Deep Learning for Massive MIMO Channel State Acquisition and Feedback

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.

This letter presents a finite-rate deep-learning (DL)-based channel state information (CSI) feedback method for massive multiple-input multiple-output (MIMO) systems. The presented method provides a finite-bit representation of the latent vector based on a vector-quantized variational autoencoder (VQ-VAE) framework while reducing its computational complexity based on shape-gain vector quantization. In this method, the magnitude of the latent vector is quantized using a non-uniform scalar codebook with a proper transformation function, while the direction of the latent vector is quantized using a trainable Grassmannian codebook. A multi-rate codebook design strategy is also developed by introducing a codeword selection rule for a nested codebook along with the design of a loss function. Simulation results demonstrate that the proposed method reduces the computational complexity of VQ-VAE while improving CSI reconstruction performance under a given feedback overhead.

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.

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.

As a combination of spatial modulation (SM) system and massive multiple-input multiple-output (MIMO) system, massive SM aided MIMO (SM-MIMO) system is recently proposed. In broadband scenarios, single-carrier (SC) modulation is introduced to massive SM-MIMO system, thus massive SC-SM MIMO system is proposed for uplink multi-user transmission over frequency-selective fading channels. In this study, the uplink spectral efficiency (SE) of multi-cell massive SC-SM MIMO system is analysed, meanwhile the pilot contamination effect is taken into consideration. A tight SE lower bound of multi-cell massive SC-SM MIMO system is proposed with maximum ratio (MR) combining, which also takes into account the imperfect channel estimation, transmit antenna correlation and path loss. The tightness of the authors' proposed closed-form SE lower bound is shown via simulation results. The optimal pilot reuse factor can be determined with different system configurations by simulations, and the pilot reuse factor that is larger than one is more suitable for less TAs and user equipments.

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.

In order to unlock the full advantages of massive multiple input multiple output (MIMO) in the downlink, channel state information (CSI) is required at the base station (BS) to optimize the beamforming matrices. In frequency division duplex (FDD) systems, full channel reciprocity does not hold, and CSI acquisition generally requires downlink pilot transmission followed by uplink feedback. Prior work proposed the end-to-end design of pilot transmission, feedback, and CSI estimation via deep learning. In this work, we introduce an enhanced end-to-end design that leverages partial uplink-downlink reciprocity and temporal correlation of the fading processes by utilizing jointly downlink and uplink pilots. The proposed method is based on a novel deep learning architecture – HyperRNN – that combines hypernetworks and recurrent neural networks (RNNs) to optimize the transfer of long-term channel features from uplink to downlink. Simulation results demonstrate that the HyperRNN achieves a lower normalized mean square error (NMSE) performance, and that it reduces requirements in terms of pilot lengths.

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 this paper, we investigate the suitability of single carrier frequency domain processing (SC-FDP) as the downlink transmission scheme in a massive multiple-input multiple-output (MIMO) system. By deriving the sum-rate of the SC-FDP massive MIMO system theoretically, we show that this method obtains a sum-rate similar to that of orthogonal frequency division multiplexing (OFDM) massive MIMO. We also derive the theoretical sum-rate of both SC-FDP and OFDM in a non-synchronized massive MIMO scenario and show that the rate of the former is significantly larger than that of the latter. Moreover, we theoretically analyze the sum-rate of both systems in the presence of power amplifier non-linearity. All the sum-rates are derived for both zero forcing and matched filter precoding schemes. The results show that the effect of power amplifier non-linearity on the sum-rate of both systems is similar when the number of users is large. We also compare SC-FDP with OFDM from the peak to average power ratio (PAPR) and complexity viewpoints. Although the PAPR of SC-FDP signals is lower than that of OFDM signals, for MIMO systems, the difference between their PAPR decreases as we increase the number of users. Thus, both techniques can have similar PAPR in massive MIMO systems. The overall complexity of SC-FDP and OFDM is similar. Due to the mentioned facts, SC-FDP can be considered as a promising transmission scheme for the downlink of the massive MIMO systems in the presence of carrier frequency offset and power amplifier non-linearities.

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 $3.47 \sim 5.74 \mathrm{~dB}$.

In this paper, we establish a general framework on the reduced dimensional channel state information (CSI) estimation and pre-beamformer design for frequency-selective massive multiple-input multiple-output (MIMO) systems employing single- carrier (SC) modulation in time division duplex (TDD) mode by exploiting the joint angle-delay domain channel sparsity in millimeter (mm) wave frequencies. First, based on a generic subspace projection taking the joint angle-delay power profile and user-grouping into account, the reduced-rank minimum mean square error (RR-MMSE) instantaneous CSI estimator is derived for spatially correlated wideband MIMO channels. Second, the statistical pre-beamformer design is considered for frequency-selective SC massive MIMO channels. We examine the dimension reduction problem and subspace (beamspace) construction on which the RR-MMSE estimation can be realized as accurately as possible. It is observed that the proposed techniques show remarkable robustness to the pilot interference (or contamination) with a significant reduction in pilot overhead.

Chapter 7 - Channel feedback for mmWave massive MIMO

This work focuses on the secure beamforming problem in massive multiple input multiple output (MIMO) system. The optimization problem is modeled by the theory of reinforcement learning (RL). With asymptotic behavior of massive MIMO, detailed theoretical analysis of the proposed RL problem is presented. By policy gradient method we provide solution for the delay-aware large-scale RL problem. The proposed RL structure can dynamically optimize the system performance by observing the state of cache and acquiring feedback from the delay of packet without requiring channel estimation, which can avoid the imperfect channel state information (CSI) issue in massive MIMO system. We conduct numerical experiments by using asynchronous advantage actor critic (A3C) algorithm to solve the proposed RL problem with comparisons to the randomized policy in a time-variant wireless environment. It shows that by using the RL algorithm the delay of system can be reduced without using CSI.

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.

Massive multiple-input multiple-output (MIMO) systems have been drawing considerable interest. In the uplink, massive MIMO systems are commonly studied assuming that each base station (BS) decodes the signals of its user terminals separately and linearly while treating all interference as noise. Although this approach provides improved spectral efficiency (SE) in favorable channel conditions, it is generally sub-optimal from an information-theoretic perspective. In this work we characterize the SE of massive MIMO when the BSs are allowed to jointly decode the received signals. We consider two schemes for handling the interference, and derive their SEs for both finite and asymptotic number of antennas. Simulation tests of the proposed methods illustrate their gains in SE compared to standard separate linear decoding, and show that the standard approach fails to capture the actual achievable rates of massive MIMO systems, particularly when the interference is dominant.