and shadowing loss.) However, Ref.[7]considers only the case of a path-loss exponent of 3.5 and ashadowing loss standard deviation of 8dB. In this paper, thetotal transmit power for data relay among wireless ports isevaluated by computer simulation for various parameters, i.e.,
limited number of hops, path-loss exponent and standard
deviation of shadowing loss.

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Control station

Network

Wireless port

request message. The header of route construct request
message includes (a) the transmit power, (b) the source
wireless port address, (c) the number of hops, (d) thetransmitting wireless port address, and (e) the total required
transmit power of wireless ports along the route. The header ofroute notification message includes (a) the destination wirelessport address, (b) the transmitting wireless port address, (c) thesource wireless port address, and (d) the required transmit
power of the destination wireless port. Route construction
algorithm is as follows:
Step1: Source wireless port #k(0) (#1 in Fig. 3) sends the route
construct request message with transmit power Pt(k(0)).

Central port

Fig. 1

Virtual cellular system.

II. MULTI-HOP SYSTEM
If all wireless ports communicate with the central port
directly, the transmit powers of some wireless ports may
become very large due to path-loss, shadowing loss, andmultipath fading. To avoid this, multi-hop wireless system isapplied. In this paper, the virtual cell control layer that isinserted between the data link layer and the network layer isintroduced as illustrated in Fig. 2. The signal transmitted froma mobile terminal is received by all wireless ports. Since eachwireless port can act as a site diversity branch, the transmit
power of a mobile terminal can be significantly reduced
compared to the present cellular systems [3]. The virtual cell
control layer manages the construction of multi-hop route
between each wireless port and the central port.

NetworkPt ,req (k (n − 1), k (n))= Preq + Pt (k (n − 1)) − Pr (k (n)) in dB,(1)

where Preq is the required received signal power, Pt(k(n1)) is the transmit power of the wireless port #k(n-1),
and Pr(k(n)) is the received signal power at the wirelessport #k(n). Then, the total transmit power P of thewireless ports along the route reaching the wireless port
#k(n) is computed fromnControl station

P=Central port

∑Pt ,req ( k (i − 1), k (i ))

.

(2)

i =1

Network layer
Wireless port

Mobile terminal

Virtual cell
control layer

Data link layer

Fig. 2

Step2: Upon reception of the route construct request message
from the wireless port #k(n-1), the wireless port #k(n)checks the number n of hops and if n is less than theallowable maximum number of hops, the wireless port
#k(n) computes the required transmit power Pt,req(k(n-1),k(n)) of the wireless port #k(n-1) using the following
equation:

Layer structure.

A. Uplink（wireless port-to-central port）
Multi-hop route is constructed in order to minimize thetotal transmit power of wireless ports for data relay. Fig. 3
shows message flow of route construction. Route construct
request message is sent periodically from all wireless ports tothe central port via other wireless ports, and route notification
message is sent back from the central port to each wireless port
via other wireless ports. In order to limit the maximum numberof hops, the number of hops is included in the route construct

If the wireless port receives more than one routeconstruction request messages, the wireless port relays
the route construction request message that has theminimum total required transmit power P. For example,
wireless port #3 in Fig. 3 receives the route construction
request messages from wireless ports #1 and #2. Since
Pt ,req (1,2) + Pt , req (2,3) < Pt ,req (1,3) is assumed in Fig. 3,
the wireless port #3 relays the route construction
message received from wireless port #2.
Step3: The central port (wireless port #0 in Fig. 3) chooses theroute which minimizes the total required transmit power
and multicasts the route notification message that
includes the destination wireless port address (#3) andthe required transmit power of wireless port #3.
Step4: When the wireless port finds its address in the received
route notification message, it relays the routenotification message to the source wireless port
(wireless port #1 in Fig. 3).

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Step5: The source wireless port (wireless port #1 in Fig. 3)
receives the route notification message.
In this paper, we have introduced the route construction
algorithm in which the route construct request message is sentfrom each wireless port to the central port. An alternativealgorithm can be used wherein the central port sends the routeconstruct request message to all wireless ports.

#2#3

Central port #0A. Multi-hop routeFig. 4 shows some examples of constructed routes for K=20
and N=5, where K is the number of wireless ports and N is themaximum number of allowable hops, respectively. The
propagation path-loss exponent α of 3.5 and the log-normally
distributed shadowing loss with standard deviation σ of 7dB
are assumed. Fig. 4(a) shows that the central port needs totransmit/receive the uplink/downlink signals via only one
wireless port. This suggests that the downlink transmit powerof central port can be reduced considerably. Of course, thisdoes not always happen. Sometimes, the central port needs tohave multiple connections with surrounding wireless ports.

Source wirelessport #1

Step1Wireless port
Central port
#2

Source wirelessport #1#3

Central port #0
Step2

#2(a)

Source wirelessport #1#3

Central port #0
Step3

#2

Source wirelessport #1#3

Central port #0

Wireless port
Central port

Step4

Fig. 3 Example of route construction message flow.

B. Downlink（central port-to-wireless port）
The downlink multi-hop route is the same as the uplinkroute. The central port can multicast the downlink signal,transmitted from the control station in the network, to all
wireless ports. The total required transmit power of the central
port and wireless ports for downlink data relay is smaller thanthat for uplink data relay.
III.

COMPUTER SIMULATION

Signal-to-noise power ratio (SNR)-based slow transmit
power control is assumed. Wireless ports are randomly locatedin an entire virtual cell.

(b)
Fig.4 Some examples of constructed routes.

B. Average total transmit power for data relay
The total transmit power of wireless ports in an entire
virtual cell is evaluated by computer simulation. The totaltransmit power is defined as the ensemble average of the sumof transmit power of wireless ports and the central wireless port
in an entire virtual cell.

0-7803-7955-1/03/$17.00 (C) 2003 IEEENormalized total transmit power

1

1uplink K=10uplink K=20uplink K=50
downlink K=10
downlink K=20
downlink K=50

0.1

α=4.0
α=3.5 uplink
α=3.0
α=2.0
α=4.0
α=3.5 downlink
α=3.0
α=2.0

σ=7
K =20
Normalized total transmit power

Fig. 5 plots the total transmit power normalized by that ofsingle hop case as a function of the maximum number N ofallowable hops with the number K of wireless ports per virtual
cell as a parameter for α= 3.5 and σ= 7dB. It is clearly seenthat multi-hop transmission can significantly reduce the totaltransmit power. When N=4 and K=20, the uplink (downlink)
total transmit power can be reduced to 0.008 (0.004) of that of
the single hop case. The transmit power of uplink is larger thanthat of downlink. This is because that same signal can be
multicast to many wireless ports simultaneously in thedownlink. It can also be seen that the normalized total transmit
power is almost the same for N>4, 6 and 8 when K=10, 20 and50, respectively. This suggests that the maximum number ofallowable hops can be limited in order to avoid unnecessary
long time delay.

0.1

0.01

0.001
02

4

6810Maximum number N of allowable hops

Fig. 6 Normalized total transmit power as a function of themaximum number N of allowable hops with the pathloss exponent α as a parameter.
0.01
124
68Maximum number N of allowable hops

10Fig. 5 Normalized total transmit power as a function of themaximum number N of allowable hops with the number
K of wireless ports as a parameter.
Fig. 6 plots the total transmit power normalized by that ofsingle hop case as a function of the maximum number N ofallowable hops with α as a parameter for K=20 and σ=7dB. It
can be seen from the figure that as α becomes larger, thenormalized total transmit power reduces. This is because of asignificantly shorter link distance between transmitting andreceiving wireless ports. Fig. 7 plots the total transmit power
normalized by that of single hop case as a function of themaximum number N of allowable hops with the shadowing
loss standard deviation σ as a parameter for K=20 and α=3.5.
As σ becomes larger, the normalized total transmit power
reduces. This is because the route diversity effect increases as
the fluctuation of propagation loss between wireless ports
becomes larger. Irrespective of the values of α and σ, the totaltransmit power is almost the same for N>4, 6 and 8 when K=10,
20 and 50, respectively, as seen in Fig. 5.

Normalized total transmit power

0.001
0σ=8σ=7 uplinkσ=6σ=8σ=7 downlink

α=3.5K =20α =3.5
σ =70.1

σ=60.01

0.001
0246810Maximum number N of allowable hops

Fig. 7 Normalized total transmit power as a function of themaximum number N of allowable hops with theshadowing loss standard deviation σ as a parameter.

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C. Cdf of transmit power
Knowing the transmit power distribution of each wirelessport as well as the total transmit power is important to design
the wireless port [8]. The cumulative distribution function (cdf)of uplink transmit power is evaluated by computer simulation.
Fig.8 plots the cdf of wireless port transmit power normalized
by the average transmit power for the single hop case (N=1) for
K=20, α=3.5 and σ=7dB. It can be seen that multi-hop
communication can reduce the transmit power of each wirelessport considerably. When N ≥ 5, the transmit power at theprobability of 90% can be made significantly smaller than thatof N=1 case. This suggests that in order to avoid unnecessary
long time delay, the maximum number of allowable hops canbe limited to 5 without increasing the transmit power.

In this paper, the frequency efficiency for data relay in thevirtual cell was not discussed. A possibility of significant
transmit power reductions implies that the same frequencies
can be reused for data relay at different wireless ports within
the virtual cell as well as in the different virtual cells assuggested in Ref. [3]. The frequency reuse problem for data
relay is an interesting future study.

10.8

total transmit power of wireless ports for data relay wasevaluated by computer simulation to show that the multi-hop
system can reduce considerably the total transmit power while
limiting the number of hops. It was found that as thepropagation path-loss exponent α or the shadowing loss
standard deviation σ becomes larger, the total transmit power
normalized by that of single hop case reduces. It was also
found that the maximum number of hops can be limited to fiveirrespective of the values of propagation path-loss exponent α
and the shadowing loss standard deviation σ. The evaluation ofcumulative distribution function of uplink transmit power ofeach wireless port showed that in order to avoid unnecessary
large time delay, the maximum number of allowable hops canbe limited while significantly reducing the transmit power.

10570.6

3cdf

2

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

K=20
α =3.5
σ=7REFERENCES
[1]

[2]

[3]

0-25-20-15-10-50[4]Normalized transmit power(dB)

Fig. 8 Cdf of normalized transmit power of wireless port.

[5][6]

IV. CONCLUSIONSIn the virtual cellular system, data relay between central
port and wireless ports is necessary. In this paper, multi-hop
wireless system was applied for data relay and the virtual cellcontrol layer was introduced. The routing algorithm which
minimizes the total uplink transmit power was presented. The

[7]

[8]

F. Adachi, “Wireless past and future-evolving mobile communicationsystems”, IEICE Trans. Fundamentals, vol. E84-A, no.1, pp.55-60, Jan.
2001.
T. Otsu, Y. Aburakawa and Y. Yamao, “Multi-hop wireless link system
for new generation mobile radio access networks”, IEICE Trans.
Commun., vol. E85-B, no.8, pp.1542-1551, Aug. 2002.
E. Kudoh and F. Adachi, “Power and frequency efficient virtual cellularnetwork”, IEEE proc. VTC’2003 spring, Cheju, Korea, April 2003.
E. M. Royer and C. K. Toh, “A review of current routing protocols forad hoc mobile wireless networks”, IEEE Personal Commun., pp.46-55,
April 1999.
T. Mukai, H. Murata and S. Yoshida, “Study on channel selection
algorithm and number of established routes of multi-hop autonomous
distributed radio network”, (in Japanese) IEICE Trans. Commun.,
vol.J85-B, no.12, pp.2080-2086, Dec. 2002.
C. E. Perkins and E. M. Royer, “Ad-hoc on-demand distance vectorrouting”, IEEE proc. WMCSA’99, pp.90-100, Feb. 1999.
A. Fujiwara, S. Takeda, H. Yoshino, T. Otsu and Y. Yamao, “Capacity
improvement with a multi-hop access scheme in broadband CDMAcellular systems”, (in Japanese) IEICE Trans. Commun., vol.J85-B,
no.12, pp.2073-2079, Dec. 2002.
E. Kudoh and F. Adachi, “Study of a Multi-hop communication in a
virtual cellular system”, submitted to WPMC’2003, Yokosuka, Japan,
Oct. 2003.

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