Mean Square Error Channel Estimation Research Articles

Detecting Abrupt Change in Channel Covariance Matrix for MIMO Communication

The acquisition of the channel covariance matrix is of paramount importance to many strategies in multiple-input-multiple-output (MIMO) communications, such as the minimum mean-square error (MMSE) channel estimation. Therefore, plenty of efficient channel covariance matrix estimation schemes have been proposed in the literature. However, an abrupt change in the channel covariance matrix may happen occasionally in practice due to the change in the scattering environment and the user location. Our paper aims to adopt the classic change detection theory to detect the change in the channel covariance matrix as accurately and quickly as possible such that the new covariance matrix can be re-estimated in time. Specifically, this paper first considers the technique of on-line change detection (also known as quickest/sequential change detection), where we need to detect whether a change in the channel covariance matrix occurs at each channel coherence time interval. Next, because the complexity of detecting the change in a high-dimension covariance matrix at each coherence time interval is too high, we devise a low-complexity off-line strategy in massive MIMO systems, where change detection is merely performed at the last channel coherence time interval of a given time period. Numerical results show that our proposed on-line and off-line schemes can detect the channel covariance change with a small delay and a low false alarm rate. Therefore, our paper theoretically and numerically verifies the feasibility of detecting the channel covariance change accurately and quickly in practice.

Joint CFO and Channel Estimation for RIS-Aided Multi-User Massive MIMO Systems

Accurate channel estimation is essential to achieve the performance gains promised by the use of reconfigurable intelligent surfaces (RISs) in wireless communications. In the uplink of multi-user orthogonal frequency division multiple access (OFDMA) systems, synchronization errors such as carrier frequency offsets (CFOs) can significantly degrade the channel estimation performance. This becomes more critical in RIS-aided communications, as the RIS phases are adjusted based on the channel estimates and even a small channel estimation error leads to a significant performance loss. Motivated by this, we propose a joint CFO and channel estimation method for RIS-aided multi-user massive multiple-input multiple-output (MIMO) systems. Our proposed pilot structure makes it possible to accurately estimate the CFOs without multi-user interference (MUI), using the same pilot resources for both CFO estimation and channel estimation. For optimization of the RIS phase shifts at the data transmission stage, we propose a projected gradient method (PGM) which achieves the same performance as a more computationally demanding grid search technique while having a significantly lower computational complexity. Simulation results demonstrate that the proposed method provides an improvement in the normalized mean-square error (NMSE) of channel es-timation as well as in the bit error rate (BER) performance. Moreover, analyzing the computational complexity and the pilot resource efficiency of the proposed method, we demonstrate that the proposed estimation approach requires low computational load and no extra cost in pilot overhead.

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.

Improving spectral efficiency via pilot assignment and subarray selection under realistic XL-MIMO channels

The main requirements for 5G and beyond connectivity include a uniform high quality of service, which can be attained in crowded scenarios by extra-large MIMO (XL-MIMO) systems. Another requirement is to support an increasing number of connected users in (over)crowded machine-type communication (mMTC). In such scenarios, pilot assignment (PA) becomes paramount to reduce pilot contamination and consequently improve spectral efficiency (SE). We propose a novel quasi-optimal low-complexity iterative pilot assignment strategy for XL-MIMO systems, based on a genetic algorithm (GA). The proposed GA-based PA procedure turns the quality of service more uniform, taking into account the normalized mean-square error (NMSE) of channel estimation from each candidate of the population. The simulations reveal that the proposed iterative procedure minimizes the channel estimation NMSE averaged over the UEs. The second procedure is the subarray (SA) selection. In XL-MIMO systems, commonly a UE is close to an SA antenna subset such that a sufficient data rate can be achieved if only a specific SA serves that UE. Thus, an SA selection procedure is investigated to make the system scalable by defining the maximum number of UEs each SA can help. Hence, the SA clusters are formatted based on the PA decision. Furthermore, we introduce an appropriate channel model for XL-MIMO, which considers a deterministic LoS component with a distance-dependent probability of existence combined with a stochastic spatially correlated Rayleigh NLoS fading component. The developed simulations and analyses rely on this suitable channel model under realistic assumptions of pilot contamination and correlated channels.

Multiuser-MIMO Systems Using Comparator Network-Aided Receivers With 1-Bit Quantization

Low-resolution analog-to-digital converters (ADCs) are promising for reducing energy consumption and costs of multiuser multiple-input multiple-output (MIMO) systems with many antennas. We propose low-resolution multiuser MIMO receivers where the signals are simultaneously processed by 1-bit ADCs and a comparator network, which can be interpreted as additional virtual channels with binary outputs. We distinguish the proposed comparator networks in fully and partially connected. For such receivers, we develop the low-resolution aware linear minimum mean-squared error (LRA-LMMSE) channel estimator and detector according to the Bussgang theorem. We also develop a robust detector which takes into account the channel state information (CSI) mismatch statistics. By exploiting knowledge of the channel coefficients we devise a mean-square error (MSE) greedy search and a sequential signal-to-interference-plus-noise ratio (SINR) search for optimization of partially connected networks. Numerical results show that a system with extra virtual channels can outperform a system with additional receive antennas, in terms of bit error rate (BER). Furthermore, by employing the proposed channel estimation with its error statistics, we construct a lower bound on the ergodic sum rate for a linear receiver. Simulation results confirm that the proposed approach outperforms the conventional 1-bit MIMO system in terms of BER, MSE and sum rate.

Block Sparse Bayesian Learning Based Joint User Activity Detection and Channel Estimation in Grant-Free MIMO-NOMA

In the massive machine type of communication (mMTC), grant-free non-orthogonal multiple access (NOMA) is receiving more and more attention because it can skip the complex grant process to allocate non-orthogonal resources to serve more users. To address the limited wireless resources and substantial connection challenges, combining grant-free NOMA and multiple-input multiple-output (MIMO) is crucial to further improve the system’s capacity. In the grant-free MIMO-NOMA system, the base station should obtain the relevant information of the user before data detection. Thus, user activity detection (UAD) and channel estimation (CE) are two problems that should be solved urgently. In this paper, we fully consider the sparse characteristics of signals and the spatial correlation between multiple antennas in the grant-free MIMO-NOMA system. Then, we propose a spatial correlation block sparse Bayesian learning (SC-BSBL) algorithm to address the joint UAD and CE problems. First, by fully mining the block sparsity of signals in the grant-free MIMO-NOMA system, we model the joint UAD and CE problem as a three-dimensional block sparse signal recovery problem. Second, we derive the cost function based on the hierarchical Bayesian theory and spatial correlation. Finally, to estimate the channel and the set of active users, we optimize the cost function with fast marginal likelihood maximization. The simulation results indicate that, compared with the existing algorithms, SC-BSBL can always fully use the signal sparsity and spatial correlation to accurately complete UAD and CE under various user activation probabilities, SNRs, and the number of antennas. The normalized mean square error of CE can be reduced to 0.01, and the UAD error rate can be less than 10−5.

Hierarchical BEM Based Channel Estimation With Very Low Pilot Overhead for High Mobility MIMO-OFDM Systems

Channel estimation for multi-input multi-output orthogonal frequency division multiplexing (MIMO-OFDM) systems is a challenging issue in high mobility scenarios due to prohibitive pilot overhead and complexity. In this paper, a hierarchical basis expansion model (BEM) based channel estimation scheme is proposed for doubly selective channels, which requires a low pilot overhead and computational complexity. A mixed-BEM is proposed for time-varying channels alongside a complex exponential-BEM (CE-BEM), resulting in very few unknown parameters required for channel estimation. Based on the hierarchical BEM structure, an analytical channel estimation model is derived. By employing the block-structured sparsity and a small number of mixed-BEM coefficients in the antenna-time-BEM domain, a low-complexity estimator is proposed to recover the mixed-BEM coefficients accurately. The lower bound on the mean square error (MSE) of channel estimation is derived to verify the effectiveness of the proposed scheme. Simulation results show that the proposed channel estimation scheme significantly outperforms the existing methods in terms of MSE of channel estimation and bit error rate, with much lower pilot overhead and computational complexity.

Universal Performance Bounds for Joint Self-Interference Cancellation and Data Detection in Full-Duplex Communications

This paper studies the joint digital self-interference (SI) cancellation and data detection in an orthogonal-frequency-division-multiplexing (OFDM) full-duplex (FD) system, considering the effect of phase noise introduced by the oscillators at both the local transmitter and receiver. In particular, an universal iterative two-stage joint SI cancellation and data detection framework is considered and its performance bound independent of any specific estimation and detection methods is derived. First, the channel and phase noise estimation mean square error (MSE) lower bounds in each iteration are derived by analyzing the Fisher information of the received signal. Then, by substituting the derived MSE lower bound into the SINR expression, which is related to the channel and phase noise estimation MSE, the SINR upper bound in each iteration is computed. Finally, by exploiting the SINR upper bound and the transition information of the detection errors between two adjacent iterations, the universal bit error rate (BER) lower bound for data detection is derived.

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.

Orthogonal frequency division multiplexing system with an indexed-pilot channel estimation

In this paper, we examine an orthogonal frequency division multiplexing (OFDM) system under imperfect channel conditions and pilot-insertion- based channel estimation. However, unlike conventional pilot-insertion-based channel estimation, some inserted pilot symbols are set to zero where the index of the zero-pilot symbols is employed to transmit extra data bits. In this paper, we employ a minimum mean squared error (MMSE) to detect transmitted pilot symbols; these symbols are then used to estimate channel coefficients. Furthermore, the impact of zero-pilot symbols on the mean-squared error of channel estimation and on system error performance is examined. Our findings show that the index of zero-pilot symbols can be used to improve system throughput by carrying extra information bits without harming channel estimation accuracy or degrading system error performance. Simulation results show that, at a high signal-to-noise ratio, the bit error rate for data bits transmitted via zero-pilot symbols index selection is lower than that of data bits transmitted over data subcarriers.

Near-Optimal BEM OTFS Receiver With Low Pilot Overhead for High-Mobility Communications

In this paper, a new receiver design based on basis expansion model (BEM) orthogonal time frequency space (OTFS) is presented for high-mobility communications with Doppler-spread channel. By deriving an analytical BEM OTFS system model, a low-order generalized complex exponential BEM (GCE-BEM) aided rough channel estimation is proposed at the initial stage with low pilot overhead, followed by equalization. Then, the refinement of channel estimation and equalization is conducted iteratively, in which a high-resolution GCE-BEM model with a large BEM order is adopted and the detected data symbols are exploited as pseudo-pilots, leading to higher estimation accuracy. Simulation results show that the proposed BEM OTFS receiver significantly outperforms the existing OTFS receivers in terms of the mean square error (MSE) of channel estimation and bit error rate (BER), while featuring low pilot overhead. Results also show the near-optimal performance of the novel solution, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i.e.</i> , achieved BER is very close to the case of perfect channel estimation. The theoretical lower bound on MSE of channel estimation is derived to verify the effectiveness of the proposed BEM OTFS receiver, which is shown to be close to simulation results.

Training Signal Design for Sparse Channel Estimation in Intelligent Reflecting Surface-Assisted Millimeter-Wave Communication

In this paper, the problem of training signal design for intelligent reflecting surface (IRS)-assisted millimeter-wave (mmWave) communication under a sparse channel model is considered. The problem is approached based on the Cramér-Rao lower bound (CRB) on the mean-square error (MSE) of channel estimation. By exploiting the sparse structure of mmWave channels, the CRB for the channel parameter composed of path gains and path angles is derived in closed form under Bayesian and hybrid parameter assumptions. Based on the derivation and analysis, an IRS reflection pattern design method is proposed by minimizing the CRB as a function of design variables under constant modulus constraint on reflection coefficients. Extensions of the proposed design to a multi-antenna transceiver, a uniform planar array (UPA)-based IRS, and multi-user case are discussed. Numerical results validate the effectiveness of the proposed design method for sparse mmWave channel estimation.

Channel Estimation for Intelligent Reflecting Surface Assisted Backscatter Communication

Intelligent reflecting surface (IRS) is a promising technology to improve the performance of backscatter communication systems by smartly reconfiguring the multi-reflection channel. To fully exploit the passive beamforming gain of IRS in backscatter communication, channel state information (CSI) is indispensable but more practically challenging to acquire than conventional IRS-assisted systems, since IRS passively reflects signals over both the forward and backward (backscattering) links between the reader and tag. To address this issue, we propose in this letter a new and efficient channel estimation scheme for the IRS-assisted backscatter communication system. To minimize the mean-square error (MSE) of channel estimation, we formulate and solve an optimization problem by designing the IRS training reflection matrix for channel estimation under the constraints of unit-modulus elements and full rank. Simulation results verify the effectiveness of the proposed channel estimation scheme as compared to other baseline schemes.

Deep Learning-Based Phase Noise Compensation in Multicarrier Systems

This letter presents a deep learning (DL) algorithm for compensating the impacts of phase noise in channel estimation and data detection for multicarrier systems. The proposed DL algorithm replaces conventional estimators’ iterative process and therefore reduces complexity. The input to this algorithm is the first iteration of the conventional least squares (LS) estimator, which requires no knowledge of channel and phase-noise statistics. The proposed algorithm is trained offline using simulation data and then exploited for online phase noise compensation. The simulation results show that the proposed DL algorithm outperforms the conventional estimators and achieves a 6 dB reduction in the mean-squared error (MSE) of channel estimation and a 45% improvement in the bit-error rate (BER).

A Low Complexity Learning-Based Channel Estimation for OFDM Systems With Online Training

In this paper, we devise a highly efficient machine learning-based channel estimation for orthogonal frequency division multiplexing (OFDM) systems, in which the training of the estimator is performed online. A simple learning module is employed for the proposed learning-based estimator. The training process is thus much faster and the required training data is reduced significantly. Besides, a training data construction approach utilizing least square (LS) estimation results is proposed so that the training data can be collected during the data transmission. The feasibility of this novel construction approach is verified by theoretical analysis and simulations. Based on this construction approach, two alternative training data generation schemes are proposed. One scheme transmits additional block pilot symbols to create training data, while the other scheme adopts a decision-directed method and does not require extra pilot overhead. Simulation results show the robustness of the proposed channel estimation method. Furthermore, the proposed method shows better adaptation to practical imperfections compared with the conventional minimum mean-square error (MMSE) channel estimation. It outperforms the existing machine learning-based channel estimation techniques under varying channel conditions.

Uplink transmission design for crowded correlated cell-free massive MIMO-OFDM systems

In cell-free massive multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems, user equipments (UEs) are served by many distributed access points (APs), where channels are correlated owing to finite angle-delay spread in realistic outdoor wireless propagation environments. Meanwhile, the number of UEs is growing rapidly for future fully networked society. In this paper, we focus on the uplink transmission design in crowded correlated cell-free massive MIMO-OFDM systems with a limited number of orthogonal pilots. For the pilot transmission phase, we identify active UEs based on non-orthogonal pilot phase shift hopping patterns and non-orthogonal adjustable phase shift pilots (APSP). We derive a closed-form expression of mean square error of channel estimation (MSE-CE) and obtain an optimal condition for minimizing MSE-CE. According to this condition, the APSP set allocation scheme is proposed. Furthermore, for the data transmission, the max-min power control algorithm is devised to maximize the minimum spectral efficiency (SE) lower bound among active UEs. Simulation results indicate significant performance gains in terms of MSE-CE for the proposed APSP set allocation scheme. The proposed power control scheme can further improve the minimum SE among active UEs. Hence, they are crucial for crowded correlated cell-free massive MIMO-OFDM systems.

Adaptive-Slope Squashing-Function-Based ANN for CSI Estimation and Symbol Detection in SFBC-OFDM System

This paper presents an adaptive-slope squashing-function (ASF)-based artificial neural network (ANN) for efficient estimation of smoothly time-varying multipath fading channels, in a $$4 \times 1$$ space-frequency-block-coded orthogonal-frequency-division-multiplexing (SFBC-OFDM) system using 64 subcarriers. The channel-state-information (CSI) estimated at first stage is further used for OFDM information symbol detection (through minimum mean square error criterion-based detection) at second stage. To combat the impact of smoothly time-varying environment, we emphasize on the utilization of ASF-ANN using backpropagation (BP) algorithm for the estimation of channel tap coefficients in frequency domain. The underlying ANN is modeled as feedforward multi-layered perceptron that updates the network weights. The major focus is on the gradient-descent algorithm-based adaptation of the slope of squashing-function (SF) along with other ANN parameters, which enhances the training efficiency of ASF-ANN in terms of the lower mean-squared channel estimation error in comparison with the traditional fixed-slope squashing-function (FSF) ANN technique. Simulation results corresponding to the underlying $$4 \times 1$$ SFBC-OFDM system are presented to depict that ASF-ANN-based approach outperforms the FSF-ANN technique by providing lower bit-error-rate (BER) due to the usage of well-estimated CSI. At 15 dB SNR and fade rate = 0.001, the average BER reduces to $$2.85 \times 10^{ - 4}$$ for the ASF-ANN based approach, due to improved CSI estimation, which accounts for approximately 5% improvement in the detection success rate as compared to the FSF-ANN-based approach.

Application-Based Coexistence of Different Waveforms on Non-Orthogonal Multiple Access

In the study, the coexistence of different waveform structures on the same resource element is studied under the theory of non-orthogonal multiple access (NOMA). This study introduces a paradigm-shift on NOMA towards the application-centric waveform coexistence. Throughout this article, the coexistence of different waveforms is explained with two specific use cases, which are power-balanced NOMA and joint radar-sensing and communication with NOMA. For the first use case, block error rate (BLER) performance in the power-balanced regime for two user is improved compared to conventional NOMA transmission with the same waveform. For the joint radar-sensing and communication aspect, the superiority of proposed NOMA scheme over orthogonal frequency division multiplexing (OFDM) joint radar-communication (JRC) scheme is demonstrated regarding radar ambiguity, channel estimation mean-square error (MSE) and bit-error rate (BER) performances. In addition, some of the previous works in the literature are reviewed regarding waveform coexistence in a non-orthogonal manner. However, the concept is not limited to these use cases. With the rapid development of wireless technology, next-generation wireless systems are proposed to be flexible and hybrid, having different kinds of capabilities such as sensing, security, intelligence, control, and computing. Therefore, the concept of different waveforms’ coexistence to meet these concerns are becoming impressive for researchers.

Joint Power Control and LSFD for Wireless-Powered Cell-Free Massive MIMO

This paper considers wireless uplink information and downlink power transfer in cell-free massive multiple-input multiple-output systems. The single-antenna user equipments (UEs) utilize the energy harvested in the downlink to transmit uplink pilot and information signals to the multiple-antenna access points (APs). We consider Rician fading and maximum ratio processing based on either linear minimum mean-squared error (LMMSE) or least-squares (LS) channel estimation. We derive the average harvested energy by using a practical non-linear energy harvesting circuit model for both coherent and non-coherent transmission schemes. Furthermore, the uplink spectral efficiency (SE) is derived for all the considered methods and the max-min fairness problem is cast where the optimization variables are the AP and UE power control coefficients together with the large-scale fading decoding vectors. The objective is to maximize the minimum SE of the UEs’ under APs’ and UEs’ transmission power constraints. A novel alternating optimization algorithm with guaranteed convergence and improvement at each step is proposed to solve the highly-coupled non-convex problem.

Preamble Power Optimization Based on Intrinsic Interference Utilization for OQAM/FBMC Channel Estimation

Benefiting from high spectral efficiency, agility of carrier aggregation and support for asynchronous transmissions, offset quadrature amplitude modulation based filter bank multicarrier (OQAM/FBMC) is being developed as an attractive alternative to cyclic-prefix based orthogonal frequency division multiplexing (CP-OFDM) as the air interface technology for future communications. However, its non-orthogonal nature results in intrinsic interference among symbols and subcarriers, which makes channel estimation in OQAM/FBMC significantly more difficult than that in CP-OFDM. In this paper, we propose a novel preamble design method based on intrinsic interference utilization for OQAM/FBMC channel estimation. Specifically, we build a preamble by triplets of subcarriers, each of which is determined by a preamble power optimization problem that minimizes the channel estimation mean square error (MSE) at the central subcarrier. We derive the optimal closed-form solution by exploiting the linearly dependent relationship between preamble symbols and intrinsic interference weights. Moreover, extensions to multiple-input multiple-output (MIMO) setup capable of improving both spectral efficiency and channel estimation performance are investigated. Theoretical analysis and simulation results show the superiority of the proposed preamble design method over the conventional methods in terms of channel estimation MSE, bit error ratio (BER) and peak-to-average power ratio (PAPR).