be used, deploying matrix-vector calculus. Discrete- time variables will be denoted by vectors which are given as lower case characters in bold face italics.
MIMO Schemes In UTRA LTE, A Comparison Christoph Spiegel1, Jens Berkmann2, Zijian Bai1, Tobias Scholand3, Christian Drewes2, Guido H. Bruck1, Bertram Gunzelmann2, Peter Jung1 1
Universität Duisburg-Essen, Lehrstuhl für KommunikationsTechnik, 47048 Duisburg, Germany 2 Infineon Technologies AG, Am Campeon 1-12, 85579 Neubiberg, Germany 3 Infineon Technologies AG, Düsseldorfer Landstraße 401, 47259 Duisburg, Germany
Abstract— The long term evolution of UMTS (Universal Mobile Telecommunications System) Terrestrial Radio Access, abbreviated as UTRA LTE, will be based on OFDM (orthogonal frequency division multiplexing). Furthermore, MIMO (multiple-input multiple-output) techniques have been considered as a means for the improvement of wireless connectivity. In wireless systems, high data rates in the downlink are desirable: Furthermore, with respect to an efficient implementation, the downlink requires a thorough assessment. In particular, the Alamouti and the V-BLAST (Vertical Bell Labs Layered Space Time) schemes are seen as interesting concepts. In this communication, the authors will compare these two MIMO schemes w.r.t. the achievable performance in the UTRA LTE downlink using up to two transmit and two receive antennas. Furthermore, the authors will discuss the deployment of spatial multiplexing in the UTRA LTE downlink and will show that the performance of successive interference cancellation (SIC) based data detection techniques for MIMO-OFDM is beneficial. Index terms— Alamouti, Diversity, MIMO, OFDM (Orthogonal Frequency Division Multiplexing), Spatial Multiplexing, Successive Interference Cancellation (SIC), UMTS, UTRA LTE, V-BLAST
I. INTRODUCTION Mobile radio systems like UTRA (Universal Mobile Telecommunication System Terrestrial Radio Access) [1],[2], direct sequence code division multiple access (DS-CDMA) has been used as the basic multiple access method, forming the basic PHY and MAC concepts. Despite many advantageous features, DS-CDMA techniques do not facilitate a flexible adaptive engineering of the used frequency resource. Owing to its inherent flexibility and its attractive implementation potential, OFDM (orthogonal frequency division multiplexing) has therefore become a preferred candidate for the downlink of the long term evolution of UTRA, termed UTRA LTE. To allow high user data rates which are required for the realization of wireless multimedia, the combination of OFDM with MIMO (multiple-input multipleoutput) antenna schemes has been considered as a preferred way forward. This combination is termed MIMO-OFDM. The data detection in MIMOOFDM can be done in various ways. In order to limit the additional implementation complexity, 978-1-4244-1645-5/08/$25.00 ©2008 IEEE
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linear equalization, e.g. zero-forcing (ZF) and minimum mean squared error (MMSE) equalization, or serial interference cancellation (SIC) is preferred. Besides transmit diversity, i.e. the Alamouti scheme [3], V-BLAST (Vertical Bell Labs Layered Space Time) [4], a SIC version of ZF equalization, and the corresponding SIC-MMSE receiver are considered an interesting concept for this purpose. In what follows, complex base band notation will be used, deploying matrix-vector calculus. Discretetime variables will be denoted by vectors which are given as lower case characters in bold face italics. Matrices will be denoted by upper case characters in bold face italics. Complex values will be T underlined. Furthermore, ( ⋅) denotes vector or H matrix transposition, ( ⋅) denotes Hermitian of a vector or a matrix. This communication is organized as follows: After this introductory section, Sect. II will present the system model underlying the analysis. In Sect. III simulation results will be presented. Sect. IV will conclude the manuscript. II. SYSTEM MODEL A. General Remarks It has been known that MIMO schemes can facilitate an improved receiver robustness by exploiting transmitter (TX) and receiver (RX) antenna diversity as well as the maximization of data rates by deploying spatial multiplexing (SM). For this reason, K T , K T ∈ ` , TX antennas are deployed for communication with at least K R , K R ∈ ` , RX antennas. Between each pair of TX/RX antennas there is a radio path. The RX antennas receive the signals of the TX antennas. To allow the data detection in the case of SM, K R ≥ KT must be fulfilled [4]. In SM, the overall achievable data rate at the TX is K T times the data rate of a single TX antenna transmitter. Alamouti type TX antenna diversity does not impose any requirements on the number of RX antennas.
Therefore, K R > 1 always yields additional RX antenna diversity. In what follows, a system concept for the SM and a system model for the Alamouti approach will be presented. Each data symbol is assumed to be taken from an M -ary symbol alphabet. B. Spatial Multiplexing In this section, we will deploy the mathematical model introduced in [5]. We will consider a single slot, i.e. a single OFDM symbol period, in a time transmission interval (TTI). Let us assume that K T 1 k K data symbols d l( ) "d (l T ) "d (l T ) are transmitted on each subcarrier l , l = 1" L . In what follows, we will arrange these K T data symbols in the subcarrier specific data vector
(
d l = d l( ) "d l( 1
kT )
"d l(
)
KT )
T
, l = 1" L .
(1)
Assuming cyclic prefixes being removed at the RX input, the frequency domain received sample associated with subcarrier l , l = 1" L , is given by r (l
kR )
KT
= ¦ H (l ,lR
k , kT )
d l(
kT )
+ n(l
kR )
, l = 1" L .
(2)
kT =1
In (2), n(l R ) is the sample of the noise measured at RX antenna kR , kR ∈ {1" K R } , and associated with k ,k the l th subcarrier, l = 1" L . H l(,lR T ) denotes the channel coefficient associated with the l th subcarrier and, thus, with the subcarrier specific k ,k data vector d l of (1). H (l ,lR T ) describes the connection between TX antenna kT , kT ∈{1" K T } , with RX antenna kR , kR ∈ {1" K R } . Owing to (2), the subcarriers do not mutually interfere, i.e. intercarrier interference (ICI) is absent. With the subcarrier specific channel matrix k
H l ,l
) § H l(1,1 ,l ¨ ¨ H ( 2,1) = ¨ l ,l ¨ # ¨ H ( KR ,1) © l ,l
H (l ,l
1,2 )
H
H l(,l
1, K T )
· ¸ ¸ " H ¸ , l = 1" L , (3) % # ¸ ( KR , KT ) ¸ " H l ,l ¹ "
( 2,2) l ,l
( 2, KT ) l ,l
# ( KR ,2)
H l ,l
and with the subcarrier specific noise vector
(
nl = nl( ) "nl( 1
kR )
" nl(
KR )
)
T
, l = 1" L ,
(4)
, l = 1" L ,
(5)
the received vector
(
r l = r (l ) "r (l 1
kR )
"r (l
KR )
)
T
associated with the l th subcarrier is given by r l = H l ,l d l + nl , l = 1" L .
(6)
The V-BLAST scheme [4] is a viable detection approach for SM. The RX sets out from r l defined 1 in (5) and (6) to detect first data symbol d (l ) . This 2229
is done by nulling like in the case of the nullsteering beamformer. The mentioned nulling can be performed by applying a weight vector
(
w i = w(i ) " w(i 1
kR )
" w(i
KR )
)
T
(7)
with the weights being determined according to 0 ∀kT ≥ i, 1, k 2, k K ,k (8) H l( ,l T ) , H l(,l T ) " H (l ,l R T ) w i = ® ¯1 ∀kT = i,
(
)
to the received vector r l . (8) means that the weight vector w i is orthogonal to the subspace spanned by those contributions to r l which have not yet been cancelled. (8) can be solved by first deleting the first ( kT − 1) columns of H l ,l defined by (3) , j , and then which yields the modified matrix H l ,l computing the Moore-Penrose pseudo inverse
(
+ j jH H j H l ,l = H l ,l l ,l
)
−1
jH H l ,l
(9) +
j . In the Then, w i is given by the i th row of H l ,l + j is the Moorecase of the first data symbol, the H l ,l Penrose pseudo inverse of the full matrix H l ,l of j + . With Q {a} (3) and w 1 is the first row of H l ,l denoting the complex quantizing operation, quantizing a to the nearest allowed data symbol realization, we find (1) T (10) d = Q w r , l = 1" L . l
{
1
l
}
(1) Now, the influence of the detected symbol d l is subtracted from r l , resulting in the modified vector (1)
r l ,2 = r l − dl
(H(
1,1) l ,l
, H (l ,l ) " H (l ,l R 2,1
K ,1)
)
T
, l = 1" L ,
(11)
which contains less interference. Since the influence of the first data symbol has been removed, the modified received vector r l ,2 , l = 1" L , contains less interference than r l . Hence, the detection of the remaining symbols can be improved. This procedure is then repeated with the 2 new vector r l ,2 , detecting d l( ) . This procedure is repeated until all data symbols have been detected. Obviously, the V-BLAST receiver is a ZF (ZeroForcing) based SIC (Successive Interference Cancellation) receiver, also termed SIC-ZF in what follows. In the above description it is assumed that the symbols are detected in the order of the data vector d l . However, as stated in [4] the order of detection is critical. Because the signal-to-noise ratio (SNR) in each data detection stage varies, each data symbol is prone to a different error probability. Hence, the ordering of the data detection effects the
overall symbol error. It turns out that an optimal strategy is a greedy approach. One hence chooses the particular data symbol with the greatest SNR of the remaining undetected data symbols in each detection stage. This data symbol is then detected with the minimum error probability of all remaining data symbols. Subtracting the influence of the newly detected data symbol from the remaining data symbols yields an improvement of their respective SNR, leading to a favorable error performance. The SNR can be estimated using the MoorePenrose pseudo inverse of the modified channel matrix, see (9), also used to determine the appropriate weights for symbol nulling. The sought cardinal number of the next data symbols is simply the row number of this matrix with the smallest L2 vector norm [4]. In V-BLAST receivers, the aforementioned separation is done straight forwardly by matrix inversion of the channel matrix, provided that its inverse exists. However, this ZF approach yields poor results if the channel matrix H l ,l of (3) is ill conditioned. This happens when the cross correlations between the different elements of H l ,l are high, e.g. when there is a significant line-ofsight (LOS) component. As an alternative to the ZF based V-BLAST, an MMSE (Minimum Mean Squared Error) based approach facilitates more favorable results. In the case of MMSE receivers, the orthogonality principle is fulfilled which guarantees that the estimation error and the estimates are orthogonal in average [6]. The V-BLAST algorithm can be modified accordingly by replacing (9) with +
j H l ,l
§ ¨ N0 =¨I + k ¨¨ E d l( T ) ©
{
2
}
( Hj
H l ,l
j H l ,l
· −1 ¸ ¸ ¸¸ ¹
T
(
d l = d (l ) , d (l
) ( Hj
H l ,l
j H l ,l
)
−1
H
j , H l ,l
H l ,l
}
2230
1
2)
)
T
, l = 1" L .
(13)
In the OFDM symbol period (ν + 1) , the data 2∗ symbol −d l( ) is transmitted on the l th subcarrier over the first TX antenna and the data symbol 1∗ + d l( ) is transmitted on the l th subcarrier over the second TX antenna. With (13), with the subcarrier specific 2 K R × 2 channel matrix
−1
(12) where N 0 equal to kBT0 is the spectral noise power 2 is the symbol energy. The density and E d (l k ) resulting receiver is termed SIC-MMSE in what follows. C. Alamouti Type TX Diversity If the radio paths between the K T , K T ∈ ` , TX antennas and the K R , K R ∈ ` , RX antennas are sufficiently uncorrelated, the exploitation of diversity is possible which makes the reception
{
more robust against the detrimental effects of interference, noise and fading. Therefore, it will be possible to increase the data rate by deploying higher order modulation (HOM) thus providing a higher throughput. A simple way of realizing such a system is by using the Space-Time Block Code (STBC) discovered by Alamouti [3]. This scheme combines diversity with a low-complexity receiver structure. The key idea of [3] is to transmit two symbols simultaneously over the two TX antennas. At the next symbol period the same symbols are transmitted again, swapping the TX antenna elements for transmission of each symbol. A simple coding of the symbols makes it possible for the receiver, to detect the received symbols with only small effort. In order to describe the OFDM version of the Alamouti scheme we must consider the transmission at two consecutive OFDM symbol periods, OFDM symbol period ν and OFDM symbol period (ν + 1) . In the OFDM symbol period ν , the data symbol d l(1) is transmitted on the l th subcarrier over the first TX antenna and the data 2 symbol d l( ) is transmitted on the l th subcarrier over the second TX antenna. Both data symbols form the data vector
) § + H (l1,1 ,l ¨ )∗ ¨ + H l(1,2 ,l ¨ # =¨ ¨ + H ( KR ,1) l ,l ¨ ¨ + H ( KR ,2)∗ l ,l ©
+ H (l ,l
1,2 )
· ¸ − H l ,l ¸ ¸ # ¸ , l = 1" L , ( KR ,2 ) ¸ + H l ,l ¸ K ,1 ∗ − H (l ,l R ) ¸¹ (1,1)∗
(14)
and with the subcarrier specific noise vector
(
nl = n(l )( ) , n(l )( 1 ν
1 ν +1)
" nl(
K R )(ν )
, n(l
K R )(ν +1)
the received vector
(
r l = r l( )( ) , r l( )( 1 ν
1 ν +1)
"r l(
K R )(ν )
, r l(
K R )(ν +1)
)
)
T
T
, l = 1" L . (15)
, l = 1" L , (16)
associated with the l th subcarrier is given by
r l = H l ,l d l + nl , l = 1" L .
Fig. 1.
(17)
(Quadrature Amplitude Modulation) Alamouti and 16-QAM V-BLAST as well as 16-QAM SICMMSE will be compared to 256-QAM Alamouti, respectively, as the V-BLAST and SIC-MMSE schemes have twice the symbol rate for 2 × 2 MIMO. In all cases, real decision feedback equalization (rDFE) [5] will be taken into account when analyzing the V-BLAST and SIC-MMSE performance. Furthermore, we will focus on a 2x2 MIMO channel with uncorrelated MIMO branches. In all simulations, perfect channel estimation is considered.
Uncoded BER for QPSK modulation, 2x2-MIMO, uncorrelated MIMO branches
In order to detect the received symbols the maximum-likelihood (ML) rule 2 H ½ H d l = arg max ®2 Re d l H l ,l r l − H l ,l d l ¾ , k ¯ ¿ (18) dl
{
}
l = 1" L,
can be applied [3]. The ML rule in (18) can be simplified by noting that the channel matrix H l ,l is always orthogonal, regardless of the actual values of the channel coefficients. Then, H l ,l H l ,l = H
§1 0· H + H ⋅¨ ¸, { } 0 1 © ¹ KR
¦
( kR ,1)
2
( kR ,2 )
l ,l
2
l ,l
Fig. 2.
Uncoded BER for 16-QAM modulation, 2x2MIMO, uncorrelated MIMO branches
Fig. 3.
Uncoded bit error ratio (BER) performance, 2x2 spatial channel model with uncorrelated MIMO branches
l = 1" L .
kR =1
=I
= EH
2
(19)
Therefore, (18) becomes 2 H ½ H d l = arg max ®2 Re d l H l ,l r l − EH d l ¾ , k ¯ ¿ dl
{
}
(20)
l = 1" L. H l ,l
H r l in (20) is the Alamouti linear equalizer in the case of K R , 2K R ∈ ` , RX antennas. In the case of constant d l , e.g. when phase shift keying modulations are deployed, (20) further simplifies to become H H (21) d = arg max Re d H r , l = 1" L. l
k
dl
{ {
l
l ,l
l
}}
III. SIMULATION RESULTS In [1], a spatial channel model, termed SCM, has been introduced for MIMO reference simulation purpose. To have a fair comparison, QPSK (Quadrature Phase Shift Keying) V-BLAST and QPSK SIC-MMSE will be compared to 16-QAM 2231
First the uncoded bit error ratio (BER) Pe shall be addressed. Fig. 1, Fig. 2 and Fig. 3 show simulation results for the BER as a function of the overall signal to noise ratio 10log10 ( Eb N 0 ) for the V-BLAST and the SIC-MMSE detectors as well as
for Alamouti TX diversity with dual RX antenna diversity. At low SNR values, the SIC schemes exhibit steeper BER curves than their linear variants. At high SNR values, the SIC schemes and the linear receiver performance curves show the same slopes. The ML receiver provides the steepest BER curves. Nevertheless, the SIC-MMSE receiver provides an overwhelmingly promising performance. At high SNR values, the linear receivers, i.e. the MMSE and the ZF receivers, again provide the worst performance whereas the SIC versions facilitate performance improvements.
Fig. 4.
Measured throughput η in bit/s/Hz for the SICMMSE receiver, Chase combining (CC) or incremental redundancy (IR), 2x2 spatial channel model with uncorrelated MIMO branches
Fig. 4 shows the evaluated throughput η , measured in bit/s/Hz, in the case of coded transmission and SIC-MMSE reception using the UMTS Turbo Code according to release 5 with varying code rates. The simulation results consider the hybrid automatic repeat request (H-ARQ) procedure specified in the UMTS standard. Both Chase combining (CC) as well as the selected incremental redundancy (IR) scheme of UMTS have been considered. The chosen code rates vary between 1/3, 1/2, 2/3 and 3/4. The data modulation schemes are either QPSK or 16-QAM with maximum throughput values of 3.36 bit/s/Hz and 6.72 bit/s/Hz, respectively. It has been found that spatial multiplexing techniques are inferior w.r.t. the robustness of the transmission. Nevertheless, throughput analyses showed that maximum throughputs can also be
2232
achieved by using spatial multiplexing, although a higher SNR requirement must be met. Therefore, both spatial multiplexing as well as diversity schemes are seen as competing and viable means to increase the data rate in future mobile radio systems. IV. CONCLUSIONS In this manuscript, the authors discussed spatial multiplexing compared with transmit and receive diversity schemes for MIMO transmission. In particular, V-BLAST, SIC-MMSE and Alamouti type transmission were taken into account. Special focus was laid on the downlink transmission of UTRA LTE. The SIC-MMSE receiver structure was illustrated and its performance was analyzed in simulations. It was found that the SIC-MMSE outperforms the V-BLAST scheme. Although the SIC-MMSE cannot provide reception as robust as in the case of spatial ML receivers, it allows a beneficially low implementation complexity and therefore is a viable candidate for terminals using MIMO techniques. Furthermore, simulation results showed that both diversity and spatial multiplexing are viable means to improve the data rates. V. ACKNOWLEDGMENT The authors wish to grateful to their colleagues at Infineon Technologies and at the Lehrstuhl für KommunikationsTechnik of the Universität Duisburg-Essen. Parts of this work have been carried out within the scope of the EUREKA MEDEA+ project MIMOWA, partly funded by the German BMBF. REFERENCES [1]
[2]
[3]
[4]
[5]
[6]
Third Generation Partnership Project; Technical Specification Group Radio Access Network: “Physical Layer Aspects for Evolved UTRA“; 3GPP TR 25.814. Third Generation Partnership Project; Technical Specification Group Radio Access Network: “Requirements for Evolved UTRA (E-UTRA) and Evolved UTRAN (E-UTRAN); (Release 7)“; 3GPP TR 25.913 V7.0.0. Alamouti, S.: A Simple Transmit Diversity Technique for Wireless Communica-tions. IEEE Journal on Selected Areas in Communications, vol. 16 (1998), pp. 1451 – 1458. Wolniansky, P. W.; Foschini, G. J.; Golden, G. D.; Valenzuela, R. A.: V BLAST: An Architecture for Realizing Very High Data Rates Over the Rich-Scattering Wireless Channel. Proceedings of the URSI International Symposium on Signals, Systems, and Electronics (1998). New York/NY, pp. 295 – 300. Scholand, T.; Spiegel, C.; Berkmann, J.; Bai, Z.; Drewes, C.; Gunzelmann, B.; Bruck, G.H.; Jung, P.: MIMO Succesive Interference Cancellation for UTRA LTE. Proceedings of the 12th International OFDM-Workshop (InOWo'07), 29-30 August 2007, Hamburg. Kay, S.M.: Fundamentals of Statistical Signal Processing – Estimation Theory. Page 386, Englewood Cliffs: Prentice Hall, 1993.
