FDD Massive MIMO Research Articles

Disentangled Representation Learning Empowered CSI Feedback Using Implicit Channel Reciprocity in FDD Massive MIMO

Disentangled Representation Learning Empowered CSI Feedback Using Implicit Channel Reciprocity in FDD Massive MIMO

Utilizing Partial Reciprocity to Efficient Codebook Design for FDD Massive MIMO Systems

Utilizing Partial Reciprocity to Efficient Codebook Design for FDD Massive MIMO Systems

Spectral Efficient TSB Scheme With User Scheduling for FDD Massive MIMO Systems

Spectral Efficient TSB Scheme With User Scheduling for FDD Massive MIMO Systems

A Manifold Learning-based CSI Feedback Framework for FDD Massive MIMO

A Manifold Learning-based CSI Feedback Framework for FDD Massive MIMO

Downlink Channel Covariance Matrix Reconstruction for FDD Massive MIMO Systems With Limited Feedback

Downlink Channel Covariance Matrix Reconstruction for FDD Massive MIMO Systems With Limited Feedback

FDD Massive MIMO Channel Training: Optimal Rate-Distortion Bounds and the Spectral Efficiency of “One-Shot” Schemes

We study the problem of providing channel state information (CSI) at the transmitter in multi-user “massive” MIMO systems operating in frequency division duplexing (FDD). The wideband MIMO channel is a vector-valued random process correlated in time, space (antennas), and frequency (subcarriers). The base station (BS) broadcasts periodically β <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">tr</sub> pilot symbols from its <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> antenna ports to <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> single-antenna users (UEs). Correspondingly, the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> UEs send feedback messages about their channel state using β <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">fb</sub> symbols in the uplink (UL). Using results from remote rate-distortion theory, we show that, as snr → ∞, the optimal feedback strategy achieves a channel state estimation mean squared error (MSE) that behaves as Θ(1) if β <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">tr</sub> < <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</i> and as Θ(snr <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">–α</sup> ) when β <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">tr</sub> ⩾ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</i> , where α = min(β <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">fb</sub> / <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</i> , 1), where <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</i> is the rank of the channel covariance matrix. The MSE-optimal rate-distortion strategy implies encoding of long sequences of channel states, which would yield completely stale CSI and therefore poor multiuser precoding performance. Hence, we consider three practical “one-shot” CSI strategies with minimum one-slot delay and analyze their large-SNR channel estimation MSE behavior. These are: (1) digital feedback via entropy-coded scalar quantization (ECSQ), (2) analog feedback (AF), and (3) local channel estimation at the UEs via compressed sensing and digital feedback. These schemes have different requirements in terms of knowledge of the channel statistics at the UE and at the BS. In particular, the latter strategy requires no statistical knowledge and is closely inspired by a CSI feedback scheme currently proposed in 3GPP standardization. It is shown that ECSQ achieves optimal MSE at the price of a slight increase in feedback rate which vanishes for large SNR. AF achieves the optimal MSE decay rate of Θ(snr <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">–1</sup> ) whenever β <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">tr</sub> , β <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">fb</sub> ⩾ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</i> but is sub-optimal if β⩾ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</i> and β <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">fb</sub> < <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</i> . The <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3GPP-inspired</i> scheme is shown, via numerical simulations, to achieves performance similar to ECSQ and AF when the multipath channel is sufficiently sparse in the angle-delay domain, but suffers from a large performance gap if this requirement is not met.

Analysis of scalable channel estimation in FDD massive MIMO

One of the key ideas for reducing downlink channel acquisition overhead for FDD massive MIMO systems is to exploit a combination of two assumptions: (i) the dimension of channel models in propagation domain may be much smaller than the next-generation base-station array sizes (e.g., 64 or more antennas), and (ii) uplink and downlink channels may share the same low-dimensional propagation domain. Our channel measurements demonstrate that the two assumptions may not always hold, thereby impacting the predicted performance of methods that rely on the above assumptions. In this paper, we analyze the error in modeling the downlink channel using uplink measurements, caused by the mismatch from the above two assumptions. We investigate how modeling error varies with base-station array size and provide both numerical and experimental results. We observe that modeling error increases with the number of base-station antennas, and channels with larger angular spreads have larger modeling error. Utilizing our modeling error analysis, we then investigate the resulting beamforming performance rate loss. Accordingly, we observe that the rate loss increases with the number of base-station antennas, and channels with larger angular spreads suffer from higher rate loss.

Optimization of resource allocation in FDD massive MIMO systems

The performance of massive MIMO systems relies heavily on the availability of Channel State Information at the Transmitter (CSIT). A large amount of work has been devoted to reducing the CSIT acquisition overhead at the pilot training and/or CSI feedback stage. In fact, the downlink communication generally includes three stages, i.e., pilot training, CSI feedback, and data transmission. These three stages are mutually related and jointly determine the overall system performance. Unfortunately, there exist few studies on the reduction of CSIT acquisition overhead from the global point of view. In this paper, we integrate the Minimum Mean Square Error (MMSE) channel estimation, Random Vector Quantization (RVQ) based limited feedback and Maximal Ratio Combining (MRC) precoding into a unified framework for investigating the resource allocation problem. In particular, we first approximate the covariance matrix of the quantization error with a simple expression and derive an analytical expression of the received Signal-to-Noise Ratio (SNR) based on the deterministic equivalence theory. Then the three performance metrics (the spectral efficiency, energy efficiency, and total energy consumption) oriented problems are formulated analytically. With practical system requirements, these three metrics can be collaboratively optimized. Finally, we propose an optimization solver to derive the optimal partition of channel coherence time. Experiment results verify the benefits of the proposed resource allocation schemes under three different scenarios and illustrate the tradeoff of resource allocation between three stages.

Self-Supervised Learning for CSI Compression in FDD Massive MIMO Systems

In frequency division duplexing systems, the user equipment frequently reports the channel state information (CSI) to the base station. This information is crucial for link adaptation and beamforming tasks in massive MIMO systems. However, it consumes a large amount of bandwidth when the number of antennas and subcarriers increases. Currently, compression techniques have been used to reduce this bandwidth overhead. In this letter, we propose a novel learning-based technique for CSI compression. Our method exploits the bias/variance tradeoff for CSI compression based on a shallow neural network to approximate a sufficient statistic function for each sampled channel. Unlike prior work that adopts projection-based techniques for compression, our method interprets the model weights as the compressed representation. The experimental results confirm the advantages of the proposed method compared with other state-of-the-art models.

CAnet: Uplink-Aided Downlink Channel Acquisition in FDD Massive MIMO Using Deep Learning

In frequency-division duplexing systems, the downlink channel state information (CSI) acquisition scheme leads to high training and feedback overhead. In this work, we propose an uplink-aided downlink channel acquisition framework using deep learning to reduce such overhead. We consider the entire downlink CSI acquisition process, including the downlink pilot design, channel estimation, and feedback. First, we propose an adaptive pilot design module by exploiting the correlation in magnitude among bidirectional channels in the angular domain to improve channel estimation. Second, to avoid the bit allocation problem during the feedback module, we concatenate the complex channel and embed the uplink channel magnitude to the channel reconstruction at the base station. Finally, we combine the two modules and compare two popular uplink-aided downlink channel acquisition frameworks. One framework estimates and subsequently feeds back the channel at the user equipment. In the other framework, the user equipment directly feeds back the received pilot signals to the base station. Results reveal that with the help of the uplink channel, directly feeding back pilot signals can save approximately 20% of feedback bits. This work thus provides a guideline for future research.

Fully Analog Precoding Scheme Based on Sequential Pre-Codebooks in Fdd Massive Mimo Systems

Fully Analog Precoding Scheme Based on Sequential Pre-Codebooks in Fdd Massive Mimo Systems

Comments on “Spatially Common Sparsity Based Adaptive Channel Estimation and Feedback for FDD Massive MIMO”

In the generalized multiple measurement vectors (GMMV) setup of compressive sensing, we consider the problem of jointly recovering multiple sparse signal vectors sharing a common sparsity pattern based on joint analysis of their linear measurements. The important aspect of the GMMV setup is that the linear measurements of different sparse signal vectors are acquired by using different sensing matrices. It is not yet well understood how the GMMV setup affects identifiability of sparse signal vectors from the measurements, in particular compared to the single measurement vector (SMV) setup wherein we perform recovery of each sparse signal vector independently. Gao et al. [1] presented the first theorem on identifiability of sparse signal vectors in the GMMV setup, in which it is stated that the GMMV setup allows signal vectors with more nonzero rows to be identifiable compared to the SMV setup. In this correspondence, we aim to present a contrasting perspective on sparse signal identifiability in the GMMV setup. In particular, it is shown that the GMMV setup does not result in an improved identifiability condition for some signal vectors even when their entries are diverse.

Deep Learning for Distributed Channel Feedback and Multiuser Precoding in FDD Massive MIMO

This paper shows that deep neural network (DNN) can be used for efficient and distributed channel estimation, quantization, feedback, and downlink multiuser precoding for a frequency-division duplex massive multiple-input multiple-output system in which a base station (BS) serves multiple mobile users, but with rate-limited feedback from the users to the BS. A key observation is that the multiuser channel estimation and feedback problem can be thought of as a distributed source coding problem. In contrast to the traditional approach where the channel state information (CSI) is estimated and quantized at each user independently, this paper shows that a joint design of pilots and a new DNN architecture, which maps the received pilots directly into feedback bits at the user side then maps the feedback bits from all the users directly into the precoding matrix at the BS, can significantly improve the overall performance. This paper further proposes robust design strategies with respect to channel parameters and also a generalizable DNN architecture for varying number of users and number of feedback bits. Numerical results show that the DNN-based approach with short pilot sequences and very limited feedback overhead can already approach the performance of conventional linear precoding schemes with full CSI.

Downlink channel estimation of FDD based massive MIMO using spatial partial-common sparsity modeling

Downlink channel estimation in FDD massive MIMO systems is a challenge in 5G wireless communication systems. Using orthogonal pilots for downlink channel estimation leads to the pilot overhead problem. To cope with this problem, spatio-temporal common sparsity feature of delay domain beside the compressive sensing algorithm has used for channel estimation. In a practical affair, the spatial common sparsity of the adjacent antennas groups is not entirely separate. In this paper, we model the FDD massive MIMO downlink frequency selective channel estimation problem by a spatial partial-common sparsity, in which it is assumed that the spatial sparsity pattern of antennas in each group has a common part and an uncommon part. For the proposed model, we design a proper pilot sequence, and finally, we propose an estimation method associated with this model to solve the problem. Our proposed method has better NMSE and BER performance than reference methods in the same pilot overhead ratio, which is shown in the simulation results.

On Optimal Scheduling for Joint Spatial Division and Multiplexing Approach in FDD Massive MIMO

Massive MIMO is widely considered as a key enabler of the next generation 5G networks. With a large number of antennas at the Base Station, both spectral and energy efficiencies can be enhanced. Unfortunately, the downlink channel estimation overhead scales linearly with the number of antennas. This burden is easily mitigated in TDD systems by the use of the channel reciprocity property. However, this is unfeasible for FDD systems and the method of two-stage beamforming was therefore developed to reduce the amount of channel state information feedback. The performance of this scheme being highly dependent on the users grouping and scheduling mechanims, we introduce in this paper a new similarity measure coupled with a novel clustering procedure to achieve the appropriate users grouping. We also proceed to formulate the optimal users scheduling policy in JSDM and prove that it is NP-hard. This result is of paramount importance since it suggests that, unless P=NP, there are no polynomial time algorithms that solve the general scheduling problem to global optimality and the use of sub-optimal scheduling strategies is more realistic in practice. We therefore use graph theory to develop a sub-optimal users scheduling scheme that runs in polynomial time and outperforms the scheduling schemes previously introduced in the literature for JSDM in both sum-rate and throughput fairness.

Compressive Channel Estimation Based on Weighted IRLS in FDD Massive MIMO

In this letter a weighted iteratively reweighted least-square (IRLS) algorithm is proposed for FDD massive MIMO channel estimation. The priori support information is merged into the weighted IRLS to improve the recovery performance. The priori support information is obtained from the uplink channel by reciprocity in angle domain, and a support estimation algorithm is proposed from the analysis of basis mismatch and angle deviation between uplink and downlink which is more practical in the real scenario. A brief convergence analysis of weighted IRLS is given out. Simulations show that the proposed weighted IRLS outperforms the standard IRLS, subspace pursuit (SP) and weighted SP.

Downlink Training Overhead Reduction Technique for FDD Massive MIMO Systems

In this letter, a novel minimum mean square error (MSE) based channel estimation framework is proposed to reduce the downlink channel training overhead in frequency division duplexing massive multiple-input multiple-output systems, where the overhead reduction is achieved through training only a subset of antennas and by exploiting the spatial correlation between the antennas at the base station. Closed-form expressions of the analytical MSE and the asymptotic MSE of the system are obtained. Furthermore, a perfect match between theoretical and simulation results is observed, where the channel training overhead can be reduced by half with an acceptable performance.

Dictionary Learning-Based Sparse Channel Representation and Estimation for FDD Massive MIMO Systems

This paper addresses the problem of uplink and downlink channel estimation in FDD Massive MIMO systems. By utilizing sparse recovery and compressive sensing algorithms, we are able to improve the accuracy of the uplink/downlink channel estimation and reduce the number of uplink/downlink pilot symbols. Such successful channel estimation builds upon the assumption that the channel can be sparsely represented under some basis/dictionary. Previous works model the channel using some predefined basis/dictionary, while in this work, we present a dictionary learning based channel model such that a dictionary is learned from comprehensively collected channel measurements. The learned dictionary adapts specifically to the cell characteristics and promotes a more efficient and robust channel representation, which in turn improves the performance of the channel estimation. Furthermore, we extend the dictionary learning based channel model into a joint uplink/downlink learning framework by observing the reciprocity of the AOA/AOD between the uplink/downlink transmission, and propose a joint channel estimation algorithm that combines the uplink and downlink received training signals to obtain a more accurate channel estimate. In other words, the downlink training overhead, which is a bottleneck in FDD Massive MIMO system, can be reduced by utilizing the information from simpler uplink training.

Channel Estimation for TDD/FDD Massive MIMO Systems With Channel Covariance Computing

In this paper, we propose a new channel estimation scheme for TDD/FDD massive MIMO systems by reconstructing (sometimes also referred to as covariance computing or covariance fitting) uplink/downlink channel covariance matrices (CCMs) with the aid of array signal processing techniques. Specifically, the angle parameters and power angular spectrum (PAS) of channel are extracted from the instantaneous uplink channel state information (CSI). Then, the uplink CCM is reconstructed and can be used to improve the uplink channel estimation without any additional training cost. By virtue of angle reciprocity as well as PAS reciprocity between uplink and downlink channels, the downlink CCM could also be inferred with a similar approach even for the FDD massive MIMO systems. Then, the downlink instantaneous CSI can be obtained by training toward the dominant eigen-directions of each user. The proposed strategy is applicable to various PAS distributions. Numerical results are provided to demonstrate the superiority of the proposed methods over the existing ones.

Large System Analysis of Two-Stage Beamforming With Limited Feedback in FDD Massive MIMO Systems

Two-stage beamforming is a transmit strategy that uses two types of beamformers to reduce the feedback overhead of frequency-division-duplexing massive multiple-input multiple-output systems that are spatially correlated. In this paper, we present large system analysis of two-stage beamforming when a transmitter has limited channel information from feedback and when regularized-zero-forcing (RZF) is used as a second-stage beamformer. We consider two random-vector-quantization-based feedback schemes that can be respectively applied when users have perfect channel information or perfect effective channel information. For each feedback method, we analyze both expected signal-to-interference-plus-noise ratio (SINR) and expected rate loss and then characterize their bounds as a function of the number of feedback bits. From the characterization, we reveal that the sum rate of two-stage beamforming is very sensitive to the regularization parameter of RZF, especially when the number of feedback bits is limited. Motivated by this, we derive the optimal regularization parameter that maximizes the SINR of two-stage beamforming with limited feedback. Using simulations, we verify the tightness of the characterized bounds and quantify how the use of the optimal regularization parameter improves the sum rate of two-stage beamforming.