Channel Estimation for mmWave Massive MIMO With Convolutional Blind Denoising Network

In this paper, we develop the channel estimation algorithm for a massive multiple input multiple output (MIMO) system using one-bit analog-to-digital converters (ADCs). Although, one-bit quantization significantly reduces the deployment cost and power consumption of the massive MIMO, the great distortion induced by one-bit quantization makes channel estimation more difficult. Therefore, a channel estimation method by executing a deep neural network (DNN) over multiple signal segments is proposed for the uplink of one-bit massive MIMO. The average of the DNN’s outputs throughout all the segments is the final channel estimate for a transmission block. In order to improve the estimation accuracy without increasing the length of pilot, the data symbols got based on the initial channel estimates are used as the other part of pilots to refine the estimation result. Moreover, a sliding window based pilot segment method is adopted to increase the number of signal segments with a same pilot length. The simulation results show that the proposed scheme outperforms least squares (LS) and Bussgang linear minimum mean squared error (BLMMSE) channel estimators in the whole signal-to-noise-ratio (SNR) region.

With the large number of antennas and subcarriers the overhead due to pilot transmission for channel estimation can be prohibitive in wideband massive multiple-input multiple-output (MIMO) systems. This can degrade the overall spectral efficiency significantly, and as a result, curtail the potential benefits of massive MIMO. In this paper, we propose a neural network (NN)-based joint pilot design and downlink channel estimation scheme for frequency division duplex (FDD) MIMO orthogonal frequency division multiplex (OFDM) systems. The proposed NN architecture uses fully connected layers for frequency-aware pilot design, and outperforms linear minimum mean square error (LMMSE) estimation by exploiting inherent correlations in MIMO channel matrices utilizing convolutional NN layers. Our proposed NN architecture uses a non-local attention module to learn longer range correlations in the channel matrix to further improve the channel estimation performance.We also propose an effective pilot reduction technique by gradually pruning less significant neurons from the dense NN layers during training. This constitutes a novel application of NN pruning to reduce the pilot transmission overhead. Our pruning-based pilot reduction technique reduces the overhead by allocating pilots across subcarriers non-uniformly and exploiting the inter-frequency and inter-antenna correlations in the channel matrix efficiently through convolutional layers and attention module.

A novel asymmetrical massive multiple-input multiple-output (MIMO) system has recently emerged as a crucial solution for reducing hardware complexity and alleviating the data processing pressure. However, the absence of channel reciprocity in this system presents unique challenges when directly applying traditional channel estimation methods, inevitably leading to performance loss. Deep learning approaches hold promise for achieving improved channel estimation performance by implicitly learning channel features. Unfortunately, deep learning approaches are often designed empirically. It is critical to utilize prior knowledge to develop an efficient deep neural network (DNN), especially for wireless communication systems. This paper explores a knowledge-driven DNN design approach and introduces a deep learning-based channel estimation framework for asymmetrical transceivers. The channel estimation problem is decoupled into channel denoising and information inference problems. Two novel DNNs are proposed to eliminate noise and exploit correlative features for reconstructing the missing channel information, respectively. Extensive simulations demonstrate that our proposed channel estimation framework can significantly eliminate noise effects, even in low signal-to-noise ratio regimes, and outperform traditional estimators and other deep learning-based methods. Moreover, ablation studies also validate the effectiveness of our knowledge-driven network structure design approach.

Chapter 6 - Channel estimation for mmWave massive MIMO systems

Hybrid beamformer design plays very crucial role in the next generation millimeter-wave (mm-Wave) massive MIMO (multiple-input multiple-output) systems. Previous works assume the perfect channel state information (CSI) which results heavy feedback overhead. To lower complexity, channel statistics can be utilized such that only infrequent update of the channel information is needed. To reduce the complexity and provide robustness, in this work, we propose a deep learning (DL) framework to deal with both hybrid beamforming and channel estimation. For this purpose, we introduce three deep convolutional neural network (CNN) architectures. We assume that the base station (BS) has the channel statistics only and feeds the channel covariance matrix into a CNN to obtain the hybrid precoders. At the receiver, two CNNs are employed. The first one is used for channel estimation purposes and the another is employed to design the hybrid combiners. The proposed DL framework does not require the instantaneous feedback of the CSI at the BS. We have shown that the proposed approach has higher spectral efficiency with comparison to the conventional techniques. The trained CNN structures do not need to be re-trained due to the changes in the propagation environment such as the deviations in the number of received paths and the fluctuations in the received path angles up to 4 degrees. Also, the proposed DL framework exhibits at least 10 times lower computational complexity as compared to the conventional optimization-based approaches.

The huge pilot overhead required for channel estimation is one of the key issues for massive multiple-input multiple-output (MIMO) systems. Existing compressed sensing and deep learning methods generally implement pilot compression under the assumption of the huge number of antennas and strict channel sparsity, while the channel estimation performance decreases sharply under quasi-sparse channel environment. Motivated by the powerful learning ability of deep learning for extracting the major characteristics of the target, we propose approximate message passing (AMP) algorithm-based multi-stage training optimization architecture to solve the above problem, where the whole system is considered as a deep neural network (DNN). In the first stage, the optimized sensing matrix of the AMP algorithm is learned by training to match the quasi-sparse channel. In the second stage, we optimize the linear coefficients and nonlinear shrinkage parameters of AMP to further improve the performance. In the third stage, all parameters are jointly optimized by training to make the whole system optimal. Numerical simulation results show that the proposed architecture can achieve high precision channel estimation under the premise of reducing pilot overhead effectively.

Channel estimation and beamforming play critical roles in frequency-division duplexing (FDD) massive multiple-input multiple-output (MIMO) systems. However, these two modules have been treated as two stand-alone components, which makes it difficult to achieve a global system optimality. In this paper, we propose a deep learning-based approach that directly optimizes the beamformers at the base station according to the received uplink pilots, thereby, bypassing the explicit channel estimation. Different from the existing fully data-driven approach where all the modules are replaced by deep neural networks (DNNs), a neural calibration method is proposed to improve the scalability of the end-to-end design. In particular, the backbone of conventional time-efficient algorithms, i.e., the least-squares (LS) channel estimator and the zero-forcing (ZF) beamformer, is preserved and DNNs are leveraged to calibrate their inputs for better performance. The permutation equivariance property of the formulated resource allocation problem is then identified to design a low-complexity neural network architecture. Simulation results will show the superiority of the proposed neural calibration method over benchmark schemes in terms of both the spectral efficiency and scalability in large-scale wireless networks.

Massive multiple-input multiple-output (MIMO) technology for wireless communication is considered a key technology for the future fifth-generation (5G) communication networks. To reduce the propagation loss of channel, MIMO systems with analog or digital hybrid precoders and combiners (HPC) architecture have been used. This review paper presents the various types of analog and digital HPC designs for the massive MIMO communication systems that were investigated within the last decade. The reviewed systems are useful for both single-user (SU) and multi-user MIMO (MU-MIMO) systems. The key parameter of the study was spectral efficiency (SE), signal-to-noise ratio (SNR), signal-to-interference pulse noise ratio (SINR), system sum-rate (SR) performance, computational complexity (CC), co-channel interference (CCI), inter-primary base station interference (IPBSI), multiuser interference (MUI), effective desired channel gain (EDCG), and minimum mean square error (MMSE).

User-segregation based channel estimation in the MIMO system

Large-scale channel matrices in massive multiple-input multiple-output (MIMO) systems increase the difficulty of channel estimation. Conventional best linear unbiased estimator (BLUE) algorithms include multiple inverse operations for large-scale matrices; however this typically reduces algorithm efficiency. Efficiency can be improved by converting inverse operations into a system of linear equations, which are more easily solved for large matrices. This approach is used in the conjugate gradient (CG) method, which exhibits higher efficiency and precision when solving for approximate optimal solutions. As such, we propose a hybrid conjugate gradient (CG BLUE) algorithm, an improved version of the conventional BLUE technique. This algorithm reduces the dimensions of the channel model through a vectorization transform and uses the CG method to improve algorithm process efficiency during channel estimation for massive MIMO systems. Simulated results of NMSE and algorithm processing time show the proposed CG-BLUE algorithm resulted in nearly one order of magnitude higher calculation efficiency while maintaining the same level of accuracy as conventional BLUE.

This paper reports on investigations into the effects of spatial correlation on channel estimation and capacity of a multiple input multiple output (MIMO) system. Minimum mean square error (MMSE) method is applied for channel estimation under a correlated channel scenario. Simulation results for a 4 times 4 MIMO system with the Jakes model describing a channel between a base station and a mobile station demonstrate a trade-off between the effects of spatial correlation, channel estimation and capacity. For low values of signal to noise ratio (SNR), spatial correlation decreases channel estimation errors and improves capacity. For high values of SNR, spatial correlation has a less pronounced effect on improving channel estimation and thus the MIMO capacity is adversely affected by the decreased channel matrix rank.

In time division duplexing (TDD) millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems, downlink channel state information (CSI) can be obtained from uplink channel estimation thanks to channel reciprocity. However, under high-mobility scenarios, frequent uplink channel estimation is needed due to channel aging. Additionally, large amounts of antennas and subcarriers result in high-dimensional CSI matrices, aggravating pilot training overhead. To address this, we propose a three-domain (3D) channel extrapolation framework across spatial, frequency, and temporal domains. First, considering the effectiveness of traditional knowledge-driven channel estimation methods and the marginal effects of pilots in the spatial and frequency domains, a knowledge-and-data driven spatial-frequency channel extrapolation network (KDD-SFCEN) is proposed for uplink channel estimation via joint spatial-frequency channel extrapolation to reduce spatial-frequency domain pilot overhead. Then, leveraging channel reciprocity and temporal dependencies, we propose a temporal uplink-downlink channel extrapolation network (TUDCEN) powered by generative artificial intelligence for slot-level channel extrapolation, aiming to reduce the tremendous temporal domain pilot overhead caused by high mobility. Numerical results demonstrate the superiority of the proposed framework in significantly reducing the pilot training overhead by 16 times and improving the system’s spectral efficiency under high-mobility scenarios compared with state-of-the-art channel estimation/extrapolation methods.

Channel estimation is very challenging for millimeter wave (mmWave) massive multiple input multiple output (MIMO) systems with low-resolution analog-to-digital converters (ADCs) owing to the severe nonlinear distortion introduced by quantization. In this paper, we develop an advanced channel estimation method based on generalized expectation consistent signal recovery (GEC-SR) algorithm, which can obtain accurate channel state information from quantized signal. Specifically, we consider Laplacian prior to model angular domain mmWave channel coefficients and embed the expectation-maximization (EM) principle into GEC-SR algorithm to learn the unknown prior parameters. Numerical results show that our method outperforms state-of-the-art generalized-approximate-message-passing-based channel estimator, and can reduce the required pilot overhead significantly by using orthogonal pilot. © 2019 IEEE.

Hardware problems are the most detrimental issues to channel estimates in wireless communication systems. Because of the enormous number of antennas at the base station (BS) in cellular massive multiple-input multiple-output (MIMO) systems and because one radio frequency (RF) chain per antenna is required, hardware impairments in such systems will be quite severe. Many research publications have used a quality-cost tradeoff to adjust for RF unit hardware issues. In this study, we have taken a different approach by reducing the error floor caused by impairments in the predicted channels. Here are two steps to remedy the problem. In phase 1, a single active user channel in a single cell was calculated statistically rather than parametrically. In phase 2, a convex optimization approach was used to regularize the estimated channel in phase 1 to reduce error and provide a robust channel estimate. The results of our proposed procedure are measured by the normalized minimum mean squared error (NMSE) versus a range from the effective signal-to-noise ratio, and it shows a significant reduction (nearly one order of magnitude) in the error floor as compared with the conventional one, especially at high signal-to-noise ratio (SNR) in the range of (20 dB-30 dB). Simulation results were extracted in MATLAB R2020a.

Massive multiple-input multiple-output (MIMO) systems with 1-bit analog-to-digital converters (ADCs) are promising to reduce the energy consumption. However, the serious quantization error caused by 1-bit ADCs will potentially limit the feasibility of high order modulations. This paper focuses on the analysis of the high order phase-shift keying (PSK) signal transmission in the 1-bit ADC massive MIMO system. Firstly, assuming ideal channel estimation and a single mobile station (MS), we theoretically prove that with an asymptotically large number of antennas at the base station, PSK signals with arbitrary modulation order can be recovered in the 1-bit ADC massive MIMO system. Secondly, we analyze the impact of pilot based channel estimation on the recovery of the high order PSK signals, which leads to a periodic asymptotic detection phase error (ADPE) at high signal to noise ratio (SNR). Furthermore, we also propose to optimize the pilot sequence for minimizing the cumulative absolute ADPE. Finally, the analysis is extended to the multi-MS case and the performance with different pilot patterns is discussed. Simulation results validate our analysis and show that using our proposed optimized pilot sequence can significantly improve the detection performance for both single-MS and multi-MS 1-bit ADC massive MIMO systems.