756 research outputs found

    Closed-Loop Beam Alignment for Massive MIMO Channel Estimation

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    Training sequences are designed to probe wireless channels in order to obtain channel state information for block-fading channels. Optimal training sounds the channel using orthogonal beamforming vectors to find an estimate that optimizes some cost function, such as mean square error. As the number of transmit antennas increases, however, the training overhead becomes significant. This creates a need for alternative channel estimation schemes for increasingly large transmit arrays. In this work, we relax the orthogonal restriction on sounding vectors. The use of a feedback channel after each forward channel use during training enables closed-loop sounding vector design. A misalignment cost function is introduced, which provides a metric to sequentially design sounding vectors. In turn, the structure of the sounding vectors aligns the transmit beamformer with the true channel direction, thereby increasing beamforming gain. This beam alignment scheme for massive MIMO is shown to improve beamforming gain over conventional orthogonal training for a MISO channel

    Training Sequence Design for Feedback Assisted Hybrid Beamforming in Massive MIMO Systems

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    The use of large-scale antenna systems in future commercial wireless communications is an emerging technology that uses an excess of transmit antennas to realize high spectral efficiency. Achieving potential gains with large-scale antenna arrays in practice hinges on sufficient channel estimation accuracy. Much prior work focuses on TDD based networks, relying on reciprocity between the uplink and downlink channels. However, most currently deployed commercial wireless systems are FDD based, making it difficult to exploit channel reciprocity. In massive MIMO FDD systems, the problem of channel estimation becomes even more challenging due to the attendant substantial training resources and feedback requirements which scale with the number of antennas. In this paper, we consider the problem of training sequence design that employs a set of training signals and its mapping to the training periods. We focus on reduced-dimension training sequence designs, along with transmit precoder designs, aimed at reducing both hardware complexity and power consumption. The resulting designs are extended to hybrid analog-digital beamforming systems, which employ a limited number of active RF chains for transmit precoding, by applying the Toeplitz distribution theorem to large-scale linear antenna systems. A practical guideline for training sequence parameter selection is presented along with performance analysis.Comment: 16 pages, 9 figures, replaced with revised versio

    Framework of Channel Estimation for Hybrid Analog-and-Digital Processing Enabled Massive MIMO Communications

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    We investigate a general channel estimation problem in the massive multiple-input multiple-output (MIMO) system which employs the hybrid analog/digital precoding structure with limited radio-frequency (RF) chains. By properly designing RF combiners and performing multiple trainings, the proposed channel estimation can approach the performance of fully-digital estimations depending on the degree of channel spatial correlation and the number of RF chains. Dealing with the hybrid channel estimation, the optimal combiner is theoretically derived by relaxing the constant-magnitude constraint in a specific single-training scenario, which is then extended to the design of combiners for multiple trainings by Sequential and Alternating methods. Further, we develop a technique to generate the phase-only RF combiners based on the corresponding unconstrained ones to satisfy the constant-magnitude constraints. The performance of the proposed hybrid channel estimation scheme is examined by simulations under both nonparametric and spatial channel models. The simulation results demonstrate that the estimated CSI can approach the performance of fully-digital estimations in terms of both mean square error and spectral efficiency. Moreover, a practical spatial channel covariance estimation method is proposed and its effectiveness in hybrid channel estimation is verified by simulations

    Channel Estimation and Hybrid Precoding for Distributed Phased Arrays Based MIMO Wireless Communications

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    Distributed phased arrays based multiple-input multiple-output (DPA-MIMO) is a newly introduced architecture that enables both spatial multiplexing and beamforming while facilitating highly reconfigurable hardware implementation in millimeter-wave (mmWave) frequency bands. With a DPA-MIMO system, we focus on channel state information (CSI) acquisition and hybrid precoding. As benefited from a coordinated and open-loop pilot beam pattern design, all the sub-arrays can perform channel sounding with less training overhead compared with the traditional orthogonal operation of each sub-array. Furthermore, two sparse channel recovery algorithms, known as joint orthogonal matching pursuit (JOMP) and joint sparse Bayesian learning with â„“2\ell_2 reweighting (JSBL-â„“2\ell_2), are proposed to exploit the hidden structured sparsity in the beam-domain channel vector. Finally, successive interference cancellation (SIC) based hybrid precoding through sub-array grouping is illustrated for the DPA-MIMO system, which decomposes the joint sub-array RF beamformer design into an interactive per-sub-array-group handle. Simulation results show that the proposed two channel estimators fully take advantage of the partial coupling characteristic of DPA-MIMO channels to perform channel recovery, and the proposed hybrid precoding algorithm is suitable for such array-of-sub-arrays architecture with satisfactory performance and low complexity.Comment: accepted by IEEE Transactions on Vehicular Technolog

    Limited Feedback Massive MISO Systems with Trellis Coded Quantization for Correlated Channels

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    In this paper, we propose trellis coded quantization (TCQ) based limited feedback techniques for massive multiple-input single-output (MISO) frequency division duplexing (FDD) systems in temporally and spatially correlated channels. We exploit the correlation present in the channel to effectively quantize channel direction information (CDI). For multiuser (MU) systems with matched-filter (MF) precoding, we show that the number of feedback bits required by the random vector quantization (RVQ) codebook to match even a small fraction of the perfect CDI signal-to-interference-plus-noise ratio (SINR) performance is large. With such large numbers of bits, the exhaustive search required by conventional codebook approaches make them infeasible for massive MISO systems. Motivated by this, we propose a differential TCQ scheme for temporally correlated channels that transforms the source constellation at each stage in a trellis using 2D translation and scaling techniques. We derive a scaling parameter for the source constellation as a function of the temporal correlation and the number of BS antennas. We also propose a TCQ based limited feedback scheme for spatially correlated channels where the channel is quantized directly without performing decorrelation at the receiver. Simulation results show that the proposed TCQ schemes outperform the existing noncoherent TCQ (NTCQ) schemes, by improving the spectral efficiency and beamforming gain of the system. The proposed differential TCQ also reduces the feedback overhead of the system compared to the differential NTCQ method.Comment: 13 pages, 18 figures, IEEE Transactions on Vehicular Technology, accepted for publicatio

    Two-Stage Beamformer Design for Massive MIMO Downlink By Trace Quotient Formulation

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    In this paper, the problem of outer beamformer design based only on channel statistic information is considered for two-stage beamforming for multi-user massive MIMO downlink, and the problem is approached based on signal-to-leakage-plus-noise ratio (SLNR). To eliminate the dependence on the instantaneous channel state information, a lower bound on the average SLNR is derived by assuming zero-forcing (ZF) inner beamforming, and an outer beamformer design method that maximizes the lower bound on the average SLNR is proposed. It is shown that the proposed SLNR-based outer beamformer design problem reduces to a trace quotient problem (TQP), which is often encountered in the field of machine learning. An iterative algorithm is presented to obtain an optimal solution to the proposed TQP. The proposed method has the capability of optimally controlling the weighting factor between the signal power to the desired user and the interference leakage power to undesired users according to different channel statistics. Numerical results show that the proposed outer beamformer design method yields significant performance gain over existing methods.Comment: 27 pages, 5 figures, submitted to IEEE Transactions on Communication

    Pilot Signal Design for Massive MIMO Systems: A Received Signal-To-Noise-Ratio-Based Approach

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    In this paper, the pilot signal design for massive MIMO systems to maximize the training-based received signal-to-noise ratio (SNR) is considered under two channel models: block Gauss-Markov and block independent and identically distributed (i.i.d.) channel models. First, it is shown that under the block Gauss-Markov channel model, the optimal pilot design problem reduces to a semi-definite programming (SDP) problem, which can be solved numerically by a standard convex optimization tool. Second, under the block i.i.d. channel model, an optimal solution is obtained in closed form. Numerical results show that the proposed method yields noticeably better performance than other existing pilot design methods in terms of received SNR.Comment: 5 pages, double column, 1 figure. Submitted to IEEE Signal Processing Letter

    Trellis-Extended Codebooks and Successive Phase Adjustment: A Path from LTE-Advanced to FDD Massive MIMO Systems

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    It is of great interest to develop efficient ways to acquire accurate channel state information (CSI) for frequency division duplexing (FDD) massive multiple-input multiple-output (MIMO) systems for backward compatibility. It is theoretically well known that the codebook size for CSI quantization should be increased as the number of transmit antennas becomes larger, and 3GPP long term evolution (LTE) and LTE-Advanced codebooks also follow this trend. Thus, in massive MIMO, it is hard to apply the conventional approach of using pre-defined vector-quantized codebooks for CSI quantization mainly because of codeword search complexity. In this paper, we propose a trellis-extended codebook (TEC) that can be easily harmonized with current wireless standards such as LTE or LTE-Advanced by extending standardized codebooks designed for 2, 4, or 8 antennas with trellis structures. TEC exploits a Viterbi decoder and convolutional encoder in channel coding as the CSI quantizer and the CSI reconstructer, respectively. By quantizing multiple channel entries simultaneously using standardized codebooks in a state transition of trellis search, TEC can achieve fractional bits per channel entry quantization to have a practical feedback overhead. Thus, TEC can solve both the complexity and the feedback overhead issues of CSI quantization in massive MIMO systems. We also develop trellis-extended successive phase adjustment (TE-SPA) which works as a differential codebook of TEC. This is similar to the dual codebook concept of LTE-Advanced. TE-SPA can reduce CSI quantization error even with lower feedback overhead in temporally correlated channels. Numerical results verify the effectiveness of the proposed schemes in FDD massive MIMO systems.Comment: 10 pages, 11 figures, accepted to IEEE Transactions on Wireless Communications, Nov. 201

    Leveraging the Restricted Isometry Property: Improved Low-Rank Subspace Decomposition for Hybrid Millimeter-Wave Systems

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    Communication at millimeter wave frequencies will be one of the essential new technologies in 5G. Acquiring an accurate channel estimate is the key to facilitate advanced millimeter wave hybrid multiple-input multiple-output (MIMO) precoding techniques. Millimeter wave MIMO channel estimation, however, suffers from a considerably increased channel use overhead. This happens due to the limited number of radio frequency (RF) chains that prevent the digital baseband from directly accessing the signal at each antenna. To address this issue, recent research has focused on adaptive closed-loop and two-way channel estimation techniques. In this paper, unlike the prior approaches, we study a non-adaptive, hence rather simple, open-loop millimeter wave MIMO channel estimation technique. We present a simple random design of channel subspace sampling signals and show that they obey the restricted isometry property (RIP) with high probability. We then formulate the channel estimation as a low-rank subspace decomposition problem and, based on the RIP, show that the proposed framework reveals resilience to a low signal-to-noise ratio. It is revealed that the required number of channel uses ensuring a bounded estimation error is linearly proportional to the degrees of freedom of the channel, whereas it converges to a constant value if the number of RF chains can grow proportionally to the channel dimension while keeping the channel rank fixed. In particular, we show that the tighter the RIP characterization the lower the channel estimation error is. We also devise an iterative technique that effectively finds a suboptimal but stationary solution to the formulated problem. The proposed technique is shown to have improved channel estimation accuracy with a low channel use overhead as compared to that of previous closed-loop and two-way adaptation techniques

    A Hardware-Efficient Hybrid Beamforming Solution for mmWave MIMO Systems

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    In millimeter wave (mmWave) communication systems, existing hybrid beamforming solutions generally require a large number of high-resolution phase shifters (PSs) to realize analog beamformers, which still suffer from high hardware complexity and power consumption. Targeting at this problem, this article introduces a novel hardware-efficient hybrid precoding/combining architecture, which only employs a limited number of simple phase over-samplers (POSs) and a switch (SW) network to achieve maximum hardware efficiency while maintaining satisfactory spectral efficiency performance. The POS can be realized by a simple circuit and simultaneously outputs several parallel signals with different phases. With the aid of a simple switch network, the analog precoder/combiner is implemented by feeding the signals with appropriate phases to antenna arrays or RF chains. We analyze the design challenges of this POS-SW-based hybrid beamforming architecture and present potential solutions to the fundamental issues, especially the precoder/combiner design and the channel estimation strategy. Simulation results demonstrate that this hardware-efficient structure can achieve comparable spectral efficiency but much higher energy efficiency than that of the traditional structures
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