Downlink Beamforming for WCDMA Based on Uplink Channel Parameters

Downlink Beamforming for WCDMA based on Uplink Channel Parameters

Christopher Brunner,1, 2 Michael Joham,2 Wolfgang Utschick,2 Martin Haardt,1 and Josef A. Nossek 2

1. Siemens AG, ICN CA CTO 71 2. Institute for Network Theory and Circuit Design Hofmannstr. 51, D-81359 Munich, Germany Munich Univ. of Technology, D-80290 Munich, Germany Phone/Fax:+49(89)722-29480/-44958 Phone/Fax:+49(89)289-28511 / -28504

E-Mail: [email protected] E-Mail: [email protected] (1)

Abstract – The downlink spectral efﬁciency of third w 1

generation mobile radio systems is especially important (2)

w DAC HF PA

since several serviceswill be asymmetric, i.e., on the av- 1 + (3)

erage the downlink data rates will be higher than on w 1

the uplink. We propose to utilize adaptive antennas at

(1) w

the base stations because spatial interference suppres- 2

s (t) 1 sion is able to reduce the near-far effect caused by high (2) w DAC HF PA

2 +

s (t)

data rate connections in the downlink of single-user de- 2

(3) w

tection DS-CDMA systems. The algorithm that calcu- 2

s (t)

lates the downlink beamforming vectors takes into ac- 3

(1) w count the correlation properties of the spreading and M

scrambling codes. It is also based on estimates of the (2)

w DAC HF PA M +

downlink channel parameters in terms of the domi-

(3) w nant directions of arrival, corresponding delays, and M corresponding medium-term average path losses. A non-linear minimization problem with non-linear con- Figure 1: Illustration of downlink beamforming for K =3 users straints is set up, where the total transmit power is min- and M antenna elements. imized while each mobile is provided with the required signal to interference and noise ratio (SINR) at the output of its rake receiver. data rate connections in order to compensate for the lower processing gain. If the spreading factors differ significantly, the near-far effect may degrade the performance of 1 Introduction the low data rate mobiles significantly. Downlink beamforming, cf. Figure 1, leads to spatial interference suppres- Future mobile communication systems require a signif- sion and, therefore, reduces the near-far effect. Moreover, icant increase in capacity to accommodate the growing fast fading can be mitigated by exploiting the spatial trans- number of users and to allow new services with higher data mit diversity. In the sequel, we assume that the BS is en- rates and a variety of quality of service requirements. The hanced with an antenna array. The mobiles are equipped proposed concepts for third generation mobile radio sys- with a single antenna and a conventional maximum ratio tems allow an easy and flexible implementation of new and combining rake receiver [11]. Notice that the simplicity more sophisticated services. Recently, ETSI SMG selected of the mobile is very important from an economic point of the TD-CDMA concept for time-division duplex (TDD) view. systems and the WCDMA concept for frequency-division duplex (FDD) systems1 [5]. Adaptive antennas exploit the Depending on the service, each mobile requires a certain inherent spatial diversity of the mobile radio channel and transmission rate and bit error ratio. These parameters perform spatial interference suppression. Therefore, they set the target SINR required at the output of the mobile are an important technology to meet the high spectral effi- maximum ratio combining rake receiver. In [7], a down- ciency and quality requirements. We have investigated the link beamforming approach is introduced which provides uplink data detection in WCDMA utilizing adaptive anten- each user with a given SINR. To this end, a complex non- nas at the base station (BS) in [2, 3]. linear constrained optimization problem is set up and several approximations are discussed. However, the users In this paper, we focus on the downlink of WCDMA. In in [7] are separated by space only, whereas for WCDMA, general, high data rate connections on the downlink of separation takes place in the space and the code domain. WCDMA must be transmitted with more power than low Therefore, the calculation of the downlink beamforming vectors for WCDMA should also consider the auto- and 1This solution has been contributed to the International Telecommu- nication Union - as the European proposal for IMT-2000 transmission cross-correlation properties of the spreading and scram- technology. bling codes in addition to the (medium-term) downlink

chips chips

Q Q

k C D

channel parameters. The intercell interference and thermal k

b ol symb ol noise are considered as well. Notice that we average the sym downlink channel parameters over fast fading. Therefore, the beamforming vectors are not updated at the rate of fast

fading but at the rate the medium-term downlink channel

control symb ols

N N data symb ols

k C D parameters change. This leads to a signiﬁcant reduction in k computational complexity. Moreover, all processing takes

place in the BS.

chips

N cps This paper is organized as follows. The downlink channel parameters can be obtained in different ways as ex-

Figure 2: Downlink slot structure of WCDMA for the k -th mo- plained in Section 2. Section 3 describes the downlink sig- bile: The DPDCH and DPCCH are time-multiplexed. The num-

nal model, and we illustrate the complete downlink data

N N

ber of chips per slot equals cps. Moreover, k P dedicated pilot

model in Section 4. Section 5 gives the scheme which de- symbols are broadcasted at the beginning of each DPCCH slot.

= Q = Q k

termines the downlink beamforming vectors. Finally, Sec- Q

k k For simplicity, we assume k D C . tion 6 examines the scheme with respect to complexity and bit error ratios by means of Monte-Carlo simulations. 3 Downlink Signal Model

2 Channel Parameter Estimation An extensive overview of WCDMA is given in [6, 5]. WCDMA has two types of dedicated physical channels, the dedicated physical control channel (DPCCH) and In [8], the (medium-term) downlink channel parameter es- the dedicated physical data channel (DPDCH). On the timates are obtained by feedback information on the up- downlink, the DPDCH and DPCCH are time-multiplexed, link. To this end, each antenna element transmits different cf. Figure 2. In case of data rates not exceeding 2 Mb/s, pilot signals. The channel estimates at each mobile are one connection consists of one DPCCH and one DPDCH. then transmitted to the BS. To keep feedback rates reason- For the sake of notational simplicity, we assume that the ably low, the estimates are averaged over fast fading. power and spreading codes are identical for the DPDCH However, channel information estimated on the uplink can and the DPCCH of each mobile. Moreover, we do not in- also be applied to the downlink. The frequency offset clude scrambling in our notation. The downlink baseband

between up- and downlink in WCDMA is approximately signal for the mobile k may then be expressed as

equal to 190 MHz. We assume that the reciprocity be- 1

tween up- and downlink comprises the directions of ar- X

(m)

s (t) = b c (t mT )

k k k (1)

rival (DOAs), the delays, and the medium-term average k

path losses2. Note that the reciprocity does not hold for m

Q k

the phases. X

c (t) = d p(t q T )

k c k q (2)

Since the DOAs, delays, and medium-term average path

q =1

losses of the impinging wavefronts are much less time- and

T = 4096 frequency-variant than the phases, the medium-term uplink 1

The chip rate in WCDMA equals c Mchips/s.

(t) T =

channel information may be obtained by averaging over c k

Moreover, the spreading code, k , is of length

Q d f1 1g T

several consecutive uplink slots [5], i.e., by averaging over Q

k k q c

k and is composed of chips ,

fast fading. Moreover, averaging reduces the inﬂuence of (

1 q Q b f1 1 g

k . The symbols, j j , are

interference and noise considerably. In [2], we describe k

(t) QPSK modulated. Furthermore, p R denotes the how to obtain a signal-and-interference-plus-noise as well chip-waveform which has a square-root raised cosine spec-

as an interference-plus-noise space-frequency covariance

= 022 trum with a rolloff factor of . matrix for each WCDMA uplink slot and each mobile. In order to obtain the channel parameters listed below, the Notice that downlink transmission is synchronized on the covariance matrices are averaged and applied to the 3-D symbol level to exploit the orthogonality of the spreading channel sounding algorithm based on 3-D Unitary ESPRIT sequences. Of course, this orthogonality is degraded by as described in [10]. multipath propagation. On the other hand, downlink transmission is (intentionally) not synchronized with respect to

For downlink processing, the DOAs in terms of azimuth the slots to be able to take full advantage of discontinous

k k

k and elevation , the delays , and the medium- transmission (DTX) or packet services .

term average path losses k of the dominant wavefronts

k 1 L 1 k K

of each mobile , where k and , L

are required. Here, k denotes the number of dominant 4 Downlink Data Model K wavefronts of mobile k and is the number of co-channel mobiles in one cell. We assume that the mobiles are equipped with a conventional maximum ratio combining rake receiver [11]. The 2Experimental measurements at 900 MHz have shown that the DOAs remain relatively stable over the frequency range used for uplink and 3Note that the DPDCH part of the slot may be empty. However, the downlink transmission in GSM [1]. control channel is always transmitted due to uplink power control, etc.

required signal to noise and interference ratio after com- not known. However, the BS can calculate the averaged

k v k bining in the -th mobile (SINR ) is deﬁned according to absolute value of k nf as follows:

au cr

(k n )

(I + I + N ) k S =

k k

k SINR (3) k

k H f

jv j = j w j y

k n (4) k f k nf and must be chosen with respect to the QoS (Quality of Moreover, the norm of the ﬁnger weights of each mobile

Service) requirements. Here, the noise power of the k -th

rake can be chosen freely without inﬂuencing its SINR. N user k comprises the thermal noise and intercell interference. Intracell interference occurs due to intersymbol in- Therefore, we set

terference (ISI) and multi-user access interference (MAI). H

k[v v v ] k

kv k = = 1

k 1 k 2 k N 2 2 k (5) The auto-correlation interference power caused by ISI and f the cross-correlation interference power caused by MAI

au cr The intracell interference in terms of ISI and MAI is I

are denoted by I and , respectively. If the wavefronts k k caused by non-ideal auto-correlation and cross-correlation

for the mobile k arrive at the mobile with different delays, c

properties of the spreading codes k according to

its rake is able to correct the unknown downlink phases.

L 2

Then the received and combined signal power at the rake f k

X X

(k n

au H )

w I j = y v

output of mobile is given by j

k n

k k

n =1

=16=n

f f

f z

X X

(k n )

(m) K 2

H f k

A X X

f X

z S = y b jv j

k k n (k n )

E k n k

k n cr H

z f f

j w y = I jv

k n

k k

=1 =1 n

nf z f

0 0

=1 n

=1 k =1k 6=k

f z

X X

) (k n

f A where

= y jv j z

k n k n

z k n f

n n =1 =1

(k n

f z f )

y ) = a (

k k k n ACFk k f

4 0

(k n

where f )

0 0

) y ( = a

(k n )

k k k k n k CCF

f k f

y = a (0) k n ACFk k nf f

hold. Note that the medium-term post-correlation down- N

The mobile rake has f ﬁngers and the number of down- 0

) k n

( f y

N link channel vector is calculated from the averaged

link beamforming vectors used per mobile equals z. The k

M a channel information estimated on the uplink, cf. Section 2. weighted steering vector k nf C depends on azimuth,

elevation, and medium-term path loss, cf. Section 2. The The number of dominant wavefronts of the k -th mobile is

k M subscript denotes the mobile and is the number of BS denoted by k . In addition to (3), we require the total

0 downlink transmit power k k antenna elements. ACFk and CCF stand for the auto-

correlation function and the cross-correlation function of K

5 X

c c k

the spreading codes k and , respectively . The down- H

w P = w

k (6)

link beamforming vectors are denoted as k nz C . The

k =1 k

averaged weight applied to the nf-th rake ﬁnger in the -th v to be as small as possible in order to reduce the intercell mobile equals k nf C. interference.

If the wavefronts are transmitted at the same time, the

z k N Fast fading is not taken into account since we use the z beamforming vectors k nz of the -th mobile can be

w medium-term downlink channel parameters. However, if merged to one beamforming vector k according to

the SINR target is not reached (exceeded) at the rake re-

X ceiver output, power control can trigger an increase (de-

k n )

H (

y S = jv j w

k k n

k k

k n crease) of the noise and intercell interference power

f f

n =1

f of mobile k . Macro-diversity which is required for soft N where handoff can also be taken into account by adapting k of

6 N z k

X mobile at the involved base stations .

w = z k n

k z n z =1 5 Estimation of the Downlink Beam-

In general, the wavefronts arrive at each mobile at different forming Vectors

1 n N times due to different delays k nf f f, when transmitted at the same time. Here, we assume that the We must avoid more than one wavefront assigned to a mo- delays differ sufﬁciently so that the rake receivers are able bile arriving at that mobile at the same time. Otherwise, to resolve the multipaths and, thus, are able to combine the rake receiver fails to resolve the impinging wavefronts

coherently. independently which may lead to combined wavefronts v Of course, the phases of k nf in the mobile rake receiver weakened or even eliminated by superposition (noncoher- are not available in the BS since the downlink phases are ent addition). The simplest approach consists of serving

4Here, the wavefronts of each user are transmitted at the same time. 6Notice that intercell interference determines the minimum downlink

5 Q

An extension of this notation is required if the spreading factors k receive power at each mobile, especially if the mobile is close to the cell

are not equal for all K mobiles. border.

each mobile only on the strongest multipath component

H H H

C u A u u C u u u

N = 1

1K K 1 1 12 2

1 2

( z ). Without loss of generality, we assume that K

H H H

u C u C u u A u u

ka k ka k k 1

2K K 21 1 2 2

1 2

1 2 k 2

k holds for . In this case,

. . .

v k = 1 k

k .

1 2

constraint (5) reduces to k and can, there- . . .. .

fore, be ignored. Equations (3) and (6) take the following H H H

C u u C u u u A u

K1 1 K2 2 K K

1 2 form: K

Minimize

u K

Each normalized beamforming vector k is the eigenvec-

X H

w P = w tor corresponding to the positive eigenvalue of the matrix

k (7)

k =1 K

subject to X

C A

k k k

(k )

H 2 cr au

0 0

kw y k + I + N ) = (I

k =1k 6=k k

SINRk (8)

k k k 2

k 1

= w C w k

k k k Note that each user’s transmit signal generates more sig-

where nal power than interference power if all columns of matrix

L add up to be positive. Then the eigenvalue correspond-

k 1) (k 1)

au H ( H ing to the eigenvector which is the normalized beamform-

I w = y y w

k k

k k u

ing vector k must be positive. Moreover, the transmit

=2 P

H au power k for each mobile will also be positive. Since the

= w C w

k k

k medium-term channel parameters change slowly, the inver-

K K

k sion of C which is required to obtain the trans-

X X

0 0

k 1) (k 1)

cr H ( H

0 k

w w y y I

= mit powers can be performed iteratively [9] at reduced

k k

0 0

=1 =1k 6=k

k computational complexity. K

X With initial estimates of the normalized beamforming vec-

H cr

w = C w

0 0

k k k

k tors and the correspondingpowers according to (9), we can

0 0

=1k 6=k k apply a linear iterative algorithm described in [7] which hold. A very similar problem has been examined in [7] offers a performance close to the non-linear schemes at a for a TDMA system such as GSM enhanced with adap- signiﬁcantly reduced computational complexity. tive antennas at the BS. Several solutions to this prob- Notice that the dimension of matrix is increased by one lem are listed in [7], e.g., a computationally complex non- when a new mobile starts to communicate. However, the linear method such as the augmented Lagrangianalgorithm system may not be able to meet the service requirements

for non-linear equalities. In an SDMA system based on of the new mobile depending on the current load. By eval-

K +1)(K +1)

GSM, no more than ﬁve mobiles must be taken into ac- ( uating matrix C , we are able to perform count jointly. However, more than 60 mobiles can operate admission control very efﬁciently, since all columns sim- in the same channel in WCDMA. Therefore, it is essential ply must add up to be positive. to utilize less complex schemes. To this end, we rewrite the beamforming vectors as fol-

lows: 6 Simulations

w = P u ku k = 1 k

k k k 2 k and To ensure realistic simulation scenarios, propagation data The basic idea of the following scheme is to transform the of the downtown of Munich is utilized generated by a sophisticated ray tracing tool developed at the Univer- joint optimization problem for all K beamforming vectors

sity of Karlsruhe [4]. The scenario is based on a three-

w K

k into decoupled problems and to separately estimate

dimensional topographical model of downtown Munich,

u P k the normalized beamforming vector k and the power where the height of the base station is 26 meters and the required for the k -th mobile. If the constraints given in equation (8) are rewritten according to height of the transmitter at the mobiles is 2 meters, cf. Fig-

ure 3. K

H X H

0 0

P u u P = 1 C u A u

0 In the sequel, we assume optimum downlink channel pa-

k k k k k k

k k

0 0

=1k 6=k

k rameter estimation in the BS, i.e., the medium-term post-

(k 1)

correlation downlink channel vectors y have been de-

where k

L = 5

au cr termined with the ray-trace parameters of k dom-

C C

k k

= = C

A inant wavefronts of each user. Here, we have used long k k

k and

N N N

k k k SINR k scrambling codes which comprise 40960 chips. Therefore, hold, we can set up the following set of linear equations: the signal, auto-, and cross-correlation covariance matri-

au cr

C C C 0

ces k , , and must be averaged over a sufﬁcient

k k k

1 P

1 number of symbols. Even though the scheme described

1 P

in Section 5 takes only the dominant multipath component

. . (9)

. . into accountfor signal transmission, the rakes are equipped

N = 5 1

P with rake ﬁngers which are set to the exact delays K f In the next simulation, we take strong intercell interference into account as well, cf. Figure 5. Intercell interference (and thermal noise) is modeled as white additive Gaussian noise and the signal to noise ratio (SNR) at the receiving

antenna of the mobile (before the correlator) is set to 0 dB. Accordingly, the improvements attained by calculating the beamforming vectors and corresponding transmit powers with equation (9) are less pronounced.

7 Conclusion

In general, separation is neither orthogonal in space nor by code in contrast to separation in frequency or time. Here, the mobiles are separated not only by code or space but by code and space. Therefore, we have presented a data model for WCDMA that takes into account BS adaptive antennas and comprises the correlation properties of the codes as well as the spatial and temporal downlink channel parameters. Preliminary simulation results have shown that the performance and, thus, the capacity can be increased signiﬁcantly by taking into account the correlation Figure 3: Map of downtown Munich showing the location of the properties. base station (TX) and the mobiles. The propagation data in terms of DOAs, delays, Dopplers, and attenuations of each impinging wavefront is available for 57 different mobile positions. References

[1] L. Bigler, H. P. Lin, S. S. Jeng, and G. Xu, “Experimental direction of arrival

and spatial signature measurements at 900 MHz for smart antenna systems”,

v k n k nf and weights f. Hence, the SINR at the rake out- in Proc. IEEE Vehicular Techn. Conf., pp. 55–58, Chicago, IL, July 1995. puts will be slightly better than expected according to (7) [2] C. Brunner, M. Haardt, and J. A. Nossek, “2-D rake receiver in the space- and (8). Moreover, it is assumed that the mobiles are not frequency domain for the uplink of WCDMA”, in Proc. 6th IEEE Interna- moving. Then the Doppler is zero and (fast) fading does tional Workshop on Intelligent Signal Processing and Communication Sys- tems. (ISPACS '98), vol. 2, pp. 551–555, Melbourne, Australia, Nov. 1998. not occur. We chose a scenario with 4 high-data-rate users

[3] C. Brunner, M. Haardt, and J. A. Nossek, “Adaptive space-frequency rake

Q = 16 in one cell with a spreading factor of k which cor- receivers for WCDMA”, in Proc. IEEE Int. Conf. Acoust., Speech, Signal

responds to a raw data rate of 512 kb/s. Processing, Phoenix, Arizona, Mar. 1999, accepted for publication.

In the first simulation, we only consider intracell interfer- [4] D. J. Cichon, Strahlenoptische Modellierung der Wellenausbreitung in urba- nen Mikro- und Pikofunkzellen, Ph. D. dissertation, University of Karlsruhe, ence and set the intercell interference to zero. The raw Karlsruhe, Germany, Dec. 1994, in German. bit error ratio (BER) of user 1 is plotted as a function of [5] E. Dahlman, B. Gudmundson, M. Nilsson, and J. Sköld, “UMTS/IMT-2000 the number of antenna elements (of a uniform linear array) based on wideband CDMA”, IEEE Communication Magazine, vol. 36, pp. with intracell interference, cf. Figure 5. The target SINR 70–80, Sept. 1998. is set to 10 dB for each user. The dashed BER-curve is [6] E. H. Dinan and B. Jabbari, “Spreading codes for direct sequence CDMA and obtained by calculating the power and normalized beam- wideband CDMA cellular networks”, IEEE Communication Magazine, vol. forming vector for each user separately taking into account 36, pp. 48–54, Sept. 1998. only the dominant path. The power is set to the inverse [7] C. Farsakh and J. A. Nossek, “Spatial covariance based downlink beamforming in an SDMA mobile radio system”, IEEE Trans. Communications, vol. of the attenuation of the dominant path and the normal- 46, pp. 1497–1506, 1998. ized beamforming vector is equivalent with the normalized [8] D. Gerlach and A. Paulraj, “Base station transmitting antenna arrays for mul- steering vector of the dominant path. We achieve a signif- tipath environments”, Signal Processing, vol. 54, pp. 59–74, Oct. 1996. icant improvement, cf. solid BER-curve in Figure 5, by [9] G. H. Golub and C. F. van Loan, Matrix Computations, Johns Hopkins Uni- determining the normalized beamforming vector and the versity Press, Baltimore, MD, 2nd edition, 1989. corresponding transmit power by jointly considering all [10] M. Haardt, C. Brunner, and J. A. Nossek, “Efficient high-resolution 3-D chan- mobiles in the cell according to equation (9), thus serving nel sounding”, in Proc. 48th IEEE Vehicular Technology Conf. (VTC '98), pp. each mobile on its strongest multipath component. In both 164–168, Ottawa, Canada, May 1998. cases,users 2, 3, and 4 had a BER of zero. In Figure 4, the [11] J. G. Proakis, Digital Communications, McGraw-Hill, New York, NY, 2nd beamforming patterns of user 1 and user 2 are plotted with edition, 1989. dashed and solid lines in case of separately taking into account the dominant path of each user and in case of utilizing equation (9), respectively. By taking into account the correlation properties, the beamforming patterns of users 2, 3, and 4 change significantly which corresponds with the improvements seen in Figure 5 for user 1. Obviously, user 1 is the weakest of the 4 users since its beamforming pattern does not change. 90 90 separated downlink processing 2.2361 separated downlink processing 2.2361 120 60 120 60 joint downlink processing joint downlink processing

1.6771 1.677 directions of arrival directions of arrival

150 1.118 30 150 1.118 30

0.55902 0.55901

180 0 180 0

210 330 210 330

240 300 240 300

270 270

Figure 4: The beamforming patterns of user 1 and user 2 are plotted on the left and right side, respectively. The dashed (normalized) pattern is obtained by taking the dominant path into account for each user separately (separated downlink processing), whereas the solid (normalized) pattern is determined by solving equation (9) (joint downlink processing). The directions of arrival are plotted as dashed lines. Note that the length does not indicate the attenuation but only which path is dominant. By taking into account the correlation properties, the beamforming pattern of user 2 changes signiﬁcantly. On the other hand, the beamforming pattern of user

1 does not change. (The dashed and solid curves on the left side are the same.) These plots are based on a uniform linear array with = 5 M antenna elements.

user 1, no intercell interference user 1, intercell interference: SNR = 0 0 0 10 10

−1 10

−1 10 raw bit error ratio raw bit error ratio

−2 10

separated downlink processing separated downlink processing

joint downlink processing joint downlink processing

−3 −2 10 10 1 1.5 2 2.5 3 3.5 4 4.5 5 1 1.5 2 2.5 3 3.5 4 4.5 5 # of antenna elements # of antenna elements

Figure 5: The raw bit error ratio of user 1 is plotted as a function of the number of antenna elements (of a uniform linear array) with intracell interference (on the left), and (on the right) with intracell and intercell interference. Intercell interference (and thermal noise) is modeled as white additive Gaussian noise. The dashed curves are obtained when taking the dominant path of each user into account separately, whereas the solid curves are based on the beamforming vectors and corresponding transmit powers determined by equation (9).