Analysis and Improvements of Linear Multi-user user MIMO Precoding Techniques
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1 1 Analysis and Improvements of Linear Multi-user user MIMO Precoding Techniques Bin Song and Martin Haardt
2 Outline 2 Multi-user user MIMO System (main topic in phase I and phase II) critical problem Downlink main strategy Space Division Multiple Access (SDMA( SDMA) sub-optimal Linear Precoding
3 Outline 3 Three main contributions: B. Song and M. Haardt, Achievable throughput approximation for RBD precoding at high SNR, in IEEE International Acoust., Speech, and Signal Processing (ICASSP( 2009). B. Song and M. Haardt, Effects of imperfect channel state information on achievable rates of precoded multi-user MIMO broadcast channels with limited feedback, in IEEE International Conference on Communication (ICC 2009). B. Song, M. Haardt, T. F. Maciel and A. Klein, Multi-user MIMO downlink precoding for time-variant correlated channels, International ITG/IEEE Workshop on Smart Antennas (WSA( 2009). Conclusions
4 RBD Throughput Approximation at high SNRs 4 Motivation Linear precoding techniques, as sub-optimal SDMA strategies, can transmit the same number of data streams as a DPC based system. But does incur a sum rate loss compared to DPC. The ratio between the achievable sum rates of DPC and block diagonalization (BD) precoding has been studied in [1]. In [2] the absolute rate and power offsets between these algorithms have been analyzed. In this work, we further consider regularized block diagonalization (RBD) precoding and analyze the absolute rate and power offsets among DPC, RBD, and BD. [1] Z. Shen, R. Chen, J. G. Andrews, R. W. Health, and B. L. Evans, Sum capacity of multiuser MIMO broadcast channel, in Proc. IEEE Int. Symp. on Inform. Theory (ISIT), Seattle, WA, July [2] J. Lee and N. Jindal, High SNR analysis for MIMO broadcast channels: Dirty paper coding vs. linear precoding, IEEE Trans. Information Theory,, vol. 53, pp , 4792, Dec
5 System Model and Capacity Approximation Framework 5 System Model users, transmit antennas, receive antennas per user Capacity approximation framework [3], where the channel capacity is well approximated at high SNRs as : multiplexing gain (i.e., the asymptotic slope of the spectral efficiency in bps/hz per 3 db) : power offset in 3 db units : the first derivative of the capacity with respect to [3] S. Shamai and S. Verdú, The impact of frequency-flat flat fading on the spectral efficiency of CDMA, IEEE Trans. Information Theory,, vol. 47, May 2001.
6 DPC and Linear Precoding 6 DPC Sum capacity via BC-MAC duality: Linear precoding User has precoding matrix Transmit vector is with covariance matrix Define equivalent channel
7 Sum Rates Approximation for RBD 7 The RBD precoding matrix: We further approximate We set uniform power allocation: Apply the capacity approximation framework for the achievable sum rates of RBD precoding
8 Sum Rates Approximation for RBD 8 Give a bound to We approximate the RBD sum rates at high SNRs as Sum rates approximation for DPC and BD in high SNRs
9 Average Rate and Power Offset 9 RBD vs. BD rate offset per channel realization RBD vs. DPC rate offset per channel realization average rate offset average rate offset Theorem 1. The average rate offset between RBD and BD at high SNRs is upper bounded by Theorem 2. The average rate offset between DPC and RBD at high SNRs is low bounded by power offset: power offset:
10 Simulation Results vs. Approximation Results 10 Rayleigh fading channels, no correlation
11 Effects of Imperfect CSI on Rates Loss 11 Motivation The quality of the available CSI at the BS directly influences the performance of a multi-user MIMO system with linear precoding. In frequency division duplex (FDD) systems, a feedback channel is needed for the BS to acquire the knowledge of CSI from each receiver. In order to further reduce the feedback overhead we consider the feedback of quantized CSI instead of analog feedback. RBD precoding increases the challenge of channel quantization at the receiver side in contrast to zero-forcing (ZF) or BD precoding, where the transmitter only requires the channel direction information. For RBD, the transmitter additionally requires the channel magnitude information. The channel estimation error, quantization error, and feedback delay cause a degradation of the quality of the CSI provided at the BS. The aim of this work is to assess this effect on the achievable data rates of a multiuser MIMO system employing RBD precoding.
12 System Model and Quantization Scheme System Model users, transmit antennas, receive antennas for user constant over one block of L symbols. Training phase: 12 Data transmission phase: Quantization scheme is proposed in [4]. Random vector quantization (RVQ) [4] B. Song, F. Roemer, and M. Haardt, Efficient channel quantization scheme for multi-user user MIMO broadcast channels with RBD precoding, in Proc. IEEE ICASSP, Las Vegas,, pp , 2392, Apr
13 System Performance Analysis 13 Channel estimation error model We denote the estimation of the matrix and the channel estimation error by and, respectively. Feedback delay model A simple Markov chain model allows us to track the channel state given the knowledge of the past. MMSE estimator Channel quantization error Here is the temporal correlation coefficient and is a complex Gaussian matrix where each elements has zero mean and unit variance.
14 System Performance Analysis 14 Effect of channel estimation error, quantization error, and feedback delay Theorem 3. The rate loss per user incurred due to the channel estimation error, quantization error, and feedback delay relative to RBD with perfect CSI can be upper bounded by Theorem 4. In order to maintain the above rate loss that is not larger than a given bound, the number of feedback bits per user is calculated as:
15 Simulation Results 15 2 users, 4 x {2,2} Rayleigh fading channels
16 Simulation Results 16
17 A New Approach to Precoding Based on long-term CSI 17 Motivation Linear precoding is a low-complexity transmission technique to utilize all available spatial degrees and can significantly improve the capacity of a multi- user MIMO system with perfect channel state information (CSI) at the transmitter. If it is impossible to acquire perfect instantaneous CSI at the transmitter, the spatial channel correlation can alternatively be used to reduce the multi-user interference (MUI) and improve the system performance. In this work we consider the multi-user MIMO OFDM downlink and assume that the channel is correlated and varies too rapidly to obtain short-term CSI. We propose a new approach to exploit the knowledge of the spatial correlation at the BS, which allows us to use existing precoding techniques (e.g.,bd and RBD) designed for perfect CSI at the BS.
18 Multi-user user MIMO Downlink 18 Combined network channel matrix of all users freq. Precoder matrix time Decoder matrix Chunk-wise precoding and decoding are performed. Input output data model for all users
19 ROLT-CSI 19 We propose a new approach called rank-one approximated long-term CSI (ROLT-CSI). ROLT-CSI is designed to effectively represent the channel by using a rank one approximation of the estimated long-term channel spatial correlation matrix per receive antenna. We use to denote the row of the channel matrix. The index indicates the receive antenna of user. We estimate the spatial correlation matrix of the receive antenna of user by averaging over one chunk. Let denotes the estimated spatial correlation matrix of user, chunk, and receive antenna. We have and its SVD as
20 ROLT-CSI 20 According to [5], when only second-order channel statistics are available at the BS, the optimal strategy is to transmit along the dominant eigenmode of the matrix. Therefore, we define the equivalent channel matrix of user in chunk as Based on ROLT-CSI, any linear precoding technique can be modified for longterm CSI. In this work we evaluate the throughputs for BD and RBD precoding. [5] M. Bengtsson and B. Ottersten, Optimum and suboptimum transmit beamforming, in Handbook of antennas in wireless communication (L. C. Godara, eds.) s.),, CRC Press, 2002.
21 Simulation Scenario 21 OFDM parameters [6] Parameter Values Carrier Freq. 5 GHz Subcarrier Spacing MHz Useful Symbol Duration µs System Bandwidth MHz Used Subcarrier [-128 : +128] 0 not used Chunk size 8 subcarriers, 15 OFDM symbols Duplexing Mode TDD 3 users, 8 transmit antennas at the BS, 2 receive antennas per user User 1 and user 2: non-line of sight (NLOS) channels User 3: a line of sight (LOS) channel. Velocities of the three users: 10 km/h. [6] G. Del Galdo, M. Haardt, and C. Schneider Geometry-based channel modelling of MIMO channels in comparison with channel sounder measurements, Advances in Radio Science-Kleinheubacher Berichte, pp , October 2003, more information on the model, as well as the source code and some exemplary scenarios can be found at ilmenau.de/ilmprop.
22 Estimation of the Equivalent Channel 22 We use uplink dedicated pilots to estimate the channel between the user terminal and all BS antennas. For each chunk, there are several pilots available. We compute one channel estimate per pilot and then interpolate between these estimates for every symbol in the chunk. Then we calculate the equivalent channel of the chunk for the ROLT-CSI approach and the longterm CSI method of [7,8], respectively. freq. time [7] V. Stankovic and M. Haardt, Multi-user user MIMO downlink beamforming over correlated MIMO channels, in Proc. International ITG/IEEE Workshop on Smart Antennas (WSA 05) 05),, Apr [8] F. Roemer, M. Fuchs, and M. Haardt, Distributed MIMO systems with spatial reuse for high-speed speed- indoor mobile radio access, in of the 20-th Meeting of the Wireless World Research Forum (WWRF), (Ottawa, ON, Canada), April 2008.
23 Simulation Results (1) 23 CCDF of the system sum rates with BD and RBD precoding The channel estimate per pilot of each chunk is perfectly performed. We can see that RBD precoding can achieve a higher data rate than BD precoding. When linear precoding is performed based on long-term CSI, a significant performance gain can be achieved by our new approach relative to the previous long-term CSI method.
24 Simulation Results (2) 24 BD precoding, individual user throughput RBD precoding, individual user throughput The channel estimate per pilot of each chunk is perfectly performed. It is shown that ROLT-CSI is particularly efficient for the user who has the LOS channel. Even for the users who only have NLOS channels, relative to the previous long-term CSI method there are still some performance gains available for ROLT-CSI approach.
25 Conclusions 25 We consider multi-user MIMO downlink system with linear precoding techniques. Firstly, we approximate the achievable sum rates of RBD precoding at high SNRs. The sum rates difference relative to DPC and BD are analyzed and bounded as simple functions of the system parameters. Secondly, we evaluate the effects of the channel estimation error, quantization error, and feedback delay on the rate loss for multi-user MIMO broadcast channels with limited feedback. Lastly, We propose a new precoding approach called rank-one approximated long-term CSI (ROLT-CSI), which allows the use of previously defined linear precoding techniques originally requiring perfect CSI at the transmitter in cases when only long-term CSI is available.
26 26 Thank you for your attention!
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