Power and Frequency Efficient
Virtual Cellular Network
Eisuke KUDOH and Fumiyuki ADACHIElectrical 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: Recently, major services provided by mobilecommunications systems are shifting from voice conversations todata communications over the Internet. There is a strong
demand for increasing the data transmission rate. However, an
important problem arises; larger peak transmit power isrequired as transmission rate becomes higher. In this paper, avirtual cellular concept is proposed to avoid this power problem
and its transmit power and frequency efficiencies are evaluatedby computer simulation to compare with that of the present
cellular systems.
Keyword: Virtual cellular system, frequency reuse distance,transmit power efficiency, transmit power control

I. INTRODUCTION
The 3rd generation mobile communication systems,
known as IMT-2000 systems, have data transmission
capability of up to 2 Mbps. However, since informationtransferred over the Internet is becoming increasingly rich,even IMT-2000 data transmission rate capability will sooner
or later become insufficient. Probably, there will be a demandof peak data transmission rates of around 100Mbps ~1Gbps
even in mobile communications systems. This will be the taskof the 4th generation (4G) mobile communications systems,
which is expected to emerge around 2010. A major objectiveof 4G systems will be to offer mobile users broadband
multimedia services. However, there will be an important
problem to overcome; as data transmission rate becomes
higher, the peak transmit power becomes larger. Reducing thecell size is an efficient way to avoid larger peak transmit
powers while increasing the data transmission rate [1], [2].
However, in realizing nano- or even pico-cell wirelessnetwork, the use of present cellular concept may not be
optimal. In this paper, a virtual cellular concept is proposed
and its transmit power and frequency efficiencies areevaluated by computer simulation to compare with the present
cellular systems.

II. VIRTUAL CELLULAR CONCEPT
Figure 1 compares the virtual cellular system and thepresent cellular system. Many wireless ports are distributed ineach virtual cell. One of the wireless ports distributed in each
virtual cell acts as a gateway (this is called the central porthere) to the network, similar to a base station in the present
cellular system. A mobile station communicates with multiple
wireless ports simultaneously. The features of the virtual

cellular concept are summarized below.
(a) Grouping of distributed wireless ports, to construct each
virtual cell, can be different for each user (i.e., the virtual
cell can be different for each user) and the virtual cell sizefor the uplink may not necessarily be the same as for thedownlink.
(b) The control signal traffic for handover and location
registration to/from the network increases as the cell size
becomes smaller. However, in the virtual cellular system,
since a group of distributed wireless ports acts as one
virtual base station, the control traffic will not increase.
(c) Each wireless port is designed to communicate with thecentral port via other wireless ports. Installation andremoval of wireless ports are made whenever necessary.
(d) Since each wireless port acts as a site diversity branch,
the transmit power of a mobile station and the total transmit
power of wireless ports in each virtual cell can be madesignificantly smaller than the present cellular system.
(e) Reducing the transmit power contributes to the reductionin the interference power to other virtual cells, and thus thefrequency efficiency improves significantly. Even in theTDMA case, the same frequency may be reused in the same
virtual cell.
In the virtual cellular system, traffic routing and wirelessaccess methods among wireless ports are important technicalissues. If all wireless ports communicate with the central port
directly, some wireless ports may need significantly largetransmit powers due to path loss, shadowing loss, andmultipath fading. To avoid this situation, adhoc network andmultihop network can be applied [4],[5]. Since the objectiveof this paper is to evaluate the power and frequency
efficiencies of the virtual cellular system, ideal
communication among wireless ports is assumed.

Network6Control station
Wireless port

Base station

5n=1

DInterferenceCentral port(a)Virtual cellular system

R(b)Present cellular system

Figure 1 Comparison of virtual cellular system and presentcellular system.

n=0
4
Virtual cell ofinterest

III. NUMERICAL EXPRESSION FOR TRANSMIT POWER
AND RECEIVED SINRTDMA wireless access method is assumed (the samefrequency is not reused within a virtual cell). Figure 2illustrates the virtual cell of interest surrounded by six nearest
co-channel virtual cells. The 0-th virtual cell is considered as
the virtual cell of interest. Only the first tier (6 nearest
co-channel virtual cells) is considered because theinterference power from the second tier of co-channel virtualcells is much smaller than the first tier. D is the distance
between the co-channel virtual cells and R is the virtual cellradius. The instantaneous propagation loss is modeled as theproduct of the distance dependent path loss, log-normally
distributed shadowing loss and multipath fading power gain.
Assuming a short distance between a mobile and its nearest
wireless port, frequency non-selective fading is assumed.
Signal-to-noise power ratio (SNR)-based fast transmit
power control (TPC) is considered with the target SNR(S/N)target given by [3]§S·= χ ⋅ γ req ,¨ ¸© N ¹ target(1)where N is the background noise power, χ represents theallowable interference rise factor, defined as the interferenceplus background noise-to-background noise power ratio andγreq is the required signal-to-interference plus noise powerratio (SINR) for the required bit error rate (BER) Pbreq. The
sum of the background noise and interference is approximatedas a Gaussian noise. Assuming coherent quadrature phaseshift keying (QPSK) data modulation, the required SINR γreq
is obtained usingPbreq =§ γ req ·1¸.
erfc¨¨ 2 ¸2©
¹(2)Interferingvirtual cell

23

Figure 2 Geometry of co-channel virtual cells.

A. UPLINKIn the uplink, the received signals at wireless ports aretransferred to the central port to be diversity combined. Then,the combined signal at the central port is transferred to thecontrol station in the network. Two diversity combining
methods are considered: maximal ratio combining (MRC) andselection combining (SC). The transmit power of mobile
station is controlled by TPC command that is sent from thecentral port. It is assumed that there are K wireless ports ineach virtual cell, each wireless port being equipped with M
receive antennas.
(1) MRCThe SINR γ0 at the central port in the 0-th virtual cell andthe transmit power Pt,n of the mobile station in the n-th virtual
cell are given byη 0 ,k ( 0 )M­
2§ Pt ,0 · − 10−α°¨¸10ξ 0,k (0 ) (m )r
0 , k (0 )K ¨ N ¸°©
¹m =1°γ 0 =η n ,k ( 0 )−°k =1§S·10 10 rn,k (0 )−α°6 ¨N ¸© ¹ target°1+
η n ,k ( n )°K−n =1°(M − 1) 10 10 rn ,k (n )−α°k =1°°
, (3)
®
°
§S·°
¨ ¸
°§ Pt ,n ·© N ¹ target¸¸ =°¨¨ηn ,k ( n )KM−2°© N ¹
10 10 rn,k (n )−αξ n ,k ( n ) (m )°°k =1m =1°°°
¯°

¦¦¦

¦

¦

¦

wireless port only.
where rn,k (n) is the distance from the mobile station in the n-thvirtual cell to the k-th wireless port in the n-th virtual cell, α isthe path loss exponent, ηn,k(n) is the shadowing loss (dB) andξn,k(n)(m) is the complex fading gain for the propagation
channel between the mobile station in the n-th virtual cell andthe m-th antenna of the k-th wireless port in the n-th virtualcell.
(2) SCThe wireless port with the largest signal power isselected for data demodulation at the central port. The SINR
γ0 at the central port in the 0-th virtual cell and the transmit
power Pt,n of the mobile station in the n-th virtual cell are
given by­§S·¨ ¸°© N ¹ target°γ =η n ,k (0 )° 0−§S·°
10 10 rn,k (0 )−α6 ¨N¸°
© ¹ target1+°η n ,k ( n )°−n =1(M − 1)10 10 rn,k (n )−α°°,
®
°
§S·°
¨ ¸
°§ Pt ,n ·© N ¹ target¸¸ =°¨¨ηn,k(n)M−°© N ¹2−α10 r
10ξ n,k (n ) (m )°n , k (n )°m =1°°
¯

¦

(4)

¦( )

η , j (n )Mºmax ª − n102
«10rn , j (n )−αξ n, j (n ) (m) »=j∈{1,.., K } «»m =1
¬¼

¦¦

¦

¦

(2) SSTDThe SINR γ0 at the mobile station in the 0-th virtual celland the transmit power Pt,k(n) of the k-th wireless port in then-th virtual cell are given by

where the k-th wireless port is assumed to have the maximum
received signal power, i.e.,η n ,k ( n )M2ξ n , k (n ) m
10 10 rn, k (n )−αm =1

­§S·
¨ ¸°
© N ¹ target°γ =0η k ( n ), 0°−§S·−α10 r°
10¨¸k (n ), 06 K°© N ¹ target1+°η k ( n ),nK−°
n =1 k =1(M − 1) 10 10 rk (n ),n −α°°k =1°. (6)
®
°
§S·°
¨ ¸
°§ Pt ,k ( n ) ·© N ¹ target¸=°¨¨η¸k ( n ),nK
M−°© N ¹
2
10 10 rk (n ),n −αξ k (n ),n (m )°°k =1m =1°°°¯¦¦−(1) Multi-TD
The signals transmitted from the wireless ports arereceived and coherently combined based on MRC at themobile station. The SINR γ0 at the mobile station in the 0-thvirtual cell and the transmit power Pt,k(n) of the k-th wirelessport in the n-th virtual cell are given by

­
§S·
¨ ¸°
© N ¹ target°γ =0η k ( n ), 0°−§S·°
10 10 rk (n ),0 −α
6 ¨N¸°© ¹ target1+°η k ( n ),n−°n =1−α10 r−()M
110°
k (n ), n°,
®
°
§S·°
¨ ¸
°§ Pt ,k ( n ) ·© N ¹ target¸=°¨¨η¸k ( n ),nM−°© N ¹2−α10 10 rk (n ),nξ k (n ),n (m )°°
m =1°°¯¦.

(5)¦(3) Present cellular system
For comparison, the present cellular system is considered.
The SINR γ0 at the base station in the 0-th cell of interest andthe transmit power Pt,n of the mobile station in the n-th cellare given by Eq.(4) with k(n) replaced by n.

B. DOWNLINK
Two transmit diversity schemes are considered:multi-transmit diversity (Multi-TD) where the same signal istransmitted from all wireless ports, and site selection transmit
diversity (SSTD) where the signal is transmitted from the best(7)¦where the k-th wireless port is assumed to provide the least
instantaneous propagation loss.
(3) Present cellular system
For comparison, the present cellular system is considered. TheSINR γ0 at the mobile station in the 0-th cell of interest andthe transmit power Pt,n of the base station in the n-th cell are
given by by Eq.(7) with k(n) replaced by n.

means that the transmit power of each wireless port is lessthan 1/70 of that of a base station in the present cellularsystem.

IV. COMPUTER SIMULATION

A. TRANSMIT POWER EFFICIENCY

Normalized average transmit power

1
uplink MRCuplink SC
downlink Multi-TD
downlink SSTD

1
Normalized average transmit power

For simplicity, hexagonal layout of the virtual cells isassumed. A mobile station is randomly located in each virtualcell. The average transmit power of mobile station (uplink),
the total average transmit powers of K wireless ports(downlink), and the frequency reuse distance are evaluated byMonte Carlo simulation. It is assumed that χ=10dB and-3
Pbreq=10 .

K =10
α =3.5σ =7(dB)

uplink MRC

0.1

uplink SC
downlink Multi-TD
downlink SSTD0.010.001

0.10Figure 4
0.01
M =2
α =3.5σ =7(dB)

0.001
051015
Number K of wireless ports per virtual cell

Present cellular system

20

Figure 3 Normalized average transmit power per virtual cell.
Figure 3 shows the average transmit power normalized
by the transmit power in a present cellular system as afunction of the number K of wireless ports per virtual cell forthe pass loss exponent α=3.5, the standard deviation of
log-normal shadowing σ=7dB and Rayleigh fading.
Two-branch antenna diversity reception (M=2) at both themobile and wireless port is assumed. It is seen that theaverage transmit power of the virtual cellular system can besignificantly reduced from that of the present cellular system.
When K=8 and MRC is used at the central port, the mobiletransmit power (uplink) can be reduced to less than 1/100 ofthat of the present cellular system. The use of SC at thecentral port instead of MRC increases the mobile transmit
power by about 2 times. The total transmit power of wirelessports (downlink) is smaller with SSTD than with Multi-TD.
This is because with Multi-TD, all wireless ports transmit thesame signal to a mobile, while only the best wireless port
transmits with SSTD. However, even with Multi-TD, when
K=7, the total transmit power of wireless ports can be reducedby 10 times from that of the present cellular system. This2468
Number M of receive antennas

10

Normalized average transmit power as a functionof the number M of antennas.

Figure 4 plots the average transmit power, normalized by
the average transmit power of the present cellular system withM=2, as a function of the number M of antennas for K=10.
The virtual cellular system can reduce the average transmit
power significantly. Similar to the Fig.3, the average transmit
power of the mobile station (uplink) is smaller with MRC
than the case with SC and the total average transmit power ofwireless ports (downlink) is smaller with SSTD than withMulti-TD.

3.5

Present cellular system

Present cellular sytem
uplink MRC
uplink SC
downlink Multi-TD
downlink SSTD

31
2.5

K =10
M =2
σ =7(dB)

0.1

2D/R

Normalized average transmit power

101.5

uplink MRC
uplink SC
downlink Multi-TDdownlink SSTD

0.01

0.001
22.5

33.5
Pass loss exponent α

0.5

4Figure 5 Normalized average transmit power as a function of
the path loss exponent α.
Figure 5 shows the average transmit power, normalized
by the average transmit power of the present cellular system
for α=3.5, as a function of the path loss exponent α.
Irrespective of the value of α, the average transmit power ofthe virtual cellular system can be reduced significantly. As α
becomes larger, the average transmit power reduces since theinterference power from other virtual cells decreases.

B. FREQUENCY EFFICIENCY
A good indicator of the frequency efficiency in a cellular
type communication system is the reuse distance D of thesame frequency normalized by the virtual cell radius of R for
keeping the outage probability at the allowable value. The
outage probability is defined as the probability that the SINR
at a central port (uplink) or a mobile station (downlink)
becomes less than the required value. When the hexagonallayout of virtual cells is assumed, the allocated channels canbe grouped into F groups, where F is called the cluster size
and is given by F = (1 3)(D / R )2 [6], each channel group
being assigned to different virtual cell.
Figure 6 plots the normalized frequency reuse distanceD/R for the allowable outage probability of 10% as a functionof the number K of wireless ports per virtual cell for the pathloss exponent α=3.5, the standard deviation of log-normal
shadowing σ=7dB, and the number of antennas M=2. The
normalized reuse distance of the present cellular system isalso plotted for comparison. It is found that increasing thevalue of K can reduce the D/R. It should be pointed out thatwhen D / R < 3 , the same frequency can be reused within
the virtual cell.

M =2α =3.5
σ =7(dB)

100

246810

Number K of wireless ports per virtual cell

Figure 6 Frequency reuse distance D/R.

V. CONCLUSIONS
The virtual cellular concept was proposed to realize apico-cell network for broadband wireless communication
systems. A virtual cell consists of many distributed wirelessports and a group of distributed wireless ports acts as one basestation. The transmit power and frequency efficiencies of thevirtual cellular system were evaluated by Monte Carlosimulation to show that the virtual cellular system canconsiderably reduce the transmit power, irrespective of thevalue of path loss exponent α and the number M of receiveantennas. Reducing the transmit power contributes toreducing the frequency reuse distance. Even in TDMA, thesame frequency can be reused within the same virtual cell.
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