Minimum Mean Square Error Channel Estimation Research Articles

Enhancing spectral efficiency in uplink/downlink channels of multi-cell massive MIMO for 5G networks

Massive multiple-input multiple-output (MIMO) systems are at the forefront of 5G technology, significantly improving energy efficiency compared to earlier wireless communication systems. This study develops an optimal model for energy-efficient massive MIMO systems, aiming to increase spectral efficiency (SE) within a multi-cell framework. Base stations (BSs) use various techniques for channel estimations during uplink (UL) transmission, including minimum mean-squared error (MMSE), Least Squares, and Element-wise MMSE (EW-MMSE) estimators. The research evaluates the SE achievable through MMSE channel estimation by applying different receive combining schemes. Additionally, it explores downlink (DL) transmission using various precoding schemes, utilizing vectors similar to those in combining schemes. Simulations show a significant improvement in SE by advancing UL and DL transmission models. The study highlights that optimized MMSE channel estimation, along with an increased number of BS antennas and the ability to serve multiple user equipment (UEs) per cell, can enhance the average SE per cell. The findings indicate that optimizing channel estimation is crucial for the development of massive MIMO systems, especially for improving SE in both UL and DL transmissions.

Subspace-Based Pilot Decontamination in User-Centric Scalable Cell-Free Wireless Networks

We consider a cell-free wireless system operated in Time Division Duplex (TDD) mode with user-centric clusters of remote radio units (RUs). Since the uplink pilot dimensions per channel coherence slot is limited, co-pilot users might incur mutual pilot contamination. In the current literature, it is assumed that the long-term statistical knowledge of all user channels is available. This enables Minimum Mean-Square Error channel estimation or simplified dominant subspace projection, which achieves significant pilot decontamination under certain assumptions on the channel covariance matrices. However, estimating the channel covariance matrix or even just its dominant subspace at all RUs forming a user cluster is not an easy task. In fact, if not properly designed, a piloting scheme for such long-term statistics estimation will also be subject to the contamination problem. In this paper, we propose a new channel subspace estimation scheme explicitly designed for cell-free wireless networks. Our scheme is based on 1) a sounding reference signal (SRS) using latin squares wideband frequency hopping, and 2) a subspace estimation method based on robust Principal Component Analysis (R-PCA). The SRS hopping scheme ensures that for any user and any RU participating in its cluster, only a few pilot measurements will contain strong co-pilot interference. These few heavily contaminated measurements are (implicitly) eliminated by R-PCA, which is designed to regularize the estimation and discount the “outlier” measurements. Our simulation results show that the proposed scheme achieves almost perfect subspace knowledge, which in turns yields system performance very close to that with ideal channel state information, thus essentially solving the problem of pilot contamination in cell-free user-centric TDD wireless networks.

Massive MIMO With Dual-Polarized Antennas

This paper considers a single-cell massive MIMO (multiple-input multiple-output) system with dual-polarized antennas at both the base station and users. We study a channel model that includes the key practical aspects that arise when utilizing dual-polarization: channel cross-polar discrimination (XPD) and cross-polar correlations (XPC) at the transmitter and receiver. We derive the achievable uplink and downlink spectral efficiencies (SE) with and without successive interference cancellation (SIC) when using the linear minimum mean squared error (MMSE), zero-forcing (ZF), and maximum ratio (MR) combining/precoding schemes. The expressions depend on the statistical properties of the MMSE channel estimator obtained for the dual-polarized channel model. Closed-form uplink and downlink SE expressions for MR combining/precoding are derived. Using these expressions, we propose power-control algorithms that maximize the uplink and downlink sum SEs under uncorrelated fading but can be used to enhance performance also with correlated fading. We compare the SEs achieved in dual-polarized and uni-polarized setups numerically and evaluate the impact of XPD and XPC conditions. The simulations reveal that dual-polarized setups achieve 40-60\% higher SEs and the gains remain also under severe XPD and XPC. Dual-polarized also systems benefit more from advanced signal processing that compensates for imperfections.

Wideband Cell-Free mmWave Massive MIMO-OFDM: Beam Squint-Aware Channel Covariance-Based Hybrid Beamforming

This paper considers the design of beam squint-aware channel covariance-based hybrid beamformers for wideband cell-free millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO)-orthogonal frequency division multiplexing (OFDM) systems. Single and double phase shifter-based analog radio frequency (RF) precoder/combiner strategies are proposed that are based on dissimilar beam squint awareness assumptions. The digital precoding/combining stage is implemented using centralized designs maximizing the signal-to-interference-plus-noise-ratio (SINR) and relying on the uplink (UL)/downlink (DL) duality enabled by the time division duplex (TDD) protocol and the use of either phase shift-aware minimum mean square error (MMSE) or phase shift-unaware linear MMSE (LMMSE) channel estimators. The performance of the proposed beam squint-aware hybrid beamforming strategies is assessed through extensive numerical simulations under different scenarios. Numerical results show that beam squint-aware designs outperform the beam squint-unaware strategies, specially in typical wideband cell free mmWave massive MIMO-OFDM scenarios where a combination of a very high carrier frequency, a large system bandwidth, and a large-scale antenna array causes the spatial-wideband effect.

Performance Evaluation of Spectral Efficiency for Uplink and Downlink Multi-Cell Massive MIMO Systems

Massive multiple-input and multiple-output (MIMO) systems have become the most persuasive technology for 5G as it increased the energy efficiency gigantically as compared to other wireless communication systems. Being the most vibrant research technology in the communication sector, this research work is based on the optimal model development of energy-efficient massive MIMO systems. The proposed model is a realistic model that augmented the spectral efficiency (SE) of massive MIMO systems where a multi-cell model scenario is considered. Channel estimation is carried out at the base stations (BSs) based on uplink (UL) transmission while the minimum mean-squared error (MMSE), Element-wise MMSE, and Least-square (LS) estimators are used for the estimation. We analyze the achievable SE of the UL based on the MMSE channel estimator with different receive combining schemes. Moreover, the downlink (DL) transmission model is also modelled with different precoding schemes by taking the same vectors used in combining schemes. The simulation results show a significant improvement in spectral efficiency by developing UL and DL transmission models and also realized that the average sum of SE per cell can be improved by optimized MMSE channel estimation, installing multiple BS antennas, and serving multiple UEs per cell. The findings of this work specify that the massive MIMO system can be developed by optimizing the channel estimation for the augmentation of SE in UL and DL transmissions. Conclusively, it can be summarized that some complex computations of MMSE channel estimators can enhance the average sum of SE per cell as per the results verified in this model.

Spatial Multiplexing Superimposed Pilots for Multicell Multiuser MIMO Uplink Systems

For a multiple-input multiple-output (MIMO) system, or a multiuser MIMO system, it is important to acquire the accurate channel state information. In this article, a superimposed-pilot-based channel estimation scheme is proposed for multicell multiuser MIMO uplink systems. In this scheme, the pilot sequences and data sequences are superimposed, but the space generated by the pilot sequences and the space spanned by data sequences are separated far enough in order to reduce interference. Based on this scheme, the minimum mean-square error channel estimation is deduced, and the optimal power allocation between the pilots and the data signals is derived to maximize throughput. These results show that our proposed scheme can overcome the pilot contamination and achieve better performance than the traditional time-multiplexing scheme with mutually orthogonal pilot sequences for different users when the coherent time slot is limited.

Resource efficiency and pilot decontamination in XL‐MIMO double‐scattering correlated channels

AbstractIn extra‐large scale massive MIMO (XL‐MIMO) systems, due to the large antenna array physical dimensions, the received signal at the base‐station (BS) results in spatial non‐stationarities and visibility regions (VRs), limited regions of the array which are visible to the users equipments (UEs). In crowded XL‐MIMO scenarios, the reuse of pilot sequences is a path to provide massive connectivity, principally when the radio resources are scarce. However, such reuse increases the intra‐cell interference, since UEs sharing the same pilot sequences may have overlapped VRs. Thus, despite the minimum mean‐squared error (MMSE) combiner having a high computational complexity, its capability in mitigating the pilot contamination, and even in eliminating such effect in asymptotic antenna regime, justify its use to provide massive connectivity with high spectral efficiency (SE). In this work, we evaluate the performance of the MMSE combiner in XL‐MIMO systems in terms of the SE, energy efficiency (EE), resource efficiency (RE), and capability of eliminating the intra‐cell pilot contamination. The MMSE channel estimator is deployed to estimate the channel vectors. Indeed, the performance of the zero‐forcing combiner and the randomized Kaczmarz regularized zero‐forcing combiner is evaluated and compared with the MMSE scheme. For modeling the XL‐MIMO propagation channel, we use the double‐scattering channel model, which considers clusters of scatterers on both the BS‐side and the UE‐side to model the spatial channel correlation. In parallel, we develop the analysis considering the single‐scattering channel model, a useful simplification of the double‐scattering channel model. The numerical results reveal that, at the cost of a high computational complexity, the MMSE combiner achieves remarkable SE and EE results. However, such superior performance is limited by the number of antennas, being recommended for cases where the size of the VR (number of active antennas) is reduced.

MMSE channel estimation for two-port demodulation reference signals in new radio

Two-port demodulation reference signals (DMRS) have been employed in new radio (NR) recently. In this paper, we firstly propose a minimum mean square error (MMSE) scheme with full priori knowledge (F-MMSE) to achieve the channel estimation of two-port DMRS in NR. When the two ports are assigned to different users, the full priori knowledge of two ports is not easy to be obtained for one user. Then, we present a MMSE scheme with partial priori knowledge (P-MMSE). Finally, numerical results show that the proposed schemes achieve satisfactory channel estimation performance. Moreover, for both mean square error and bit error ratio metrics, the proposed schemes can achieve better performance compared with the classical discrete Fourier transform based channel estimation. Particularly, P-MMSE scheme delivers almost the same performance compared with F-MMSE scheme by a small amount of prior knowledge.

Channel Estimation for Reconfigurable Intelligent Surface Aided MISO Communications: From LMMSE to Deep Learning Solutions

We consider multi-antenna wireless systems aided by reconfigurable intelligent surfaces (RIS). RIS presents a new physical layer technology for improving coverage and energy efficiency by intelligently controlling the propagation environment. In practice however, achieving the anticipated gains of RIS requires accurate channel estimation. Recent attempts to solve this problem have considered the least-squares (LS) approach, which is simple but also sub-optimal. The optimal channel estimator, based on the minimum mean-squared-error (MMSE) criterion, is challenging to obtain and is non-linear due to the non-Gaussianity of the effective channel seen at the receiver. Here we present approaches to approximate the optimal MMSE channel estimator. As a first approach, we analytically develop the best linear estimator, the LMMSE, together with a corresponding majorization-minimization-based algorithm designed to optimize the RIS phase shift matrix during the training phase. This estimator is shown to yield improved accuracy over the LS approach by exploiting second-order statistical properties of the wireless channel and the noise. To further improve performance and better approximate the globally-optimal MMSE channel estimator, we propose data-driven non-linear solutions based on deep learning. Specifically, by posing the MMSE channel estimation problem as an image denoising problem, we propose two convolutional neural network (CNN)-based methods to perform the denoising and approximate the optimal MMSE channel estimation solution. Our numerical results show that these CNN-based estimators give superior performance compared with linear estimation approaches. They also have low computational complexity requirements, thereby motivating their potential use in future RIS-aided wireless communication systems.

Ergodic spectral efficiency of massive MIMO with correlated Rician channel and MRC detection based on LS and MMSE channel estimation

The authors study the spectral efficiency (SE) of a multi-cell massive multiple-input multiple-output (MIMO) system with a spatially correlated Rician channel. The correlation between least squares (LS) estimator and its error complicates SE analysis, since signal and interference components become cross-correlated, too. Minimum mean square error (MMSE) estimators do not suffer from this burden. In some previous works, a proper part of the signal is referred to interference, which makes them cross-uncorrelated, and leads to a SE lower bound. In their modified approach, the authors extract and refer the cross-correlated part of interference to the signal to attain this objective. Here, they use this approach for calculating the instantaneous SE of maximum ratio combining (MRC) detector under LS and MMSE estimation methods. They further derive closed-form approximations of their ergodic SE. This approach is also applicable to other linear channel estimators or data detectors. Numerical results show that achievable SE surpasses that of the previous approach. Moreover, they show that their approximation is close enough to Monte Carlo simulation results, especially at the high number of the base station antennas.

Spectral and Energy Efficiency in Cell-Free Massive MIMO Systems Over Correlated Rician Fading

In this article, we investigate the downlink (DL) of a cell-free massive multiple-input multiple-output (MIMO) system over spatially correlated Rician fading, in which many distributed access points (APs) equipped with multiple antennas serve single-antenna users. The APs apply minimum mean-square error channel estimation to obtain the uplink channel state information (CSI). Furthermore, in order to obtain DL CSI at users, this article considers the use of maximum-ratio transmission to beamform DL pilots in the DL beamforming training (BT) phase. For such a system, we derive the closed-form expressions of the sum spectral efficiency (SE) and total energy efficiency (EE). Based on the obtained closed-form expressions, we develop two successive approximation algorithms to improve the sum SE and total EE by optimizing the power control coefficients of DL data and pilot. Numerical results are provided to demonstrate the superiority of the proposed algorithms in improving the sum SE and total EE. In addition, the numerical results also show that the sum SE of a cell-free massive MIMO system with exploiting the BT scheme can be significantly improved over the system without employing the BT scheme.

Neural Network-Optimized Channel Estimator and Training Signal Design for MIMO Systems With Few-Bit ADCs

This paper is concerned with channel estimation in MIMO systems with few-bit ADCs. In these systems, a linear minimum mean-squared error (MMSE) channel estimator obtained in closed-form is not an optimal solution. We first consider a deep neural network (DNN) and train it as a nonlinear MMSE channel estimator for few-bit MIMO systems. We then present a first attempt to use DNN in optimizing the training signal and the MMSE channel estimator concurrently. Specifically, we propose an autoencoder with a specialized first layer, whose weights embed the training signal matrix. Consequently, the trained autoencoder prompts a new training signal designed specifically for the MIMO channel model under consideration.

Low-Complexity Subspace MMSE Channel Estimation in Massive MU-MIMO System

Massive multi-user multiple-input multiple-output (massive MU-MIMO) technology is considered as a promising enabler to fulfill the rapid growth of traffic requirement for wireless mobile communications. The massive MU-MIMO system can achieve unlimited capacity when the base station (BS) has accurate channel state information (CSI). In time-division-duplex (TDD) mode, the BS estimates CSI by receiving pilot signals sent from user terminals (UEs). However, because of using non-orthogonal pilots, pilot contamination happens to degrade the quality of the CSI estimation. To deal with pilot contamination problem, a low-complexity subspace minimum mean square error (MMSE) estimation method is proposed in this paper. Specifically, our approach operates the MMSE estimation in a low-dimensional subspace to avoid large matrix manipulation. Meanwhile, subspace projection helps to discriminate the desired signal and interfering signals in the power domain. Interference analysis shows the MMSE estimation can achieve interference-free estimation even in a low-dimensional subspace with a large number of BS antennas, and non-overlapping angles of arrival (AoAs) between desired and interfering UEs. Furthermore, thanks to the low-rank property of the channel covariance matrix in massive MU-MIMO systems, a two-step covariance matrix subspace projection method is proposed for further computational complexity reduction. The complexity analysis and simulation results indicate that our proposed approach has better channel estimation accuracy with lower complexity than the conventional MMSE estimation when the number of BS antennas is large.

Deep Learning-Based Wireless Channel Estimation for MIMO Uncoded Space-Time Labeling Diversity

Uncoded space-time labeling diversity (USTLD) is a space-time block coded (STBC) system with labeling diversity applied to it to increase wireless link reliability without compromising the spectral efficiency. USTLD achieves higher link reliability relative to the traditional Alamouti STBC system. This work aims to design a bandwidth-efficient and blind wireless channel estimator for the USTLD system. Traditional channel estimation techniques like the least-squares (LS) and the minimum mean squared error (MMSE) methods are generally inefficient in using the channel bandwidth. The LS and MMSE channel estimation schemes require the prior knowledge of transmitted pilot symbols and/or channel statistics, together with the receiver noise variance, for channel estimation. A neural network machine learning (NN-ML) channel estimator with transmit power-sharing is proposed to facilitate blind channel estimation for the USTLD system and to minimize the required channel estimation bandwidth utilization. We mathematically model the equivalent noise power and derive the optimal transmit power fraction that minimizes the channel estimation bandwidth utilization. The blind NN-ML channel estimator with transmit power-sharing is shown to utilize 20% of the LS and MMSE wireless channel estimators’ bandwidth to achieve the same bit error rate (BER) performance for the USTLD system in the case of 16-QAM and 16-PSK modulation.

Coexistence of Direct and Relayed Transmission Users in Multi-Cell Massive MIMO Systems

In this paper, we investigate the uplink performance of a multi-cell massive MIMO relay network, where the base stations (BSs) and the relay stations (RSs) are equipped with large scale antennas and conventional number of antennas, respectively. In each cell, a portion of users communicate with the BS directly while others are aided by the RSs, which are called direct transmission users (DTUs) and relayed transmission users (RTUs), respectively. The two types of users and RSs of all cells share the same time-frequency resource and thus interfere with each other. After describing the system model, we investigate linear minimum mean-squared error channel estimation for the DTUs and RTUs and derive tractable expressions of channel estimation accuracy. With maximal ratio combining and zero-forcing detections based on the estimated channel state information (CSI), we derive the closed-form lower bound and approximation of the achievable rates for DTUs and RTUs to reveal their mutual impact, including intra- and inter-cell interference and pilot contamination. Then, we propose the power scaling law, which proves to be a simple and energy-efficient way to enable the coexistence of DTUs and RTUs in all cells. Furthermore, an optimal power allocation (OPA) scheme is designed based on the proposed power scaling law to maximize the system sum rate. Numerical results verify the accuracy of our theoretical analysis and the effectiveness of the OPA scheme to guarantee performance improvement and fairness simultaneously.

Multiuser Massive MIMO Systems With Time-Offset Pilots and Successive Interference Cancellation

This paper proposes time-offset pilots for a single-cell multiuser massive multiple-input multiple-output (MIMO) system and studies its performance under the minimum mean-squared error channel estimator and successive interference cancellation. With the proposed time-offset pilots, users are divided into two groups and the uplink pilots from one group are transmitted simultaneously with the uplink data of the other group, which allows the system to accommodate more users for a given number of pilots. Successive interference cancellation is developed to ease the effect of pilot contamination and enhance data detection. Closed-form expressions for lower bounds of the uplink spectral efficiencies in both the training and data phases are derived when the maximum-ratio combining receiver is used at the base station. The power control problem is formulated with the objective of either maximizing the quality of service that can be equally provided to all users, or minimizing the total transmit power. Since the original power control problems are NP-hard, we also propose algorithms based on the bisection method to solve the problems separately in training and data phases. Analysis and numerical results show that the effect of pilot contamination can be mitigated by successive interference cancellation and proper power control.

Performance Analysis for the ${N}$ -Continuous Precoded SM-OFDM System

Combined with N -continuous (NC) precoding, the spatial modulation (SM) orthogonal frequency division multiplexing (OFDM) system offers considerable sidelobe suppression for the downlink transmission, at the cost of additional interference to the transmit signal. Therefore, this paper focuses on investigating the impact of the NC precoder on the bit error rate (BER) performance of the SM-OFDM system. The BER performance is analyzed over the frequency-selective Rayleigh fading channel under two distinct scenarios, i.e., perfect channel estimation and interference suppression based minimum mean square error (MMSE) channel estimation. First, we propose an approximate system model for the NC precoded SM-OFDM system along with an analysis on the introduced interference, and then derive the average BER performance of the system with perfect channel estimation. Based on the above proposed approximate system model, we further analyze the interference based upon MMSE channel estimation, and investigate the characteristics of channel estimation errors. Furthermore, we derive the average BER performance of the NC precoded SM-OFDM system with imperfect channel estimation. The numerical results show that the analytical BER closely matches its simulated counterpart under different system configurations, and demonstrate that the proposed approximate system model is in good agreement with the precise one.

Comparison of Compressed Sensing MMSE Channel estimation with conventional LS and MMSE

Multiple-input multiple-output (MIMO) Orthogonal frequency division multiplexing (OFDM) technology is becoming mature in wireless communication systems. It has led to the third and fourth generation wireless systems which have been providing good range, reliability and higher data rates. To extract the benefits provided by the MIMO systems, it is necessary to estimate the noisy channel through which the information is transmitted. To acquire the channel parameters, we propose compressed sensing (CS) method based on priority which considers the channel with few dominant taps, i.e., sparse nature of the channel is exploited. In this method, priority is taken into consideration, where all user equipments (UE) are not of equivalent significance and more inclination is given to the user with high need. When the number of UEs is more than the available channels, rating is given to UEs based on some heuristics. With this proposed method, we can obtain better performance in-terms of BER and SNR when compared to the conventional methods such as least square (LS) and minimum mean square error (MMSE) techniques. Simulation results show the comparison between the proposed method and the conventional method which proves that the compressed sensing technique outperforms the LS and MMSE techniques. Keywords: Channel Estimation, Compressed Sensing, MIMO-OFDM, MMSE, LS, UE

Power Allocation Optimization for Energy-Efficient Massive MIMO Aided Multi-Pair Decode-and-Forward Relay Systems

We investigate power allocation optimization for global energy efficiency (GEE) maximization in the massive multiple-input multiple-output technique aided multi-pair one-way decode-and-forward relay systems. Assuming that the minimum mean-square error channel estimator and zero-forcing transceivers are employed at the relay, we first derive an accurate closed-form expression of the GEE of this complex system. Based on our analytical results, a non-convex power allocation optimization problem with the objective of GEE maximization is formulated under specific quality-of-service (QoS) and transmit power constraints. To solve this challenging problem, the successive convex approximation technique is invoked to transform the original optimization problem into a concave fractional programming problem, which is then efficiently solved by Dinkelbach’s method and by the Charnes–Cooper transformation-based method. In addition, as a special case, the GEE maximization problem under the assumption of using the equal power allocation strategy at both the source users and the relay is also considered. Simulation results demonstrate the accuracy of our analytical results and the effectiveness of the proposed algorithms. Furthermore, the impact of several important system parameters (i.e., the QoS constraint, the transmit power constraints at both the source users and the relay, as well as the quality of channel estimation) on the maximum GEE achieved by the proposed algorithms is also illustrated.

An Universal MMSE Channel Estimator for OFDM Receiver

In this paper, we re-derived the new auto-correlation function based on Jake's Model, and an universal minimum mean square error (MMSE) channel estimator are proposed based on the new auto-correlation function. Therefore, the proposed MMSE channel estimator can be adopted to various channel scenarios owing its inherent robustness. The performance of the MMSE channel estimator is investigated through a practise DVB-T standard, which shown that the MMSE channel estimator can achieve the extraordinary minimum square error performance at a low complexity.