- Open Access
Distributed user selection scheme for uplink multiuser MIMO systems in a multicell environment
© Lee et al.; licensee Springer. 2012
- Received: 4 February 2012
- Accepted: 12 May 2012
- Published: 21 June 2012
We propose an interference-aware user selection scheme for uplink multiuser multiple-input multiple-output systems in a multicell environment. The proposed scheme works in a distributed manner. Each mobile station determines its transmit beamforming vector based on the locally available channel state information, and informs the associated base station (BS) of the amount of potential interference caused to adjacent cells along with the resulting beamforming vector. Then, the BS selects a set of users to be served simultaneously with consideration of intercell interference. The user selection scheme is devised either to maximize the sum rate or to achieve proportional fairness among users. For each case, we derive an optimal user selection criterion and propose a suboptimal distributed user selection algorithm with low complexity. Simulation results confirm that the proposed scheme offers significant throughput enhancement due to reduction of the intercell interference in a multicell environment.
- Channel State Information
- Proportional Fairness
- User Selection
- Intercell Interference
- Precoding Scheme
Multiuser multiple-input multiple-output (MU-MIMO) is widely accepted as a key technology for enabling high-speed wireless access. In the uplink MU-MIMO systems, multiple mobile stations (MSs) are allowed to simultaneously transmit their signals to the base station (BS) to increase the system capacity. Under this scenario, the system performance may depend on the set of transmitting users and their transmit beamforming vectors [1–3]. In , a general framework for transmit beamforming and user selection was developed based upon general convex utility functions. In , successive user selection algorithms were proposed along with optimization of transmit beamforming vectors. In , various low-complexity beamforming and user selection schemes were proposed. All these works, however, have dealt with only a single cell environment where the intercell interference does not exist.
Intercell interference is one of the most critical factors that limit the performance of cellular systems, especially for low-frequency reuse factor. There have been several works on MIMO that account for the intercell interference in a multicell environment [4–7]. In , it was reported that the performance of spatial multiplexing MIMO scheme is significantly degraded in an interference-limited multicell environment. In , an optimal MIMO transmission strategy was studied when the channel state information (CSI) is not available at the transmitter. For the case when the CSI is available at the transmitter, a centralized precoding scheme that maximizes the total sum rate was proposed in . In , a precoding scheme was proposed to maximize the total sum rate in a distributed manner. However, these works have been based on a single user MIMO system where only one MS is served at a time. MU-MIMO systems were only recently investigated in a multicell environment [8–10]. In , downlink multicell MU-MIMO systems were discussed from the aspects of tradeoffs, overhead, and interference control. In , scheduling schemes were developed for the downlink multicell MIMO systems. Uplink MU-MIMO systems were analyzed in  in the case that the adjacent BS’s are allowed to cooperate.
In this article, we develop an interference-aware user selection scheme for uplink MU-MIMO systems in a multicell environment. The scheme comprises of two steps and works in a distributed manner. In the first step, each MS determines its transmit beamforming vector. By utilizing the previous result on the interference-aware beamforming proposed in , we can effectively reduce the interference caused to adjacent cells. In the second step, each BS selects a set of users to be served simultaneously to realize multiuser diversity with consideration of interference caused to adjacent cells as well as the desired link performance. The user selection scheme is developed so to maximize the sum rate or to achieve proportional fairness among users. For each objective, we derive an optimal user selection criterion and propose a suboptimal distributed user selection algorithm with low complexity. Simulation results are provided to show the throughput enhancement of the proposed scheme.
The rest of this article is organized as follows. Section 2 describes the system model. In Section 3, we explain distributed beamforming schemes. In Section 4, we propose an uplink user selection algorithm based on the beamforming vectors. Simulation results are presented in Section 5, and conclusions are drawn in Section 6.
We define here some notation used throughout this article. We use boldface capital letters and boldface small letters to denote matrices and vectors, respectively, (·)T and (·)H to denote transpose and conjugate transpose, respectively, det(·) to denote determinant of a matrix, tr(·) to denote trace of a matrix, (·)−1 to denote matrix inversion, ||·|| to denote Euclidean norm of a vector, I N to denote the N × N identity matrix.
We consider the uplink of an MU-MIMO system comprised of L cells where there are K users in each cell. Each MS and each BS are equipped with N t transmit antennas and N r receive antennas, respectively. The k th MS in the i th cell is assumed to communicate with the BS in the i th cell by using a transmit beamforming vector .
where S i denotes the set of selected users to be simultaneously served in the i th cell. We assume that the maximum number of selected users per cell is N r . denotes the input symbol transmitted from the k th MS in the i th cell, denotes an N r × N t channel matrix between the k th MS in the j th cell and the BS in the i th cell. We assume a flat fading channel in both time and frequency. The elements of and are assumed to be independent and identically distributed (i.i.d.) circularly symmetric complex Gaussian random variables with zero mean and unit variance. In (1), n i denotes the additive white Gaussian noise (AWGN) vector at the BS in the i th cell with each element having unit variance, denotes the signal-to-noise ratio (SNR) of the k th MS in the i th cell, and denotes the interference-to-noise ratio (INR) for the interference that the k th MS in the j th cell causes to the BS in the i th cell.
We assume that the k th MS can obtain and by exploiting the channel reciprocity. This is possible for time division duplex systems. For example, the MS in the i th cell can estimate through downlink signal that comes from the BS in the i th cell. Similarly, the MS can determine by estimating the covariance matrix of aggregate interference signals that come from adjacent cells during the downlink period. Based on the above assumptions, we introduce two distributed transmit beamforming schemes proposed in : MAX-SNR beamforming and MAX-SGINR beamforming.
The solution of (8) can be obtained as the eigenvector corresponding to the largest eigenvalue of .
The solution of (10) can be obtained as the eigenvector corresponding to the largest eigenvalue of . The MAX-SGINR beamforming effectively reduces the interference to adjacent cells while maintaining the desired signal power. It is shown in  that the MAX-SGINR beamforming approximately maximizes the total sum rate for multiple-input single-output systems in a two-cell environment.
where denotes the amount of interference caused to adjacent cell by the k th MS in the i th cell. Note that depends on the transmit beamforming vector. Each MS informs the associated BS of and for user selection.
In this section, we develop user selection schemes with two different objectives: sum rate maximization, and proportional fairness (PF). For each objective, we first derive an optimal user selection criterion and then propose a suboptimal distributed algorithm with low complexity.
Sum rate maximization
The solution of (13) can only be obtained through centralized optimization among cells, which requires perfect CSI, a lot of signaling overhead among cells, and very high computational complexity. As a more practical solution, we propose a suboptimal distributed user selection algorithm with low complexity. The algorithm is described as in the following steps.
Step 1. Initialization:
Step 2. . Step 3. If , then and go back to the Step 2; otherwise terminate the algorithm.
Each BS independently selects users to be served by using the above algorithm. In Step 1, the set S i of selected users is initialized. In Step 2, the BS chooses one user among the users not in S i so as to maximize the amount of the change in the total sum rate. Note that denotes the amount of the change in the total sum rate when the k th user is added to S i . In Step 3, if the addition of the selected user in Step 2 increases the total sum rate, then the BS adds the user to S i and goes back to Step 2. Otherwise, the algorithm terminates and the final set of selected users is given by S i .
The proposed algorithm requires at most KN r computations of per cell, since users are successively selected.
where Tc is the time constant of the averaging window. The solution of (21), however, does not guarantee the system-wide PF due to the intercell interference.
As provided in the Appendix, the optimization problem (23) remains the same even though U1 is replaced with U2. The use of U2 enables the user selection algorithm to work in a distributed fashion with low computational complexity. Based on the newly defined utility function U2, the proposed algorithm works as follows.
Step 1. Initialization: .
Step 2. .
Step 3. If , then and go back to the Step 2, otherwise terminate the algorithm.
Note that the above algorithm is the same as the distributed algorithm developed in Section 4.1, except that is replaced by , which denotes the amount of the change in U2 when the k th user is added to Si.
This algorithm also requires at most KN r computations of per cell.
In this article, we have developed an interference-aware distributed user selection scheme for uplink MU-MIMO systems in a multicell environment. Multiple transmit antennas at each MS are utilized for transmit beamforming to reduce the interference caused to adjacent cells. Multiple receive antennas at each BS are utilized for receiving the signals from the selected users and suppressing intercell interference. We have derived system-wide optimal user selection criteria and proposed distributed user selection algorithms with low complexity. Simulation results have shown that the proposed user selection scheme provides significant performance improvement in a multicell environment.
This work was supported in part by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (No. 2009–0085604), and in part by the KCC (Korea Communications Commission), Korea, under the R&D program supervised by the KCA (Korea Communications Agency) (KCA-2011-08911-04003).
- Lau KN: Analytical framework for multiuser uplink MIMO space-time scheduling design with convex utility functions. IEEE Trans. Wirel. Commun. 2004, 3(9):1832-1843.View ArticleGoogle Scholar
- Hara Y, Brunel L, Oshima K: Uplink spatial scheduling with adaptive transmit beamforming in multiuser MIMO systems. Proceeding of IEEE International Symposium on Personal, Indoor and Mobile Radio Communications 2004. 10.1109/PIMRC.2006.254006Google Scholar
- Serbetli S, Yener A: Beamforming and scheduling strategies for time slotted multiuser MIMO systems. Proceeding of Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA USA 1st edition. 2004, 1227-1231.Google Scholar
- Catreux S, Driessen PF, Greenstein LJ: Simulation results for an interference-limited multiple-input multiple-output cellular system. IEEE Commun. Lett 2000, 4(11):334-336.View ArticleGoogle Scholar
- Blum RS: MIMO capacity with interference. IEEE J. Sel. Areas Commun 2003, 21(6):793-801.View ArticleGoogle Scholar
- Ye S, Blum RS: Optimized signaling for MIMO interference systems with feedback. IEEE Trans. Signal Process 2003, 51(11):2939-2848.Google Scholar
- Lee BO, Je HW, Shin OS, Lee KB: A novel uplink MIMO transmission scheme in a multicell environment. IEEE Trans. Wirel. Commun 2009, 8(10):4981-4987.View ArticleGoogle Scholar
- Ramprashad SA, Papadopoulos HC, Benjebbour A, Kishiyama Y, Jindal N, Caire G: Cooperative cellular networks using multi-user MIMO: tradeoffs, overheads, and interference control across architectures. IEEE Commun. Mag 2011, 49(5):70-77.View ArticleGoogle Scholar
- Kobayashi M, Debbah M, Belfiore J: Outage efficient strategies for network MIMO with partial CSIT. In Proceeding of IEEE International Symposium on Information Theory. Seoul, Korea; 2009:249-253.Google Scholar
- Hoydis J, Kobayashi M, Debbah M: Optimal channel training in uplink network MIMO systems. IEEE Trans. Signal Process 2011, 59(6):2824-2833.MathSciNetView ArticleGoogle Scholar
- Jalali A, Padovani R, Pankaj R: Data throughput of CDMA-HDR a high efficiency-high data rate personal communication wireless system. In Proceeding of IEEE Vehicular Technology Conference-Spring. Tokyo, Japan; 2000:1854-1858. vol. 3Google Scholar
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