Vector Quantization for Deep-Learning-Based CSI Feedback in Massive MIMO Systems

Aiming at the problem of high complexity and low feedback accuracy of existing channel state information (CSI) feedback algorithms for frequency-division duplexing (FDD) massive multiple-input multiple-output (MIMO) systems, this paper proposes a CSI compression feedback algorithm based on deep learning (DL), which is suitable for single-user and multi-user scenarios in massive MIMO systems. This algorithm considers the spatial correlation of massive MIMO channel and uses bidirectional long short-term memory (Bi-LSTM) and bidirectional convolutional long short-term memory (Bi-ConvLSTM) network to decompress and recover the CSI for single-user and multi-user, respectively. The proposed DL-based CSI feedback network is trained offline by massive MIMO channel data and could learn the structural characteristics of the massive MIMO channel by fully exploiting the channel information in the training samples. The simulation results show that compared with several classical CSI compression feedback algorithms, the proposed CSI compression feedback algorithm has lower computational complexity, higher feedback accuracy, and better system performance in massive MIMO systems.

Massive multiple-input multiple-output (MIMO) systems are a main enabler of the excessive throughput requirements in 5G and future generation wireless networks as they can serve many users simultaneously with high spectral and energy efficiency. To achieve this massive MIMO systems require accurate and timely channel state information (CSI), which is acquired by a training process that involves pilot transmission, CSI estimation, and feedback. This training process incurs a training overhead, which scales with the number of antennas, users, and subcarriers. Reducing the training overhead in massive MIMO systems has been a major topic of research since the emergence of the concept. Recently, deep learning (DL)-based approaches have been proposed and shown to provide significant reduction in the CSI acquisition and feedback overhead in massive MIMO systems compared to traditional techniques. In this paper, we present an overview of the state-of-the-art DL architectures and algorithms used for CSI acquisition and feedback, and provide further research directions.

Deep learning (DL)-based channel state information (CSI) feedback improves the capacity and energy efficiency of massive multiple-input multiple-output (MIMO) systems in frequency division duplexing mode. However, multiple neural networks with different lengths of feedback overhead are required by time-varying bandwidth resources. The storage space required at the user equipment (UE) and the base station (BS) for these models increases linearly with the number of models. In this paper, we propose a DL-based changeable-rate framework with novel quantization scheme to improve the efficiency and feasibility of CSI feedback systems. This framework can reutilize all the network layers to achieve overhead-changeable CSI feedback to optimize the storage efficiency at the UE and the BS sides. Designed quantizer in this framework can avoid the normalization and gradient problems faced by traditional quantization schemes. Specifically, we propose two DL-based changeable-rate CSI feedback networks CH- CsiNetPro and CH- DualNetSph by introducing a feedback overhead control unit. Then, a pluggable quantization block (PQB) is developed to further improve the encoding efficiency of CSI feedback in an end-to-end way. Compared with existing CSI feedback methods, the proposed framework saves the storage space by about 50% with changeable-rate scheme and improves the encoding efficiency with the quantization module.

Large language models (LLMs) have revolutionized natural language processing by learning rich representations from massive and diverse text data. While pre-trained LLMs have been widely customized for a variety of text-related tasks, their potential in wireless communications remains largely untapped. In this paper, we propose a novel channel state information (CSI) feedback framework for massive multiple-input multiple-output (MIMO) systems that leverages pre-trained LLMs to bridge the gap between natural language processing and wireless communication. To adapt LLMs for the CSI feedback task, we design specialized pre-processing, embedding, and post-processing modules that convert CSI data into token representations compatible with LLMs. Moreover, to address the limitations of a single model and enhance performance in diverse environments and under various compression ratios, we introduce a mixture-of-agents (MoA)based framework that integrates the complementary strengths of multiple LLMs. Simulation results demonstrate that our approach achieves superior CSI reconstruction performance, robust generalization to unseen scenarios, and significant training cost reduction even with limited data. These findings confirm that the transferable knowledge acquired from large-scale natural language pre-training can effectively enhance CSI feedback, offering a promising direction for intelligent and efficient nextgeneration wireless communication systems.

In this paper, we propose a cross-attention and self-attention Transformer-based network (CASA-TransNet) for channel state information (CSI) feedback in dual-polarized massive multiple-input multiple-output (MIMO) systems. In dualpolarized massive MIMO systems, the channels in the horizontal and vertical polarization directions have a high correlation, which can be exploited for joint compression and reconstruction of the dual-polarized channels to improve the CSI feedback performance. The proposed CASA-TransNet employs a twostream cross-attention Transformer architecture and extracts the correlation between horizontal and vertical polarization CSI via cross-stream exchange of the query embeddings. Furthermore, a self-attention Transformer is utilized to model long-term dependencies of the dual-polarized CSI. Simulation results show that the proposed CASA-TransNet outperforms other deep learningbased methods, achieving better CSI reconstruction performance even at high compression ratios. Compared to state-of-the-art schemes, CASA-TransNet achieves a performance gain of $3.47 \sim 5.74 \mathrm{~dB}$.

Accurate downlink channel state information (CSI) is required to be fed back to the base station (BS) in frequency division duplexing (FDD) massive multiple-input multiple-output (MIMO) systems in order to achieve maximum antenna diversity and multiplexing. However, downlink CSI feedback overhead scales with the number of transceiver antennas, a major hurdle for practical deployment of FDD massive MIMO systems. To solve this problem, we propose a compressive sampled CSI feedback method based on deep learning (SampleDL). In SampleDL, the massive MIMO channel matrix is sampled uniformly in time/frequency dimension before being fed into neural networks (NNs), which will reduce the computational resource/time at user equipment (UE) as well as enhance the CSI recovery accuracy at the BS. Both theoretical analysis and normalized mean square errors (NMSE) results confirm the advantages of the proposed method in terms of time complexity and recovery accuracy. Besides, a suitable CSI feedback period is explored by link level simulations, which aims to further reduce the overhead of CSI feedback without degrading the communication quality.

For massive multiple-input multiple-output (MIMO) systems, downlink channel state information (CSI) feedback is critical for exploiting the performance potentials. Recognized by the 3rd Generation Partnership Project as a key use case for the artificial intelligence-native air interface, deep learning (DL)-based CSI feedback has attracted extensive research from academia and industry. However, one of the most significant obstacles to its practical deployment is the limited generalization capabilities of DL models. In this article, we first illustrate the generalization challenge faced by DL-based CSI feedback with the main factors. Then, we systematically analyze its feasible solutions from two perspectives: initial model acquisition and efficient online updating. Finally, to address knowledge-forgetting problems in online updating, a novel alternating optimization framework is proposed to further improve the generalization ability through knowledge review. Hopefully, this article can give inspiring insights for the optimization of deployment and generalization for DL-based CSI feedback systems.

In a massive multiple-input multiple-output (MIMO) system, channel state information (CSI) is essential for the base station (BS) to achieve high performance gain. The user equipment (UE) needs to estimate CSI and then feeds it back to the BS in the frequency division duplexing (FDD) mode. Effective compression of CSI will significantly reduce the cost of channel feedback, and many deep learning (DL) based channel compression schemes have been proposed to achieve this goal. In this paper, rather than viewing CSI as images as in most existing works, we propose a new perspective of viewing CSI as an information sequence and analogize CSI feedback to a machine translation task. Further, we propose a novel sequence to sequence (Seq2Seq) model for CSI feedback composed of only recurrent neural networks and a small-scale fully connected layer, avoiding the convolution and pooling structure commonly used in current DL-based works. The advantage of this scheme is that it fully integrates the physical characteristics of the MIMO channel in the spatial domain into the structure of the neural network and avoids the loss of some prominent unsmooth or discontinuous features caused by the inappropriate convolution and pooling operation. Simulation results show that the proposed Seq2Seq model outperforms other DL-based CSI compression techniques under various communication scenarios.

Channel state information (CSI) feedback is critical for achieving the promised advantages of enhancing spectral and energy efficiencies in massive multiple-input multiple-output (MIMO) wireless communication systems. Deep learning (DL)-based methods have been proven effective in reducing the required signaling overhead for CSI feedback. In practical dual-polarized MIMO scenarios, channels in the vertical and horizontal polarization directions tend to exhibit high polarization correlation. To fully exploit the inherent propagation similarity within dual-polarized channels, we propose a disentangled representation neural network (NN) for CSI feedback, referred to as DiReNet. The proposed DiReNet disentangles dual-polarized CSI into three components: polarization-shared information, vertical polarization-specific information, and horizontal polarization-specific information. This disentanglement of dual-polarized CSI enables the minimization of information redundancy caused by the polarization correlation and improves the performance of CSI compression and recovery. Additionally, flexible quantization and network extension schemes are designed. Consequently, our method provides a pragmatic solution for CSI feedback to harness the physical MIMO polarization as a priori information. Our experimental results show that the performance of our proposed DiReNet surpasses that of existing DL-based networks, while also effectively reducing the number of network parameters by nearly one third.

Unlike the time-division duplexing (TDD) systems, the downlink (DL) and uplink (UL) channels are not reciprocal anymore in the case of frequency-division duplexing (FDD). However, some long-term parameters, e.g. the time delays and angles of arrival (AoAs) of the channel paths, still enjoy reciprocity. In this paper, by efficiently exploiting the aforementioned limited reciprocity, we address the DL channel state information (CSI) feedback in a practical wideband massive multiple-input multiple-output (MIMO) system operating in the FDD mode. In particular, the base station (BS) can transmit the FFT-based pilots with the carefully-selected phase shifts to align the DL paths. Then the user can rely on the so-called time-domain aggregate channel (TAC) to derive the estimate of the DL CSI. Next, with the knowledge about the second-order statistics of the DL channels, the user is also able to compute feedback of reduced dimensionality. We demonstrate that each user can just feed back one scalar number per DL channel path for the BS to recover the DL CSIs. Comprehensive numerical results corroborate our designs.

Massive MIMO is a promising technique to provide high data rate with good energy efficiency for the future wireless cellular communication. However, its performance benefit often can be realized only when accurate channel state information (CSI) is available at the transmitter to perform accurate beamforming. With large number of antennas, full CSI consumes too much overhead to feed back without compression. To reduce CSI feedback overhead, CSI feedback scheme with dual stage precoding structure is designed to quantize the long term spatial channel correlation information and short term linear precoder information. In this paper, we discuss how to optimize this dual stage precoding scheme in the typical dual-polarized massive MIMO system. The eigenvalues of spatial correlation matrix are used to improve feedback efficiency. By relaxing the constant modulus constraint in codebook design, more flexible long term precoding can be used and adapt to the channel. A specific structure of long term precoding matrix for dual-polarized MIMO system is proposed to ensure the orthogonality of the final precoder for multi-layer transmission.

Accurate channel state information (CSI) at base station (BS) is the key to achieve full multiplexing and diversity gain in traditional multiple-input multiple-output (MIMO) systems. In frequency-division-duplex (FDD) systems, it is obtained through downlink training and uplink feedback. However, the training and feedback overhead in massive MIMO systems is unacceptable for the large number of antennas equipped at BS. To reduce the CSI feedback overhead and improve CSI quantization accuracy, we propose a limited feedback scheme for spatio-temporal correlated massive MIMO channel. The proposed scheme jointly performs Karhunen-Loève transform (KLT) and polar-cap quantization on CSI. For the compactly deployed antennas at BS, there exists spatial correlation in massive MIMO channel. When the user equipment (UE) moves slowly, adjacent channels feature temporal correlation. The high dimensional and spatial correlated CSI is compressed through KLT. Then the compressed CSI is normalized to be isotropic to perform polar-cap quantization. Simulation results show that the proposed scheme is capable of improving the sum-rate performance with limited feedback bits for massive MIMO systems.

In frequency division duplex model, the massive multiple-input multiple-output (MIMO) systems rely on feedback of channel state information (CSI) to perform precoding operations. This can increase the potential transmission gain of the system. The use of large scale antennas increases the feedback overhead of CSI exponentially. Therefore, CSI must be compressed for feedback. However, convolution based feedback methods lack long-range dependency modeling of the CSI, resulting in limited effects at high compression ratios. In this letter, we propose a novel neural network based on the convolutional transformer architecture to improve the performance of CSI compression and reconstruction at high compression rates. The experimental results show that the average accuracy of ours is improved by 5.39% over the state-of-the-art method at a high compression rate of 1/64. At the same time, the overall performance of the system has been improved.

In frequency-division duplexing (FDD) massive multiple-input multiple-output (MIMO) systems, 1-bit compressed sensing (CS)-based superimposed channel state information (CSI) feedback has shown many advantages, while still faces many challenges, such as low accuracy of the downlink CSI recovery and large processing delays. To overcome these drawbacks, this paper proposes a deep learning (DL) scheme to improve the 1-bit compressed sensing-based superimposed CSI feedback. On the user side, the downlink CSI is compressed with the 1-bit CS technique, superimposed on the uplink user data sequences (UL-US), and then sent back to the base station (BS). At the BS, based on the model-driven approach and assisted by the superimposition-interference cancellation technology, a multi-task detection network is first constructed for detecting both the UL-US and downlink CSI. In particular, this detection network is jointly trained to detect the UL-US and downlink CSI simultaneously, capturing a globally optimized network parameter. Then, with the recovered bits for the downlink CSI, a lightweight reconstruction scheme, which consists of an initial feature extraction of the downlink CSI with the simplified traditional method and a single hidden layer network, is utilized to reconstruct the downlink CSI with low processing delay. Compared with the 1-bit CS-based superimposed CSI feedback scheme, the proposed scheme improves the recovery accuracy of the UL-US and downlink CSI with lower processing delay and possesses robustness against parameter variations.

To enhance the performance of a massive multiple-input multiple-output (MIMO) system, the downlink channel state information (CSI) should be compressed and fed back to the base station (BS) effectively in a frequency division duplex (FDD) mode. In contrast to traditional compression methods that rely on the particular prior assumptions, deep learning (DL) based CSI feedback has the potential to learn informatively from the hidden complex models behind the data. However, most of the current DL based methods stay in the early stage that uses DL modules directly from image processing, while the distinctive channel semantic information has been largely ignored. In this letter, considering the spatial-temporal correlation property of CSI matrices, we propose an architecture based on criss-cross attention, called CCA-Net, which extracts the channel features more precisely by leveraging the contextual information along the delay and angle domain. Meanwhile, a real and imaginary part combination module is used to assist in extracting the internal features of CSI. In addition, to reap the computational resources at BSs, a scalable decoder is designed to extend the reconstruction abilities. Experiments demonstrate that our network achieves better normalized mean square error with lower flops than existing state-of-the-art algorithms.