Beamspace Channel Estimation Research Articles

Millimeter wave–3D massive MIMO: Deep prior‐aided graph neural network combining with hierarchical residual learning for beamspace channel estimation

SummaryMillimeter Wave (mmWave) communication has emerged as a transformative technology at the forefront of wireless communication. One of the key challenges in harnessing the potential of mmWave technology is overcoming the increased susceptibility to propagation losses and environmental obstacles. To address these challenges, Three‐Dimensional Massive Multiple‐Input Multiple‐Output (3D Massive MIMO) systems have gained traction. The 3D aspect extends this concept by considering the elevation dimension, allowing for enhanced spatial resolution and coverage. Accurate estimation of the channel in 3D Massive MIMO scenarios is particularly challenging because of the complex propagation characteristics of mmWave signals. This paper introduces an efficient‐Aided Graph Neural Network Combining with Hierarchical Residual Learning (DPrGNN‐HrResNetL), designed specifically for beamspace Channel Estimation (CE)in mmWave‐Massive MIMO environments. The proposed model leverages deep priors and GNN mechanisms to enhance the extraction of spatial features, while hierarchical residual connections facilitate effective information flow through the network. DPrGNN enables the model to capture and understand complex spatial relationships among different antenna elements. The incorporation of deep priors provides a mechanism for leveraging prior knowledge about channel characteristics. This enhances the efficiency of the learning process, allowing the model to learn and adapt more effectively. The integration of hierarchical residual connections facilitates effective information flow through the network. This is particularly important for modeling complex dependencies within the beamspace channel data, enhancing the learning capacity of the network. The performance of the DPrGNN‐HrResNetL model is evaluated across a range of Signal‐to‐Noise Ratios (SNRs), utilizing metrics such as Normalized Mean Squared Error (NMSE) to measure the accuracy of the estimation. The outcomes underscore the resilience and efficacy of the DPrGNN‐HrResNetL approach in achieving precise CE within demanding mmWave scenarios.

Simplified Learned Approximate Message Passing Network for Beamspace Channel Estimation in mmWave Massive MIMO Systems

Simplified Learned Approximate Message Passing Network for Beamspace Channel Estimation in mmWave Massive MIMO Systems

A Survey on Beamspace Millimeter-wave Massive Mimo Systems: An Overview of Open Issues, Challenges, and Future Research Trends

Abstract: The channel sparsity is exploited by transforming the channel into an angular domain from the spatial domain at millimeter wave frequencies in Beamspace Multiple-Input Multiple-Output (B-MIMO) systems. Every beam in B-MIMO corresponds to an individual radio frequency (RF) chain, and thus, beam selection techniques can reduce the RF hardware complexity. RF chain limitation is needed for an ideal beamspace precoding scheme to attain good system performance across the entire bandwidth. New methods of beamspace channel estimation with a small amount of estimation error and low computational complexity are challenging in the beam domain due to the larger antenna arrays deployed. A novel beamspace processing technique to improve the direction of arrival estimation performance for different array configurations with improvement in system performance is desired in a 5G system. A detailed review of the B-MIMO system with its architecture and various beam selection techniques is presented in this paper. The scope of the work is elaborated by incorporating various existing beamspace precoding and channel estimation methods. The paper also presents various beamspace processing schemes for parameter estimation with a focus on the direction of arrival estimation performance.

A Beamspace Channel Estimation based on Deep Convolutional Reconstruction Networks

A Beamspace Channel Estimation based on Deep Convolutional Reconstruction Networks

Channel Estimation for mmWave Massive MIMO Systems With Mixed-ADC Architecture

Millimeter wave (mmWave) communications are widely preferred due to the rich bandwidth and potentially huge spectrum resources. Nowadays, mixed-ADC architecture combined with mmWave massive MIMO has become a communication mainstream, which can effectively solve the issue of high total power consumption and cost of base station (BS) circuits. However, the channel estimation problem for mmWave massive MIMO systems with mixed-ADC architecture has not been studied yet. In this paper, we develop the sparse channel estimation method on this framework. Specifically, by exploiting the sparsity of mmWave channels, the beamspace channel estimation problem can be transformed into a sparse matrix recovery problem, the channel parameters are recovered using compressive sensing (CS) techniques. Simulation results show that the algorithms quantized by the mixed-ADC outperforms the low-resolution ADC, and the best performance can be achieved when the low-resolution ADC in the mixed-ADC architecture reaches five-bit.

An enhanced beamspace channel estimation algorithm for wideband millimeter-wave massive MIMO systems

Accurate beamspace channel estimation is critical in wideband millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) communication systems. However, the beam squint effect caused by the increase in bandwidth and array dimension can bring additional challenges to the wideband channel estimation. In this study, we propose a wideband channel estimation scheme based on compressed sensing to solve the beam squint effect in broadband mmWave massive MIMO systems. First, the channel estimation problem is transformed into a beamspace direction estimation problem by exploiting the special frequency-dependent sparse structure of a broadband beamspace channel. Then, we propose a beam-band function-based orthogonal matching pursuit algorithm, in which a beam-band function is constructed and used to capture the power of each path component to estimate the spatial direction. In addition, the support of each path component at different sub-carriers is estimated to reduce the influence of the beam squint effect. Moreover, the support is estimated adaptively to improve the estimation accuracy further. Simulation results demonstrate that the proposed scheme reduces the pilot overhead under the beam squint effect and improve the estimation accuracy significantly.

Deep Learning-Based Channel Estimation for mmWave Massive MIMO Systems in Mixed-ADC Architecture.

Millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) systems can significantly reduce the number of radio frequency (RF) chains by using lens antenna arrays, because it is usually the case that the number of RF chains is often much smaller than the number of antennas, so channel estimation becomes very challenging in practical wireless communication. In this paper, we investigated channel estimation for mmWave massive MIMO system with lens antenna array, in which we use a mixed (low/high) resolution analog-to-digital converter (ADC) architecture to trade-off the power consumption and performance of the system. Specifically, most antennas are equipped with low-resolution ADC and the rest of the antennas use high-resolution ADC. By utilizing the sparsity of the mmWave channel, the beamspace channel estimation can be expressed as a sparse signal recovery problem, and the channel can be recovered by the algorithm based on compressed sensing. We compare the traditional channel estimation scheme with the deep learning channel-estimation scheme, which has a better advantage, such as that the estimation scheme based on deep neural network is significantly better than the traditional channel-estimation algorithm.

Beamspace channel estimation in wideband lens antenna array-based mmWave mMIMO-OFDM systems under beam squint

Sparse Bayesian learning (SBL) and particularly relevant vector machines (RVMs) have drawn much attention to improving the performance of existing machine learning models. The methodology depends on a parameterized prior that enforces models with weight sparsity, where only a few are non-zeros. Wideband mmWave massive multiple-input multiple-output (mMIMO) systems with lens antenna array (LAA), expect to play a key role in future fifth-generation (5G) wireless systems. To provide the beamforming gain required to overcome path loss, we consider a lens antenna array (LAA)-based beamspace mMIMO system. However, the spatial-wideband influence causes the beam squint effect to emerge, making the beamspace channel path components exhibit a unique frequency-dependent sparse structure, and thus nullifies the frequency domain common support assumption. In this paper, we first propose a channel estimation (CE) algorithm, namely a reduced-antenna selection progressive support-detection (RAS-PSD), for the wideband mmWave mMIMO-OFDM systems with LAA, which considers the beam squint effect. Secondly, by exploring Bayesian learning (BL), a Gaussian Process hyperparameter optimization-based CE (GP-HOCE) algorithm is proposed for the considered system, where both its own hyperparameter and the hyperparameters of its adjacent neighbors governs the sparsity of each coefficient. The simulation results show that the wideband beamspace channel coefficients can be estimated more efficiently than those of the existing state-of-the-art algorithms in terms of normalized mean square error (NMSE) of CE for wideband mmWave mMIMO-OFDM systems.

Nonconvex Regularized Gradient Projection Sparse Reconstruction for Massive MIMO Channel Estimation

Novel sparse reconstruction algorithms are proposed for beamspace channel estimation in massive multiple-input multiple-output systems. The proposed algorithms minimize a least-squares objective having a nonconvex regularizer. This regularizer removes the penalties on a few large-magnitude elements from the conventional <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell _{1}$ </tex-math></inline-formula> -norm regularizer, and thus it only forces penalties on the remaining elements that are expected to be zeros. Accurate and fast reconstructions can be achieved by performing gradient projection updates within the framework of difference of convex functions (DC) programming. A double-loop algorithm and a single-loop algorithm are proposed via different DC decompositions, and these two algorithms have distinct computational complexities and convergence rates. An extension algorithm is further proposed by designing new step sizes for the single-loop algorithm. The extension algorithm has a faster convergence rate and can achieve approximately the same level of accuracy as the proposed double-loop algorithm. Numerical results show significant advantages of the proposed algorithms over existing reconstruction algorithms in terms of reconstruction accuracies and runtimes. Compared with the benchmark channel estimation approaches, the proposed algorithms can achieve smaller channel reconstruction error and higher achievable spectral efficiency.

3D Metallic Plate Lens Antenna based Beamspace Channel Estimation Technique for 5G Mmwave Massive MIMO Systems

Beamspace channel estimation mechanism for massive MIMO (multiple input multiple output) antenna system presents a major process to compensate the 5G spectrum challenges caused by the proliferation of information from mobile devices. However, this estimation is required to ensure the perfect channel state information (CSI) for lower amount of Radio Frequency (RF) chains for each beam. In addition, phase shifter (PS) components used in this estimation need high power to select the beam in the desired direction. To overcome these limitations, in this work, we propose Regular Scanning Support Detection (RSSD) based channel estimation mechanism. Moreover, we utilise a 3D lens antenna array having metallic plate and a switch in our model which compensates the limitation of phase shifters. Simulation results show that the proposed RSSD based channel estimation surpasses traditional technique and SD based channel estimation even in lower SNR area which is highly desirable in the millimeter wave (mmWave) massive MIMO systems.

3D Metallic Plate Lens Antenna based Beamspace Channel Estimation Technique for 5G Mmwave Massive MIMO Systems

3D Metallic Plate Lens Antenna based Beamspace Channel Estimation Technique for 5G Mmwave Massive MIMO Systems

Beamspace Channel Estimation With Beam Squint Effect for the Millimeter-Wave MIMO-OFDM Systems

In this paper, we investigate two novel beamspace channel estimation schemes for millimeter-wave MIMO-OFDM systems relying on a uniform linear antenna array. Based on the sparse nature of the beamspace channel, compressive sensing-based methods can be adopted. Most of the existing wideband beamspace channel estimation schemes take the common support assumption that the support of all sub-carriers from a single path component keeps unchanged. However, due to the beam squint effect caused by time delays among different antennas, this assumption is no longer satisfied. Based on the above, we analyze the frequency-dependent sparse structure of the beamspace channel due to beam squint and propose the block simultaneous orthogonal matching pursuit algorithm where support is jointly estimated by using beamspace windows. Moreover, considering the power focusing effect of beam squint, we propose the two-stage beamspace channel estimation scheme, where the first stage is for the angle of arrival estimation, and the second stage is for updating path gain to reconstruct the beamspace channel. Simulation results demonstrate that proposed schemes can estimate the channel under the beam squint effect with high accuracy but low pilot overheads.

Deep Learning for Beamspace Channel Estimation in Millimeter-Wave Massive MIMO Systems

Millimeter-wave massive multiple-input multiple-output (MIMO) can use a lens antenna array to considerably reduce the number of radio frequency (RF) chains, but channel estimation is challenging due to the number of RF chains is much smaller than that of antennas. By exploiting the sparsity of beamspace channels, the beamspace channel estimation can be formulated as a sparse signal recovery problem, which can be solved by the classical iterative algorithm named approximate message passing (AMP), and its corresponding version learned AMP (LAMP) realized by a deep neural network (DNN). However, these existing schemes cannot achieve satisfactory estimation accuracy. To improve the channel estimation performance, we propose a prior-aided Gaussian mixture LAMP (GM-LAMP) based beamspace channel estimation scheme in this paper. Specifically, based on the prior information that beamspace channel elements can be modeled by the Gaussian mixture distribution, we first derive a new shrinkage function to refine the AMP algorithm. Then, by replacing the original shrinkage function in the LAMP network with the derived Gaussian mixture shrinkage function, a prior-aided GM-LAMP network is developed to estimate the beamspace channel more accurately. Simulation results by using both the theoretical channel model and the ray-tracing based channel dataset show that, the proposed GM-LAMP network can achieve better channel estimation accuracy.

Lower Performance Bound for Beamspace Channel Estimation in Massive MIMO

In this letter, we present a lower performance bound for discrete Fourier transform (DFT)-based beamspace channel estimation (CE) in 64 antennas Massive Multiple-Input Multiple-Output (MIMO) receiver. The beamspace CE is implemented after antennas digital signal transformation to a priori estimated DFT sub-space resulting in less complexity. To estimate the performance, we calculate noise power after the beamspace CE unit by decomposing an ideal channel response into separate taps and transforming them into the beam domain. Then the minimum mean squared error (MMSE) method is employed with taps to estimate the CE error power. An artificial CE is calculated as a sum of the ideal beamspace channel and additive Gaussian noise with the same error power. The artificial CE is utilized in the MIMO detector and decoder to achieve performance bound. Simulation results are presented for the non-line-of-sight model of the 5G QuaDRiGa 2.0 channel.

Beamspace Channel Estimation for Massive MIMO mmWave Systems: Algorithm and VLSI Design

Millimeter-wave (mmWave) communication in combination with massive multiuser multiple-input multiple-output (MU-MIMO) enables high-bandwidth data transmission to multiple users in the same time-frequency resource. The strong path loss of wave propagation at such high frequencies necessitates accurate channel state information to ensure reliable data transmission. We propose a novel channel estimation algorithm called BEAmspace CHannel EStimation (BEACHES), which leverages the fact that wave propagation at mmWave frequencies is predominantly directional. BEACHES adaptively denoises the channel vectors in the beamspace domain using an adaptive shrinkage procedure that relies on Stein's unbiased risk estimator (SURE). Simulation results for line-of-sight (LoS) and non-LoS mmWave channels reveal that BEACHES performs on par with state-of-the-art channel estimation methods while requiring orders-of-magnitude lower complexity. To demonstrate the effectiveness of BEACHES in practice, we develop a very large-scale integration (VLSI) architecture and provide field-programmable gate array (FPGA) implementation results. Our results show that adaptive channel denoising can be performed at high throughput and in a hardware-friendly manner for massive MU-MIMO mmWave systems with hundreds of antennas.

Wideband Beamspace Channel Estimation for Millimeter-Wave MIMO Systems Relying on Lens Antenna Arrays

Beamspace channel estimation is indispensable for millimeter-wave MIMO systems relying on lens antenna arrays for achieving substantially increased data rates, despite using a small number of radio-frequency chains. However, most of the existing beamspace channel estimation schemes have been designed for narrowband systems, while the rather scarce wideband solutions tend to assume that the sparse beamspace channel exhibits a common support in the frequency domain, which has a limited validity owing to the effect of beam squint caused by the wide bandwidth in practice. In this paper, we investigate the wideband beamspace channel estimation problem without the common support assumption. Specifically, by exploiting the effect of beam squint, we first prove that each path component of the wideband beamspace channel exhibits a unique frequency-dependent sparse structure. Inspired by this structure, we then propose a successive support detection (SSD) based beamspace channel estimation scheme, which successively estimates all the sparse path components following the classical idea of successive interference cancellation. For each path component, its support at different frequencies is jointly estimated to improve the accuracy by utilizing the proved sparse structure, and its influence is removed to estimate the remaining path components. The performance analysis shows that the proposed SSD-based scheme can accurately estimate the wideband beamspace channel at a low complexity. Simulation results verify that the proposed SSD-based scheme enjoys a reduced pilot overhead, and yet achieves an improved channel estimation accuracy.

An AMP-Based Network With Deep Residual Learning for mmWave Beamspace Channel Estimation

Beamspace channel estimation in millimeter-wave (mmWave) massive MIMO system is a very challenging task, especially when the number of radio-frequency chains is limited. To address this problem, we present a novel approximate message passing (AMP)-based network with deep residual learning, referred to as LampResNet. It mainly consists of two components: 1) a learned AMP (LAMP) network and 2) a deep residual learning network (ResNet). The former utilizes the sparsity property of beamspace channel matrix and is employed to obtain a preliminary estimation result, while the latter is designed to reduce the impact of channel noise and further refine the coarse estimation obtained by the LAMP network. Simulation results validate the efficiency of the proposed network.

Beamspace Channel Estimation for Millimeter Wave Massive MIMO System With Hybrid Precoding and Combining

In this paper, a framework of beamspace channel estimation in millimeter wave (mmWave) massive MIMO system is proposed. The framework includes the design of hybrid precoding and combining matrix as well as the search method for the largest entry of over-sampled beamspace receiving matrix. Then based on the framework, three channel estimation schemes including identity matrix approximation (IA)-based scheme, scattered zero off-diagonal (SZO)-based scheme and concentrated zero off-diagonal (CZO)-based scheme are proposed. These schemes together with the existing channel estimation schemes are compared in terms of computational complexity, estimation error and total time slots for channel training. Simulation results show that the proposed schemes outperform the existing schemes and can approach the performance of the ideal case. In particular, total time slots for channel training can be substantially reduced.

Beamspace Channel Estimation in mmWave Systems via Cosparse Image Reconstruction Technique

This paper considers the beamspace channel estimation problem in 3D lens antenna array under a millimeter-wave communication system. We analyze the focusing capability of the 3D lens antenna array and the sparsity of the beamspace channel response matrix. Considering the analysis, we observe that the channel matrix can be treated as a 2D natural image; that is, the channel is sparse, and the changes between adjacent elements are subtle. Thus, for the channel estimation, we incorporate an image reconstruction technique called sparse non-informative parameter estimator-based cosparse analysis AMP for imaging (SCAMPI) algorithm. The SCAMPI algorithm is faster and more accurate than earlier algorithms such as orthogonal matching pursuit and support detection algorithms. To further improve the SCAMPI algorithm, we model the channel distribution as a generic Gaussian mixture (GM) probability and embed the expectation maximization learning algorithm into the SCAMPI algorithm to learn the parameters in the GM probability. We show that the GM probability outperforms the common uniform distribution used in image reconstruction. We also propose a phase-shifter-reduced selection network structure to decrease the power consumption of the system and prove that the SCAMPI algorithm is robust even if the number of phase shifters is reduced by 10%.

Reliable Beamspace Channel Estimation for Millimeter-Wave Massive MIMO Systems with Lens Antenna Array

Millimeter-wave massive MIMO with lens antenna array can considerably reduce the number of required radio-frequency (RF) chains by beam selection. However, beam selection requires the base station to acquire the accurate information of beamspace channel. This is a challenging task, as the size of beamspace channel is large while the number of RF chains is limited. In this paper, we investigate the beamspace channel estimation problem in mmWave massive MIMO systems with lens antenna array. Specifically, we first design an adaptive selecting network for mmWave massive MIMO systems with lens antenna array, and based on this network, we further formulate the beamspace channel estimation problem as a sparse signal recovery problem. Then, by fully utilizing the structural characteristics of mmWave beamspace channel, we propose a support detection (SD)-based channel estimation scheme with reliable performance and low pilot overhead. Finally, the performance and complexity analyses are provided to prove that the proposed SD-based channel estimation scheme can estimate the support of sparse beamspace channel with comparable or higher accuracy than conventional schemes. Simulation results verify that the proposed SD-based channel estimation scheme outperforms conventional schemes and enjoys satisfying accuracy, even in the low SNR region as the structural characteristics of beamspace channel can be exploited.