Employing Directional Antennas in Double-Directional Radio Channel

Chen Sun, Thomas Hunziker, and Makoto TaromaruATR Wave Engineering Laboratories, 2-2-2 Hikaridai, 619-0288, Kyoto, Japan

sun@atr.jp

Abstract-A novel scheme that jointly utilizes switched beamantennas in double-directional radio channel (DDRC) is proposed.Employing directional beam pattern at both transmitter (Tx) andreceiver (Rx) sides in DDRC provides distributed directivity gain(DDG). Jointly switching directional patterns at both endsprovides extra diversity gain. We employ two electronicallysteerable parasitic array radiator (ESPAR) antennas as theswitched beam antennas. The scheme features a lower systemcomplexity. The achieved capacity is even higher than that of a 2-by-2 multiple-input multiple-output (MIMO) system in the samechannel environment.

I. INTRODUCTIONThe evolution of wireless communications system has

ushered in better quality, higher data rate, and new value addedservices. The multiple-input multiple-output (MIMO) systempromises a much higher channel capacity in comparison withthat of a single-input single-output (SISO) system. Transmittingspace-time codes through the MIMO systems dramaticallyincreases the data rate [1]. This potentially achievable data rateand channel capacity of MIMO systems have been calculatedusing various wireless propagation models.

The double-directional radio channel (DDRC) model wasrecently introduced as an indoor or microscopic wirelesschannel model which incorporates angular information at bothtransmitter (Tx) and receiver (Rx) of a wireless link [2].Incorporating this spatial information, the statistical modelbetter describes the wireless channels, thus allowing a betterevaluation of the system performance in a practical situation. In[3] Wallace et al. extend the Spencer's model [4] to includeboth angle-of-arrival (AOA) and angle-of-departure (AOD)information. The calculated MIMO channel capacity using theDDRC model matches the measured results. The achievedcapacity in DDRC is lower than that reported in [5] owing to thepropagation wave clustering phenomenon [6].

The concept of DDRC indicates that the main energy ofsignals is transmitted spatially through the wave clusters' AODsat the Tx side, and received through the wave clusters' AOAs atthe Rx side. Therefore, both Tx and Rx array antennas shouldbe optimized to distribute and collect signals spatially accordingto the channel's directional property. In this paper, we employswitched beam antennas instead of multiple-element arrayantennas. The antenna has one RF port and produces directionalbeam pattems by changing the tunable reactance loaded at theparasitic elements [8]. The advantages of the proposed scheme

are that, firstly the system complexity is lower than a MIMOsystem as only one RF channel is required at the Tx/Rx sides;secondly, we will show that the directivity gain provided by thesimple switched beam antennas increases the channel capacityto a level that is higher than that of a 2-by-2 MIMO system.

Il. SYSTEM MODELThe DDRC impulse response is written as [3]h ( , t) = A 6(b eAA)6(k A ) ( )

LK /=0 k=Owhere superscripts r and t denote, respectively, the Rx and Txsides of a wireless link. or and b' are the AOA and AOD,respectively. Dr and VI are the nominal AOA and AOD of theIth cluster that are uniformly distributed over the azimuthalplane [4], and L is the total number of clusters. '4k and d/kare the kth AOA and AOD of rays within the Ith cluster thatfollow Laplacian distribution over the clusters' nominaldirections with angular spread a as

Pr(a)1,k D) 1 (2)

K is the total number of rays within each cluster. /3,k is thecorresponding random phase shift that is uniformly distributedover (-xr ir]. alk is the Rayleigh fading amplitude correspondingto the kth ray of the Ith cluster. Its mean power decay followsdouble-exponential distribution

E [a,k ] = E[o] e We X*(3)a is the power decay of the first ray of the first cluster and we

set E[a] = 1 . E[] is the expectation operator. F and y are theconstant delay time of cluster and rays, respectively. TI is thedelay of the first arrival ray of the Ith cluster and Fo = 0 nsec. Itis exponentially distributed and conditioned on F_1l as

Pr(1 IF,)= Ae-A( -0I.)o< r <1 <oo (4)The delay of rays within each cluster is also exponentiallydistributed and conditioned on the previous delay as

Pr("Vk r-llk ) = AeT"k °-', < "I-I,k <1,k <00 (5)A and k are the constant arrival rates of clusters and rays. Themodel in [3], [4] is based on the assumption that statistics ofrays and clusters are independent and the temporal and spatialstatistics are independent, thus

This work is part of "Research and development of ultra-high speed giga-bit rate wireless LAN systems" granted by the National Institute of Informationand Communications Technology (NICT)

0-7803-9206-X/05/$20.00 ©2005 IEEE

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Figure 1. Structure of a 7-element ESPAR antenna. The elements aremonopoles with inter-element spacing of a quarter wavelength.

Pr(Trk I ,k|T,,k- ) = Pr(zl,k 1,k- )Pr(ak) - (6)The directional antennas we employed in this paper are

called electronically steerable parasitic array radiator (ESPAR)[7]. In comparison with a multi-element array antenna, theESPAR antenna features low power consumption andfabrication cost. Fig. I shows the structure of a seven-elementESPAR antenna. There, one active central monopole issurrounded by six parasitic elements on a circle of radius of aquarter wavelength on the circular grounded baseplate. Thecentral monopole is connected to a RF receiver and eachparasitic monopole is loaded with a tunable reactor. Let s(t) bethe far-field impinging wave from direction b, the outputsignal at the RF port is written as

y(t) = WT a (0) s(t) + n(t), (7)where a(0) is the 7-by-I dimensional steering vector definedbased upon the array geometry of the ESPAR antenna. It iswritten as

T

a (o) = e2 ) ei 2os@j2.3) e 1 (8)

-1 (8)n(t) is the additive white Gaussian noise (AWGN) component.Superscript T denotes transpose. WESP is written as

WESP (Y + X) Ul (9)Y is the mutual impedance matrix of array elements and X isrepresented as diag[zo, x1, , x6] Q, where xj (i = 1, 2, , 6) arethe reactance loaded at the array parasitic elements as shown inFig. 1 and zo = 50 Q is the characteristic impedance at thecentral RF port. ul = [1 0 0 0 0 0O ]T. Therefore, the normalizedazimuthal array beam pattem can be written as

g(o) = w WESP a (0) d

-, W Pa(0)a' ((I)w,* d {l^

90

180 $ Q' ~

210 3

24 300270

Figure 2. Six consecutive directional patterns generated by shifting thereactance values.

Laplacian DistributedAngular Spread

Transmitter ESPAR Receiver ESPARAntenna Antenna

Cluster 2Scatering at

rough surface andsmall objects

Figure 3. System model ofemploying switched beam antennas at both endsof the wireless link within a DDRC.

where superscript * is the complex-conjugate. For simplicity weonly consider impinging waves in the azimuthal plane and areco-polarized with the array elements. Since WESp is a function ofthe reactances at those parasitic elements, by changing thevalues of reactance the beam pattem can be adjusted [7]. Forexample, when the reactance values are set to (-90 0 0 0 0 0) Q2,the ESPAR antenna forms a directional pattem pointing to 0degree in the azimuthal plane. By shifting the reactance values,the antenna produces six consecutive directional beam pattemsas shown in Fig. 2. In this paper we employ ESPAR antennas asswitched beam directional antennas. Other forms of switchedbeam antennas also can be deployed.

In Fig. 3, two clusters ofwaves can be observed at the Tx andRx sides. Both the Tx and Rx choose one out of six directionalbeam pattems produced by the ESPAR antennas as shown inFig. 2. When the two pattems at both ends of link, respectively,are steered towards a common existing cluster, the link is set up.This requires a cluster identification process. In [1], waveclusters are identified in spatial-temporal domain through visualobservation. Here, we assume that both the Tx and Rx know thepositions of clusters and the nominal directions of the clustersare aligned with the centers of the directional patterns.Employing directional beam pattems in accordance with thechannel's directional property provides antenna directivity gain.

582

v

4

co'2-c

-T---- -. .

'5

C/3 -8_ .I

-12.n no 30 60 90 120 150Azimuthal Angle 0 of Cluster [degree]

Cu

a)0

xc

180

Figure 4. DDG for the directional beam pattern by the ESPAR antennasgo(@) (a beam pattem pointing to 00 in the azimuthal plane) in different

spatially distributed radio channels. Because of symmetry, the lines for x-

axis from 1800 to 3600 are not plotted.

Directing Tx and Rx directional patterns towards anothercommon cluster provides an alternative signal propagationchannel. Switching among different beam patterns pointing todifferent clusters provides diversity freedom. In this paper, weassume that the channel has two clusters. Here we designate thelinks through clusters I and 2 as CHI and CH2, respectively.

III. PERFORMANCE EVALUATIONFirstly, we examine the array directivity gain in the presence

of angular distribution of the impinging waves. This involvescalculating the array distributed directivity gain (DDG) [10]. Aswe only consider waves in the azimuthal plane, the DDG for agiven cluster is defined as

Do (4, Ila) =|(0|101)go (O)doQ(where AV40) is the probability density function (pdf) of theangular distribution of impinging waves given the clusternominal direction (D, and go() describes the Tx/Rx directionalradiation pattern pointing to azimuthal direction 6. Fig. 4 givesthe DDG for the directional pattern pointing to 0°. We alsoshow that using omni-directional beam patterns in DDRC doesnot provide DDG. For different angular spread situations theDDG reduces as the nominal direction of the cluster movesaway from the beam direction. When we consider the DDG atboth ends of the link, the joint gain of the link for a given set ofTx/Rx directional patterns is written as

E[hhH]= LK KEE E[a.kcx g (@;+'dk)| g4'+od )2] (12)

To simplify the model, we assume a/ k CI 0,(, a, ) where

CAf (., a2) denotes complex normal distribution with mean u

and variance G2 . Therefore, we haveIK-1

-~E E(a,k°l k)= e X , for I = 0,, L-1 (13)k=o

which is the mean power decay of the Ith cluster.

0 60 120 180 240 300 360Pattern Azimuthal Angular Seperation [degree]

Figure 5. Complex correlation ofbeam patterns in the presence of a givenangular distribution property of the channel. The antenna beam pattems are

assumed pointing to the clusters' nominal directions.

After taking the expectation over time and angulardistribution, the joint link gain when there are two clusters asshown in Fig. 3 is simplified to

E[hht'(] D (O,)J+e§ (FD,ojD((4aj] (14)

where el/AF gives the cluster mean power decay [1]. Here we

set F = 30 nsec and 1/A = 30 nsec. Let us assume cD' = (D' = O'and FD = OD = 120' . Jointly employing Tx/Rx patterns go(Sb) or

Tx/Rx patterns g120(f) provides two alternative links. Therefore,switching among different links provides diversity freedom. Inthe following, we will examine their correlation and the averagelink gain ratio.Because Do(Q1,a) and D120(o0,a) represent the DDGs with

120° angular mismatch between the pattern and clusterdirections, which have small values (c.f., Fig. 4), the averagegain ratio between these two alternative links is expressed as

Do (4or, a) Do ((D>,oa) +e A14J (dI,o)Jul20 (DtI)2 (4(D, a)DL20 (0, )+e Do ((Dr,C)D0((DI-I

-eAr =4.34dBHere, we observe that the average gain ratio is determined bythe cluster power decay, which is determined by the clusterarrival time. The correlation of two directional patterns g6, (0)and g9 (0) is expresses as

(16)flu(0)g, (0)j(0)d¢j f(0)g,"(0)g9(O)dO

wherefO) is the angular distribution of waves. For two clusters,the angular distribution is expressed as:

f(0)= l e-j(O-O,)/Uf +e-1(0-02)/la2lj (17)

We assume that the centers of the two directional beam patternsare aligned with clusters' nominal directions, respectively. The

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I Lapo=20-. -T ......Lap a= 40

II.... Lapo=60T ----- Omni-pattem

, I.. Fo *_-_*,,Ls_I _____I_____L_____I_____I_

... <;> Lap o=20./ .'

_ __ ,1_,__ _I _ __,_I*V _____..1.

'. Lapa 40O.' '.

Lap,a60Q.----

I--

|- -- -|- -_

Lktrm- -- --------------_'.. .. '*" ..

c

c

1-

,) f(0) g, (0) g; (0) d.

-1 ---- vrw-i, jv***_0, w I-I10 f-{ Theo, SC, p = O, = 0 dB - - - - - - - - - -

< - - -- - --- - - -- - - - - -_--co - - - - - - - - - -- -:CD)

102

t - = = ==I== =,r1= - = s G = H- = - - - - -=

-N __to

_ _=~~~~I--

-50 -40 -30 -20 -10o 1 o 20SNR [dB], relative to mean SNR of stronger channel

Figure 6. The outage rates of different channels using directional antennasat both ends of the wireless links.

correlation for different beam pattern angular separation 01-02and a is shown in Fig. 5. We observe that as the angular spreadincreases the pattern correlation reduces. However, as we havepreviously studied that DDG reduces when angular spreadincreases. Therefore there exists a trade-off between DDG anddiversity. In our model, the azimuthal positions of the twoclusters are O° and 1200 as viewed from both Tx and Rx sides.We can read the correlation for 1200 angular separation fromthe figure. When considering both sides of the link, we obtainthe correlation for a = 20° as p = prp, = 0.8 x 0.8 = 0.64.

IV. SIMULATION STUDYGiven the average gain ratio and correlation between the two

alternative links, we can easily obtain the outage performance.The outage rate of selection combining these two channels isobtained by calculating [1 1]

Pr(r<x)=1-exp Q(b,alpl)(18)

-exp R- )(lQ(bjpj,a))R2

Q(a,b) is the Marcum's Q-function.

Q(a,b) = 7exp{-1/2(a2 +X2)}Io (ax)xdx, (19)

and Io is the modified Bessel function.

a= 1 2x (20)RI (1 -IP2

and

b=2x

R2 (1- IPI)(21)

RI and R2 are the average link gain of the two alternative links.The outage rates of the link channels without and with SCtechnique are shown in Fig. 6. Simulation is also carried out thecompare with theoretical results. The system jointly switches

.0ci

A

Zn0

C)

I,-,...... OC)nn-omrni, Gain 0dB

° - ''Vl - ; ---- Fosctiri's2x2MUO0.9 r6 "¢ \"""d.t"" Waiace's 2x2 MMO,a=20CH#,Gain=9.8dB,o=20'_ _ _ ...+___s_...eCH#2, Gair=5.5dB, c=20* \ .

V Joint SC CH#1 & #2, p=0.64

0.6 --'B - - - - -

,0.6 SNFt 10 dB*- * *.

,0.5 - - T- - - -I I-

0.4 ___|q__ ___>_^W_V| I___I

0.3

0.2 - -- - - -I- - - 1

0.1

0 1 2 3 4 5 6 7 8 9Channel Capacity [bits/sec/Hz]

Figure 7. Shannon's theoretical channel capacity of different channels indifferent scenarios.

the Tx/Rx patterns to select a radio link that gives a higher linkgain. The system requests a feedback channel to inform thetransmitter which pattern should be selected. This is muchsimpler in comparison with feeding back the channel stateinformation.The DDRC model has been introduced to better describe an

indoor or microscopic area wireless channel. This has led to thereexamination ofMIMO channel capacity predicted by Foschini[5] for ideal stochastic channels. It is found in [6] that thecapacity of a DDRC is lower than Foschini's theoreticalcapacity. The capacities for both Foschini' stochastic model andWallace's DDRC model of 200 angular spread are plotted inFig. 7 for two transmit and two receive omni-directionalantennas with half-wavelength inter-element separation. In ourscheme, instead of using multiple array antennas, switchedbeam directional antennas are employed. The channel capacityis therefore expressed as

C = log (1 + pSNR) (22)where p is the normalized link gain. Here we can observe thatthe DDG increases the channel capacity. To compare ourproposed system that employs switched beam antennas to theconventional multiple-input multiple output (MIMO) systemthat employs antenna arrays, we give their channel capacities inFig. 7. When the switched beam antennas are employed and theTx/Rx radiation patterns are switched towards wave clusters,the capacity is increased by the array DDG to a level higherthan that of the 2x2 MIMO channel. This justifies theadvantages of employing directional antennas in DDRC.Switching between two alternative links further improves thecapacity and increases the system robustness to multipathfading.

V. CONCLUSIONSIn this paper we have proposed the application of switched

beam antennas in DDRC. Since both the switched beam antennahas only one RF channel, the system complexity is much lowerthan that of a multi-element array antenna MIMO system. Thismay pose potential for commercial high data rate wireless

584

-- Theo, nodiversity _ j - _Simu, no diversity _ z___ _l I___

-G- Theo, joint SC,p= 0.64, rT = 4.3dB - 1 - - - -

S-- .imu- ioirtSC de-1 I----

10°1

applications. Study has shown that this simple structureincreases the spectrum efficiency to a level that is higher thanthat achievable through a MIMO system in the same channelcondition. The directional patterns at the Tx and Rx are jointlyswitched towards a common cluster of waves to exploit thedirectional property of the channel. The DDG increasesspectrum efficiency. By jointly switching to a different cluster,the system also provides diversity freedom to counteractmultipath fading.

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