High Bit Rates for 3G and Beyond using MIMO channels
Ari Hottinen, Jussi Vesma, Olav Tirkkonen, and Nikolai Nefedov
Nokia Research Center
P.O.Box 407, FIN-00045 Nokia Group
Finland
Abstract— This paper studies the applicability of
se-lected high rate open-loop space-time codes and closed-loop beamforming concepts for future wireless systems, such as WCDMA/HSDPA. Several spectrally efficient space-time codes are evaluated and their performance is compared to related closed-loop concepts, where a feedback link from the receiver is used to aid (downlink) beamforming. The comparison is based on schemes that attain 4bps/Hz spec-tral efficiency, where either two parallel QPSK streams or a single 16-QAM stream is transmitted using up to four transmit antennas, and one or two receive antennas.
I. Introduction
Future evolutions of the WCDMA system are likely to support very high (instantaneous) data rates. High instan-taneous data rates enable efficient application of multiuser diversity[15] and rate allocation concepts. As an example, with multiuser diversity the channel resources are allocated or prioritized to the user or service with the best channel conditions. This involves rapid rate allocation and joint coordination of multiple users’ transmissions.
The peak bit rates currently considered for WCDMA High Speed Downlink Packet Access (HSDPA) are between 10−20M bps. To achieve such data rates a high rate channel code (e.g. rate ≥ 3/4 Turbo code) and in addition most of the available downlink channelization codes need to be assigned to a given user. Given that the current HSDPA specification supports 16-QAM modulation, the peak data rates above 10M bps become feasible[34]. Such high rates can be provisioned to users with sufficiently good channel conditions.
Multiple-Input-Multiple-Output channels open the way for new modulation and coding schemes with either in-creased bandwidth efficiency or better power efficiency[19], [4]. These can be considered as alternatives to 16-QAM and other single-stream high-order modulation methods. The MIMO transmission methods typically send multiple symbol streams, each with low modulation order. These streams interfere with each other and an efficient decoder (e.g. Maximum Likelihood, ML) is required to capture the gains due to parallel transmission. Provided with a ML receiver space-time codes designed for MIMO chan-nels have been shown to outperform conventional high or-der modulation concepts by several decibels[23]. This sug-gests that further performance increase for HSDPA, or any other similar system, could be sought from novel multi-antenna transceiver concepts that deliberately exploit the additional degrees-of-freedom inherent in highly scattering
environments. On the other hand, in MIMO channels the number of channel parameters is increased, which degrades the overall performance of MIMO systems. Efficient chan-nel estimation is needed to overcome performance satura-tion due to channel estimasatura-tion errors.
Many of the MIMO capacity results assume an open-loop MIMO system with no channel state information in the transmitter. If feedback link exists for conveying such infor-mation, conventional single-stream transmission becomes again competitive. This is expected, as MIMO modulation schemes require that the channel rank is sufficiently high. However, if the channel state information is used to control a beamformer, the channel rank (conditioned on feedback) collapses. In this case MIMO transmission method also converges to the special case where only a single stream is transmitted. The prevailing WCDMA closed-loop concepts (Mode 1 and Mode 2), or extensions thereof, can be used to provide the channel state information to the transmitter.
This paper is structured as follows. Section 2 summa-rizes selected spectrally efficient multi-antenna transmis-sion concepts. Section 3 discusses the closed-loop concepts adopted in WCDMA and their multi-antenna extensions. Section 4 provides numerical results where open and closed-loop schemes are compared. Finally, Section 5 concludes and proposes possible new directions.
II. High Rate MIMO transmission A. Unconstrained transmission
The commonly known BLAST receiver and associated parallel transmission[4] applied unconstrained transmission using several transmit antennas. The signal transmitted withNttransmit antennas is simply
X= [x1 · · · xNt], (1) wherex1, ..., xNt are modulated symbols (e.g. QPSK) and different columns designate different antennas. The re-ceived signal for the block is
r=Xh+n, (2)
wherenis white (complex) Gaussian noise andhis a vector comprising the complex channel coefficients between trans-mit and receive antenna. Multiple receive antennas are needed to decode the transmitted signal. Unconstrained signaling above does not provide any transmit diversity gain. In contrast the BLAST receiver requires multiple receive antennas in order to decouple the parallel streams and to enjoy some receive diversity gain. Employing a large number of receive antennas is not cost-effective and there-fore alternative solutions are desired for real systems.
B. Orthogonal space-time block codes
Unconstrained transmission is a highly non-orthogonal transmission method, which deliberately avoids almost all design principles. Another extreme, which requires only linear processing at the transmitter, is provided by or-thogonal space-time block codes proposed in [1]. How-ever, orthogonal space–time block codes are suitable for relative low rate transmission due to the inherent rate con-straints. In particular, symbol rate one space-time block codes (STBC) exist only when there are 2 antenna ele-ments in the transmitter. This code is known is applied in the STTD concept in WCDMA.
With increased transmit diversity order (with more than two antenna elements), the rate diminishes. As an exam-ple, with space-time block codes for 3 or 4 transmit anten-nas, the maximal code/symbol rate is reduced to 3/4 [17], [18]. Bearing in mind the desire to increase the data rate, such reductions in symbol rate are not desired, and alter-native encoding schemes are needed. Nevertheless, despite inherent suboptimality at symbol level in a MIMO channel, simple yet efficient multi-antenna extensions of the Alam-outi code [8], [16] may be useful even when combined with high order modulation and an outer channel code.
C. Double STTD
Double STTD (DSTTD)[26] transmits two STTD (or Alamouti) codes in parallel from four transmit antennas using code matrix
X(x1, ..., x4) = £
X(x1, x2) X(x3, x4) ¤
. (3) The philosophy behind this solution is analogous to that of the unconstrained signaling concept. That is, with a suffi-ciently complex decoder, and with suffisuffi-ciently uncorrelated channels, spectral efficiency can be increased by transmit-ting two streams of data in parallel through independent spatial channels. Multiple receive antennas reduce the sig-nal correlations and enhance reception considerably, as was shown by [19], [4]. DSTTD yields transmit diversity order two and receive diversity order of two, when the receiver applies a Maximum Likelihood decoder.
D. Non-orthogonal space-time block codes
Solutions that address the tradeoffs between diversity or-der, code rate, and performance were proposed in [20], [13], [5]. We review particular instances of non-orthogonal codes below. The choice below is motivated by its robustness to Ricean fading [11].
D.1 Symbol rate one code with rotated constellations Consider a transmitter with Nt transmit antennas and
square space-time code matrices. Let X1 ∈ CNt/2×Nt/2
and X2 ∈ CNt/2×Nt/2 be arbitrary rate r constituent
or-thogonal space-time block codes, andU is unitary matrix of the form U(α, φ) = · µ ν −ν∗ µ∗ ¸ ⊗INt/2, (4)
where we assume thatµ=√αandν =√1−αexp(−jφπ). The transformed code is obtained e.g. by constructing a space-time matrix: Xtr= · 1 0 1 0 ¸ ⊗X˜1+ · 0 1 0 −1 ¸ ⊗X˜2, (5) where ˜ X1 = X1(y1, ..., yNt/2) ˜ X2 = X2(yNt+1, ..., yNt) (6) with transformed input symbols
(y1, ..., yNt) = (s1, ..., sNt)U
T(α, φ). (7)
Assume thatX1andX2are of the Alamouti form. Ifα= 0
orα= 1 we obtain the STTD-OTD concept of [14]. When
α = 0.5 the code has a correlation structure of ABBA type[20]. However, the the form of the effective channel correlations is more favorable in correlated channels, as will be seen below.
The received signal is
r=Xtrh+n. (8)
As before, we can write (8) using the effective channel ma-trix as ˜r = HUs+n, where ˜r is obtained from r using complex conjugations and linear transformations. WithNr
receive antennasNr analogous models are stacked on top
of each other. Direct calculation reveals that the correla-tion matrix of the transformed code with multiple receive antennas (withα= 0.5) is U†H†HU=aI Nt+ · 0 b b∗ 0 ¸ ⊗INt/2, (9) where a = Nr X j=1 Nt X i=1 |hi,j|2 (10) b = exp(jπφ)( Nr X j=1 NXt/2 i=1 |hi,j|2− Nr X j=1 Nt X i=Nt/2+1 |hi,j|2)(11).
The rate of the code is identical to the rate of the con-stituent space-time block codes X1 andX2. As an
exam-ple, when Alamouti codes are used as constituent codes, we have four element transmission and symbol rate 1. When all channel coefficients are i.i.d Rayleigh we obtain identi-cal correlation properties with a transmitter employing four transmit and two receive antennas (4Tx-2Rx), and with a transmitter using eight transmit antennas and one receive antenna (8Tx-1Rx). With 8 transmit antennas the rate would be reduced to 3/4 and 3dB would be lost in perfor-mance gain due to absence of receive antenna diversity. D.2 Symbol Rate Two Transformed Code
A four antenna transformed code with symbol rate two can be constructed e.g. as
X(x1, ..., x8) = · ˜ X1 X˜3 ˜ X4 X˜2 ¸ . (12)
Above ˜X1and ˜X2are borrowed from the transformed code
to obtain symbol rate one. To increase the symbol rate ˜X3
modulates symbolsx5 andx6, and ˜X4symbolsx7andx8.
Hence, eight symbols are transmitted in four time epochs. The code inherits the correlation properties of the sym-bol rate one transformed code for blocks ˜X1 and ˜X2, and
blocks ˜X3 and ˜X2, respectively. In essence, when BLAST
[4] transmits uncoded symbol streams in parallel, DSTTD transmits orthogonal space-time codes in parallel, the dual rate transformed code transmits two non-orthogonal space-time block codes in parallel using multiple transmit an-tennas [10]. Just like with symbol rate one code above, here also increasing the number of receive and transmit antennas reduces the magnitude of the non-orthogonality coefficient. In practice, with maximum likelihood detec-tion the code attains diversity order eight in a 4 Tx- 2Rx channel. Therefore, it is a strong candidate especially for MIMO channels, where the number of receive antennas is increased beyond one.
E. Channel estimation issues
Design of STBC, originally proposed for flat fading chan-nels, recently is extended for frequency selective channels [27], such that Alamouti scheme [1] is applied not for sym-bols, but for data blocks.
It may be shown that STBC according to [27] allows to decouple data corresponding to different blocks and makes noise samples before detection uncorrelated. As a result, it eliminates a need for joint data detection and allows to use simple detectors for different data blocks.
Application of the STBC for EDGE is proposed in [28] [29]. However, in practice the diversity gain from STBC in a channel with significant ISI may be not very pronounced due to significant degradation of channel estimation ac-curacy. Similar problems may arise with applications in WCDMA systems. However, it is possible to recover diver-sity gain by using iterative data processing, as addressed in [30]. On the other hand, complexity of iterative receiver for CDMA is very high and a more feasible way to im-prove MIMO channel estimates may be seen in application non-iterative semiblind subspace methods based on second order statistics.
In blind subspace methods the observation space is first partitioned into signal subspace and noise subspace. Then MIMO channel parameters are estimated based on orthog-onality between subspaces. This method allows to identify MIMO channel up to a right multiplication of an invertible matrix. To resolve the ambiguity a small amount of trans-mitted symbols (e.g., tailing symbols) should be known at the receiver.
If available, prior information on MIMO channel (e.g., obtained from pilot signals) is to be used to improve accu-racy and robustness of blind estimation. It may be done by projecting the LS estimates obtained from known data to the signal subspace [31]. Another method, semiblind reg-ularization, is based on minimization of a combined cost function including cost functions from blind and data-aided estimators [31].
To facilitate subspace estimation of MIMO channels a precoding for space-time codes is proposed in [32]. To avoid MIMO channel estimation differentially-encoded space-time transmission is suggested in [33].
III. Closed-loop transmit diversity
The closed-loop transmit diversity techniques are de-signed to improve the system performance over the open-loop techniques in particular in low-mobility environments. The closed-loop concepts modify the complex weights in each transmit antenna such that the signals are combined coherently at the receiver. The current WCDMA specifi-cation supports two elements in the transmitter, but the concept can be directly extended to multi-element trans-mission. In closed-loop modes the transmit antennas need to be sufficiently close to each other so that the propagation delays between each transmitting element and the terminal are effectively identical. However, the antennas need not be calibrated.
The terminal determines the optimum transmit weight (due to channel matched beamforming) using the following principle. First the downlink channels are estimated using common pilot channels. This allows to construct a channel matrixH= (h1, ...,hM), wherehmis the impulse response
between them’th array element and the terminal. Second, the optimal beamforming vector is calculated as the domi-nant eigenvector ofH†H. Third, the elements of this vector
are quantized, and signaled to the base station. Naturally, the signaling overhead should be minimized and therefore the resolution of the beamforming vector is compromised. The WCDMA system incorporates currently two feedback modes with slightly different tradeoffs in effective channel resolution and signaling robustness.
With closed-loop beamforming only one symbol stream is transmitted and the received signal is
y=H†wx+n, (13)
where w is the beamforming vector. Spectral efficiency 4bps/Hz is attained e.g. whenxis a 16-QAM symbol.
The closed-loop transmit diversity concept above applies beams that maximize the received signal power for a given channel realization. Alternatively, a set of long-term eigen-beams can be determined as the dominant eigenvectors of
E(H†H), where expectation is with respect to channel
co-efficients. This approach is useful when feedback capacity is limited, the transmit antennas are correlated, and some downlink beams on average convey more information than others. Here, the columns of a selected space-time code can be transmitted to different eigenbeams [9], [12]. The par-allel space-time coded streams may be allocated different transmit powers[7].
IV. Performance
In Figures 1 and 2, several open-loop (OL) and closed-loop (CL) MIMO transmission concepts are compared in spatially uncorrelated flat Rayleigh fading channel. All these achieve the same spectral efficiency of 4bps/Hz by
using either one 16-QAM stream or two parallel 4-PSK streams. Bit-error rates shown in the figure assume un-coded transmission with optimal ML detection in the re-ceiver.
The OL concepts shown in Fig 1 include single an-tenna transmission, STTD with one and 2 receive anan-tennas, DSTTD, ABBA with one and 2 receive antennas, trans-formed symbol rate one code with one and two receive antennas, transformed symbol rate two code, BLAST [4], as well as a particular case of TxD-MIMO [21]. The pa-rameter values for the transformed code are α= 0.5 and
φ= 0.25. In the legends, the number of transmit and re-ceive antennas are denoted by (Nt×Nr).
The CL concepts in Fig 2 loosely correspond to the closed-loop transmit diversity (mode1 and mode2) defined in 3GPP for WCDMA, where the dominant eigenvector of the spatial correlation matrix is fed back to the transmitter (error free) and which is then used for beamforming.
In the simulations, two feedback bits per slot were used which approximately corresponds to FB rate of 3000bps. The eigenvector was quantized before transmission. The number of quantization bits for phase and amplitude were
Nphase= 2 andNamp= 0 or alternativelyNphase= 3 and
Namp= 1. The former values were mostly used for 10km/h
and later values for 3km/h.
As it is expected, the CL concepts with low mobile speed offer some dB gain compared to the corresponding OL con-cepts with the same number of transmit and receive anten-nas (see Figs. 1 and 2). The symbol rate two transformed code outperforms other OL candidates.
In Fig 3, some of the above-mentioned concepts are sim-ulated in a channel having high spatial correlation. The correlation matrix for the transmit antennas was generated using the following parameters resulting to the maximum correlation value of 0.98: angle of arrival 50deg, angular spread 5deg, and 0.5λspacing between elements, where λ
is the carrier wavelength. In the receiver side, the maxi-mum correlation value of 0.3 was used between two receive antennas.
In this highly correlated case, the OL concepts with sym-bol rate two, i.e., DSTTD, BLAST, and transformed code, do not work very well. Actually symbol rate one ST codes (STTD and transformed code) work better with low signal-to-noise ratios. The gain offered by the CL concepts is higher than in uncorrelated case.
V. Conclusion
Multiple transmit and receive antennas can be used to increase bandwidth efficiency for 3G systems and beyond. Recent modulation concepts for MIMO (e.g. symbol rate two codes using rotated constellations) yield a promis-ing performance improvement over conventional high or-der modulation. This improvement comes at the ex-pense of increased demodulation complexity. With chan-nel state information in the transmitter, e.g. provided by WCDMA closed-loop modes or their extensions, simpler single-stream transmission methods become again attrac-tive. In this paper we concentrated on 4bps/Hz
transmis-2 3 4 5 6 7 8 9 10 11 12 10−4 10−3 10−2 10−1 EbNo [dB] BER (1x1) (2x1) STTD (2x2) STTD (4x2) DSTTD (4x1) ABBA (4x2) ABBA (4x1) Tr: 16−QAM (4x2) Tr: 16−QAM (4x2) Tr: 2x4PSK (2x2) BLAST (2x2) TxD−MIMO
Fig. 1. Bit-error rates in spatially uncorrelated channel for open-loop concepts with one 16-QAM stream (dashed and dash-dotted lines) or with two 4-PSK streams solid lines).
2 3 4 5 6 7 8 9 10 11 12 10−4 10−3 10−2 10−1 EbNo [dB] BER (2x1) CL 10km/h (4x1) CL 10km/h (2x2) CL 10km/h (4x2) CL 10km/h (2x1) CL 3km/h (4x1) CL 3km/h (2x2) CL 3km/h (4x2) CL 3km/h
Fig. 2. Bit-error rates in spatially uncorrelated channel for closed-loop concepts with one 16-QAM stream and with two different mobile speeds. 2 3 4 5 6 7 8 9 10 11 12 10−4 10−3 10−2 10−1 EbNo [dB] BER (1x1) (2x1) STTD (2x2) STTD (4x2) DSTTD (4x2) Tr: 16−QAM (4x2) Tr: 2x4PSK (2x2) BLAST (2x2) CL 3km/h (4x2) CL 3km/h
Fig. 3. Bit-error rates for OL and CL concepts in the case where the transmit antennas are highly correlated.
sion. Direct extensions to higher spectral efficiencies are possible e.g. by increasing the constellation size in each individual stream, transmitting several streams in paral-lel, and simultaneously increasing the number of receive antennas.
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