- Research
- Open Access
User scheduling for MU-MIMO transmission with active CSI feedback
- Kyu-haeng Lee^{1} and
- Chong-kwon Kim^{1}Email author
https://doi.org/10.1186/s13638-015-0331-4
© Lee and Kim; licensee Springer. 2015
Received: 21 October 2014
Accepted: 22 February 2015
Published: 18 April 2015
Abstract
User scheduling boosts the multi-user multi-input multi-output (MU-MIMO) gain by selecting an optimal set of users to increase the 802.11 Wi-Fi system capacities. Many kinds of user scheduling algorithms, however, fail to fully realize the advantages of MU-MIMO due to considerable channel state information (CSI) overhead. In this paper, we propose a new MU-MIMO MAC protocol, called 802.11ac+, including a novel user scheduling algorithm. Unlike most proposals, where user scheduling is performed after an access point (AP) receives CSI from all users, 802.11ac+ determines the best user set during the CSI feedback phase. In particular, the AP broadcasts a channel hint about previously scheduled users, and the remaining users actively send CSI reports according to their effective channel gains (ECGs) calculated from the hint. Based on the proposed scheme, we develop two fair scheduling protocols, Round-Robin 802.11ac+ (RR-11ac+) and Proportional-Fair 802.11ac+ (PF-11ac+). Through trace-driven MATLAB simulations, we prove that the proposed schemes not only improve the throughput gain but also enhance the fairness among users.
Keywords
- Access Point
- Channel State Information
- User Selection
- Throughput Gain
- User Schedule
1 Introduction
Most significant throughput gains of recent wireless communication systems come from multi-user multi-input multi-output (MU-MIMO) transmission using beamforming, which focuses energy toward a user so that the SNR and data rates increase. Wi-Fi standards as well as LTE-based cellular systems [1,2] have been adopting the MU-MIMO as a key technology for the next-generation wireless communication, and recently, several commercial products have been successfully deployed on the market.
The performance of MU-MIMO can be significantly improved when proper user scheduling is performed by multi-antenna nodes such as access points (APs) or base stations (BSs). Users with high received power or with an orthogonal channel can be chosen for increasing diversity gain or multiplexing gain, respectively. However, determining an optimal user set is nontrivial since it is generally integrated with finding optimal beamforming weights and powers. Even though we employ a simple beamforming strategy (e.g., zero-forcing beam forming (ZFBF)), a brute force search over all possible user sets is required and thus still creates a heavy burden. This motivates greedy user selection algorithms aimed at providing sub-optimal performance with a practical low complexity [3-9].
In this paper, we present an MU-MIMO MAC protocol for Wi-Fi systems, called 802.11ac+. In particular, 802.11ac+ provides a novel and practical user scheduling solution. Our idea is very intuitive: perform the user scheduling during the CSI feedback phase. To do this, the AP broadcasts channel information about previously scheduled users by appending it to a poll frame. We refer to this channel information as a channel hint. Then, users calculate their effective channel gains (ECGs) from the channel hint, and the user with the largest gain actively sends a CSI report back to the AP. Upon receiving the CSI report, the AP includes the user in the multi-user transmission schedule and repeats this process while its degrees of freedom (DoF) constraint is satisfied. As a result, the performance of 802.11ac+ is comparable to other user scheduling heuristics, with the key difference that it requires a much smaller amount of CSI feedback.
The design of 802.11ac+ is challenging for the following reasons. First, the channel hint should be well designed to balance between overhead and efficiency. In order to reduce the overhead, the channel hint should be succinct, but at the same time, it should include all channel information of already scheduled users such that the remaining users can estimate their ECGs. To deal with such a trade-off, we propose an efficient channel hint broadcasting mechanism. More specifically, an AP extracts the effective channel vector of the last scheduled user from the received CSI reports and uses it as a channel hint. The second challenging issue comes from the fact that users hardly know how much better their ECGs are in a fully distributed manner, which leads us to adopt a contention for users to get a feedback opportunity. Due to the nature of contention, there may be a frame collision if more than one user sends a CSI report at the same time. To address the collision problem, we use a delayed feedback approach, where users delay their CSI feedback according to their ECGs: the bigger the ECG a user has, the faster the CSI report will be. To improve the performance, we focus on maximizing the probability of feedback success. Additionally, we extend our user selection algorithm to well-known fair scheduling protocols, Round-Robin (RR) and Proportional-Fair (PF), to achieve fairness among users.
To evaluate the performance of our approach, we implement the 802.11ac+ and its fair scheduling protocols on a MATLAB simulator. The extensive trace-driven simulation results show that 802.11ac+ obtains much higher throughput gain than 802.11ac and a MAC protocol employing a well-known user scheduling algorithm. Also, we demonstrate that two fair scheduling protocols of 802.11ac+ give a much better throughput fairness than 802.11ac, especially when users experience different channel qualities.
We summarize our main contributions as follows. First, we propose the design of an MU-MIMO MAC protocol, called 802.11ac+, which accomplishes user scheduling gain with a far smaller amount of CSI feedback. Second, in order to realize the protocol, we provide a channel hint broadcasting mechanism and an active CSI feedback scheme. Third, we build two fair scheduling protocols based on the user scheduling of 802.11ac+ to achieve fairness among users. Lastly, the performance of 802.11ac+ has been evaluated through trace-driven simulations in MATLAB.
The remainder of the paper is organized as follows. Section 2 provides the related work, and we next describe the 802.11ac+ mechanism in greater detail in Section 3. In Section 4, we discuss the fair scheduling protocols of 802.11ac+, and Section 5 shows the performance evaluation. We finally conclude our paper in Section 6.
2 Related work
We survey the research results on the user scheduling schemes and channel feedback overhead reduction techniques related to 802.11ac+.
2.1 User scheduling schemes
User selection has been highlighted since it can improve the MU-MIMO performance significantly. In user scheduling, it is challenging and often impractical to determine the optimal user set due to the large search space. Therefore, some protocols based on heuristics have been proposed. Many publications study the problem of maximizing sum capacity [3,7-9]. SUS [6] selects one user in each round by exploiting channel orthogonality between users. However, the selected users cannot guarantee that they always increase the sum rate. GUSS [7] considers ‘delete’ and ‘swap’ operations to guarantee a positive increment of channel capacity in each selecting round. Jin et al. propose a volume metric as the product of diagonal elements of an upper-triangular matrix by performing QR factorization to the selected user channels [8]. Shen et al. [9] propose and compare two algorithms for both approaches with block diagonalization [11] which is a generalized concept of channel inversion.
In addition to the sum rate maximization, the rate balancing problem aimed at maximizing the throughput subject to the constraint that the rates of the different users need to have certain fixed ratios has also been considered in many literatures [12,13]. Hellings et al. propose a gradient projection-based solution [12], and Guthy et al. propose a user classification scheme based on perturbation analysis [13], in order to handle the rate balancing problem. Along this line, Lima et al. consider a frequency allocation problem for MIMO-OFDMA networks [14]. Unfortunately, these schemes come with a nonnegligible performance loss due to the excessive feedback overhead.
2.2 Channel feedback overhead reduction techniques
One way of overcoming the CSI overhead is to use the compression techniques for reducing CSI feedback bits. Codebook and quantization are already adopted in LTE and MIMO-based Wi-Fi systems [1,2,15-17]; however, selecting the optimal quantization level is still an open problem. In Wi-Fi systems, it is proposed to compress the CSI report along three dimensions: time, frequency, and quantization level. Even though compression is used, it is reported that the feedback can take about 25 times longer than the data transmission time when sending a small packet with a high data rate [10]. A vast literature of work has aimed to design an efficient CSI quantization mechanism [18-22]. Recently, compressive sensing has also been used for feedback reduction in MIMO communications [23,24]. The downside of compressions is, as expected, a throughput loss of MU-MIMO transmission: fewer bits may offer diminishing returns.
In addition to the compression, the reduction of feedback loads by adaptively sending feedback can be used. One possible solution is to allow only users whose signal quality (e.g., SNR, carrier-to-noise ratio (CNR)) is higher than a pre-defined threshold to report their CSI [10,25-28]. However, these approaches may fail to obtain higher effective channel gain because their CSI reports are sent without considering the relationship between user channels.
3 802.11ac+
3.1 System model
where (·)^{†}, H(S), and H ^{∗} stand for a pseudo-inverse, the channel matrix of S, and the conjugate transpose of H, respectively.
3.2 Overview
The intuition behind our user scheduling method is that users actively participate in scheduling decisions, unlike in most user scheduling algorithms, which are executed at only the multi-antenna transmitters. As a result, user scheduling in 802.11ac+ can limit the number of sounding exchanges to the number of AP antennas, while still keeping the scheduling gain. In the next section, we introduce two main mechanisms to realize 802.11ac+: channel hint broadcasting and active CSI feedback.
3.3 Channel hint broadcasting
3.3.1 3.3.1 Effective channel gain
where I is the identity matrix and Q(S) is a projection matrix. Then, the ECG of user k is denoted as ∥e _{ k }∥^{2}.
where N _{ c } is the total number of subcarriers.
3.3.2 3.3.2 Channel hint design
There are many ways to implement a channel hint. In a simple way, the AP can use a projection matrix as a channel hint. Although this simplifies the computation burden at the receiver, it always consumes significant bits for representing an M×M matrix per each subcarrier (the maximum required number of appended channel vectors is (M−1)M N _{ c }.). By contrast, if we use the received CSI as a channel hint, then this will increase the receiver side computing complexity.
Our proposed design exploits a compromise between the above two schemes. Every time the AP receives a CSI report, it computes the effective channel vector from that CSI and uses it as a channel hint. Hence, in every poll frame, the effective channel vector of the last scheduled user will be included. On the receiver side, users should maintain the value of summation in Equation 3 during the feedback phase so that they can update a projection matrix and obtain their ECGs much faster.
where τ _{SIFS} stands for 802.11 Short InterFrame Space, which is μs in 802.11ac [2]. Here, τ _{contention} is an overhead from the feedback contention of 802.11ac+, which will be discussed in the next section. As will be discussed later, the maximum value of a τ _{contention} is about 2τ _{SIFS} (four slots per each round).
Even if taking τ _{ECV}≃τ _{CSI}, overhead_{802.11a c+}<overhead_{add}. Also, since the AP has no choice but to poll users randomly in this scheme, the user selection gain could be small, as shown in the case of M=4 in Figure 2.
When sending a channel hint, since the AP may not intend all users to participate in the feedback procedure, it requires a method to notify only some dedicated users. For example, an AP should prevent users from sending CSI reports when it has no frames for them. For target user notification, we utilize the legacy Null Data Packet Announcement (NDPA) frame, by using fewer bits for the Association ID in the STA Info field and mapping bit positions to each user ID. This method maintains the same frame format and thus is efficient. A detailed description of the notification is out of the scope of this paper.
3.4 Active CSI feedback
3.4.1 3.4.1 Feedback contention
In 802.11ac+, only the user with the highest ECG should respond to the poll. However, this is a challenging task since users cannot know the ECG of the others in a distributed manner. If two users, who might think their gains are the best, feed back their CSI reports simultaneously, a frame collision will occur. Without any coordination between users, they should get opportunities to send feedback through a contention like the 802.11 distributed coordinate function (DCF). We call this a feedback contention in this paper.
In order to resolve the feedback contention, we adopt a delayed transmission approach. In this approach, users delay their feedback transmission regarding their ECGs, such that a user with higher value can access the feedback opportunity faster. To realize this, we first apply slotted time in our scheme, where the slot duration is fixed and each slot has a pre-defined threshold. We refer to this threshold as a slot threshold. A user is assigned to the specific slot according to its ECG and is allowed to transmit feedback only at the slot. If a user senses a feedback transmission earlier than its slot, it gives up and waits until the next poll.
Since users should listen to the medium until they obtain a transmission opportunity, the minimum duration of the slot requires at least one slot time of 802.11 (e.g., 4 μs for CCA + 5 μs for RX/TX turnaround). To limit the expense of delayed feedback, an AP uses the timeout threshold (γ). If the AP does not receive any feedback reports before γ, then, it finishes the scheduling. When feedback collision or timeout occurs in the first contention round, the scheduling may be stopped with only one user (i.e., the first user) remaining in S. In this case, the AP just sends a frame to that user in diversity mode, which guarantees the minimal level of system performance.
An example of the thresholds
CR | ( w _{s} , w _{c} , w _{t} ) | α _{1} | α _{2} | α _{3} | α _{4} | α _{5} |
---|---|---|---|---|---|---|
1 | (1,1,1) | 3.667 | 3.543 | 3.453 | 3.371 | 3.280 |
(0.4,0.4,0.2) | 3.680 | 3.558 | 3.472 | 3.396 | 3.318 | |
2 | (1,1,1) | 2.541 | 2.436 | 2.360 | 2.291 | 2.215 |
(0.4,0.4,0.2) | 2.552 | 2.449 | 2.376 | 2.312 | 2.246 | |
3 | (1,1,1) | 1.384 | 1.304 | 1.247 | 1.196 | 1.140 |
(0.4,0.4,0.2) | 1.392 | 1.314 | 1.259 | 1.212 | 1.163 |
3.4.2 3.4.2 Slot threshold optimization
The performance of the active feedback mainly relies on how to select the thresholds: γ and slot thresholds. As described before, active feedback fails when a collision or timeout occurs; however, their impacts are different from each other. The loss from collision is much bigger than that from timeout, due to the relatively long time wasted in the collision. Thus, we first fix γ and find optimal values of the slot thresholds for each contention round. Now, we describe how to determine the thresholds as below.
where F(α;N _{ c } L,1/N _{ c }) is the cumulative distribution function (CDF) of the Gamma distribution for α, N _{ c } and L. For fixed N _{ c } and L, we use F(α) and F(α;N _{ c } L,1/N _{ c }) in the same sense. Note that L varies every contention round.
where K ^{′} is the number of contending users in the contention round. We note that K ^{′}≤K−1 because the first user is already selected by AP, and K ^{′} can be estimated by using the target user notification.
where w _{ s },w _{ c }, and w _{ t } are weights for the probabilities of success, collision, and timeout, respectively.
The optimization problem described in Equation 15 is nonconvex and is solved using nonlinear optimization technique. Note that it only needs to be solved whenever the network configuration (N _{ c }, M, K) is changed or we can construct a set of solutions offline. Once a set of thresholds has been constructed, users can refer to them at any time.
Table 1 shows an example of the thresholds in the case of γ=5,M=4,K ^{′}=14, and N _{ c }=30, where CR stands for contention round. Recall that there are maximum (M−1) contention rounds, and each round consists of γ time slots. From the table, we can see that the thresholds decrease during the course of a contention round because successful feedback reduces L one by one and hence decreases the DoF of the chi-square distribution. In addition, the reduced number of contending users also results in lower thresholds in further contention rounds. The thresholds of nonequal weights are slightly bigger than those of equal weights. In this case, the probability of success as well as the probability of collision decreases.
The graph also demonstrates that nonequal weights reduce both the feedback success probability and the collision probability (omitted here), as expected, thereby decreasing the scheduling gain. As a result, the throughput of nonequal weights is lower than that of the equal weights over all cases. Additionally, we can see that too large a γ decreases the effective channel gain while too small a γ decreases the user diversity gain. For the real trace scenario, both downlink throughputs increase as γ reaches four; after that, they decrease (for the synthetic trace, maximum downlink throughput is obtained when γ is three).
4 Fair scheduling
where \(\mathcal {R}_{k}\) is the average data rate of user k and A is a target user set. For the remaining users, each fair scheduling protocol uses a different scheduling strategy, but the main idea is the same as that of 802.11ac+. We describe the details of RR-11ac+ and PF-11ac+ in the next subsections.
4.1 RR-11ac+
This is the simplest way to obtain the fairness that gives users equal transmission opportunities. Most Round-Robin schedulers use the average data rates of all users, and they can be monitored at the scheduler, which is very easy to implement.
In RR-11ac+, we use the same metric to schedule users, but a simple change is made for multi-user transmission: before the active CSI feedback, an AP limits the contending users according to their average data rates. Specifically, among remaining users in A, the AP selects top (M−1+o) users in ascending order of average data rates such that users who have been served less have more feedback opportunities. If the nonnegative parameter o is set to 0, then RR-11ac+ is reduced to the 802.11ac with the legacy Round-Robin scheduling; however, it still considers the ECG of users. For example, if one’s ECG is too low so joining it into S is no longer helpful for multi-user transmission, then it will be discarded.
4.2 PF-11ac+
where \(\mathcal {T}_{k}\) is the current available data rate of user k.
The difficulty of legacy Proportional-Fair scheduling is that the scheduler cannot know the exact data rates of users (\(\mathcal {T}_{k}\)) when the scheduling decision has to be made. However, the active feedback of 802.11ac+ provides a simple implementation of the Proportional-Fair scheduling since users can actively join the scheduling decision. In particular, they can estimate \(\mathcal {T}_{k}\) by using their ECGs (i.e., \(\mathcal {T}_{k}\sim \text {log}({\left \| \mathbf {e}_{\mathbf {k}} \right \|}^{2})\)). Note that in PF-11ac+, users should maintain their average data rates, and the slot thresholds should be redefined according to Equation 17 by adopting the technique in Section 3.
4.3 Summary
Comparison between three schemes
Size of target user set | First user selection | Metric for n (>1)th user selection | |
---|---|---|---|
802.11ac+ | K | random or argmax∥e _{k}∥^{2} | ∥e _{k}∥^{2} |
RR-11ac+ | M−1+o | \( \text {argmax} \frac {1}{\mathcal {R}_{k}}\) | \(\frac {\mathcal {T}_{k}}{\mathcal {R}_{k}}\) |
PF-11ac+ | K |
5 Performance evaluation
In this section, simulation results for the throughput and fairness performance of the proposed schemes are presented.
5.1 Setting
We implement 802.11ac, an SUS [6] based MAC protocol, 802.11ac+, RR-11ac+, and PF-11ac+ on the MATLAB simulator. To conduct high-fidelity emulation of real-world settings, we use the 802.11n data traces provided by the authors of [30]. The traces contain per-subcarrier (30 subcarriers for 20 MHz) CSI and SNR readings (ranging from 4 to 43 dB) for 18 users. By using the traces, we reconfigure 25 users and a maximum of four AP antennas in our simulations.
Default simulation parameters
Parameter | Value |
---|---|
Downlink traffic intensity | 5 (Mb p s) |
Uplink traffic intensity | 0.5 (Mb p s) |
K | 15 |
The number of polls used in SUS | 10 |
M | 4 |
SNR | 16.7 (dB) |
γ | 4 |
o | 4 |
5.2 802.11ac+ performance
5.2.1 5.2.1 Impact of K
where \(\text {throughput}^{\text {scheme}}_{k}\) denotes the target scheme throughput when K=k.
5.2.2 5.2.2 Impact of M
5.2.3 5.2.3 Impact of the number of polls
5.3 Fair scheduling protocol performance
5.3.1 5.3.1 System throughput
5.3.2 5.3.2 Fairness
To evaluate the fairness performance of RR-11ac+ and PF-11ac+, users are subjected to different average SNRs from 4 to 43 dB, and a user with a higher ID has a bigger SNR than one with a lower ID, unlike in the previous set of simulations.
6 Conclusions
In this work, we propose a new MU-MIMO MAC protocol, 802.11ac+, which obtains significant user scheduling gain with a far smaller amount of CSI feedback by exploiting channel hint-based polling and active CSI feedback. Trace-driven MATLAB simulation results show that 802.11ac+ achieves downlink throughput gains of up to 100% and 168% over 802.11ac and SUS-based MAC protocols. Additionally, two fair scheduling protocols of 802.11ac+ give close-to-perfect user fairness even when the users experience different channel qualities.
7 Endnotes
^{a} The effective channel vector of the first user is the same as its channel vector, e _{(1)}=h _{(1)}.
^{b} In this paper, we do not consider a per-subcarrier decision. We leave this issue to our future work.
^{c} For better graph representation, we omit the graphs for the uplink.
Declarations
Acknowledgements
This work was supported in part by the IT R&D program of MSIP/KEIT. [10041861, Development of Wired/Wireless i-AVB System Technology for Concurrent Transmission of HD Media and Control Data].
Authors’ Affiliations
References
- Evolved Universal Terrestrial Radio Access (E-UTRA), Downlink Multiple Input Multiple Output (MIMO) enhancement for LTE-Advanced (Release 11). 3GPP TR V11.0.0. http://www.3gpp.org/ (2015).
- IEEE Approved Draft Standard for IT - Telecommunications and Information Exchange Between Systems - LAN/MAN - Specific Requirements - Part 11: Wireless LAN Medium Access Control and Physical Layer Specifications. IEEE P802.11ac/D7.0, 1–456 (2013).Google Scholar
- G Dimic, ND Sidiropoulos, On downlink beamforming with greedy user selection: performance analysis and a simple new algorithm. Signal Process. IEEE Trans. 53(10), 3857–3868 (2005).View ArticleMathSciNetGoogle Scholar
- J Wang, DJ Love, MD Zoltowski, User selection with zero-forcing beamforming achieves the asymptotically optimal sum rate. Signal Process. IEEE Trans. 56(8), 3713–3726 (2008).View ArticleMathSciNetGoogle Scholar
- M Kobayashi, G Caire, Joint beamforming and scheduling for a multi-antenna downlink with imperfect transmitter channel knowledge. IEEE J Sel A Commun. 25(7), 1468–1477 (2007).View ArticleGoogle Scholar
- T Yoo, A Goldsmith, On the optimality of multiantenna broadcast scheduling using zero-forcing beamforming. Selected Areas Commun. IEEE J. 24(3), 528–541 (2006).View ArticleGoogle Scholar
- S Huang, H Yin, J Wu, VCM Leung, User selection for multi-user MIMO downlink with zero-forcing beamforming. Vehicular Techn. IEEE Trans. 62(7), 3084–3097 (2012).View ArticleGoogle Scholar
- L Jin, X Gu, Z Hu, Low-complexity scheduling strategy for wireless multiuser multiple-input multiple-output downlink system. Commun. IET. 5(7), 990–995 (2011).View ArticleGoogle Scholar
- Z Shen, R Chen, JG Andrews, RW Heath, BL Evans, in Signals, Systems and Computers, 2005. Conference Record of the Thirty-Ninth Asilomar Conference On. Low complexity user selection algorithms for multiuser MIMO systems with block diagonalization (Pacific Grove, California, USA, 2006).Google Scholar
- X Zhang, X Xie, K Sundaresan, in ACM MOBICOM. Adaptive feedback compression for MIMO networks (Miami, Florida, USA, 2013).Google Scholar
- QH Spencer, AL Swindlehurst, M Haardt, Zero-forcing methods for downlink spatial multiplexing in multiuser MIMO channels. Signal Process. IEEE Trans. 52(2), 461–471 (2004).View ArticleMathSciNetGoogle Scholar
- C Hellings, M Joham, W Utschick, in Smart Antennas (WSA), 2011 International ITG Workshop On. Gradient-based rate balancing for mimo broadcast channels with linear precoding (IEEEAachen, Germany, 2011), pp. 1–8.View ArticleGoogle Scholar
- C Guthy, W Utschick, in Proceedings of ITG/IEEE Workshop on Smart Antennas (WSA). Sum throughput maximization in quality of service constraint multiuser mimo systems based on perturbation analysis (Vienna, Austria, 2007).Google Scholar
- FRM Lima, T Ferreira Maciel, WC Freitas, FR Porto Cavalcanti, Improved spectral efficiency with acceptable service provision in multiuser MIMO scenarios. Vehicular Tech. IEEE Trans. 63(6), 2697–2711 (2014).View ArticleGoogle Scholar
- DJ Love, RW Heath, W Santipach, ML Honig, What is the value of limited feedback for MIMO channels?Commun. Mag. IEEE. 42(10), 54–59 (2004).View ArticleGoogle Scholar
- P Frank, A Muller, J Speidel, in Wireless Conference (EW), 2010 European. Fair performance comparison between CQI- and CSI-based MU-MIMO, for the LTE downlink (Lucca, Italy, 2010).Google Scholar
- IEEE Std 802.11n. IEEE Standard for Information technology - Local and metropolitan area networks - Specific requirements - Part 11: Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) Specifications. IEEE P802.11 (2009).Google Scholar
- K Huang, RW Heath, JG Andrews, Limited feedback beamforming over temporally-correlated channels. Signal Process. IEEE Trans. 57(5), 1959–1975 (2009).View ArticleMathSciNetGoogle Scholar
- V Pohl, PH Nguyen, V Jungnickel, C Von Helmolt, in IEEE Global Telecommunications Conference. How often channel estimation is needed in MIMO systems (San Francisco, USA, 2003).Google Scholar
- W Wang, A Harada, Enhanced limited feedback schemes for DL MU-MIMO ZF precoding. Wireless Commun. IEEE Trans. 12(4), 1554–1561 (2013).View ArticleGoogle Scholar
- JH Lee, W Choi, Optimal feedback rate sharing strategy in zero-forcing MIMO broadcast channels. Wireless Commun. IEEE Trans. 12(6), 3000–3011 (2013).View ArticleMathSciNetGoogle Scholar
- DJ Love, RW Heath, VKN Lau, D Gesbert, BD Rao, M Andrews, An overview of limited feedback in wireless communication systems. Selected Areas Commun. IEEE J. 26(8), 1341–1365 (2008).View ArticleGoogle Scholar
- EJ Candes, MB Wakin, An introduction to compressive sampling. Signal Process. Mag. IEEE. 25(2), 21–30 (2008).View ArticleGoogle Scholar
- ST Qaseem, TY Al-Naffouri, S Alghadhban, in Telecommunications (ICT), IEEE International Conference On. Compressive sensing for feedback reduction in MIMO broadcast channels (Doha, Qatar, 2010).Google Scholar
- D Gesbert, M-S Alouini, in Signal Processing and Information Technology, IEEE International Symposium On. Selective multi-user diversity (Darmstadt, Germany, 2003).Google Scholar
- D Gesbert, M-S Alouini, in Communications, IEEE International Conference On. How much feedback is multi-user diversity really worth? (Paris, France, 2004).Google Scholar
- V Hassel, D Gesbert, M-S Alouini, GE Oien, A threshold-based channel state feedback algorithm for modern cellular systems. Wireless Commun. IEEE Trans. 6(7), 2422–2426 (2007).View ArticleGoogle Scholar
- W Zhang, KB Letaief, MIMO broadcast scheduling with limited feedback. Selected Areas Commun. IEEE J. 25(7), 1457–1467 (2007).View ArticleGoogle Scholar
- Q Yang, X Li, H Yao, J Fang, K Tan, W Hu, J Zhang, Y Zhang, in Proc. of ACM SIGCOMM. Bigstation: enabling scalable real-time signal processing in large MU-MIMO systems (Hong Kong, China, 2013).Google Scholar
- A Bhartia, Y-C Chen, S Rallapalli, L Qiu, in ACM MOBICOM. Harnessing frequency diversity in Wi-Fi networks (Las Vegas, Nevada, USA, 2011).Google Scholar
Copyright
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited.