Interference Mitigation for MIMO Systems Employing User-specific, Linear Precoding

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1 Interference Mitigation for MIMO Systems Employing User-specific, Linear Precoding Afif Osseiran 1, Kambiz Zangi, Dennis Hui and Leonid Krasny 1 Ericsson Research, Stockholm, Sweden, Ericsson Research, Research Triangle Park, North Carolina, US {Afif.Osseiran, Kambiz.Zangi, Dennis.Hui, Leonid.Krasny}@ericsson.com Abstract User-specific, linear precoding is used extensively by almost all existing and emerging wireless MIMO standards [1], [], [3], []. With user-specific, linear precoding, the data symbols to be transmitted to each user are passed through a linear transformation before being sent to the transmit antennas, and a different precoder is used for each user depending on his/her channel. For example, with transmit antennas at the BS, receive antennas at the mobile, and instant channel quality indicator (CQI), the cell capacity of a x -clustered system with user-specific, linear precoding is more than 8% higher than the cell capacity of a system with one transmit antenna [1]. But such schemes are vulnerable to delayed CQI due to fast variations of interference, leading in some cases to performance that is worse than a SISO system. In this paper, we will present a method that mitigates the degradation due to fast-varying interference in MIMO systems that use linear precoding. We will show that the temporal variation of other-cell interference is almost eliminated with this method. Our results indicate that for a x -Clustered transmit array with the proposed method, the performance loss due to delayed CQI is reduced from 35% to 5%. Key Words: Array Gain, Array Geometry, Interference Mitigation, OFDM, Spatial multiplexing, System Performance. I. INTRODUCTION Multiple-input, multiple-output (MIMO) transmission schemes are being proposed as one of the key radio access technologies for enhancing cellular wireless systems [5], [6]. User-specific, linear precoding is used extensively by almost all existing and emerging wireless MIMO standards [1], [], [3], []. With user-specific, linear precoding, the data symbols to be transmitted to each user are passed through a linear transformation before being sent to the transmit antennas, and a different precoder is used for each user to adapt the covariance matrix of the transmitted signal to the specific channel of the intended user. Uniform linear array (ULA) is the most widely used transmit antenna geometry. ULA s can be divided in two groups: (a) uniform linear phased arrays, and (b) uniform linear diversity arrays (ULDA). In (a), the spacing between consecutive antenna elements are chosen small enough relative to (the wavelength at the carrier frequency) to ensure that all antennas are highly correlated, and typically just one stream of data is transmitted to each User Terminal (UT). In (b) the N tx transmit antennas are positioned far apart relative to such that every pair of transmit antennas are essentially independent, and typically N tx independent streams are transmitted to each UT. From a single-link perspective, [7] and [8] found that a particular non-uniform linear transmit array geometry (the socalled -clustered transmit array geometry) outperforms most other transmit array geometries over a wide range of SNRs. Motivated by these results, for N tx = and 8, it was shown in [9], [1] that the system-level performance of a cellular system using the -clustered transmit antenna geometry at each Base Station (BS) can be improved significantly compared to the performance of a cellular system using the traditional uniform diversity linear arrays with the same number of transmit antennas. However, [9] and most studies in the literature tend to neglect the impact of the rapid interference variation on the system performance (i.e. a perfect Channel Quality Indicator (CQI) at the BS is typically assumed). In fact, it is well known that the deployment of multiple antennas in radio networks impacts the spatial and/or temporal characteristics of the interference. In particular, the interference variation is more acute when user-specific precoding is used at the transmitter. Changing the precoder at the BS transmitter changes the spatial covariance matrix of the interference that is observed by each UT having multiple receive antennas, i.e. the spatial characteristics of the interference at the UTs change as the percoder at the BS is changed. In addition, if the radio channel is varying fast, both the temporal and spatial characteristics of the interference will vary rapidly. This fastvarying interference makes any required feedback to a system (e.g. CQI) obsolete yielding a CQI mismatch, also called flashlight effect. This phenomenon was already known in HSDPA system [11]. In [1], it was shown that linear MU- MIMO precoding schemes such as successive Minimum Mean Square Error (MMSE) and Regularized Block Diagonalization (RBD) in a multi-cell scenario can even perform worse than a Single Input Single Output (SISO) system. It can be easily understood that any kind of scheme where the precoding weights are changing rapidly (e.g. adaptive beamforming or fast codebook-based precoding), will lead to a fast-varying interference which is very hard to predict accurately. This is especially true at medium to high system loads where the interference is mostly dominated by other-cell interference which is changing fast. In case of isolated cells like in the local area scenario [13], the performance degradation would be minor due to low or nonexistence other-cell interference. Predicting the interference variation appears to be a challenging task. Instead it is perhaps more practical to try to stabilize the interference. In the this paper, we will present a method that

2 mitigates the degradation due to fast-varying interference. We will call this method slow fixed beam reuse. The rest of this paper is organized as follows. The transmit antenna geometry is presented in Section II. In Section III, the signal to interference plus noise ratio is derived. Section IV introduces the slow fixed beam reuse method. In Section V, our network deployment model is explained. The systemlevel simulation results are presented in Section VI. Lastly, conclusions are given in Section VII. De-MUX FEC1 Π MOD1 w 1 w 1 II. TRANSMIT ANTENNA CONFIGURATION We will consider in this paper the -Clustered non-uniform linear array geometry. The antennas in each cluster form a uniform, linear, phased array; since, the antennas within each cluster are highly correlated due to the half wave length,, spacing between consecutive antennas in each cluster. In fact, it was shown in [8], [7] that grouping the antennas in two independent clusters is an optimal geometry for almost all SNRs (except for very low SNRs where it is best to use all transmit antennas to form a uniform linear array with / spacing). The -Clustered geometry with N tx =transmit antennas is depicted in Fig. 1. The N tx transmit antennas are grouped in clusters where each cluster is configured as a ULA with spacing between consecutive antenna elements within each cluster. The two clusters are placed such that the intra-cluster spacing is 1. As shown in Figure 1, the data bits are demultiplexed into two streams where each stream is separately encoded then interleaved and modulated. A beamforming weight is applied on each stream of each cluster before the data symbols are transmitted. We assume the transmitter has access only to the second order statistics of the channel, and the receiver knows the channel perfectly. It is further assumed that both clusters use the same set of beamforming weights, hence the beamforming matrix at the b-th BS for each subcarrier belongs to the following set: 1 e jθn 1 e jθn n=1, (1) where the angle θ n represents one of the four fixed pointing angles of each beam in the coordinate system of the sector in which the beam is used. The integer n {1,, 3, } is chosen such that θ n is as close as possible to the direction of arrival of the signal transmitted by UT. III. SIGNAL TO INTERFERENCE AND NOISE DERIVATION In the following the expression of the received signal and the SINR is derived. A. Received Signal: The signal on the f-th subcarrier at the k th TTI transmitted from the b-th BS is denoted by x b (f,k), a vector of size N X 1, where 1 N X N tx. N X is the number of transmitted Fig. 1. FEC Π MOD Clustered configuration with transmit antennas. streams. Here, without loss of generality, we assume the signal of interest is transmitted from the -th BS. Let W b (f,k) and H b (f,k) denote that complex antenna weights (of size N tx N X ) and the channel coefficients (of size N r N tx )onthefth subcarrier and time index k of the bth BS at UT, respectively. The received signal on the f-th subcarrier at the k-th TTI, is given by y(f,k) =H (f,k)w (f,k)x (f,k)+ξ(f,k) () where ξ(f,k) contains the received inter-cell interference and thermal noise, and is equal to Nb 1 b=1 H b (f,k)w b (f,k)x m (f,k)+n(f,k). N b denotes the total number of BSs, and the term H b (f,k)w b (f,k)x m (f,k) is the interference signal from the m-th BS. Finally, n(f,k), denotes the zero mean Additive White Gaussian Noise (AWGN). Since equalization and symbol detection operate on a subcarrier basis and block-by-block basis, in the next section we will omit the subcarrier index f and the time index k, respectively. B. SINR Calculation A successive interference cancellation (SIC) receiver is assumed for the multi-stream transmission. The receiver operates in several stages or steps. In the first step, it simply detects the signal with the highest SINR. This is done by computing the SINR for all streams using the MMSE receiver. The second step consists of reconstructing the signal, subtracting it from the received remaining signal. Finally the third stage consists of repeating the first steps until all signals are detected. Let us first compute the SINR of the first step. The estimate of the signal x is denoted by x, and we assume that the instantaneous channel matrix H, and the second order statistics of the noise and the interference are known at the receiver. The MMSE estimate per subcarrier is simply obtained using the Wiener Filter [1] as follows: x = Λy, (3) where the filter weight Λ is defined as Λ = E { yy H} 1 E { x y H}. () w 1 w

3 Assuming the transmitted signals x b have unit power then using Eq., Λ reduces to Λ = S 1 W H H H, (5) where S is given by R S = H W W H H H + R. (6) is the interference plus noise covariance matrix and is given by R = N b 1 b=1 H b W b W H b H H b + N. (7) Furthermore, N, the covariance matrices of the noise is given by N = E { nn H} = σi Nr, (8) where σ is the thermal noise variance. Let e l denote the l th column of the N X N X identity matrix I NX, then using the above Equations the SINR of the l element of x is given by Γ (l) = eh l ΛH W e l e H l ΛR Λ H. (9) e l Then the receiver will select the stream with the highest SINR denoted, that is, i = arg max l {1,...,N X } Γ(l), (1) where i denotes the stream number with the highest SINR, and Γ (l) the SINR of the l th element given in (9). The second step consists of inserting zeros on the ith column of H. This operation models the signal cancellation step. H is thus updated as follows H H H e i e H i. (11) Then the matrix S and filter weight Λ have to be recomputed using the updated H. Finally the third stage consists of going back to the first step until all steams are detected. IV. FIXED BEAM REUSE In general, the transmit weight vector W b (f,k) depends on the long-term statistics of the channel between the BSs and the UTs being served by these BSs on the k-th TTI. The statistics of the channel of each user varies very slowly; hence, the best precoding matrix for a given user changes very slowly over time. In other words, the best precoding matrix for a given user depends mostly on the geometry of the location of the UT relative to its serving BS, and this geometry varies quite slowly compared to fast fading. In each cell, the scheduler decides which user is served at the f-th subcarrier on the k-th TTI; hence, the scheduler decides the precoding matrix W b (f,k) as an indirect consequence of what user this scheduler decides to serve on the f th sub-carrier and on the k th TTI. With beamforming on the downlink, the precoding matrix W b (f,k) is solely determined from one scalar angle θ(f,k), where θ(f,k) is determined by the direction of the UT served at frequency f on the k-th TTI. It is then clear that if the direction of the UT served on the k th TTI by the b-th BS is different from the direction of the UT served on the (k +1)-th TTI by this BS, then the b th term of R in Eq. 7 can change from one TTI to the next. In systems that use Link Adaptation (LA), the UT measures R (f; k) on a given TTI, and based on this measurement, the UT asks the BS to transmit to it a particular number of information bits on the f-th sub-carrier at some future TTI, i.e. there is always a delay between the time the UT measures R (f; k), and the time the UT receives information based on this measurement of R (f; k). If the covariance of othercell interference changes over the duration of this delay, the number of information bits transmitted to the UT on the f th sub-carrier will be different from the number of information bits that the channel to the UT can actually support at the time this transmission is made. In order to make the system more robust to CQI delays, a slow fixed beams method is introduced. The method consists of: Restricting the beamforming matrix to take a finite number of fixed values. Assigning in each cell, a portion of sub-carriers to each beam. Changing synchronously and slowly the beam assignments in all cells. While the first two steps (which we will refer to as the fixed beams reuse (FBreuse) ) will stabilize the interference spatially, the slow update of the beams weight (third step) will stabilize the interference temporally. An illustration of the slow fixed beam reuse is depicted in Fig., where two fixed beams are defined by θ 1 and θ and updated every T [seconds]. In a given cell, the portion of sub-carriers assigned to each beam can be proportional to the total traffic generated by the UTs having this particular beam as their favorite beam. Typically, T is chosen much larger than duration of one TTI. With fixed beam reuse, the interference seen by each UT changes at most once every T seconds compared to every TTI without fixed beam reuse. Hence, fixed beam reuse, with a properly chosen T, can significantly reduce the variations in interference observed by the UTs. f θ 1 θ 1 θ θ θ 1 θ 1 T θ 1 θ θ θ θ θ θ 1 θ 1 θ 1 θ θ 1 θ 1 θ θ 1 θ 1 θ 1 θ 1 θ 1 Fig.. The slow fixed beam reuse of period T, with two beams defined by θ 1 and θ. A. Reduction of Pilot Density In OFDM systems, typically certain known pilot tiles are transmitted from each antenna to allow the UT to estimate t

4 the downlink channel between this antenna and the UTs receive antenna. For example, in LTE standard, each transmit antenna has its own dedicated pilot tiles that are continuously transmitted. In this approach the pilots do not go through the same precoding matrix as the one that the data goes through, and this complicates the channel estimation at the UT. With fixed-beam approach presented here, only one pilot needs to be transmitted from each cluster regardless of the number of antennas that are used in each cluster. At each sub-carrier and from each cluster, one can transmit just one beamformed pilot (regardless of the number of transmit antennas used in each cluster). This approach can substantially reduce the amount of resources devoted to pilots compared to the approach where a separate pilot is transmitted from each antenna. Secondly, with this approach, the data and the pilot go through exactly the same precoding; hence, the channel estimation at the UT is simplified. V. NETWORK DEPLOYMENT MODEL A network deployment with seven sites where each site comprises three sectors is considered. The number of BS antennas per sector is four or eight. BS antennas are placed above rooftop. The network is assumed to operate at a carrier frequency of 3.5 GHz and OFDM with 18 sub-carriers is used within the 5 MHz transmission bandwidth. Table I provides a summary of the assumed system parameters. TABLE I SYSTEM AND SIMULATIONS PARAMETERS. Parameter Value Number of sites 7 Inter-site distance [m] 1 m Number of sectors per site 3 Number of BS antennas per sector or8 Sector output power 36.5 dbm BS receiver noise figure 5dB Number of UT transmit antennas UT output power dbm UT receiver noise figure 7dB Carrier frequency 3.5 GHz Transmission bandwidth 5MHz Sub-carrier bandwidth 39. khz Number of sub-carriers 18 Cyclic prefix length 3. μs A. Radio Channel Model The C metropolitan area pathloss and channel model from [15] are used in the evaluations. The model is applicable to a scenario with macro BS installation above rooftops and UTs located outdoors on street level. Shadow fading is modeled as a log-normally distributed random variable with a standard deviation of 8 db. The ray-based channel model is an extension to the 3GPP spatial channel model (SCM) [16] with correlated shadow fading, delay spread and angular spread. B. Receiver Structure UTs are equipped with antenna elements separated half a wavelength. A dual antenna MMSE receiver with successive stream cancellation is employed at the UTs. C. Radio Network Algorithms UTs connect to the sector with the lowest path-loss, shadowing included, and the downlink beamforming gain is considered in the cell selection procedure. Signals are transmitted using a fixed output power and the modulation order and channel code rate are selected to maximize the data rate. Turbo coding with rates from 1/1 to 8/9 are used in combination with QPSK, 16QAM, or 6QAM to find an appropriate transmission format. Round-robin transmission scheduling is employed. Further one user per sector is scheduled for transmission. D. Link-to-System Interface To estimate the packet decoding error probability of a channel coded block transmitted over a multi-state channel, a mutual information (MI) based link-to-system interface is used [17]. The model uses the post-receiver SINRs of the symbols in the channel coded block to calculate the average MI for bit-interleaved coded modulation. The average MI is then used to estimate the packet error probability. VI. SYSTEM-LEVEL PERFORMANCE RESULTS A. Performance Criteria The spectral efficiency per sector is defined as the number of correctly received bits divided by the product of the number of sectors, the simulation time, and total bandwidth. Two performance criteria are used: the 5 percentile and 95 percentile user data rate. The 5 (resp. 95) percentile user data rate is defined as the 5 (resp. 95) percentile of the cumulative probability distribution of the average data rate delivered to each user. While the 5 percentile criterion can be seen as a measure of the minimum desired data rate available to most users (including those on the cell edge), the 95 percentile criterion on the other hand measures the highest peak rate that can be achieved. B. Impact of CQI Delay The 5 percentile user throughput of 1x SIMO (Single Input Multiple Output), x PARC (Per Antenna Rate Control) with SIC, and x clustered array are shown in Figure 3 for round robin scheduler. It can be seen that the -Clustered architecture provides 7% spectral efficiency gain at a user bit rate of Mbps. It is interesting to notice that PARC-SIC yields negligible gain compared to SIMO. In order to check the potential gain of -clustered array in terms of spatial multiplexing, it is interesting to look at the rate of the users in good channel conditions (i.e. 95 percentile of the user bit rate). The 95 percentile of the user bit rate versus the spectral efficiency is shown in Figure 3(a). For user bit rate of 5Mbps the -Clustered array yields % and 83% gain compared to 1x SIMO and x PARC-SIC, respectively. The CDF of the user bit rate is show in Figure. It can be seen that the cumulative density function for the -Clustered array scheme provides substantially higher user throughput than SIMO and PARC-SIC.

5 95 % User bitrate[mbps] SIMO PARC SIC x, Str. Clustered x In order to assess the impact of the CQI delay on a precoded-coded MIMO system, the -Clustered array is evaluated in a multi-cell urban scenario (i.e. the WINNER wide area scenario [13]) with ideal and delayed CQI, respectively. Figure 5 plots the spectral efficiency (for the worst users) for a x -Clustered array scheme in case of ideal CQI and 3 TTIs delayed CQI (i.e. δ =3). It can be observed that a CQI delay of 3 TTIs was sufficient to cause a substantial spectral efficiency loss of 35% (at Mbps user rate). 1 1 Clustered x Clustered x, δ=3 5 % User bitrate[mbps] (a) 95 percentile. SIMO PARC SIC x, Str. Clustered x 5 % User bitrate[mbps] Fig. 5. The 5th percentile user bitrate versus the spectral efficiency for the x -Clustered array without and with CQI delay of 3 TTIs (i.e. δ =3) (b) 5 percentile. Fig. 3. The 5 and 95 percentiles user bit rate versus the sector spectral efficiency for 1x SIMO, x PARC-SIC with streams active and x - Clustered arrays. cdf SIMO PARC SIC x, Str. Clustered x User bitrate[mbps] Fig.. The cdf of the user bit rate for 1x SIMO, x PARC-SIC with streams active and x -Clustered arrays. C. Fixed Beam Reuse The proposed method, slow fixed beam (FB) reuse, was applied to the x -Clustered array scheme and evaluated in a multi-cell scenario. The following cases were simulated for comparison purposes: a) -Clustered x, where one user is scheduled per cell and assuming perfect CQI. b) -Clustered x, FBreuse, corresponds to the fixed beam reuse case where one user is scheduled per beam and assuming perfect CQI. c) -Clustered x, same as case a) but with a CQI delay of 3 TTIs. d) -Clustered x, FBreuse, same as case b) but with a CQI delay of 3 TTIs. e) -Clustered x, FBreuse, Slow update, same as case d) but with slow update of the FB reuse. The sector spectral efficiencies of the simulated cases are shown in Figure 6. The FB reuse bridges the gap between ideal and delayed CQI (for [Mbps] user rate) to around 11%. Further when the weight vector is updated on a slower pace (see the case FB reuse, slow update ), the CQI delay of 3 TTIs will only cause 5% loss compared to 35% when the FB reuse method was not used. It is interesting to notice that at very low loads the CQI delay has a minor impact on the performance since the other-cell interference is low. As mentioned previously, the fast change of the transmit weights renders the SINR (consequently the CQI) obsolete. In Figure 7, the CDF of the difference between SINR(t), the actual SINR, and ŜINR(t δ), the estimated SINR at time

6 5 % User bitrate[mbps] Clustered x, FBReuse Clustered x, FBReuse, δ=3 Clustered x, δ=3 Clustered x, FBReuse, δ=3, Slow update Fig. 6. The 5 percentile user bitrate versus the spectral efficiency for the x -clustered array. (t δ), is plotted. It can be seen that there is no mismatch between the estimated SINR and the actual SINR when there is no delay. In case of 3 TTIs delay, more than % of the users will experience a SINR mismatch greater than db. When the FB reuse is applied to the x -Clustered array, the percentage of users experiencing a mismatch greater than db reduces to 1 percent. Finally when slow FB reuse is applied, the SINR mismatch vanishes. cdf Clustered x, FBReuse Clustered x, FBReuse, δ=3 Clustered x, δ=3 Clustered x, FBReuse, δ=3, Slow update 6 6 SINR(t) SINR(t δ) [db] Fig. 7. The cdf of the difference between the instantaneous SINR at time t and the estimated SINR at time (t δ). VII. CONCLUSIONS In this paper, we presented a method that mitigates the degradation due to fast-varying interference in MIMO systems with user-specific precoding, under the assumption that the precoder for each user is determined only based on the statistics of this user s channel. We showed that the proposed method almost eliminates the spatial and temporal variation of the inter-cell interference hence eliminating the CQI mismatch. For a x -Clustered transmit array geometry, performance loss with the proposed method due to delayed CQI is only 5%, while the performance loss without this method due to delayed CQI is 35%. ACKNOWLEDGMENT Part of this work has been performed in the framework of the IST project IST WINNER II, which is partly funded by the European Union. The authors would like to acknowledge the contributions of their colleagues in WINNER II, although the views expressed are those of the authors and do not necessarily represent the project. REFERENCES [1] E. Dahlman, H. Ekstrom, A. Furuskar, etc. The 3G Long-Term Evolution - Radio Interface Concepts and Performance Evaluation, in Proc. IEEE VTC 6, Melbourne, Australia, May 6, pp [] D. Astely, E. Dahlman, P. Frenger, etc, A future radio-access framework, IEEE J. Selected Areas Communication, vol., no., March 6, pp [3] F. Wang, A. Ghosh, C. Sankaran, and P. Fleming, WiMax Overview and System Performance, IEEE VTC 6, VTC-6 Fall, Sept. 6, pp [] K. Peppas, F. Lazarakis, D. Axiotis, A. Moussa, and A. Alexiou, System level evaluation of reconfigurable MIMO Techniques Enhancements for HSDPA, Globecom, pp [5] K. Higuchi et al., Experiments on Real-Time 1-Gbps PacketTransmission Using MLD-Based Signal Detection in MIMO-OFDM Broadband Radio Access, vol., no. 6, pp , June 6. [6] H. Taoka, K. Dai, K. Higuchi,, and M. Sawahashi, Field Experiments on Ultimate Frequency Efficiency Exceeding 3 Bits/Second/Hz using MLD Signal Detection in MIMO-OFDM Broadband Packet Radio Access, in Proceedings IEEE Vehicular Technology Conference, Spring, Dublin, Ireland, April 7, pp [7] K. Zangi, L. Krasny, and D. Hui, Joint Optimization of the Transmit Antenna Array Geometry and Linear Precoding for MIMO Systems, in Proceedings IEEE Vehicular Technology Conference, Fall, Baltimore, USA, September 7. [8] K. Zangi and L. Krasny, Impact of Transmit Antenna Array Geometry on Downlink Data Rates in MIMO Systems, in Proc. European Wireless 7, Paris, France, April 7. [9] IST WINNER-II, D6.13.1, Final CG wide area description for integration into overall System Concept and assessment of key technologies, Framework Program 6, Tech. Rep. v1, November 7. [Online]. Available: [1] A. Osseiran, K. Zangi, and D. Hui, Impact of Transmit Array Geometry on Downlink System-Level Performance of MIMO Systems, in Proceedings IEEE Vehicular Technology Conference, Fall, Calgary, Canada, 8. [11] A. Osseiran and A. Logothetis, Closed Loop Transmit Diversity in WCDMA HS-DSCH, in Proceedings IEEE Vehicular Technology Conference, Spring, Stockholm, Sweden, 5. [1] IST WINNER-II, D3..1, The WINNER II Air Interface: Refined Spatial-Temporal Processing Solutions, Framework Program 6, Tech. Rep. v1, 6, Deliverables/. [13], D3.13.1, WINNER II Test scenarios and calibration cases issue 1, Framework Program 6, Tech. Rep. v1, 6. [Online]. Available: [1] S. Haykin, Adaptive Filter Theory, th ed. Prentice Hall,. [15] J. Meinilä, Ed., IST WINNER I, D5., Final report on link level and system level channel models, 5, no. v1, [16] 3GPP, Spatial channel model for multiple input multiple output (mimo) simulations, Tech. Rep. 3GPP TR V6.1., Sept. 3, [17] K. Brueninghaus et al., Link Performance Models for System Level Simulations of Broadband Radio Access Systems, in IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC), Berlin, Germany, September 5.