Proceedings of ICCT2003

'Spatial Division Multiplexing of Space-time Block Codes

Stbphanie Rouquette-Lbveil', Karine Gossel, Xiangyang Zhuang2, Frederick W. Vook2 Centre de Recherche de Motorola Paris, Espace Technologique S'Aubin, 91 193 Gif-sur-Yvette Cedex, France

Motorola Labs, 1301 E. Algonquin Road, Schaumburg, IL 60196

Abstracr --In this paper we propose to derive benefit from multi- ple antennas to achieve high data rates using a Spatial Division Multi- plexing (SDM) based scheme combined with Space-Time Block Coding (STBC). This scheme allows to transmit simultaneously NIP different streams from N antennas, each stream being encoded using a STBC designed for P outputs. Spatial Division Multiplexing of Space-Time Block Codes provides a reduced data rate compared to the classical SDM technique. However the performance gain provided by space-time block coding allows to transmit higher order constellations and then to design multiple antenna systems with same spectral efilciency and bet- ter performance. Performance of this scheme is assessed by simulations in the indoor 5GHz OFDM-based WLAN environment (IEEE802.11a. HIPERLAN/2).

I. INTRODUCTION One way to combat efficiently the severe attenuations in

the wireless propagation channel is to make use of spatial di- versity. In this category of multi-antenna approaches, space- time block codes have received a special interest, due to their remarkable performance vs complexity advantage. The first one has been proposed by Alamouti [ 11 to transmit data from two antennas. This rate 1 orthogonal code benefits from a

,. 1 1 1 diversity order of 2 with low complexity receiver since the corresponding Maximum Likelihood decoding scheme is based on linear processing only.

The theory of complex orthogonal designs shows that such a scheme with a codingrate of 1 and full spatial diversity can- not be extended to more than 2 transmit antennas (Tarokh e? aZ[2]). Nevertheless, it can be shown that the orthogonality and the diversity of the code can be preserved to the detri- ment of the coding rate: for instance rate 1/2 and rate 314 orthogonal codes with full diversity have been derived for 3 or 4 transmit antennas [2] [3] [4]. Another transmit diversity scheme, the so-called ABBA code, has been proposed first by 0. Tirkkonen et aZ[5] for 4 transmit antennas. This rate 1 scheme is derived from the permutation of two Alamouti codes, and provides spatial diversity to the detriment of the orthogonality of the code. Thus, due to the self-interference terms in the detection matrix, the performance of the ABBA code is inferior to the one of the orthogonal designs.

Space-Time Block Codes (STBC) benefit from the diver- sity provided by multiple antennas to improve the quality of the communication link. However these techniques have to face the cost of higher order constellations to achieve high data rates. Besides they are sub-optimal from a capacity point of view as soon as the receiver has more than 2 elements. Other multiple antenna schemes transmit simultaneously dif-

ferent streams from different antennas to increase the spectral efficiency of the system. At the receiver, several approaches can be used to perform the detection of these Spatial Division Multiplexing (SDM) based schemes with different levels of complexity and thus with different levels ofperformance. For instance Maximum Likelihood detection gives the best per- formance with a very high computational cost that increases exponentially with the order of the constellation. Less ex- pensive techniques are based on the Zero-Forcing (ZF) or the Minimum Mean Square Error (MMSE) criterion to perform the detection of the transmitted signals. The symbols are ei- ther detected simultaneously or successively if ZF or MMSE estimation is combined with the V-BLAST technique. This scheme was proposed by Wolniansky e? aZ[6] and is based on successive symbol cancellation combined with optimal de- tection ordering. Its performance is highly dependent on the number of available observations to cancel the interfering sig- nals. Thus the performance of square configurations (i.e. with same number of elements at the emitter and receiver) is rela- tively poor.

As an alternative to these schemes, we propose to combine the advantage of space-time block coding and spatial division multiplexing, i.e. robustness towards fading and increase of the spectral efficiency. This aim is achieved by transmitting several signals at the same time, each signal being encoded accordingly to a STBC to benefit from transmit diversity. At the receiver, detection can then be performed by applying to the new system one of the techniques already proposed for SDM schemes. In section 2, we present the hybrid scheme based on the combination of SDM and STBC in a flat hd- ing environment. We then detail the application of several detection schemes to this system in section 3. In particular we show that low cost ZF and MMSE receivers can be im- plemented without matrix inversion. Simulation results are presented in section 4 to compare the performance of SDM schemes, STBC and combination of SDM and STBC. Simu- lation are performed in indoor environment in the context of WLANs, and several receivers are considered for SDM based techniques. We hal ly conclude in section 5.

11. SPATIAL DIVISION MULTIPLEXING OF SPACE-TIME BLOCK CODES

For sake of simplicity, we restrict our study to the mul- tiplexing of Alamouti codes, but similar analysis can easily be conducted with any space-time block code. In this con-. figuration, a hybrid system with N antennas at the emitter

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can transmit simultaneously N / 2 streams, and each stream is transmitted over two antennas and two time intervals accord- ing to Alamouti coding. Thus an overall data rate of N / 2 is achieved, instead of 1 for Alamouti coding, and of A' for a classical SDM scheme.

Let us consider a system with four transmit elements. The corresponding emitter is depicted on figure 1.

c lfrna

Fig. 1. Spatial Division Multiplexing of two Alamouti codes

This results in transmitting four complex symbols s 1,s2, s3, and s4 according to the following code matrix

where the symbols of the nth column of C are sent from the n* antenna.

In this section, we assume that the system operates in a quasi-static flat fading environment, and we denote by h the M x 1 vector formed of the channel coefficients between the transmit antenna n and the M receive antennas. We also de- note by y1 and y2 the M x l signals received on the l'' and 2"d time slots, and by nl and n2 the corresponding additive noise components. The received signal can then be expressed as

s1

[ ;; ] = [ ;; -!; I ;; -!;I 3 x [ :: ] + [ 3'1' /

94 - (2)

- ' - n

S Y [HI IH2]

The channel matrix H = [HI IHz] is formed of two orthogo- nal sub-matrices H1 and H2 such as

H ~ H I = (llh1/l2 + llhz1l2) I2 = ~112

HFH2 = (llh31I2 + llh41I2) I2 = ~212.

(3)

(4) and

We can then recover the four transmitted symbols using equation (2). If we compare the characteristics of the hy- brid system to a SDM one with same number N of transmit

antennas, we first notice that the number of unknown is the same whereas the number of observations is twice more as we consider two time slots. Thus for any ZF or MMSE based receiver the minimum number of receive antennas required for the combination of SDM and STBC is equal to N / 2 in- stead of N . Moreover the hybrid scheme also benefits from the orthogonality of each Alamouti code, and in consequence benefits from transmit diversity. In the next section we detail the application of several types of receiver to the detection of the multiplexing of two Alamouti codes.

111. DETECTION OF SDM OF ALAMOUTI CODES

Different strategies can be applied to recover the trans- mitted signals, from optimal Maximum Likelihood to ZF or MMSE equalization. In the following, we focus on ZF or MMSE based receivers, possibly combined with the V- BLAST detection scheme, to get reasonable complexity.

A. Zero-Forcing Receiver In order to recover the four transmitted symbols SI , s2 ,

s3, and s4, ZF equalization can be applied to the hybrid sys- tem (2) by applying the Moore-Penrose pseudo-inverse ma- trix of H to the received signal y.

The pseudo-inverse H# of the channel matrix is defined as follows:

and can be rewritten as a b c t i o n of the sub-matrices H I and H# = ( ~ ~ ~ 1 - l H ~ , ( 5 )

H2 :

Let us introduce the orthogonal matrix P defined as:

P = HrH2. (7)

p p H = c ~ I ~ , (8)

Due to the orthogonality of this matrix, P verifies the relation

where

We can therefore derive an analytic form of the pseudo- inverse of the channel matrix:

W:' W:'

such as no matrix inversion is needed. The Zero-Forcing receiver can then be decomposed into

two stages. We first filter the received signal y by Wf" to remove the contribution from the other signal within each

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Alamouti code. Second we apply the filter WCF to the re- sulting signal in order to recover the two transmitted streams. These two stages lead to the same S N R within each Alamouti code, i.e.

(1 1) SNRl = c1 - c3/c2 for the lst stream, S N R ~ = q - c ~ / c I for the 2nd one.

The second term in the expression of the SNRs (11) corre- sponds to the cost of spatial multiplexing compared to the SNR achieved by the classical Alamouti scheme.

B. Minimum Mean Square Error Receiver

In the previous subsection we have derived an analytic form of the ZF receiver. We now conduct a similar study for the MMSE,receiver based on the filter W:

W = (HHH + u;Iq)-l HH, (12)

to be applied to the received signal y (2). 0: denotes the variance of the additive white gaussian noise and the symbols are assumed to be adequately normalized.

We can easily prove that W can be expressed without ma- trix inversion as

with

First stage of filtering using W y M S E is performed in a same way as for ZF detection to benefit from the orthogo- nality within each Alamouti code. Second stage based on the W y M S E filter then takes into account the variance of the ad- ditive noise to better detect the two transmitted streams and is specific to MMSE equalization.

C. V-BLAST receivers

The first step of the V-BLAST technique [6] consists in fil- tering the received signal by the ZF or MMSE filter dehed in the previous subsections. Hard or soft decisions on the two symbols related to the Alamouti code achieving the max- imum SNR are taken. For sake of simplicity we will only consider hard decisions in the section IV presenting simula- tion results. The contribution of these two symbols is then subtracted from the received signal. The second step of the V-BLAST receiver consists in recovering from the resulting signal the two symbols corresponding to the Alamouti code not detected yet.

Iv. SIMULATION RESULTS

In this section we consider W A N systems based on the specifications of the IEEE802.1 la (or HIPERLAN/2) stan- dard. This OFDM-based system operates at 5GHz with 20MHz bandwidth, and is characterized by a 64-point IFFT and 48 data subcarriers. The encoder is a rate 1/2 convolu- tional one with 64 states, and is followed by frequency inter- leaving. The mapping operation is then based on the BPSK, QPSK and 16QAM constellations.

The W A N system is extended here to deal with up to four antennas at the emitter and the receiver. The multiplexing of STBC was presented in section I1 for a flat fading chan- nel. In practice, as other multiple antenna techniques such as space-time block codes or SDM schemes, it can be straight- forwardly applied to CDMA-based systems having a Rake receiver and per-path processing, and to OFDM-based sys- tems, in which the channel can be equivalently modelled as parallel flat fading subchannels. Therefore, in the OFDM- based WLAN context, the space-time scheme operates per subcarrier. In addition to the frequency interleaving opera- tion, spatial interleaving must be performed to mix up the metrics related to the symbols detected during the same time slot. This can be achieved either by optimally extending the WLAN interleaver to operate over two dimensions (frequen- cies and antennas) [7], or by adding a spatial interleaver such as a symbol cyclic one after the mapper, as depicted on fig- ure 2, without modifying the WLAN interleaver. In our con- text, simulation results with respectively a two-dimensional bit interleaver and a symbol cyclic one lead to the same per- formance.

The multiple antenna approaches compared in this section include:

The Alamouti-based SDM scheme combined with the ZF and MMSE based receivers (sections 111-A and 111-B) as well with V-BLAST detection (section 111-C);

The Alamouti code; SDM schemes with ZF or MMSE receivers, in a non-

iterative or iterative (V-BLAST) mode.

Simulation results have been obtained at a data rate of 24Mbps, which corresponds to a spectral efficiency of 2b/subcanier. Consequently the multiple antenna techniques are combined with different constellations in order to achieve this data rate, namely we compare the QPSK 4x4 SDM and QPSK 4x4 hybrid schemes to the BPSK 4x4 SDM system and to the 16QAM 2x4 Alamouti code, The performance of these approaches is assessed in an indoor environment using the channel model BRAN A specified by ETSI [8] that corre- sponds to a typical office environment. We consider that the channels are uncorrelated and no mobility is assumed. Be- sides perfect knowledge of the channel coefficients is avail- able at the receiver.

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rate 1/2,64 states

64-point IFFT 48 data sub-caniers

Fig. 2. W A N system with multiplexed Alamouti codes

Figures 3 and 4 present the performance of these sys- tems where the ZF criterion is applied in both the SDM and Alamouti-based SDM receivers. Simulation results for fig- ures 3 and 4 have been obtained using respectively the simple receiver described in section 111-A and the V-BLAST detec- tion scheme. We notice that the ZF V-BLAST receivers per- form worse than ZF receivers, in particular for SDM schemes. In both cases the worst performance is achieved by the 4x4 SDM system that suffers from lack of spatial diversity. The best performance is achieved by multiplexing two Alamouti codes. Indeed this multiple antenna solution performs 1.4 to 1.6dB better at PER= than the 2x4 Alamouti code is penalized by the use of higher order constellations to achieve the same data rate. In addition, SDM of Alamouti codes has a gain of 0.7 to 1.6dB compared to the 2x4 SDM scheme thanks to transmit spatial diversity.

ZF RECEIVERS

0 2 4 6 8 1 0 1 2 SNR (de)

Fig. 3. PER performance of 2x4 SDM, 4x4 SDM, 4x4 Alamouti-based SDM (all with ZF receivers), and 2x4 Alamouti.

ZF V-BLAST RECEIVERS

-2 0 2 4 6 8 1 0 1 2 SNR (dB)

Fig. 4. PER performance of 2x4 SDM, 4x4 SDM, 4x4 Alamouti-based SDM (all with ZF V-BLAST receivers), and 2x4 Alamouti.

Figures 5 and 6 present the simulation results obtained in the same context but using the MMSE criterion instead of the ZF one. The performance of the MMSE V-BLAST receivers compared to MMSE receivers depends on the antenna con- figuration. Due to the improvement brought by the MMSE criterion for SDM-based schemes, the worst performance is now achieved by the Alamouti code. The difference of per- formance between the 2x4 and the 4x4 SDM systems is now reduced considerably as low diversity schemes benefit most from the use of the MMSE receiver in place of a ZF one. The hybrid design is still the most interesting solution as we no- tice a gain of 0.5 to 1.ldB at PER= compared to the 2x4 SDM technique, and a gain of 1.8 to 2.2dB compared to Alamouti coding.

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MMSE RECEIVERS

5 n

SNR (de)

Fig. 5. PER performance of 2x4 SDM, 4x4 SDM, 4x4 Alamouti-based SDM (all with MMSE receivers), and 2x4 Alamouti.

MMSE V-BLAST RECEIVERS

receivers such as the V-BLAST one can also be easily imple- mented to recover the signals transmitted by the hybrid space- time scheme. The multiplexing of space-time block codes is detailed for a flat fading channel, but it can be straightfor- wardly applied to CDMA-based systems and in a per subcar- rier basis to OFDM-based systems.

To put forward the good performance of the hybrid scheme, we consider the combination of two Alamouti codes, allow- ing to transmit data from four antennas with an overall data rate of 2. This Alamouti-based SDM scheme is then com- pared to Alamouti coding and SDM in an indoor WLAN context. Simulation results at 24Mbps show that the hybrid scheme outperforms the other space-time approaches for any type of receiver.

REFERENCES

SNR (de)

Fig. 6. PER performance of 2x4 SDM, 4x4.SDM, 4x4 [61 Alamouti-based SDM (all with MMSE V-BLAST re- ceivers), and 2x4 Alamouti.

[71 V. CONCLUSION

In this paper, we propose to combine a spatial division mul- tiplexing scheme with space-time block coding. Thus multi- ple antennas at the transmitter and receiver allow to benefit from spatial diversity and also to increase the spectral effi- ciency compared to a single antenna system. In that case NIP streams can be transmitted simultaneously from N an- tennas, each stream being encoded using a space-time block code with P outputs. At the receiver, simple ZF or MMSE de- tection can be performed without matrix inversion when the space-time block code is an orthogonal one. However other

L8]

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[3] 0. Tirkkonen and A. Hottinen. Complex Space-Time Block Codes for Four Tx Antennas. In GLOBECOMcon- ference records, volume 2, pages 1005-1009,2000.

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