Further Results on Space-Time Coding for UMTS

Further Results on Space-Time Coding for UMTS Roger Gaspa, Javier R. Fonollosa Departmenty of SIgnal Theory and Communications Universitat Politecnica de Catalunya Jordi Girona 1-3, Modul D5, Campus Nord UPC 08034 Barcelona SPAIN e-mail: frgaspa,[email protected] Abstract | We analyze dierent space-time architectures for the TDD mode of UTRA when employing multi-element antenna arrays at both the transmit and receive sites. We compare space-time codes that do not require channel knowledge at the transmitter with a beamforming scheme, which exploits channel reciprocity available in the TDD mode to construct a beamvector at the transmitter. I. Introduction

T is well known that employing multiple transmit and receive antennas considerably increases the capacity of the wireless channels. Transmit diversity schemes represent a powerful technique to combat and mitigate the destructive eects of multipath fading. Current generation of cellular systems consider only antenna arrays at the base station, but single antenna at the mobile. In this MISO channel con gurations space-time block codes designed using orthogonal designs [1],[2] are an eÆcient way to orthogonalise the available sub-channels. However these codes do not achieve channel capacity when there are multiple receive antennas (MIMO channel), moreover the amount of "channel capacity loss" increases as the SNR does [3]. Receivers for future generation of cellular systems, such as UMTS, will incorporate bigger displays if they are to support multimedia based services and high data rate services, which makes reasonable to assume more than one receive antenna. A layered architecture, named BLAST [4], achieves high spectral eÆciencies at reasonable decoding complexity provided that there are at least the same number of receive than transmit antennas. This layered architecture basically demultiplexes the bitstream (coded or uncoded data from previous blocks) into dierent substreams (one per each transmit antenna), modulates them and nally symbols are fed to its respective antenna, VBLAST. Recently, in [3], the authors presented a general structure for any linear space-time code, called Linear Dispersion (LD) codes, and showed that better performance can be achieved if symbols are dispersed in time and space when compared to in the BLAST architecture. On the other hand, if channel knowledge is available at the transmitter, via a feed-back channel or thanks to channel reciprocity as in the TDD mode of UTRA, the optimum combiner that maximises the received SNR is a beamformer

I

taken to be the maximum eigenvalue eigenvector [5]. In this paper we compare the performance of the beamforming approach with dierent linear space-time codes in terms of Bit Error Rate for a multi-user environment using a realistic MIMO channel model for the downlink transmission. II. System Model

We use a stochastic MIMO radio channel model that accounts for both time- and space-domain characteristics based on real environment measurements developed by Aalborg University as part of the METRA project [6]. The wideband radio channel H( ) can be modeled as:

H( ) =

LX1 l=0

Hl Æ( l )

where Hl is a nT  nR complex matrix whose elements describe the relation between transmit antenna i and receive antenna j at time delay l and takes into account the spatial correlation between antenna elements. We consider a 4  4 MIMO channel with spatial power correlation matrices for the mobile station (MS) and base station (BS), RM S and RBS respectively,

h

i;j

2

R

MS

6

=6 4 2

1 0:3394 0:0856 0:1615 0:3394 1 0:2947 0:1379 0:0856 0:2947 1 0:2490 0:1615 0:1397 0:2490 1

3 7 7 5 3

(1)

1 0:2628 0:2550 0:1216 6 0:2628 1 0:2417 0:2143 7 7 RBS = 6 (2) 4 0:2550 0:2417 1 0:2896 5 0:1216 0:2142 0:2896 1 which have been obtained through experimental measurements in real indoor scenario. The power delay pro le and delay spread are those speci ed by the ITU channel models (Indoor, Pedestrian, Vehicular). The TDD mode of UTRA does not envision using spacetime codes for the Dedicated Physical Channels (DPCH) and only considers using the Alamouti code [1] for the Primary Common Control Physical Channel (P-CCPCH). Figure 1 shows the transmit structure as speci ed by the This work was partially supported by the European Commis- 3GPP [7]. The beamvector w is constructed as the maxsion under Project IST-1999-11729 METRA and IST-2000-30148 IMETRA; the Spanish Government (CICYT) TIC99-0849, TIC2000- imum eigenvalue eigenvector of the estimated channel in 1025; and the Catalan Government (CIRIT) 2000SGR 00083. the reverse link. Both, beamvector and antenna selector,

are considered by 3GPP but we only addressed the beamforming approach in this paper.

Channel 1

Channel P

SF

ANT1 L FIR

ℑ(h) = Midamble

...

w1

ENC

INT

C(n) =

...

h

MUX Data

(N+1)SF

M

RF

SPR+SCR

...

...

ANT2 (N+1)SF FIR

RF

N+1 P(N+1)

w2

n;j ) and Fig. 2. Structure of matrices =(h

Uplink channel estimate

their real and imaginary parts denoted by superscript and I respectively, and obtain:

Fig. 1. Transmit Diversity for DPCH III. Linear Space-Time Codes

In [3] the authors de ne a Linear Dispersion code (LD) as a linear space-time code (following their notation) that transmits Q symbols si = i + j i , i = 1:::Q using nT antennas during T time instants according to a code matrix

S

x

R j

+

S=

q=1

(q Aq + j q Bq )

(3)

=

Q X

nT X

q=1

n=1

nT X

Q X

q

Q X

C

x

=1

I j

a

a

b

I R
n;j q;n

b

R I n;j q;n

=1

I I
n;j q;n

R R n;j q;n

!

=

nT X

q=1

n=1

a

R I + n;j q;n

!

q +

+ nR j q

n

Q X

R

!

I R
n;j q;n

a

q +

!

T

X X completely determined by the pairs of complex matrices R bR I bI
+ nI (5) q n ;j q;n n;j q;n j (Aq ; Bq ) of size T  nT . BLAST architecture and orthogq =1 n=1 onal space-time code designs are special cases of LD. where Let us denote with h i;j the channel impulse response from transmit antenna i and receive antenna j , assumed =(hn;j)C = n;j = Rn;j + j Rn;j (6) constant during the transmission of the sequence, with length Lc chips. The Spreading Factor is SF. Let us Gathering the real and imaginary parts we construct a rst consider the reception with a single antenna and as- single real system of equations that provides a linear relasume that Lc < SF (there is no inter-symbol interfer- tion between the input and the output vectors through the ence). Gathering T  SF samples of the received signal equivalent channel model Hj . at one antenna (receive antenna j ) into a column vector 2 3 1 xj = [xj (n):::xj (n + T  SF 1)]T , we can express: Q

xj = =

T X n

=(hn j )C ;

=1

n

Q X q=1

nT X n=1



=(hn j )Csn + nj = ;

(q aq;n + j q bq;n ) + nj

;

;

;

Hj

=



=

1

6 6 6 Hj 6 6 4

.. .



Q

7  7 7 7+ 7 5

nRj nIj



j A1 j B1


j AQ j BQ j C1 j D1


j CQ j DQ

where 2

n;j

contains the spreading sequence associated to each symbol. These matrices have the structure shown in gure 2. nj is a T  1 additive white Gaussian noise vector modeled as independent samples of a zero mean complex Gaussian random variable with variance N20 per dimension. We extend the result presented in [3] to a frequency selective channel. Following the steps in [3] we decompose equation 4 into



xRj xIj

(7)

Q

(4)

aq n ; bq n; sn are the n th column of matrices Aq ; Bq ; S respectively. =(hn j ) is the Toeplitz convolution matrix associated with channel impulse response h and C

where

n

Aq

=

6 6 6 6 6 6 6 6 4

aRq 1

3

2

;

a

.. .

7 7 7 R 7 q;nT 7 B I 7 q q;1 7 7 .. 5 . I q;nT

a

a

=

6 6 6 6 6 6 6 6 4

bIq 1 .. .

;

3

7 7 7 I 7 q;nT 7 R 7 q ;1 7 7 .. 5 . R q;nT

b b b



2

Cq

=

6 6 6 6 6 6 6 6 4

aIq 1 .. .

3

7 7 7 I 7 q;nT 7 D R 7 q q;1 7 .. 7 . 5 R q;nT

a a

2

;

=

6 6 6 6 6 6 6 6 4

3

bRq 1 .. .

;

7 7 7 R 7 q;nT 7 I 7 q;1 7 7 .. 5 . I q;nT

b

(8)

b

SAlamouti =



s1 s2 s2 s1



Finally, we consider the case of not using any beamforming, such as illustrated by the BLAST architecture shown a b in Figure 4. In this case the transmitter does not need to know the channel. Data is demultiplexed into nT dier R  ent substreams, each one transmitted from each transmit j = 1;j


RnT ;j I1;j


InT ;j antenna. Since this scheme increases the data rate by a factor of nT , we rst apply a convolutional code rate 1=nT Finally we stack the received signal from each receive an- to maintain the overall spectral eÆciency for all the artenna to obtain the nal MIMO input-output relation. The chitectures under consideration. Both space-time codes, extension to a multi-user case is straight-forward if we sub- Alamouti and V-BLAST, can be described using LD codes  = [C1 :::Cm], where Ci represents the previstitute C by C matrices[3]. At the receiver, after multiplexing detected ous de nition of matrix C but with the spreading sequence received data symbols a Viterbi decoder is used to decode associated to user i, and sn by sn = [s1 :::sm ], that is to the sequence and recover the original transmitted data. stack in a column vector those symbols si transmitted by In all schemes each user employs the same channelisation user i. If Lc > SF we gather at the beginning of vector sn code for each transmit antenna (code re-use), but dierthe previous symbols that due to the dispersive nature of the channel have distorted the received signal. Pilot

IV. Simulation Results

The signal constellation is QPSK is scaled such that the total transmitted energy is normalised to unity. The Spreading Factor (SF) is set to 16. Simulations are made in a slot by slot basis. For each run (one burst) a new channel matrix realization in chosen. Each burst contains two data sequences of length 61 symbols each, a middamble (training sequence) of 512 chips and a guard period of 96 chips, so the total burst length is 2
61
16+512+96 = 2560chips. We compare dierent schemes combining beamforming and

SPRD

c1,...,cK*m

s1,...,sK

2m-PSK, 2mQAM Modulator

G SPRD Space - Time Block Encoder

Pilot

M U X

M U X

Pilot SPRD Convolutional Code rate 1/4

Pilot SPRD

Pilot SPRD

Beamforming

Pilot

SPRD

M U X

ANT 1

M U X

ANT 2

M U X

ANT 3

M U X

ANT 4

ANT 1 W ANT 2

ANT 3 W ANT 4 Beamforming

Fig. 3. STBC and Beamforming

space-time codes. The rst one is the transmit beamforming as shown in Figure 1, where no space-time encoding is performed. A second one combines the 4 transmit antennas into two groups of 2 antennas each one, and a dierent beamforming is applied to each group, as shown in Figure 3. We take this approach in order to avoid using a space-time block code for for transmit antennas since this scheme is not full rate. Eectively, for complex constellations, there are no full rate space-time block codes for more than 2 transmit antenna [2]. Since we have 2 "eective" antennas we may employ any space-time code using nT = 2, e.g. the Alamouti code [1]:

Fig. 4. BLAST transmit architecture with code re-use

ent scrambling codes and training sequences are used by each user for each antenna. Note that in BLAST schemes all users undergo the same equivalent channel because no user-speci c beamforming is applied and we need to estimate only nT  nR = 16 channels. Hence all users transmitting from the same transmit antenna may use the same training sequence, as a result, as the number of users increases the better the channel estimation is because the power of the training sequence increases. Figure 5 shows the BER curves for a scenario with 4 intracell users. The beamforming approach gives the best performance. The layered architecture estimating only 16 channels (as mentioned before) shows a signi cant improvement when compared to estimating all channels for all users (64 channels). We can even observe a coding gain eect if we increase the number of states of the convolutional code. However, this layered architecture shows the worst BER curves, but it is worth mentioning that it does not require channel state information at the transmitter. In the TDD mode channel reciprocity can be used and hence channel

Downlink INDOOR 3 km/h

0

Downlink INDOOR 3 km/h & VEHICULAR 120 km/h

0

10

10

beamforming STBC+beamforming Layered 16ch estim −1

−1

10

10

VEHICULAR −2

−2

10

BER

BER

10

4x1

−3

10

−4

10

−3

10

INDOOR

beamforming STBC+beamforming Layered 16ch estim Layered 64ch estim Layered 16ch estim mm4

4x4

−4

10

−5

10 −25

−5

−20

−15

−10

−5

0 CIR (dB)

5

10

15

20

25

10 −25

−20

−15

−10

−5

0

5

Fig. 5. Downlink INDOOR 4 users

Fig. 7. Downlink INDOOR and VEHICULAR 4 users

estimation might be available at the transmitter. In gure 5 the variance of the channel estimation errors is set to the Cramer-Rao bound. However channel estimation errors may signi cantly degrade the performance of the beamforming approach. This eect is shown in Figure 6 where the variance of channel estimation errors is set twice the Cramer-Rao bound. We note that in this case the layered architecture performs very close to the beamforming approach.

V. Conclusions

Downlink INDOOR 3 km/h

−1

10

beamforming beamforming error*2 STBC+beamforming STBC+beamforming error*2 Layered 16ch estim Layered 16ch estim mm4

BER

In this paper, dierent space-time transmit diversity schemes have been analysed in terms of BER for the TDD mode of UTRA using a realistic channel mode. Channel state information is available at the base station due to channel reciprocity. This information is used to design a beamvector as the maximum eigenvalue eigenvector of the equivalent channel. Simulation results show that when the channel is estimated correctly at the reverse link the beamformer design exhibits the best performance. However, simulations show that if there are signi cant channel estimation errors, the layered architecture performs as close as the beamformer, which does not require channel state information. References

−2

10

−3

10

−4

10

−5

10 −25

10

CIR (dB)

−20

−15

−10

−5

0

CIR (dB)

Fig. 6. Downlink INDOOR 4 users

Figure 7 shows the performance in a Vehicular channel. Although the perform worst than in the Indoor case due to channel estimation error produced by the vehicle speed, the performance gap between the BLAST scheme and the beamforming approach is still preserved.

[1] S.M. Alamouti, \A simple transmit diversity technique for wireless communications," Selected Areas in Communications, IEEE Journal on, vol. 16, no. 8, pp. 1451{1458, Oct. 1998. [2] Calderbank A.R. Tarokh V., Jafarkhani H., \Space-time block coding for wireless communications: performance results," Selected Areas in Communications, IEEE Journal on, vol. 17, no. 3, pp. 451{460, March 1999. [3] Hochwald B. Hassibi B., \High-rate codes that are linear in space ans time," Submitted to IEEE Trans. Info. Theory, Aug. 2000. [4] Foschini G.J. Golden G.D. Valenzuela R.A. Wolniansky P.W., \Simpli ed processing for high spectral eÆciency wireless communication employing multi-element arrays," Selected Areas in Communications, IEEE Journal on, vol. 17, no. 11, pp. 1841{ 1852, Nov. 1999. [5] Stoica P. Ganesan G., \Maximum-snr space-time designs for mimo channels," ICASSP'01, 2001. [6] \Mimo channel characterisation," METRA Project Deliverable AAU-WP2-D2-V1.1.pdf, , no. D2, pp. available at http://www.ist{metra.org, Dec. 2000. [7] \Pysical layer procedures (tdd). ts 25.224 v3.1.0.," 3rd Generation Partnership Project, Technical Speci cation Group, Radio Acces Network, Working Group 1 (RAN-WG1)., Dec. 1999.