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1. Channel Extrapolation in FDD Massive MIMO: Theoretical Analysis and Numerical Validation

   Rottenberg, F. ; Zhang, J. ; Molisch, A. F. ( January 2019 , IEEE Globecom)

   Downlink channel estimation in massive MIMO systems is well known to generate a large overhead in frequency division duplex (FDD) mode as the amount of training generally scales with the number of transmit antennas. Using instead an extrapolation of the channel from the measured uplink estimates to the downlink frequency band completely removes this overhead. In this paper, we investigate the theoretical limits of channel extrapolation in frequency. We highlight the advantage of basing the extrapolation on high-resolution channel estimation. A lower bound (LB) on the mean squared error (MSE) of the extrapolated channel is derived. A simplified LB is also proposed, giving physical intuition on the SNR gain and extrapolation range that can be expected in practice. The validity of the simplified LB relies on the assumption that the paths are well separated. The SNR gain then linearly improves with the number of receive antennas while the extrapolation performance penalty quadratically scales with the ratio of the frequency and the training bandwidth. The theoretical LB is numerically evaluated using a 3GPP channel model and we show that the LB can be reached by practical high-resolution parameter extraction algorithms. Our results show that there are strong limitations on the extrapolation range than can be expected in SISO systems while much more promising results can be obtained in the multiple-antenna setting as the paths can be more easily separated in the delay-angle domain. 

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2. Performance Analysis of Channel Extrapolation in FDD Massive MIMO Systems

   Rottenberg, F. ; Choi, T ; Luo, P. ; Zhang, J. ; Molisch, A. F. ( January 2019 , ArXiv.org)

   Channel estimation for the downlink of frequency division duplex (FDD) massive MIMO systems is well known to generate a large overhead as the amount of training generally scales with the number of transmit antennas in a MIMO system. In this paper, we consider the solution of extrapolating the channel frequency response from uplink pilot estimates to the downlink frequency band, which completely removes the training overhead. We first show that conventional estimators fail to achieve reasonable accuracy. We propose instead to use high-resolution channel estimation. We derive theoretical lower bounds (LB) for the mean squared error (MSE) of the extrapolated channel. Assuming that the paths are well separated, the LB is simplified in an expression that gives considerable physical insight. It is then shown that the MSE is inversely proportional to the number of receive antennas while the extrapolation performance penalty scales with the square of the ratio of the frequency offset and the training bandwidth. The channel extrapolation performance is validated through numeric simulations and experimental measurements taken in an anechoic chamber. Our main conclusion is that channel extrapolation is a viable solution for FDD massive MIMO systems if accurate system calibration is performed and favorable propagation conditions are present. 

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3. Scalable user selection in FDD massive MIMO

   https://doi.org/10.1186/s13638-021-02073-4  

   Zhang, Xing ; Sabharwal, Ashutosh ( December 2021 , EURASIP Journal on Wireless Communications and Networking)

   User subset selection requires full downlink channel state information to realize effective multi-user beamforming in frequency-division duplexing (FDD) massive multi-input multi-output (MIMO) systems. However, the channel estimation overhead scales with the number of users in FDD systems. In this paper, we propose a novel propagation domain-based user selection scheme, labeled aszero-measurement selection, for FDD massive MIMO systems with the aim of reducing the channel estimation overhead that scales with the number of users. The key idea is to infer downlink user channel norm and inter-user channel correlation from uplink channel in the propagation domain. In zero-measurement selection, the base-station performs downlink user selection before any downlink channel estimation. As a result, the downlink channel estimation overhead for both user selection and beamforming is independent of the total number of users. Then, we evaluate zero-measurement selection with both measured and simulated channels. The results show that zero-measurement selection achieves up to 92.5% weighted sum rate of genie-aided user selection on the average and scales well with both the number of base-station antennas and the number of users. We also employ simulated channels for further performance validation, and the numerical results yield similar observations as the experimental findings.

    

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4. Massive MIMO Channel Estimation via Compressed and Quantized Feedback

   https://doi.org/10.1109/IEEECONF56349.2022.10052071  

   Shao, Mingjie ; Fu, Xiao ( October 2022 , 2022 56th Asilomar Conference on Signals, Systems, and Computers)

   This paper focuses on downlink channel state information (CSI) acquisition. A frequency division duplex (FDD) of massive MIMO system is considered. In such systems, the base station (BS) obtains the downlink CSI from the mobile users' feedback. A key consideration is to reduce the feedback overhead while ensuring that the BS accurately recovers the downlink CSI. Existing approaches often resort to dictionary-based or tensor/matrix decomposition techniques, which either exhibit unsatisfactory accuracy or induce heavy computational load at the mobile end. To circumvent these challenges, this work formulates the limited channel feedback problem as a quantized and compressed matrix recovery problem. The formulation presents a computationally challenging maximum likelihood estimation (MLE) problem. An ADMM algorithm leveraging existing harmonic retrieval tools is proposed to effectively tackle the optimization problem. Simulations show that the proposed method attains promising channel estimation accuracy, using a much smaller amount of feedback bits relative to existing methods. 

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5. Sparsity-Based Channel Estimation Exploiting Deep Unrolling for Downlink Massive MIMO

   Chen, An ; Xu, Wenbo ; Lu, Liyang ; Wang, Yue ( December 2023 , 2023 IEEE Global Communications Conference)

   Massive multiple-input multiple-output (MIMO) enjoys great advantage in 5G wireless communication systems owing to its spectrum and energy efficiency. However, hundreds of antennas require large volumes of pilot overhead to guarantee reliable channel estimation in FDD massive MIMO system. Compressive sensing (CS) has been applied for channel estimation by exploiting the inherent sparse structure of massive MIMO channel but suffer from high complexity. To overcome this challenge, this paper develops a hybrid channel estimation scheme by integrating the model-driven CS and data-driven deep unrolling technique. The proposed scheme consists of a coarse estimation part and a fine correction part to respectively exploit the inter- and intraframe sparsities of channels to greatly reduce the pilot overhead. Theoretical result is provided to indicate the convergence of the fine correction and coarse estimation net. Simulation results are provided to verify that our scheme can estimate MIMO channels with low pilot overhead while guaranteeing estimation accuracy with relatively low complexity. 

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