Comparison of Co-directional Reception usingBeamforming, Switched Beams and Multiuser

Detection Strategies in WCDMA SystemsR. Radhakrishnan and J. Caffery, Jr.

Dept. of ECECSUniversity of Cincinnati

Cincinnati OH 45221-0030{radhakri,jcaffery}@ececs.uc.edu

Abstract— Co-directional or clustered mobile users can be re-ceived using smart antennas at the base station (BS) and a mul-tiuser detector can be used to isolate their respective signals. Weconsider the scenario of clustered users in a WCDMA system andcompare the performance of beamforming and switched beamsantennas, along with multiuser detection strategies (decorrelatingdetector (DD) and the minimum mean squared (MMSE) detec-tor) for their reception at the BS. We show via simulations thatthe switched beams technique along with a multiuser detector, is abetter strategy than beamforming along with a multiuser detector,when the number of users in a cluster increases.

Index Terms— smart antennas, co-directional mobile users,beamforming, switched beam, multiuser detection

I. INTRODUCTION

Smart antennas consist of an array of antenna elements alongwith signal processing hardware that aims to receive the signalfrom a desired user and at the same time, cancel the effects ofsignals received from other mobile users. Research on the useof smart antennas on the uplink in cellular systems includingcode division multiple access (CDMA) and wideband code di-vision multiple access (WCDMA) systems has been going onfor some time now [1][2]. They have been shown to providea tremendous increase in the capacity along with benefits suchas range extension and minimization of multipath effects. Thethird generation standards such as WCDMA facilitates the useof smart antenna techniques by providing for a dedicated piloton the uplink for each user, consisting of pilot symbols, time-multiplexed with power control bits [3]. Smart antennas can beclassified into two groups: switched beam and adaptive antennasystems. A switched beam system consists of a set of beams inpre-defined directions (as illustrated in Fig. 1), of which the onethat best receives the signal from the desired user is selected.The beams have a narrow main lobe and small sidelobes so sig-nals arriving from directions other than that of the desired mainlobe direction are significantly attenuated. Adaptive antennaarrays, on the other hand, rely on beamforming algorithms tosteer the main lobe of the beam in the direction of the desireduser and simultaneously place nulls in the direction of the in-terfering users’ signals. Beamforming algorithms either use atraining sequence or rely on properties of the received signal,to determine the weights to be applied at each of the antenna

elements of the array, to obtain the desired beam pattern. Therecursive least squares (RLS) algorithm is a training sequencebased algorithm that has been popular in beamforming applica-tions [4].

We consider the smart antenna concepts used at the base sta-tion (BS) for the scenario of receiving co-directional mobileusers in a WCDMA system. Prior literature in this area consistsof work by Park and Kwak [4] that addressed the scenario ofco-directional users. The paper concluded that the RLS beam-forming and successive interference cancellation scheme givesthe best performance when compared to reception using an om-nidirectional antenna, even for large cluster sizes. The paper byKo et. al. in [5] proposes a switched beam system with mul-tiuser detection (MUD) (in the form of an interference canceler)to combat the multiuser interference and shows that the perfor-mance of this receiver is significantly better than that of usingswitched beam alone, or MUD alone, in the case of clusteredusers. There is no prior literature that compares the switchedbeam versus the beamforming technique when used along withmultiuser detection, for various cluster sizes. In this paper, wecompare the performance of beamforming and switched beamsalong with multiuser detection strategies (decorrelating detec-tor (DD) and the minimum mean squared (MMSE) detector)for reception of co-directional users, in a WCDMA system.A “Smart Antenna Simulation Environment” was implementedusing Matlab to perform the simulations. In Section II, a de-scription of the system model and the clustering model is pro-vided, while Section III provides a brief overview of beamform-ing and multiuser detection algorithms. Section IV discussesthe simulation results and Section V concludes the paper.

II. SCENARIO OF CLUSTERED USERS

The distribution of mobile stations (MSs) in a sector of a BSis usually not uniform over the geographical area. When mobileusers are clustered together in groups, using the technique ofbeamforming or switched beam alone is not the best receptionstrategy. This is primarily because other users in that cluster arealso accepted by the main lobe of the antenna array beam andare a source of multiuser interference, with respect to the de-sired user’s signal. Even the beamforming algorithm is not able

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Direction of Desired Signal

Direction of Interfering Signal 1

Direction of Interfering Signal 2

Switched Beam System

Antenna ElementsBeam 1

Beam 2

Beam 3

Fig. 1. The beams of a switched beam system.

30

60

90

120

150

180 0

Antenna pattern when performing Beamforming for user 1Antenna pattern when performing Beamforming for user 7Clustered mobile users

Antenna Array

User 7

User 1

Fig. 2. RLS beamforming polar plots for two users located in a cluster of 8users.

to null out other users in the same cluster due to their proximityto the desired user. Fig. 2 illustrates this phenomenon whenusing the beamforming algorithm to receive two users that aremembers of a cluster of 8 users. The beam formed to receive auser located at the center of the cluster (user 1) is forced to ac-cept the signals of the other users in the cluster. We also noticethat the beamforming beam formed for the user at the peripheryof the cluster (user 7) is different from the one formed to receiveuser 1. This is because there is a higher emphasis on placingnulls in the direction of the interferers than a maximum in thedirection of the desired user. This leads to ineffective receptionof the desired user and requires multiuser techniques, such asa decorrelating detector, to mitigate against the interference ofthe co-directional users.

The system model considered for the simulation is aWCDMA system with spreading sequences of the users mod-eled using Gold codes (the spreading factor being 31) and withthe BS using an antenna array with 8 elements. We assume

strict power control on the uplink for our simulation and hence,the signals received at the BS from all users have the same sig-nal to noise ratio (SNR). The signal received at the M -elementantenna array at the BS from K transmitting MSs in a sector isgiven by

r(t) =∑

i

K∑k=1

bk(i)ck(t− iT )a(φk) + n(t) (1)

where

ck(t) =L−1∑l=0

ψ(t− lTc) (2)

and r(t) is a M×1 array of the MS signals received at the an-tenna elements of the antenna array, bk(i) is the ith bit of in-formation transmitted by user k and ck(t) is the chip sequencefor user k. ψ(t) is the chip shaping pulse of duration Tc, whereTc = T/L with L being the number of chips per symbol, andT the symbol period. The steering vector of user k is repre-sented by aM×1 array a which is a function of the the angle ofarrival of each user’s signal, φk. The additive white Gaussiannoise (AWGN) at the antenna array is denoted by n(t), a M×1array, with the noise being uncorrelated between the antennaelements.

A model for the probability distribution function (pdf) of theclustered users formulated by Rooyen, et. al., is introduced in[6]. The probability distribution function of the angular distri-bution of MSs is given by (3) and (II)

pΘo(θo) =1

Anorm

1 +

Npeak∑l=1

γl

[rect

(ωlθo

π− αl

)

+rect(ωlθo

π− αl − 2π

)]cos2(ωlθo − αl)

}(3)

for 0≤θo≤2π and where Anorm is a normalizing factor to en-sure that ∫ 2π

0

pΘo(θo) dθo = 1.

The number of clusters in a cell is denoted byNpeak. The valueNpeak = 0 denotes a uniform distribution of MSs in the cell. Theparameter rect(x) is defined as follows: rect(x) = 1 if |x|≤ 1

2 ,and 0 elsewhere. The angular location of peak l is given by αl,ωl controls the angular width of peak l and γl represents the rel-ative size of peak l. Using the model in (3) above, Fig. 3 depictsthe pdf of a MS distribution where the MSs are clustered aroundfour perpendicular directions, such as in the case of the inter-secting roads. In this example, the plot indicates that the MSsare most densely clustered around the direction of α3 = 270◦

with respect to the BS. Section IV discusses our modificationsto this pdf to simulate the location of the clustered users in thegeographical area covered by a sector.

At the BS, a uniform linear array (ULA) of antenna elementsreceives the signals from the users in the sector (the angularrange covered being 120◦). When using the beamforming strat-egy, we determine the number of clusters and the users presentin each cluster by analyzing the beamforming weights of each

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0 1 2 3 4 5 60

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Angle (in radians)

Pd

f

Pdf of the distribution of MSs

Fig. 3. Example pdf of clustered mobiles.

user. Co-directional users have highly correlated weights sincethe beams are essentially formed with the main lobe pointing inthe direction of the desired user. Thus, the correlation value ρij

of the beamforming weights w of two users, i and j, is given by

ρij =wi

Hwj

‖wi‖ · ‖wj‖ (4)

A directional correlation matrix can thus be formed for allthe users and after comparing the individual correlation val-ues against a pre-determined threshold value, ρth, a decisionis made about the users belong to each cluster (if any).

In the case of the switched beam strategy, the signal to noiseratio (SNR) of the desired user’s signal as received at the BSusing each of the fixed beams of the switched beam system isascertained. The beam that received the largest SNR value isused for receiving that particular user. The identification of therespective beams to be used for all MSs in the sector results indetermining which MSs are members of a cluster.

III. ALGORITHMS

The RLS beamforming algorithm is implemented as follows

k(n) =λ−1P(n− 1)x(n)

1 + λ−1xH(n)P(n− 1)x(n)(5)

e(n) = b(n) − wH(n− 1)x(n) (6)

w(n) = w(n− 1) + k(n)e∗(n) (7)

P(n) = λ−1P(n− 1) − λ−1k(n)xH(n)P(n− 1) (8)

where x is the matched filter output for the kth user derivedfrom the received signal r at the antenna array and w is thebeamforming weight vector. The temporary variable k is calledthe gain vector and P is the inverse correlation matrix. Theterm b(n) represents the training symbols given by the pilotsymbols and e(n) is the error term used to modify the weightvector w to provide adaptation and convergence. The computa-tional complexity of the RLS algorithm is in the order of M2K

Block Diagram of the Smart Antenna Simulation Environment (SASE)

bk^

(For the 5 reception strategies)

Number of UsersNumber of Pilot Symbols Number of Data Symbols

SNR per User

Chips per symbol per userNumber of Antenna elements in the Array

Generate Gold Sequences and assign them to the Users

a( )φ

clustered and isolated usersAnalyze the weights to obtain

Simulate Angle of Arrival (AoA) forthe Users based on the modified

Rooyen Pdf distribution

Steering vector for each user

Use Decorrelating detector for Use Decorrelating detector for groups of Clustered users

Matched Filter

Parameters

AWGN at each antenna element

Reception using Switched Beam weightsReception using RLS Beamforming weights

Analyze the weights to obtainclustered and isolated users

groups of Clustered users

Obtain received signal at the Antenna Array

Fig. 4. Block Diagram of the Smart Antenna Simulation Environment imple-mentation.

where M is the number of antenna elements in the array andK denotes the number of users being received at the BS. Forthe switched beam antenna system, on the other hand, we im-plement the switched beams using Chebyshev weights appliedto each of the antenna elements, to form fixed beams in eightequally spaced directions spanning 120◦ in all.

The two multiuser detectors considered are the decorrelatingdetector and the minimum mean squared detector (MMSE) [7].The decorrelating detector is a linear, sub-optimal multiuser de-tector whose decision rule is given by

b = sgn[R−1y] (9)

whereas that of the MMSE detector is given by

b = sgn[(

A−1(R + σ2A−2

)−1)

y]

(10)

where b is the transmitted bit sequence for the users, R isthe crosscorrelation matrix of the signature sequences, y is thematched filter output vector, σ is the variance of the noise andA is the amplitude matrix of the received signals.

IV. SIMULATION RESULTS

The “Smart Antenna Simulation Environment” is a graphicaluser interface that we developed using Matlab, to perform thesimulations. The various steps in the simulation are listed in theblock diagram shown in Fig. 4.

The simulations were performed to compare average symbolerror rate (SER) for a cluster of users received using the fol-lowing strategies: (i) beamforming, (ii) switched beam system,(iii) beamforming with decorrelating detector and (iv) switchedbeam with decorrelating detector (v) beamforming with MMSEdetector and (vi) switched beam with MMSE detector. Theaverage SER was determined by computing the SER for eachuser in the cluster and then averaging over the users’ individualSERs.

The AoA values of the users were generated from the pdfin (3) as follows. We consider one of the peaks of the mobile

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-20 -15 -10 -5 0SNR for each user (dB)

10-5

10-4

10-3

10-2

10-1

SER

BFSBBF+DDSB+DD

Fig. 5. Average SER of 4 clustered users, using the various reception strate-gies.

distribution that is centered at φo = 65◦ and with an angularwidth of 2∆φ = 10◦. Thus, for the region (φo−∆φ)≤φ≤(φo+∆φ), the pdf of the AoA distribution can be written as

p(φ) =1

∆φ

[cos2

(π

2∆φ(φ− φo)

)]

To obtain AoA values from the above pdf of the desired clusterof MSs, we use the inverse transformation method [8].

Fig. 5 gives the average SER for the case of 4 clustered usersand Fig. 6 is for the case of 10 clustered users. In these plots,the users are received at the BS with equal signal strengths withSER averaged over all users and 105 data symbols, and plot-ted for various received SNR values. We infer that switchedbeam and beamforming alone perform poorly in terms of SERwhereas the addition of the decorrelating detector stage bringsabout a significant improvement. Switched beam antennascombined with the decorrelating detector is seen to outperformbeamforming with decorrelating detector, for the larger clusterof MSs. This is because the decorrelating detector works moreefficiently on signals received using the same beam for all theusers in a cluster whereas when the beamforming method is em-ployed, there is a disparity in the reception of the various usersof the cluster as depicted in Fig. 2. Also, selective decorrelat-ing detection is implemented using only the users in the clusterand is therefore computationally more efficient than strategiesthat attempt using multiuser techniques on all the users in thatsector that are received at the BS. The MMSE detector whensubstituted for the decorrelating detector in the above scenariosgave a comparable performance as the decorrelating detector.

Simulations were also performed to compare the two mul-tiuser strategies (namely DD and MMSE) when used along withbeamforming and switched beam strategies. The scenario con-sidered is 5 mobile users located in a cluster and received withdifferent signal strengths at the BS. One representative case is

-20 -15 -10 -5 0SNR for each user (dB)

10-5

10-4

10-3

10-2

10-1

SER

BFSBBF+DDSB+DD

Fig. 6. Average SER of 10 clustered users, using the various reception strate-gies.

User AoA(deg) SNR(dB)1 106.26 -52 111.19 -93 108.09 -84 110.16 -125 108.44 -10

TABLE IANGLE OF ARRIVAL (AOA) AND SNR FOR SIMULATION INVOLVING 5

CLUSTERED MSS.

given in Table I and the the SER, averaged over 106 data sym-bols, for each of the users received at the BS is listed in Ta-ble II. We infer that the MMSE detector provides insignificantimprovement over the decorrelating detector for the SNR valuesassumed.

The number of antenna elements in the array at the BS alsoinfluences the reception of co-directional users. Fig. 7 depictsthe antenna beam pattern when using RLS beamforming to re-ceive a mobile user present in a cluster of MSs, with an antennaarray with 4, 6 and 8 antenna elements, respectively. We notethat the beam width decreases with an increasing number ofantenna elements. The same is true for switched beam anten-nas and, in addition, the sidelobe levels decrease with increas-ing antenna elements, thus significantly attenuating the signalscoming from undesired directions. Further, we see in Fig. 7 thatthe center of each beam points in a slightly different direction.This reflects the attempt of the beamformer to null out interfer-ers, the influence of which is different depending on the widthof the beam (and hence, the number of antenna elements) forfixed user positions.

We compare the two smart antenna techniques using a decor-relating detector for a cluster of 8 users, for the case of differentantenna elements in Fig. 8. The plot indicates that the switched

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User BF+DD SB+DD BF+MMSE SB+MMSE1 0.007784 0 0.007746 02 0.094504 0.000498 0.09441 0.0004923 0.013918 0.00012 0.013888 0.000124 0.115182 0.006716 0.115206 0.0067125 0.043254 0.001754 0.04319 0.001744

TABLE IISER FOR THE 5 CLUSTERED MOBILE USERS USING SMART ANTENNAS

ALONG WITH MULTIUSER TECHNIQUES.

30

60

90

0

Antenna pattern for Beamforming − 4 element antenna arrayAntenna pattern for Beamforming − 6 element antenna arrayAntenna pattern for Beamforming − 8 element antenna arrayClustered mobiles users

Antenna Array

Fig. 7. Antenna beam pattern when receiving a user inside a cluster usingbeamforming with an antenna array of 4, 6 and 8 antenna elements.

beam with decorrelating detector performs better than beam-forming with decorrelating detector as the number of antennaelements increases. This is because with the narrow beamform-ing antenna patterns formed in the case of 8 antenna elements,there is a greater emphasis on nulling co-directional users thanaccepting the desired user’s signal at the expense of also accept-ing the signals from other clustered users. Thus, the decorrelat-ing detector is seen to be more effective on the switched beamantenna’s output rather than that of the beamformer. In the caseof 4 antenna elements, the beamwidths are large so all users areaccepted by the beams (both from beamforming and switchedbeams) formed for the desired user. Thus, the DD performsequally well when used after beamforming or with switchedbeams.

V. CONCLUSION

We have compared the performance of smart antenna tech-niques along with a multiuser detector for co-directional mo-bile users, in a WCDMA system. Simulation results usingthe “Smart Antenna Simulation Environment” that we devel-oped indicate that a switched beam antenna along with selec-tive multiuser detection can outperform the beamforming with

-20 -15 -10 -5SNR for each user (dB)

10-6

10-5

10-4

10-3

10-2

10-1

SER

BF+DD: 4 elementsSB+DD: 4 elementsBF+DD: 6 elementsSB+DD: 6 elementsBF+DD: 8 elementsSB+DD: 8 elements

Fig. 8. Average SER of 8 clustered users received using beamforming, withan antenna array with 4, 6 and 8 antenna elements.

multiuser detection technique, with increasing number of clus-tered users. An increase in the antenna elements is seen to favorthe switched beam antennas plus decorrelating detector strategyfor co-directional reception. For a smaller number of antennaelements, there was essentially no difference in performance.Thus, using switched beam antennas with a multiuser detec-tion strategy provides near the same performance (or better) asbeamforming with multiuser detection, without the additionalcomplexity of a beamforming algorithm.

REFERENCES

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[2] L. C. Godara,, “Applications of Adaptive Arrays to Mobile Communica-tions, Part I: Performance Improvement, Feasibility and System Consid-erations,” Proceedings of the IEEE, Vol. 85, No. 7, pp. 1031–1060, July.1997.

[3] H. Holma, and A. Toskala, WCDMA for UMTS : radio access for thirdgeneration mobile communications. J. Wiley, 2001.

[4] K. S. Kwak, and J. W. Park, “Multiuser Detection Scheme using AdaptiveAntenna Array Over Rayleigh Fading Channels,” in Vehicular TechnologyConference Proceedings (VTC), Vol. 3, pp. 2157–2161, Spring 2000.

[5] H. Ko, J. H. Lee, and B. Yu, “A Switched Beamforming System withMultiuser Detectors,” in Vehicular Technology Conference Proceedings(VTC), Vol. 2, pp. 705–709, Spring 2000.

[6] M. P. Lotter, and P. V. Rooyen, Space-time Processing for CDMA MobileCommunications. Kluwer Academic Publishers, Boston, MA, 2000.

[7] S. Verdu, Multiuser Detection. Cambridge University Press, New York,1998.

[8] R. Jain, The Art of Computer Systems Performance Analysis: Techniquesfor Experimental Design, Measurement, Simulation, and Modeling. Wi-ley, New York, 1991.

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