Efficient feedback scheme based on compressed sensing in MIMO wireless networks☆
Graphical abstract
Highlights
► Compressed sensing is applied into MIMO broadcast communication. ► Multiple measurement vectors CS is used for CSI recovery. ► Self pre-selection scheme based on channel vector norm and correlation is proposed. ► CS feedback scheme is feedback efficient compared with traditional feedback.
Introduction
Multi-user multiple-input–multiple-output (MU-MIMO) communication with partial channel state information (CSI) can substantially increase channel capacity while it requires low feedback overhead and is practical in engineering [1], [2], [3], [4]. However, it requires that each user reports its CSI, such as channel quality indicator (CQI) and channel direction information (CDI), which is resources expensive. On the other hand, there is a throughput loss because of the feedback inaccuracy induced by the feedback quantization. In order to improve the feedback performance and save the resources, we need to adopt more efficient feedback scheme for the MIMO broadcast system.
Compressed sensing (CS) is a promising technology in signal processing and communications and has attracted lots of researchers’ attention. Recently some authors have applied CS technology to the wireless broadcast channel, multiple users access channel and sensor networks to reduce the resource consumption and enhance the accuracy of the transmitted information. A high-precision feedback technique by using sparse approximation and compression called compressive feedback has been proposed in [5], which quantifies the channel vector by the linear combination of several unit vectors in the defined codebook, then the base station can obtain more accurate channel information, since the linear combination can be recovered by CS. In [6] the authors propose a CS based opportunistic feedback protocol for feedback resource reduction in MIMO broadcast channel with random beamforming (RBF), and the users in each beam with better channel quality, which means that user’s CQI is above a threshold, will feed back their CQI and will be the candidates in the user set for transmission. Signal to interference plus noise ratio (SINR) based user self-selection algorithm is proposed in [7], and the channel estimation of selected users are acquired via CS by exploiting the fact that only partial users are selected which is also a kind of sparcity. It should be noticed that analog feedback of the channel gain vector is used in [5], [6], [7].
A simple on-off random multiple access scheme is introduced in [8], in which CS can be applied to the multiple user detection. In [9] the authors propose a novel CQI feedback schemes in a wireless Orthogonal Frequency Division Multiplexing (OFDM) system. The CS is used for compressing and recovering the CQI. The orthogonal matching pursuit algorithm and subspace CS algorithm are used for the CQI recovery, and the subspace CS outperform the cosine transform based CQI feedback.
Meanwhile CS has been applied to the sensor networks and can greatly reduce the resource consumption. In [10] the sparse nature of monitored sensor network is exploited and a random access CS scheme is proposed in which the sensors transmit at random to a fusion center. Meanwhile the author has applied the random access CS scheme to the underwater sensor networks [11]. In [12] CS is applied to sensor data gathering for large-scale wireless sensor networks, which can reduce global scale communication cost without introducing intensive computation or complicated transmission control. What’s more, the proposed scheme can cope with abnormal sensor readings by using overcomplete hybrid dictionary.
It can be seen that CS can make the wireless communications more efficient in transmission or resource consumption, however, most of the above researches are based on single measurement vector (SMV) CS and recovery algorithms, which have been introduced in [13] and other related literatures. In the MIMO communication, the user selection is based on SNR or SINR which are scalars, and the analysis are with RBF [6], [7]. Since multiple-user and multiple-antenna are the essential natures of MIMO broadcast channel, the channel vector of each user is a vector and only partial users are selected and active which means that the channel vectors for all the selected users composite a sparse multiple dimensional vectors. Hence it is straightforward to apply multiple measurement vectors (MMV) CS to the MIMO broadcast channel. MMV CS has been discussed in [14], [15], [16], [17], [18]. In these literature and references therein, some conditions for MMV CS and recovery algorithm such as matching pursuit (MP), orthogonal matching pursuit (OMP), reduced MMV and boost algorithm (ReMBo) and convex relaxation, are thoroughly discussed.
In [4] the zero-forcing beamforming (ZFBF) and random vector quantization for MU-MIMO are introduced. Semi-orthogonal user selection (SUS) and greedy selection are illustrated, and the performance bounds are analyzed. In the paper, we propose a CS feedback scheme in ZFBF MU-MIMO broadcast channel with CS MMV algorithm which is different from the previous research with CS SMV and RBF, and the proposed feedback scheme can reduce the feedback resource consumption. A self pre-selection algorithm is based on the channel vector’s norm and correlation, which is different from the previous researches based on SNR and SINR. What’s more, both the analog and digital CS feedback are analyzed and compared with the quantization feedback of all users. The MMV OMP and ReMBo algorithms are used for the feedback information recovery.
The main contributions of our work are as following:
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A self pre-selection algorithm based on the channel vector’s norm and correlation is introduced which can reduce the feedback load and obtain better orthogonality among selected users at high probability.
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The CS MMV is firstly applied to the MIMO channel state information feedback. Both the analog and digital CS MMV feedback are considered, and the recovery rate and accuracy are analyzed.
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The feedback recovery performances of MMV OMP algorithm and ReMBo algorithm with noise are analyzed and simulated. MMV OMP outperforms the ReMBo algorithm.
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The impacts of CS digital/analog feedback on ZFBF are given, and the noise and quantization error on the sum throughput are presented.
The remaining of the paper is organized as follows. Section 2 presents broadcast channel model and feedback channel model. CS MMV background and CS feedback strategy are explained in Section 3. Section 4 evaluates the performances of sum throughput, feedback reduction, CS MMV recovery performance and algorithm complexity. Simulations and conclusion are given in Sections 5 Simulations and analysis, 6 Conclusion.
Section snippets
MIMO broadcast channel model
In this paper, we focus on the MIMO broadcast channel. The base station is equipped with antennas, and each user has a single antenna. There are users in the system. We assume that users are in flat Rayleigh fading, and the channel is assumed to be constant during each transmission period. For the MIMO broadcast channel, we assume that there are users scheduled simultaneously. The received signal at user k is given bywhere is the channel vector with zero mean unit
Compressed sensing feedback
Before discussing the proposed compressed sensing feedback algorithm, we present some important results for MMV CS used in our work.
Throughput of CS feedback in ZFBF
Firstly we will discuss the throughput of CS digital feedback in ZFBF. According to the broadcast channel model given in Section 2.1, the signal to interference plus noise ratio (SINR) of user k is aswhere is the normalized vector of , is the beamforming vector.
When feedback channel number M and self pre-selected users are chosen properly, the MMV recovery algorithm can perfectly recover the feedback information with
Simulation environment
In our simulations, we set the number of transmit antennas at the base station to , the total user number is 100. The semi-orthogonal user selection algorithm for zero-forcing beamforming is applied. Since the M-OMP algorithm has better performance than the ReMBo algorithm, the M-OMP is used for the CSI information recovery in our simulations. We simulate the CS analog and digital feedback algorithms, and compare their performance with ZFBF with perfect CSI and quantization CSI with all
Conclusion
We have proposed a resource-efficient feedback scheme based on compressed sensing for multiple users ZFBF MIMO systems. Due to the self pre-selection algorithm, the proposed CS feedback can greatly save the feedback resources. Compared with the ZFBF with quantified CSI of all users and numbered users, simulations and analysis show that the proposed CS analog feedback has better performance than the ZFBF with quantified feedback of all users, and the proposed CS digital feedback has a close
Acknowledgements
This work is supported by National Natural Science Foundation of China 60972015, China-EU International Scientific and Technological Cooperation Program (0902), China National Science and Technology Major Project 2009ZX03003-007-03, 2009ZX03003-003-02 and 2010ZX03003-001-02. Thanks for the reviewers’ valuable comments.
Wei Lu received the M.S. degree from the Department of Information Engineering at Wuhan University of Technology, China, in 2007. He was the system engineer of CDMA system in Nortel R&D Lab in Guangzhou, China, from 2007 to 2008. He is currently pursuing his Ph.D. degree at Huazhong University of Science and Technology and Wuhan National Laboratory for Optoelectronics, China. His main research interests include MIMO and compressed sensing.
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Wei Lu received the M.S. degree from the Department of Information Engineering at Wuhan University of Technology, China, in 2007. He was the system engineer of CDMA system in Nortel R&D Lab in Guangzhou, China, from 2007 to 2008. He is currently pursuing his Ph.D. degree at Huazhong University of Science and Technology and Wuhan National Laboratory for Optoelectronics, China. His main research interests include MIMO and compressed sensing.
Yingzhuang Liu received his Ph.D. degree in communications and information system in 2000 from Huazhong University of Science and Technology. He was the post doctor at University of Paris-Sud 11, France, from 2000 to 2001. Now he is the Professor at Huazhong University of Science and Technology and Wuhan National Laboratory for Optoelectronics in China.
Desheng Wang received his Ph.D. degree in communications and information system in 2006 from Huazhong University of Science and Technology. Now he is the Associate Professor in Department of Electronics and Information Engineering at Huazhong University of Science and Technology.
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Reviews processed and approved for publication by Editor-in-Chief Dr. Manu Malek.