downlink performance of das

8/4/2019 Downlink Performance of DAS

http://slidepdf.com/reader/full/downlink-performance-of-das 1/5

IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 6, NO. 1, JANUARY 2007 69

Downlink Performance and Capacity of Distributed Antenna Systems in a Multicell Environment

Wan Choi, Student Member, IEEE, and Jeffrey G. Andrews, Senior Member, IEEE

Abstract— Distributed antenna systems (DAS) have been

widely implemented in state-of-the art cellular communicationsystems to cover dead spots. Recent academic studies have shownthat in addition to coverage improvements, DAS can also havepotential advantages such as reduced power and increased systemcapacity in a single cell environment. This paper analyticallyquantifies downlink capacity of multicell DAS for two differenttransmission strategies: selection diversity (where just one or twoof the distributed antennas are used) and blanket transmission(where all antennas in the cell broadcast data). Simple repeatersare a special case of our analysis. A generalized informationtheoretic analysis is provided to illuminate the fundamental limitsof such systems in the cellular context. The results show that DASreduces other-cell interference in a multicell environment andhence significantly improves capacity (by about 2x), with partic-

ularly large improvements for users near cell boundaries. Lessobviously, from a communication theory standpoint, it is shownthat selection diversity is preferable to blanket transmission interms of achievable ergodic capacity. For blanket transmission,we show that the optimal transmission strategy is just phasesteering due to the per antenna module power constraints inDAS.

Index Terms— Capacity, cellular communications, distributedantennas systems, other-cell interference.

I. INTRODUCTION

FUTURE wireless systems will need to provide high data

rates to a large number of users. Experience tells usthat these networks will be interference-limited. Multiuser re-

ceivers are one potential way to reduce interference in cellular

systems (see e.g. [1] and the references therein), but this

requires a more complicated receiver. An alternative strategy is

to try to reduce the overall transmit power (and hence other-

cell interference) using distributed antennas, which has the

additional merit of providing better coverage and increasing

battery life [2]. Although distributed antennas systems (DAS)

were originally introduced to simply cover the dead spots

in indoor wireless communications [3], recent studies have

identified other potential advantages such as reduced power

and increased system capacity [4]–[9].

In DAS, antenna modules are geographically distributed to

reduce access distance instead of centralizing at a location.

Each distributed antenna module is connected to a home base

station (or central unit) via dedicated wires, fiber optics, or an

exclusive RF link. Although the connections via the same RF

Manuscript received March 31, 2005; revised November 22, 2005 and April14, 2006; accepted April 15, 2006. The associate editor coordinating thereview of this letter and approving it for publication was X. Wang. This work was supported in part by SOLiD Technologies, and the William S. LivingstonFellowship at the University of Texas at Austin and has appeared in part inthe Proc. of IEEE Wirelesscom, Maui, Hawaii, June 13-16, 2005.

The authors are with the Wireless Networking and Communications Group,Department of Electrical and Computer Engineering, The University of Texasat Austin, 1 University Station C0803, Austin, TX 78712 USA (email:

[email protected]; [email protected]).Digital Object Identifier 10.1109/TWC.2007.05207.

link as that used in a cell are possible, the connections with the

same RF link construct information-theoretic relay channels

categorized as another research area called cooperative com-

munications [10]–[13]. Since the distributed antenna modules

and the home base station together construct a macroscopic

multiple input single output (MISO) vector channel, DAS can

be also interpreted as a macroscopic multiple-antenna system.

Based on potential advantages of DAS, many cellular ser-

vice providers or system manufacturers are seriously consider-

ing replacing legacy cellular systems with distributed antenna

systems or adopting the distributed antenna architecture in

the future. However, most of the recent work on DAS has

been focused on analyzing its performance in the uplink

because of its analytical simplicity [4]–[8]. On the other hand,

there are few studies on the downlink performance of DAS

although the demand for high speed data will be dominant

in the downlink. There are also few papers that consider the

advantages of DAS in a multicell context. A recent paper

[9] addressed downlink performance of code division multiple

access (CDMA) DAS in a multiple cell environment, but it re-

lied on computer simulations and only investigated SIR levels

perceived at mobile stations. Computer simulations are useful

but mathematical analysis enables us to efficiently identify

the key design parameters and to understand their effects.

Particularly, information-theoretic analysis provides intuitionon achievable system capacity. For this reason, the authors of

[14], [15] analyzed downlink capacity in terms of multiple-

antenna (MIMO) information theory. However, they did not

consider a multicell environment, either. In addition, their

analysis was limited to the case with specific assumptions: (1)

channel state information is known to the transmitter and to the

receiver, and (2) transmit power is shared among distributed

antenna modules, i.e., there is no per antenna module power

constraint.

In this context, we analyze the realistic potential gains of

downlink DAS in a multicell environment. We investigate the

downlink advantages of DAS in terms of achievable ergodiccapacity for two different transmission strategies: selection

diversity (where just one or two of the distributed antennas

are used) and blanket transmission (where all antennas in

the cell broadcast the data). Simple repeaters are a special

case of our analysis. The result of this paper shows that a

distributed antenna architecture effectively addresses other-cell

interference (OCI) in a multicell environment, especially at the

cell boundaries, and achieves a non-trivial capacity increase

over a conventional cellular architecture.

I I . SYSTEM MODEL

A. Cellular Architecture

In DAS, the main processing modules such as channel cards

are centralized at a location (central unit) and are connected

1536-1276/07$20.00 c 2007 IEEE



70 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 6, NO. 1, JANUARY 2007

R

BS : Base station

: Remote Anteannas Module (RNA)

BS0

R2

R1

R6

R4

R5

R3

BS5

R2

R1

R6

R4

R5

R3

BS

6

R2

R1

R6

R4

R5

R3

BS

3

R2

R1

R6

R4

R5

R3BS4

R2

R1

R6

R4

R5

R3

BS

2

R2

R1

R6

R4

R5

R3

BS

1

R2

R1

R6

R4

R5

R3

W

W : Example worst case location

Fig. 1. Structure of a distributed antenna system.

with distributed antenna modules. Each distributed antenna

module is physically connected with a home base station

via dedicated wires, fiber optics, or an exclusive RF link.A general architecture of DAS in a multicell environment is

given in Fig. 1, where a cell is covered by a small base station

and six distributed antenna modules. In contrast, the same

area is covered by only a single high-power base station in

traditional cellular systems. The actual number of distributed

antenna modules would be determined by coverage, user

densities, and other environmental factors but we only consider

6 distributed antenna modules as a reasonable example. The

total transmit power of the ith distributed antenna module of

the jth cell is P (j)i , where the small base station of each cell

and home cell are indexed by i = 0 and j = 0, respectively.

Throughout this paper, we assume that6

i=0 P (j)

i = P whereP is the total transmit power of the conventional base station

for a fair comparison. The radius of a cell (a bold dotted circle)

is R and the coverage radius of a distributed antenna module is

r. We also consider the 1-tier cellular structure with universal

frequency reuse, where a given cell is surrounded by one

continuous tier of six cells as shown in Fig. 1. Although this

assumption of only 1-tier of interfering cells is optimistic, a

pessimistic assumption that all the distributed antenna modules

and the base stations are transmitting full power if they are

selected for transmission easily compensates.

B. Transmission Strategy and Multiple Access Scenario

In cellular DAS, there are several possible transmission

strategies using multiple distributed antenna modules. Al-

though many methods of using the distributed antenna mod-

ules are possible, we consider two likely transmission strate-

gies: the blanket transmission scheme and single transmit se-

lection scheme. The blanket transmission scheme is to transmit

signals through all the distributed antenna modules and the

home base station. In this scheme, the distributed antennas

construct a macroscopic multiple antenna system. In the single

transmit selection scheme, only a single distributed antenna

module or the home base station is selected for transmission

by the criterion of minimizing propagation pathloss. Although

smarter selection algorithms can potentially be used such as

maximizing SINR or capacity, we consider this simple one

for simplicity of analysis and since it should minimize the

required transmit power (and hence the interference caused

to other cells). This scheme exploits macroscopic selection

diversity and is expected to additionally reduce OCI because

the number of OCI sources is reduced.

We also assume a single user scenario for simplicity of

analysis, but this assumption holds for most practical multi-

user systems such as time division multiple access (TDMA),

frequency division multiple access (FDMA), orthogonal code

division multiple access (CDMA), and orthogonal frequency

division multiple access (OFDMA) systems.

C. Channel Model and Received Signal

When the blanket transmission scheme is used, the mul-

tiple distributed antenna modules and the home base station

together construct a macroscopic MISO vector channel given

by

h = [ L(0)0 h

(0)0 L(0)

1 h(0)1 · · · L(0)

6 h(0)6 ] (1)

where h(j)i denotes short term fading from the ith distributed

antenna module in the jth cell and is an i.i.d. complex

Gaussian random variable ∼ CN (0, 1). The fading channel

is assumed to be static during a symbol duration. L(j)i de-

notes propagation pathloss and shadow fading from the ith

distributed antenna module in the jth cell. Let the transmitted

signal vector be x = [x(0)0 x

(0)1 · · · x

(0)6 ]T , where x

(j)i is the

transmitted signal from the ith distributed antenna module in

the jth cell with E[|x(j)i |2] = P

(j)i . Then, the received signal

at a mobile station at a given symbol duration is given by

y = hx+

6j=1

6i=0

h(j)i

L(j)i x(j)

i + n (2)

where n is the additive Gaussian noise with variance

E[nnH ] = σ2n. Since the number of interfering source is

sufficiently large and interfering sources are independent of

each other, the interference plus noise is assumed to be a

complex Gaussian random variable z with variance σ2z =6

j=1

6i=0 L

(j)i P

(j)i + σ2

n by the Central Limit Theorem

(CLT), whereas the interference plus noise power of the con-

ventional cellular system is given by σ2c =

6j=1 L

(j)0 P

(j)0 +

σ2n.

When the single transmit selection scheme is used, thereceived signal is given by

y =

L(0)m h(0)

m x(0)m +

6j=1

h(j)q

L(j)q x(j)

q + n (3)




where m = arg maxi∈{0,1,··· ,6}{L(j)0 , L

(j)1 , · · · , L

(j)6 } and q is

randomly selected among {0, 1, · · · , 6}. The interference plus

noise is assumed to be a complex Gaussian random variable z1with variance σ2

z1=6

j=1 L(j)q P

(j)q + σ2

n. Since other cells

adopt the same transmission scheme as the home cell, only

one of the interfering sources in the other cell is randomly

selected in a single transmit selection scheme.

III. ACHIEVABLE CAPACITY OF DISTRIBUTED ANTENNA

NETWORKS

A. Ergodic Capacity Only With CSIR

If we assume the channel state information is known only

at the receiver (CSIR) and the channel is ergodic, the ergodic

Shannon capacity at a given location of the target mobile

station can be achieved by

C e = Eh

log2

1 +

1

σ2z

hShH

(4)

where S is the covariance matrix of the transmitted vector xand given by diag(P (0)0 , P

(0)1 , · · · , P

(0)6 ).

If ergodicity of the channel is assumed, the ergodic capacity

can be obtained as

C e = Eh

log2

1 +

1

σ2z

6i=0

|h(0)i |2L

(0)i P

(0)i

=

∞x=0

log2(1 + γ )f γ(γ )dγ (5)

where γ = 1σ2z

6i=0 |h(0)

i |2L(0)i P

(0)i is a weighted chi-squared

distributed random variable with p.d.f. given by

f γ(γ ) =6

i=0

σ2zπi

L(0)i P

(0)i

exp

− σ2zγ

L(0)i P

(0)i

where πi =6

k=0,k=i

L(0)i P

(0)i

L(0)i P

(0)i − L

(0)k P

(0)k

, (6)

Then, the ergodic capacity can be obtained in a simple form

by [16]

C e = −1

ln 2

6i=0

πi exp

−

σ2z

L(0)i P

(0)i

Ei

−

σ2z

L(0)i P

(0)i

(7)

where Ei(x) is the exponential integral function (Ei(x) =− ∞−x e−t/t dt) and can be easily calculated with popular

numerical tools such as MATLAB, MATHEMATICA, and

MAPLE.

Since the derivation for this MISO vector channel is a

generalization of a SISO channel, the ergodic capacities of the

single transmit selection scheme and the conventional cellular

system are given, respectively, by

C e,sel = −1

ln 2exp

−

σ2z1

L(0)m P

(0)m

Ei

−

σ2z1

L(0)m P

(0)m

(8)

C e,conv = −1

ln 2exp−

σ2c

L(0)0 P Ei−

σ2c

L(0)0 P (9)

Fig. 2 shows the ergodic capacity of cellular DAS versus the

normalized distance from the home base station in the direc-

tion of the worst case position W when the pathloss exponent

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

5

10

15

20

25

30

35

Normalized distance from a home base station (distance/R)

C a p a c i t y

( b i t s / H z )

Conventional cellular system

DAS w/ blanket transmission scheme

DAS w/ single transmit selection scheme

Fig. 2. Ergodic capacity with CSIR versus the normalized distance from thehome base station.

is 4.0. The transmit power of each distributed antenna module

is 0.1P and the transmit power of the home base station is

0.4P in DAS whereas the transmit power of the base station

in the conventional cellular system is P . Fig. 2 shows an

interesting non-monotonic relationship between capacity and

the normalized distance from the base station. This is because

the signal from a distributed antenna module becomes domi-

nant around 0.6R. In this figure, the single transmit selection

scheme achieves the highest throughput owing to the OCI

reduction and macroscopic selection diversity. Although the

achieved throughput of the blanket transmission scheme in the

cellular DAS is slightly lower than that of conventional cellular

system near the home base station due to reduced transmit

power, the achieved throughput of the blanket transmission

scheme in DAS has substantially higher throughput beyond

the normalized distance 0.5. Note that 80% of the users will

be in (0.5R, R) assuming a uniform distribution, while the

other 20% have very high SINR since they are close to the

home base station and farther from the interfering cells.

Assuming that the target mobile stations are uniformly dis-

tributed, we can obtain achievable average capacity, which is

plotted versus pathloss exponents in Fig. 3. When the pathloss

exponent is 3.5, the capacity of the blanket transmission

scheme and the single transmit selection scheme in cellular

DAS are about 120% and 190% of capacity of conventional

cellular system, respectively. This large improvement is due to

the fact that three times more users are outside of the radius

1/2R within a cell assuming uniform distribution.

B. Ergodic Capacity With CSIT

When channel is known to the transmitter side, the ergodic

Shannon capacity at a given location of the target mobile

station can be given by [17]

C e = Eh

max

Sii≤P (0)i

∀i

log2

1 + 1

σ2z

hShH

(10)

where S ii is the ith diagonal element of S. The maximum

capacity is achieved by a proper design of the transmit power



72 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 6, NO. 1, JANUARY 2007

2.5 3 3.5 4 4.51

2

3

4

5

6

7

8

9

Pathloss exponent

A v g . c a p a c i t y ( B p s / H z )




Fig. 3. Average Ergodic capacity with CSIR versus the pathloss exponent.

spectrum matrix S under individual power constraints of the

distributed antenna modules and the home base station. If

power cooperation among the distributed antenna modules and

the home base station is allowable, this problem reduces to a

standard water-filling problem in a macroscopic MISO vector

channel [15], [17] and the maximum capacity is simply given

by

C e = Eh

log2

1 +

P h2

σ2z

(11)

where P =

6i=0 P (0)i . We note from (11) that the capacityachieving strategy for DAS without per antenna module power

constraints is the transmit MRC. However, the per-antenna

power constraints make it meaningless to apply the simple

water-filling algorithm. Therefore, we should find another

solution instead of the conventional water-filling algorithm.

In (10), the ergodic capacity is maximized with the maxi-

mum value of hShH because the log function is a monotonic

increasing function with respect to hShH . Therefore, the

optimal transmit power spectrum matrix Sopt is obtained by

solving the following optimization problem:

maxSii≤P

(0)i

,∀i

6i=0

|h(0)i |2L

(0)i S ii+

6i=0

6j=0,j=i

hih∗j

L(0)i

L(0)j S ij

(12)

where h∗ denotes the conjugate of h and S ij is the (i, j)entry of the matrix S. It can be easily found that the first

term of the objective function (12) is maximized by set-

ting the diagonal components of Sopt to be diag(Sopt) =

(P (0)0 , P

(0)1 , · · · , P

(0)6 ) and hence we should only find the

optimal values of off-diagonal components. Although there

is no explicit constraints on off-diagonal components S ij,

they should satisfy S ij ≤

P

(0)

i P

(0)

j for ∀i,j,i = jbecause Sopt is a covariance matrix. Therefore, the second

term of the objective function (12) is maximized by setting

S ij =

P (0)i P

(0)j e−j∠hih

∗

j∠ for ∀i ,j,i = j. As a result, the

achievable ergodic capacity with per antenna module power

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

5

10

15

20

25

30

35

Normalized distance from a home base station (distance/R)

C a p a c i t y

( b i t s / H z )




Fig. 4. Ergodic capacity with CSIT versus the normalized distance from thehome base station.

constraints is given by

C e = Eh

log2

1 +

1

σ2z

6

i=0

|h(0)i |2L

(0)i P

(0)i

+6

i=0

6j=0,j=i

|hih∗j |

L(0)i L

(0)j P

(0)i P

(0)j

⎞⎠⎞⎠⎤⎦ . (13)

We can find from this result that the SINR maximizing

transmission strategy for DAS is phase steering with allowable

full power transmission, whereas the best transmission strategy

of DAS without per antenna module power constraints is

transmit MRC. This result also indicates that DAS with

per antenna module power constraints does not require any

channel amplitude information at the transmitter to exploit the

advantage of CSIT.

Fig. 4 shows the ergodic capacity when channel state

information is known to the transmitter, with the same setup

as Fig. 2. Similarly to the CSIR case, the single transmit

selection scheme achieves the highest capacity owing to the

OCI reduction and macroscopic selection diversity. Although

the achieved capacity of DAS is slightly lower than or similar

to that of conventional cellular system near the home base

station due to reduced transmit power, the achieved capacity of

DAS has substantially higher capacity beyond the normalized

distance 0.5. When the target mobile stations are uniformly

distributed in space, the average Shannon capacity is plotted

versus pathloss exponent in Fig. 5. This figure also shows a

similar trend to the CSIR case.

IV. CONCLUSIONS

In this paper, we have analyzed achievable capacity of vari-

ous transmission schemes in cellular DAS from an information

theoretic standpoint. The results of this paper suggest that dis-

tributed antenna systems effectively reduce OCI and improveSINR especially for users near cell boundaries, that normally

are performance limiting users, compared to conventional cel-

lular systems in an interference-limited multicell environment.

As a result, distributed antenna systems achieve lower symbol




2.5 3 3.5 4 4.52

3

4

5

6

7

8

9

10

Pathloss exponent

A v g . c a p a c i t y ( B p s / H z )




Fig. 5. Average Ergodic capacity with CSIT versus the pathloss exponent.

error probability and higher capacity than conventional cellularsystems. Based on the results of this paper, distributed antenna

architectures appear to be an effective solution for reducing

OCI in an interference-limited cellular environment.

REFERENCES

[1] J. G. Andrews, “Inteference cancellation for celluar systems: A con-temporary overview,” IEEE Wireless Commun. Mag., vol. 12, no. 2, pp.19–29, Apr. 2005.

[2] F. Adachi, “Wireless past and future–Evolving mobile communicationsystems,” IEICE Trans. Funamentals Elec. Commun., vol. E84-A, no. 1,pp. 55–60, Jan. 2001.

[3] A. A. M. Saleh, A. J. Rustako, and R. S. Roman, “Distributed antennasfor indoor radio communications,” IEEE Trans. Commun., vol. 35, pp.

1245–1251, Dec. 1987.

[4] M. V. Clark, et al., “Distributed versus centralized antenna arrays inbroadband wireless networks,” in Proc. IEEE Veh. Technol. Conf., May2001, pp. 33–37.

[5] L. Dai, S. Zho, and Y. Yao, “Capacity analysis in CDMA distributedantenna systems,” IEEE Trans. Wireless Commun., vol. 4, no. 6, pp.2613–2620, Nov. 2006.

[6] W. Roh and A. Paulraj, “Outage performance of the distributed antennasystems in a composite fading channel,” in Proc. IEEE Veh. Technol.

Conf., Sep. 2002, pp. 1520–1524.

[7] A. Obaid and H. Yanikomeroglu, “Reverse-link power control in CDMAdistributed antenna systems,” in Proc. IEEE Wireless Commun. Network-

ing Conf., Sep. 2000, pp. 608–612.[8] R. E. Schuh and M. Sommer, “WCDMA coverage and capacity analysis

for active and passive distributed antenna systems,” in Proc. IEEE Veh.Technol. Conf., May 2002, pp. 434–438.

[9] R. Hasegawa, M. Shirakabe, R. Esmailzadeh, and M. Nakagawa,“Downlink performance of a CDMA system with distributed basestation,” in Proc. IEEE Veh. Technol. Conf., Oct. 2003, pp. 882–886.

[10] A. Sendonaris, E. Erkip, and B. Aazhang, “User cooperation diversitypart I and part II,” IEEE Trans. Commun., vol. 51, no. 11, pp. 1927–1948, Nov. 2003.

[11] A. Nosratinia, T. Hunter, and A. Hedayat, “Cooperative communicationin wireless networks,” IEEE Commun. Mag., vol. 42, no. 10, pp. 74–80,Oct. 2004.

[12] J. N. Laneman and G. W. Wornell, “Distributed space-time codedprotocols for exploiting cooperative diversity in wireless networks,” IEEE Trans. Inform. Theory, vol. 49, no. 10, pp. 2415–2425, Oct. 2003.

[13] M. Janani, et al., “Coded cooperation in wireless communications:Space-time transmission and iterative decoding,” IEEE Trans. SignalProcessing, vol. 52, no. 2, pp. 362–371, Feb. 2004.

[14] L. Xiao, L. Dai, H. Zhuang, S. Zhou, and Y. Yao, “Information-theoreticcapacity analysis in MIMO distributed antenna systems,” in Proc. IEEE Veh. Technol. Conf., Apr. 2003, pp. 779–782.

[15] H. Zhuang, L. Dai, L. Xiao, and Y. Yao, “Spectral efficiency of dis-tributed antenna systems with random antenna layout,” IEEE Electron.

Lett., vol. 39, no. 6, pp. 495–496, Mar. 2003.

[16] I. Gradshteyn and I. Ryzhik, Table of Integrals, Series, and Products.London, UK: Academic Press, 2003.

[17] T. Cover and J. Thomas, Elements of Information Theory. New York:

Wiley-Interscience, 1991.

downlink performance of das

Documents