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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. 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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3. 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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4. 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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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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