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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. 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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3. Channel Extrapolation for FDD Massive MIMO: Procedure and Experimental Results

   Choi, T ; Rottenberg, F. ; Gomez, J. ; Akshai, R. ; Peng, L. Zhang ; Molisch, A. F. ( January 2019 , IEEE Vehicular Technology Conference Workshops)

   Application of massive multiple-input multipleoutput (MIMO) systems to frequency division duplex (FDD) is challenging mainly due to the considerable overhead required for downlink training and feedback. Channel extrapolation, i.e., estimating the channel response at the downlink frequency band based on measurements in the disjoint uplink band, is a promising solution to overcome this bottleneck. This paper presents measurement campaigns obtained by using a wideband (350 MHz) channel sounder at 3.5 GHz composed of a calibrated 64 element antenna array, in both an anechoic chamber and outdoor environment. The Space Alternating Generalized Expectation-Maximization (SAGE) algorithm was used to extract the parameters (amplitude, delay, and angular information) of the multipath components from the attained channel data within the “training” (uplink) band. The channel in the downlink band is then reconstructed based on these path parameters. The performance of the extrapolated channel is evaluated in terms of mean squared error (MSE) and reduction of beamforming gain (RBG) in comparison to the “ground truth”, i.e., the measured channel at the downlink frequency. We find strong sensitivity to calibration errors and model mismatch, and also find that performance depends on propagation conditions: LOS performs significantly better than NLOS. 

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4. Channel Feedback Based on AoD-Adaptive Subspace Codebook in FDD Massive MIMO Systems

   https://doi.org/10.1109/TCOMM.2018.2849755  

   Shen, Wenqian ; Dai, Linglong ; Shim, Byonghyo ; Wang, Zhaocheng ; Heath, Robert W. ( January 2018 , IEEE Transactions on Communications)

   Channel feedback is essential in frequency division duplexing (FDD) massive multiple-input multiple-output (MIMO) systems. Unfortunately, prior work on multiuser MIMO has shown that the feedback overhead scales linearly with the number of base station (BS) antennas, which is large in massive MIMO systems. To reduce the feedback overhead, we propose an angle-of-departure (AoD) adaptive subspace codebook for channel feedback in FDD massive MIMO systems. Our key insight is to leverage the observation that path AoDs vary more slowly than the path gains. Within the angle coherence time, by utilizing the constant AoD information, the proposed AoDadaptive subspace codebook is able to quantize the channel vector in a more accurate way. From the performance analysis, we show that the feedback overhead of the proposed codebook only scales linearly with a small number of dominant (path) AoDs instead of the large number of BS antennas. Moreover, we compare the proposed quantized feedback technique using the AoD-adaptive subspace codebook with a comparable analog feedback method. Extensive simulations show that the proposed AoD-adaptive subspace codebook achieves good channel feedback quality, while requiring low overhead. 

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5. Exploiting Partial FDD Reciprocity for Beam Based Pilot Precoding and CSI Feedback in Deep Learning

   https://doi.org/10.1109/TWC.2023.3289929  

   Lin, Yu-Chien ; Lee, Ta-Sung ; Ding, Zhi ( May 2023 , IEEE Transactions on Wireless Communications)

   Massive MIMO systems can achieve high spectrum and energy efficiency in downlink (DL) based on accurate estimate of channel state information (CSI). Existing works have developed learning-based DL CSI estimation that lowers uplink feedback overhead. One often overlooked problem is the limited number of DL pilots available for CSI estimation. One proposed solution leverages temporal CSI coherence by utilizing past CSI estimates and only sending CSI-reference symbols (CSIRS) for partial arrays to preserve CSI recovery performance. Exploiting CSI correlations, FDD channel reciprocity is helpful to base stations with direct access to uplink CSI. In this work, we propose a new learning-based feedback architecture and a reconfigurable CSI-RS placement scheme to reduce DL CSI training overhead and to improve encoding efficiency of CSI feedback. Our results demonstrate superior performance in both indoor and outdoor scenarios by the proposed framework for CSI recovery at substantial reduction of computation power and storage requirements at UEs. 

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