fact, the law of diminishing returns indicates that the maximum diversity gain is achieved when going from diversity of order one (no diversity) to diversity of order ...
Closed-Loop Space-Time Coding Scheme for Boosting Downlink Performance Marcos Katz 1,2, Esa Tiirola 1 and Juha Ylitalo 1 1
Nokia Networks Radio Access Systems P.O. Box 319 FIN-90651 OULU, FINLAND
2
University of Oulu Centre for Wireless Communications (CWC) P.O. Box 4500 FIN-90014 University of Oulu, FINLAND
tel: +358-8-5532867, fax: +358-8-5532845 email: marcos.katz, esa.tiirola, juha.t.ylitalo @ nokia.com
ABSTRACT A combination of selection diversity with space-time block coding is studied in this paper. In the proposed closed-loop scheme the N best out of M antennas are selected by the receiving end for transmitting space-time coded signals. Performance is evaluated for WCDMA parameters in typical flat-fading and frequency selective Rayleigh fading channels. Numerical results for M = 4 and N = 2 show that the additional antenna selection procedure brings a supplementary uncoded bit-error-rate performance improvement in the range of approximately 1.5 to 3 dB (BER = 10%), depending on the type of radio environment considered. The fact that considerable gains can be obtained with just minor increase in system complexity makes the proposed scheme attractive for present and future wireless applications. I.
INTRODUCTION
Space-time processing techniques for transmission have attracted considerable attention recently [1, 2]. Enhancement of link performance along with increase in link and network capacity are among the main reasons supporting signal processing in both spatial and temporal domains. Codes exploiting these two resources and designed to improve or optimize some performance measures define the rather new field of space-time coding. As with conventional coding methods, space-time coding can be divided in space-time block codes and space-time convolutional codes. In
the former approach N symbols transmitted from N antennas at N consecutive periods of time, where symbols and antennas are carefully and differently assigned during each transmission interval [1]. In the latter approach [2] the data is space-time coded and then split into the N transmitting antennas. Since the Space-Time Transmit Diversity (STTD) method exploits antenna diversity, increasing the number of transmitting antennas will lead to improvements in link performance. However, this is an attractive engineering solution only to some extent. In fact, the law of diminishing returns indicates that the maximum diversity gain is achieved when going from diversity of order one (no diversity) to diversity of order two. Then, less incremental gain is obtained each time a new diversity branch is added, though the total gain is always improved. From the engineering standpoint, for diversity orders larger than four the increase in complexity does not pay off the achieved increase in performance. In addition, a large number of transmitting antennas implies a small average power per antenna. This is a very desirable effect if power amplifier efficiency and linearity problems are taken into account but, on the other hand, the signal-to-interference-plusnoise ratio per antenna is correspondingly decreased. This is a very important issue since it is related to the quality of the channel estimates obtained at the receiving end and required to decode the space-time coded transmitted signal. In this paper we combine the conventional open-loop STTD method with simple selection diversity performed in a
closed-loop fashion. Basically, a reduced number N of antennas is selected for transmission out of the M available antennas. Since the selection of suitable antennas is done based on actual downlink information and previous to STTD transmission, fading can be somewhat compensated. Hence a substantially good link performance can be expected with a relatively low number of transmitting antennas. II. SYSTEM MODEL In this section the model of the proposed transmit diversity scheme is described. A single-antenna receiver and an M-antenna transmitter are assumed. The receiver measures the quality of the M downlink channels and informs to the transmitting end the N best channels, where N is a fixed number. Antenna selection can be done by measuring the channel response associated with each of transmitting antennas such that a1 (k ) a (k ) Select the N best 2 ⇒ a M (k ) Mx1
ai ( k ) a (k ) j , (1) ar (k ) Nx1
where al(k), l = 1,2,….,M, is the path gain of the lth frequency non-selective channel at the kth time interval. In a frequency selective environment antenna selection is carried out by comparing the average energy contained in the multiple paths corresponding to each transmitting antenna. Fig. 1 illustrates the operating principle of the studied closed-loop selection diversity STTD approach. In order to distinguish the signals from the different transmitting antennas, the signal used for antenna selection (and channel estimation) is required to have an identifying signature on antenna per antenna basis. For example dedicated pilot symbols or different channelisation codes, can be applied. This signal is represented by pl(t), l = 1,2,….,M in Fig. 1a, where the antenna selection process is depicted. The next step is the transmission of
the STTD coded signal from the selected antennas, as shown in Fig. 1b. As a good compromise between performance and implementation complexity N was selected to be two. For M = 4, for instance, there are 6 possible antenna pairs and thus three bits are required to feedback the selection information from the receiving end. The downlink transmission is carried out by using the conventional STTD approach for N = 2, but from the selected antenna pair. Antenna selection is done on a periodical basis, i.e., slot by slot. Assuming that at the kth instant of time (or slot) the ith and jth antennas are selected for transmission, then the received STTD coded signals r0 and r1 in respective time intervals [0, T) and [T, 2T) can be written as r0 = S 0γ i + S1γ j + n0 (2) r1 = − S1*γ i + S 0*γ j + n1 , where γi and γj are the channel impulse responses associated with the previously selected ith and jth transmit antennas, Sr = dr sr, r = 0,1, is the signal to be transmited, dr is a QPSK symbol, sr is a band limited pulse and nr, r = 0,1 models the effect of interference and noise corresponding to each transmission interval. Note that the same antenna selection is employed for transmitting during both time intervals, as shown by (2). The receiving end linearly combines the received signals according to the following space-time decoding rule ~ S0 = r0γˆi* + r1γˆ j (3) ~ S1 = r0γˆ *j − r1*γˆi , where "~" indicates detected soft symbols and "∧" denotes estimated channel impulse responses. Replacing (2) into (3) and neglecting the noise terms leads to 2 ~ 2 (4) S = γˆ + γˆ S , r = 0,1. r
(
i
j
)
r
It can be appreciated that the space-time combining rule leads to detected symbols proportional to sum of channels powers from each of the selected antennas. It is interesting to observe that overall transmitting process involves multiple use of diversity. In fact each of the N signals to be combined by the STTD method is already a product of selection diversity. The selection of
N out of M antennas can be decomposed in the process of first selecting one antenna out of M available antennas (i.e., corresponding to the best channel) to proceed with the selection of the next antenna out of the remaining M-1 antennas and so on until the N antennas have been selected. The selection diversity gain is largest for the first antenna selection and it decreases with the order of antenna selected. Combining M-to-N selection diversity with the STTD scheme results in a nonlinear process and thus, the analytical assessment of the overall gain may not be straightforward. In the sequel the overall diversity gain is obtained through numerical results for WCDMA parameters in typical radio environments. Finally, the larger the difference between M and N the best are the chances that the N selected channels will be not be affected by Rayleigh fading and thus, in that case one would expect that the performance of the Nth order space-time coded link will approach that of a equivalent system in a Gaussian channel. III. PERFORMANCE EVALUATION In this section the most important system and simulation parameters are presented. The principle of geometry modelling is also introduced. The performance of the radio link is studied by means of Monte-Carlo simulations. Single antenna transmission and ordinary open-loop STTD with two antennas are used as references in the performance analysis. A. Geometry modelling The performance is studied by using the socalled G-modeling principle, where G denotes geometry. In the G-model, the orthogonality of WCDMA downlink is taken into account in the interference modeling. The downlink model has besides the user of interest, a number of interfering co-channel users, which are separated from each other by orthogonal spreading codes. The G-parameter is used to define the ratio of the intra-cell to inter-cell interference plus thermal noise at the mobile station (MS). Thus, it reflects to the spatial distance between the MS and the base station (BS). At
large G-values the MS is near to its own BS where intra-cell interference is dominating. At small G-values the MS is near to the cell edge and the inter-cell interference is dominating. G-parameter is calculated as
G=
Por Pnon _ or + PN
,
(5)
where Por, Pnon_or and PN, are the average level of intra-cell interference at the MS (or = orthogonal) 1, the average level of inter-cell interference at the MS, and the power of thermal noise at the MS, respectively. The measure for performance is the required percentage of the total BS transmission power that the desired user needs to achieve a certain value for uncoded BER at the MS. The percentage is denoted as Tx Ic/Ior, where Tx Ic is the required transmission power per connection and Tx Ior is the average BS transmit power. The lower the Tx Ic/Ior, the better is the performance. For example, the value –20 dB means that this connection takes 1% of the total base station transmission power. B. System and Simulation Parameters The early specification of WCDMA [4] defines the system parameters, which have been used as a foundation in this work. It should be noted that the specification has changed slightly after the simulations have been performed. The main differences compared to the current specification are within the downlink common pilot structure and the chip rate. However, the differences can be considered to be negligible to the performance especially at low speeds of mobile, where the performance is less sensitive to the parameter estimation. The main system parameters used in this work have been summarized in Table 1. The time slot structure (number of bits in each field) used in the simulations is illustrated in Table 2 (TFI = transport format indicator, DPDCH =
1
Different users and traffic channels are orthogonal at the transmitter side. However, the orthogonality can be partly destroyed in the radio channel.
dedicated physical data channel, TPC = transmission power control). Table 1. The main system parameters
average BS transmit power. The G-parameter was set to –3 dB, which means that the MS under study is quite near to the cell edge where the inter-cell interference is dominating. The simulation parameters used in this work have been summarized in Table 4.
Multiple access scheme
DS-CDMA
Carrier frequency
2150 MHz
Chip rate
4.096 Mcps
Spreading modulation
Balanced QPSK
Antenna correlation
Uncorrelated
Data modulation
QPSK
Speed of MS
3 km/h
Channel multiplexing
Time multiplexing of data and control channels. 8 pilot bits per time slot on the control channel.
Geometry value
-3 dB
Spreading factor of desired user
128
Power control (PC)
Applied for the desired user only. Fast PC loop operates at the rate of 1600 Hz.
Spreading factor of interfering cochannel users
256
Simulation length
3000 frames per simulation point ≡ 30 s.
Table 4. The main simulation parameters Number of antennas
Table 2. The DL time slot structure Pilot
TFI
DPDCH1
TPC
DPDCH2
8
2
4
2
24
A flat-fading Rayleigh and a frequency selective modified Vehicular A channels were considered in this study. The powers and delays of the individual channel taps are described in Table 3. In the simulations, a new channel realization was generated for each transmitted time slot. The speed of mobile is assumed to be 3 km/h. The transmitter consisted of M antenna elements, where M=1,2,3,4. It is assumed that the antennas are widely separated such that the correlation between antenna elements is negligible.
1, 2, 3, 4
The modelling of MS functionality impacts significantly to the simulation results. Thus, it has to be done realistically. A smoother type of channel estimation filter is used for all simulation cases. The filter coefficients are optimised for 3 km/h. Channel estimation is performed from the common pilot channel. A narrowband SIR-estimator is used in the simulations. This means that the orthogonality of the downlink is taken into account also in the power control. The MS receiver is assumed to be a conventional Rake receiver having five temporal Rake fingers. The delay estimation is assumed to be ideal.
Table 3. The simulated radio channels Tap powers
Tap Delays
1-path Rayleigh
Modified Vehicular A
Tap 1
0 ns
0.0 dB
0.0 dB
Tap 2
260 ns
-
-2.4 dB
Tap 3
521 ns
-
-6.5 dB
Tap 4
781 ns
-
-9.4 dB
Tap 5
1.04 µs
-
-12.7 dB
In the simulations it is assumed that there are 20 interfering co-channel users in the sector of interest, and the transmit power of common pilot channel is assumed to be 10% of the
IV. NUMERICAL RESULTS In this section some simulation results are presented and analyzed. As a first approach it is assumed that the antenna selection is ideal with no delay. Selection is based on the average channel power over one time slot from each antenna. In case of a multi-tap channel, power corresponding to all the taps is averaged. These assumptions will allow determining the performance bound that can be reached under these idealized conditions. Fig. 2 depicts uncoded bit error rate (BER) performance as a function of Tx Ic/Ior in a flat-fading Rayleigh channel. Fig. 2 illustrates
that ordinary 2-antenna STTD-scheme gives about 3 dB gain over a single antenna transmission at uncoded BER level of 10%. If STTD is applied to those two antennas out of three possible ones, which have the least attenuation in the radio channel, an additional gain of 2.1 dB is achieved. If two antennas out of four can be selected for STTD the corresponding gain is 3.2 dB. In the latter case the transmit diversity gain compared to a single antenna transmission is more than 6 dB. Due to the low mobility of the receiver (v = 3 km/h) the coherence time of the radio channel is relatively large (about 90 ms). Therefore, it is presumed here that the effect of channel coding and interleaving is not very significant and uncoded BER results are a reliable measure of the performance. It is known that relative transmit diversity gains reach the largest values in a flat Rayleigh fading channel with low mobility. The reason is that the radio channel does not carry delay diversity and the feedback delay does not play an important role. Moreover, the code channels of the co-channel users remain orthogonal keeping the intra cell interference at minimum. Fig. 3 illustrates the performance of STTD with antenna selection in a frequency selective channel (modified Vehicular A). Clearly, the gains due to transmit diversity drop significantly. For example, two-antenna STTD gives only a marginal 0.2 dB gain over single antenna transmission. As discussed above one reason for the modest performance of transmit diversity is the fact that the multitap channel inherently gives delay diversity. Moreover, transmitting from two antennas instead of one antenna further destroys the orthogonality of the code channels of the co-channel users. However, two-antenna STTD with selection from three antennas improves the raw BER performance by about 1 dB compared to ordinary twoantenna STTD. If the selection is done from four antennas the gains are 1.5 dB and 1.8 dB, compared to two-antenna STTD and single antenna transmission, respectively. It can be concluded that one achieves selection diversity gain on top of transmit diversity gain.
V. CONCLUSION Transmit diversity with space-time coding and antenna selection schemes were studied in frequency selective and frequency nonselective Rayleigh fading channels. In particular, the well known STTD transmit diversity scheme was studied. It is concluded that STTD gives significant gains in flatfading channels but only marginal gains in frequency selective channels. If three or four antennas are available, STTD combined with transmit antenna selection by the receiver, gives significant gains over two-antenna STTD. These gains are at largest in radio channels in which delay dispersion and Doppler spread are negligible. For example, pico (indoor) and micro cells often represent such radio channels. Finally, the proposed scheme can be implemented with relatively low complexity.
REFERENCES [ 1 ] Alamouti S., ”A Simple Transmit Diversity Technique for Wireless Communications”, IEEE Journal on Select Areas in Communications, Vol. 16, No. 8, Oct. 1998. [ 2 ] Tarokh V., Seshadri N. and Calderbank A. ”Space-Time Codes for High Data Rate Wireless Communication: Performance Criterion and Code Construction”. IEEE Transactions on Information Theory, Vol. 44, No. 2, Mar. 1998. [ 3 ] Tiirola E. and Ylitalo J, . ”Performance Evaluation of Fixed-Beam Beamforming in WCDMA Downlink”. To be presented in VTC-Spring, Tokyo, Japan, May, 2000. [ 4 ] 3GPP (Third Generation Partnership Project), "Specification of Air-Interface for the 3G Mobile System", Ver. 3.0, 1999.
a) N out of M antenna selection (M = 4 , N = 2) 0
STTD with 2 antennas, G=-3 dB, modified Vehicular A channel, v=3 km/h
10
p2(t) p3(t) p4(t)
Receiver 2
Rx 3
raw BER
p1(t)
Single antenna transmission STTD with 2 antennas STTD with 2 antennas, 3->2 STTD with 2 antennas, 4->2
1
4
Transmitter
Antenna selection information
b) N-order STTD transmission (N = 2)
S0
-S1
*
T
0
-2
10
1
T
0
Rx
S 0*
3
2T 4
STTC tranmission with N = 2 antennas
Transmitter
Figure 1. Principle of the diversity selection STTD method (Example for M = 4 and N = 2). 0
STTD with 2 antennas, G=-3 dB, 1-tap Rayleigh channel, v=3 km/h
10
raw BER
Single antenna transmission STTD with 2 antennas STTD with 2 antennas, 3->2 STTD with 2 antennas, 4->2
-1
10
-2
10
-19
-18
-17
-16
-15 -14 -13 Tx Ic/Ior (dB)
-12
-11
-10
-17
-16
-15
-14 -13 Tx Ic/Ior (dB)
-12
-11
-10
Figure 3. Downlink performance in a Modified Vehicular A channel for N = 2 and M = 2, 3 and 4.
Receiver
2T 2
S1
-1
10
-9
Figure 2. Downlink performance in a one-path Rayleigh channel for N = 2 and M = 2, 3 and 4.
