1,384 research outputs found

    A Generalized Framework on Beamformer Design and CSI Acquisition for Single-Carrier Massive MIMO Systems in Millimeter Wave Channels

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    In this paper, we establish a general framework on the reduced dimensional channel state information (CSI) estimation and pre-beamformer design for frequency-selective massive multiple-input multiple-output MIMO systems employing single-carrier (SC) modulation in time division duplex (TDD) mode by exploiting the joint angle-delay domain channel sparsity in millimeter (mm) wave frequencies. First, based on a generic subspace projection taking the joint angle-delay power profile and user-grouping into account, the reduced rank minimum mean square error (RR-MMSE) instantaneous CSI estimator is derived for spatially correlated wideband MIMO channels. Second, the statistical pre-beamformer design is considered for frequency-selective SC massive MIMO channels. We examine the dimension reduction problem and subspace (beamspace) construction on which the RR-MMSE estimation can be realized as accurately as possible. Finally, a spatio-temporal domain correlator type reduced rank channel estimator, as an approximation of the RR-MMSE estimate, is obtained by carrying out least square (LS) estimation in a proper reduced dimensional beamspace. It is observed that the proposed techniques show remarkable robustness to the pilot interference (or contamination) with a significant reduction in pilot overhead

    A Coordinated Approach to Channel Estimation in Large-scale Multiple-antenna Systems

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    This paper addresses the problem of channel estimation in multi-cell interference-limited cellular networks. We consider systems employing multiple antennas and are interested in both the finite and large-scale antenna number regimes (so-called "massive MIMO"). Such systems deal with the multi-cell interference by way of per-cell beamforming applied at each base station. Channel estimation in such networks, which is known to be hampered by the pilot contamination effect, constitute a major bottleneck for overall performance. We present a novel approach which tackles this problem by enabling a low-rate coordination between cells during the channel estimation phase itself. The coordination makes use of the additional second-order statistical information about the user channels, which are shown to offer a powerful way of discriminating across interfering users with even strongly correlated pilot sequences. Importantly, we demonstrate analytically that in the large-number-of-antennas regime, the pilot contamination effect is made to vanish completely under certain conditions on the channel covariance. Gains over the conventional channel estimation framework are confirmed by our simulations for even small antenna array sizes.Comment: 10 pages, 6 figures, to appear in IEEE Journal on Selected Areas in Communication

    Uncoordinated pilot decontamination in massive MIMO systems

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    Abstract This work concerns wireless cellular networks applying time division duplexing (TDD) massive multiple-input multiple-output (MIMO) technology. Such systems suffer from pilot contamination during channel estimation, due to the shortage of orthogonal pilot sequences. This paper presents a solution based on pilot sequence hopping, which provides a randomization of the pilot contamination. It is shown that such randomized contamination can be significantly suppressed through appropriate filtering. The resulting channel estimation scheme requires no inter-cell coordination, which is a strong advantage for practical implementations. Comparisons with conventional estimation methods show that the MSE can be lowered as much as an order of magnitude at low mobility. Achievable uplink and downlink rates are increased by 42 and 46%, respectively, in a system with 128 antennas at the base station

    Large System Analysis of Power Normalization Techniques in Massive MIMO

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    Linear precoding has been widely studied in the context of Massive multiple-input-multiple-output (MIMO) together with two common power normalization techniques, namely, matrix normalization (MN) and vector normalization (VN). Despite this, their effect on the performance of Massive MIMO systems has not been thoroughly studied yet. The aim of this paper is to fulfill this gap by using large system analysis. Considering a system model that accounts for channel estimation, pilot contamination, arbitrary pathloss, and per-user channel correlation, we compute tight approximations for the signal-to-interference-plus-noise ratio and the rate of each user equipment in the system while employing maximum ratio transmission (MRT), zero forcing (ZF), and regularized ZF precoding under both MN and VN techniques. Such approximations are used to analytically reveal how the choice of power normalization affects the performance of MRT and ZF under uncorrelated fading channels. It turns out that ZF with VN resembles a sum rate maximizer while it provides a notion of fairness under MN. Numerical results are used to validate the accuracy of the asymptotic analysis and to show that in Massive MIMO, non-coherent interference and noise, rather than pilot contamination, are often the major limiting factors of the considered precoding schemes.Comment: 12 pages, 3 figures, Accepted for publication in the IEEE Transactions on Vehicular Technolog

    Channel Estimation in Multi-user Massive MIMO Systems by Expectation Propagation based Algorithms

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    Massive multiple input multiple output (MIMO) technology uses large antenna arrays with tens or hundreds of antennas at the base station (BS) to achieve high spectral efficiency, high diversity, and high capacity. These benefits, however, rely on obtaining accurate channel state information (CSI) at the receiver for both uplink and downlink channels. Traditionally, pilot sequences are transmitted and used at the receiver to estimate the CSI. Since the length of the pilot sequences scale with the number of transmit antennas, for massive MIMO systems downlink channel estimation requires long pilot sequences resulting in reduced spectral efficiency and the so-called pilot contamination due to sharing of the pilots in adjacent cells. In this dissertation we first review the problem of channel estimation in massive MIMO systems. Next, we study the problem of semi-blind channel estimation in the uplink in the case of spatially correlated time-varying channels. The proposed method uses the transmitted data symbols as virtual pilots to enhance channel estimation. An expectation propagation (EP) algorithm is developed to iteratively approximate the joint a posterior distribution of the unknown channel matrix and the transmitted data symbols with a distribution from an exponential family. The distribution is then used for direct estimation of the channel matrix and detection of the data symbols. A modified version of Kalman filtering algorithm referred to as KF-M emerges from our EP derivation and it is used to initialize our algorithm. Simulation results demonstrate that channel estimation error and the symbol error rate of the proposed algorithm improve with the increase in the number of BS antennas or the number of data symbols in the transmitted frame. Moreover, the proposed algorithms can mitigate the effects of pilot contamination as well as time-variations of the channel. Next, we study the problem of downlink channel estimation in multi-user massive MIMO systems. Our approach is based on Bayesian compressive sensing in which the clustered sparse structure of the channel in the angular domain is exploited to reduce the pilot overhead. To capture the clustered structure, we employ a conditionally independent identically distributed Bernoulli-Gaussian prior on the sparse vector representing the channel, and a Markov prior on its support vector. An EP algorithm is developed to approximate the intractable joint distribution on the sparse vector and its support with a distribution from an exponential family. This distribution is then used for direct estimation of the channel. The EP algorithm requires the model parameters which are unknown. We estimate these parameters using the expectation maximization (EM) algorithm. Simulation results show that the proposed combination of EM and EP referred to as EM-EP algorithm outperforms several recently-proposed algorithms in the literature

    Massive MIMO 시스템을 위한 채널 추정 및 피드백 기법

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    학위논문 (박사)-- 서울대학교 대학원 : 전기·컴퓨터공학부, 2017. 2. 이정우.To meet the demand of high throughput in next generation wireless systems, various directions for physical layer evolution are being explored. Massive multiple-input multiple-output (MIMO) systems, characterized by a large number of antennas at the transmitter, are expected to become a key enabler for spectral efficiency improvement. In massive MIMO systems, thanks to the orthogonality between different users' channels, high spectral and energy efficiency can be achieved through simple signal processing techniques. However, to get such advantages, accurate channel state information (CSI) needs to be available, and acquiring CSI in massive MIMO systems is challenging due to the increased channel dimension. In frequency division duplexing (FDD) systems, where CSI at the transmitter is achieved through downlink training and uplink feedback, the overhead for the training and feedback increases proportionally to the number of antennas, and the resource for data transmission becomes scarce in massive MIMO systems. In time division duplexing (TDD) systems, where the channel reciprocity holds and the downlink CSI can be obtained through uplink training, pilot contamination due to correlated pilots becomes a performance bottleneck when the number of antennas increases. In this dissertation, I propose efficient CSI acquisition techniques for various massive MIMO systems. First, I develop a downlink training technique for FDD massive MIMO systems, which estimates the downlink channel with small overhead. To this end, compressed sensing tools are utilized, and the training overhead can be highly reduced by exploiting the previous channel information. Next, a limited feedback scheme is developed for FDD massive MIMO systems. The proposed scheme reduces the feedback overhead using a dimension reduction technique that exploits spatial and temporal correlation of the channel. Lastly, I analyze the effect of pilot contamination, which has been regarded as a performance bottleneck in multi-cell massive MIMO systems, and propose two uplink training strategies. An iterative pilot design scheme is developed for small networks, and a scalable training framework is also proposed for networks with many cells.1 Introduction 1 1.1 Massive MIMO 1 1.2 CSI Acquisition in Massive MIMO Systems 3 1.3 Contributions and Organization 6 1.4 Notations 7 2 Compressed Sensing-Aided Downlink Training 9 2.1 Introduction 10 2.2 System Model 13 2.2.1 Channel Model 13 2.2.2 Downlink Channel Estimation 16 2.3 CS-Aided Channel Training 19 2.3.1 Training Sequence Design 20 2.3.2 Channel Estimation 21 2.3.3 Estimation Error 23 2.4 Discussions 26 2.4.1 Design of Measurement Matrix 26 2.4.2 Extension to MIMO Systems 27 2.4.3 Comparison to CS with Partial Support Information 28 2.5 Simulation Results 29 2.6 Conclusion 37 3 Projection-Based Differential Feedback 39 3.1 Introduction 40 3.2 System Model 44 3.2.1 Multi-User Beamforming with Limited Feedback 45 3.2.2 Massive MIMO Channel 47 3.3 Projection-Based Differential Feedback 48 3.3.1 Projection-Based Differential Feedback Framework 48 3.3.2 Projection for PBDF Framework 51 3.3.3 Efficient Algorithm 57 3.4 Discussions 58 3.4.1 Projection with Imperfect CSIR 58 3.4.2 Acquisition of Channel Statistics 61 3.5 Simulation Results 62 3.6 Conclusion 69 4 Mitigating Pilot Contamination via Pilot Design 71 4.1 Introduction 72 4.2 System Model 73 4.2.1 Multi-cell Massive MIMO Systems 74 4.2.2 Uplink Channel Training 75 4.2.3 Data Transmission 77 4.3 Iterative Pilot Design Algorithm 78 4.3.1 Algorithm 79 4.3.2 Proof of Convergence 81 4.4 Generalized Pilot Reuse 81 4.4.1 Concept of Pilot Reuse Schemes 81 4.4.2 Pilot Design based on Grassmannian Subspace Packing 82 4.5 Simulation Results 85 4.5.1 Iterative Pilot Design 85 4.5.2 Generalized Pilot Reuse 87 4.6 Conclusion 89 5 Conclusion 91 5.1 Summary 91 5.2 Future Directions 93 Bibliography 96 Abstract (In Korean) 109Docto
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