Linear Minimum Mean Research Articles

Identification of flame transfer functions during transient operation

Predicting thermoacoustic instabilities requires knowledge of the flame response to acoustic perturbations, which is characterized by the Impulse Response Function. Obtaining stability maps across an extensive parameter space is prohibitively costly with existing methods, both experimentally and numerically, as the data records must be obtained independently for each stationary operating condition. To address this problem, a nonparametric identification technique that enables the characterization of instantaneous Flame Transfer Functions (FTFs) under nonstationary operating conditions, based on a series expansion of the time-varying impulse response function (TV-IRF), is proposed. The technique is a direct extension of the Wiener-Hopf equation to nonstationary signals, yielding the linear minimum mean squared error estimator (LMMSEE) of the TV-IRF. This method is applied to data obtained from a model of a premixed, hydrogen-enriched swirl flame. It's hydrogen power fraction is rapidly varied from 12-43% over 100 milliseconds and the flame response to a band-limited, white-noise signal is computed. From the resulting input-output data, the TV-IRF is accurately estimated and the FTF for all hydrogen power fractions is obtained from a single data record. This method paves the way for cost-effective estimation of a map of FTF's from computational or experimental data, significantly reducing expenses in both cases.

Optimal pilot pattern for data‐aided channel estimation for MIMO‐OFDM wireless systems

AbstractThis article presents an optimal pilot pattern for the data‐aided channel estimation (DACE) scheme for both single‐input single‐output (SISO) and multiple‐input multiple‐output orthogonal frequency division multiplexing (MIMO‐OFDM) wireless systems. The research evaluates the performance of the DACE scheme using different comb‐type pilot patterns for both least square (LS) and linear minimum mean square error (LMMSE) channel estimators. In this regard, it is found that pilot spacing significantly influences system performance. Inserting pilot symbols in consecutive subcarriers cannot compensate for increased pilot spacing. Hence, the solution to this problem is to place pilot symbols at appropriate locations within the given spectrum. Moreover, data symbols which are reliably detected at the receiver are used as additional pilot signals to further enhance system performance. However, reliable data symbols need to be determined carefully because wrong detection results in severe performance degradation. In this respect, the proposed comb‐type pilot pattern using a single pilot subcarrier extracts the maximum number of reliable data symbols for the DACE scheme, improves channel estimation accuracy, and provides bandwidth optimization for MIMO‐OFDM systems. Furthermore, it outperforms all other pilot patterns in terms of system mean square error (MSE) and bit‐error‐rate (BER) performance.

Performance evaluation of symbol detection algorithms in massive MIMO communication systems

Abstract Massive MIMO (mMIMO) is the essential technique for attaining the exponential increase in the data rate needed for future communication systems. These advancements have been significantly supported by progress in VLSI technology, which enables the integration of an enormous number of antennas and the complex signal processing essential for massive MIMO systems on a single chip. This work conducts a comprehensive analysis of the intricacy of seven matrix decomposition techniques for symbol detection in future mMIMO communication systems: ADMM-based infinity norm (ADMIN), Neumann series (NS), Newton iteration (NI), Jacobi iteration (Ja), improved Gauss-Seidel (IGS), conjugate gradient (CG), and QR decomposition (QR), against linear and near-optimal minimum mean square error (MMSE). QR, GS, Ja, and CG belong to linear algebraic methods based on matrix decomposition. MMSE and ADMIN are nonlinear optimization methods; NS and NI are iterative methods. The analysis examines into the complexity of these detection algorithms, considering the symbol error rate, the convergence rate, the initial solution vector, and the correlation factor. Performance evaluations are conducted on 8 and 16-user mMIMO systems with 64 and 128 base station antennas, modulation schemes (32-QAM and 64-QAM), iteration counts (p = 1, 2, 3, 4), correlation factors (α = 0.2, 0.4, and 0.6), and initial solution vectors (zero vector, D −1 and W 2 −1 yMF ). The result clearly shows that if the initial solution and number of iterations are chosen properly, the IGS-based linear detector achieves near-optimal performance with a lower computational complexity of O(K 2) compared to the nonlinear MMSE-based detector with a computational complexity of O(K 3).

Low complexity stationary iteration based approximate inversion for signal detection in OTFS system

Orthogonal time frequency space (OTFS) system offers a high data rate and effectively exploits full diversity compared to orthogonal frequency division multiplexing (OFDM), achieving a seamless trade-off between data rate and processing gain. However, detecting OTFS signals is challenging due to the complex conversion between delay-Doppler (DD) and time domains. In this article, we propose a stationary iteration-based approximate inversion (SIAI) technique for low-complexity detection in uplink OTFS systems.The proposed SIAI detection technique features square-order computational complexity and delivers performance close to that of a linear minimum mean square error (LMMSE) detector. Simulation results demonstrate that the SIAI technique outperforms several state-of-the-art detection methods in terms of both error performance and computational complexity. Additionally, the robustness of the SIAI technique is validated in scenarios with imperfect channel state information at the receiver.

Development of hybrid sewing training-based dingo optimization algorithm for massive MIMO spectral efficiency maximization system

ABSTRACT A Base Station (BS) with several antenna elements serves a number of users in the frequency of the same time- slot in a huge multiuser “Multiple-Input Multiple-Output (MIMO)”. It has emerged as a viable method for the future generation of wireless networks due to its capacity to enhance both spectrum and efficiency of energy, even with straightforward linear processing like “Maximum Ratio Combining (MRC), Linear Minimum Mean Square Error (LMMSE) and Zero Forcing (ZF)”. In a power allocation scheduling method, only users who do not interfere with one another can change their power at any one time. These studies all take into account orthogonal channels. However, the “Spectral Efficiency (SE)” is reduced by the channels’ non-orthogonality. This encourages us to research how to maximize spectral efficiency in “Massive MIMO (M-MIMO)” systems by allocating power for both uplink and downlink transmission. Here, the Hybrid of Sewing Training and Dingo Optimization (HSTDO) is developed for executing the best resource allocation in the M-MIMO system to improve SE performance which helps to enhance the SE of the M-MIMO system. The simulation is carried out to compare the developed model with the conventional works to reveal the better spectral efficiency of the suggested algorithm.

Hybrid Optimized LMMSE-Based Channel Estimation with Low Power Trellis Coded Modulation

Data transfer in a wireless channel environment is plagued by numerous security issues and power transmission loss. Channel state information is crucial to attaining the performance benefit of reconfigurable intelligent surfaces (RISs) in wireless systems. Because of the Doppler effect, mobility makes accurate channel estimate (CE) more difficult. The parameter estimation approach is employed as an alternative to direct estimation in the channel matrix to address the aforementioned problems. Also, to lower the Mean Square Error (MSE) between the estimated and original channel, training-based CE, such as Linear Minimum Mean Square Error (LMMSE), and Least Square Error (LSE), are widely used in some wireless standards. To optimize the channel, certain intelligent optimized strategies are presented. For the Optimal CE, a Trellis Coded Modulation (TCM) with hybrid optimization in LMMSE has been provided. Moth amalgamated Elephant Herding Optimization (MAEHO) algorithm is the proposed hybrid optimization. Finally, the performance of the accepted model is determined in comparison to other existing techniques using a variety of metrics.

Phase Noise Effects on OFDM Chirp Communication Systems: Characteristics and Compensation

Orthogonal frequency-division multiplexing (OFDM) chirp waveforms are an attractive candidate to be a dual-function signal scheme for the joint radar and communication systems. OFDM chirp signals can not only be employed to transmit communication data through classic phase modulation, but also can perform radar detection by applying linear frequency modulation for subcarriers. However, the performance of the OFDM chirp communication system under the phase noise environment still remains uninvestigated. This paper tries to discuss the influence of phase noise on OFDM chirp communication systems and proposes effective phase noise estimation and compensation methods. We find that the phase noise effect on OFDM chirp communication systems consists of a common phase error (CPE) and an inter-carrier interference (ICI). If not compensated, the performance of the dual-function systems can be seriously degraded. In particular, an exact expression for the signal-plus-interference to noise ratio (SINR) for the OFDM chirp communication system is derived and some critical parameters are analyzed to exhibit the phase noise effects on system performance. Moreover, two low-complexity estimation approaches, maximum likelihood (ML) and linear minimum mean square error (LMMSE), as well as two compensation approaches, the de-correlation and cancellation algorithms, are respectively utilized to eliminate the phase noise impairment. Finally, the phase noise effects and the effectiveness of the compensation approach are verified by extensive numerical results.

An inspired chaos-based estimation-theory optimization for low-density parity-check (LDPC) code decoding

Optimization techniques have emerged as powerful tools for solving complex engineering problems in real-time applications, surpassing traditional heuristic methods. This paper introduces a novel chaos optimization algorithm that integrates the bisection search method to enhance the convergence ability, solution accuracy, and search speed of conventional optimization problems. The proposed algorithm is applied to the design and analysis of a reduced complexity decoding scheme using Low-Density Parity-Check (LDPC) codes. By leveraging the Linear Minimum Mean Square Error (LMMSE) estimation criterion, the proposed method approximates the estimated parameters acquired during the message computation process. This combined approach effectively mitigates error propagation and premature convergence issues. The presented research offers a low-complexity decoding algorithm for LDPC codes, leveraging an optimized chaos bisection search method. The adoption of the LMMSE criterion overcomes data dependency and error propagation concerns during the estimation process. The modified chaos optimization technique, integrated with the bisection search, efficiently determines optimal values from perturbed observations, leading to improved convergence rates and data processing precision by reducing the observation dimension (search space). Simulation results validate the proposed approach, showcasing its ability to mitigate error propagation and premature convergence while maintaining coding gain accuracy. Experimental validation on an FPGA RF-SoC device (model XCZU27DR) demonstrates that the proposed method achieves a maximum throughput of 8.7 Gbps at a clock frequency of 386.72 MHz, with reduced hardware complexity. The experimental verification on an FPGA RF-SoC device highlights the algorithm's minimal hardware complexity, superior decoding throughput, and Bit Error Rate (BER) performance.

Leveraging neuro-inspired AI accelerator for high-speed computing in 6G networks.

The field of wireless communication is currently being pushed to new boundaries with the emergence of 6G technology. This advanced technology requires substantially increased data rates and processing speeds while simultaneously requiring energy-efficient solutions for real-world practicality. In this work, we apply a neuroscience-inspired machine learning model called echo state network (ESN) to the critical task of symbol detection in massive MIMO-OFDM systems, a key technology for 6G networks. Our work encompasses the design of a hardware-accelerated reservoir neuron architecture to speed up the ESN-based symbol detector. The design is then validated through a proof of concept on the Xilinx Virtex-7 FPGA board in real-world scenarios. The experiment results show the great performance and scalability of our symbol detector design across a range of MIMO configurations, compared with traditional MIMO symbol detection methods like linear minimum mean square error. Our findings also confirm the performance and feasibility of our entire system, reflected in low bit error rates, low resource utilization, and high throughput.

Enhanced Dynamic Surface EMG Decomposition Using the Non-Negative Matrix Factorization and Three-Dimensional Motor Unit Localization.

Surface electromyography (sEMG) signal decomposition is of great importance in examining neuromuscular diseases and neuromuscular research, especially dynamic sEMG decomposition is even more technically challenging. A novel two-step sEMG decomposition approach was developed. The linear minimum mean square error estimation was first employed to extract estimated firing trains (EFTs) from the eigenvector matrices constructed using the non-negative matrix factorization (NMF). The firing instants of each EFT were then classified into motor units (MUs) according to their specific three-dimensional (3D) space position. The performance of the proposed approach was evaluated using simulated and experimentally recorded sEMG. The simulation results demonstrated that the proposed approach can reconstruct MUAPTs with true positive rates of 89.12 ± 2.71%, 94.34 ± 1.85% and 95.45 ± 2.11% at signal-to-noise ratios of 10, 20, and 30 dB, respectively. The experimental results also demonstrated a high decomposition accuracy of 90.13 ± 1.31% in the two-source evaluation, and a high accuracy of 91.86 ± 1.14% in decompose-synthesize-decompose- compare evaluation. The adoption of NMF reduces the dimension of random pattern under the restriction of non-negativity, as well as keeps the information unchanged as much as possible. The 3D space information of MUs enhances the classification accuracy by tackling the issue of relative movements between MUs and electrodes during dynamic contractions. The accuracy achieved in this study demonstrates the good performance and reliability of the proposed decomposition algorithm in dynamic surface EMG decomposition. The spatiotemporal information is applied to the dynamic surface EMG decomposition.

A Bayesian quantum state tomography along with adaptive frameworks based on linear minimum mean square error criterion

Quantum state tomography (QST) is essential for characterizing unknown quantum states. Several methods of estimating quantum states already exist and can be classified mainly into three broad classes. They are based on the criteria like maximum likelihood, linear inversion, and Bayesian framework. The Bayesian framework for QST gives a better reconstruction performance. However, the existing methods of the Bayesian frameworks are computationally extensive and, most of the time require knowledge about the prior distribution of the quantum state. In this paper, we propose a Bayesian method of QST based on the linear minimum mean square error criterion, where the prior statistics are estimated and the computational complexity is comparable to that of the linear inversion based QST method. We also propose an adaptive version based on the block estimation of parameters. Extensive numerical simulations are conducted to demonstrate its efficacy over the linear inversion-based QST regarding trace distance error metric.

Novel Low-Power Floating-Point Divider With Linear Approximation and Minimum Mean Relative Error

Novel Low-Power Floating-Point Divider With Linear Approximation and Minimum Mean Relative Error

Channel reconstruction for mmWave Massive MIMO systems based on Channel Path Map

For the needs of high data rate and massive device access in current fifth-generation (5G) mobile communication networks and future sixth-generation (6G) mobile communication networks, Millimeter-Wave (mmWave) Massive Multiple-Input Multiple-Output (MIMO) is a crucial technical support. However, the conventional pilot based channel estimation methods are exceedingly time-consuming and substantially degrade system performance when the number of users or antennas is high. This paper proposes a Path Clustering based Channel Reconstruction (PCCR) scheme for channel reconstruction in order to solve this issue. By leveraging channel information (such as angle of arrival, angle of departure, and path gain) at a number of geographical locations that are recorded in the Channel Path Map (CPM), we aim to reconstruct the mmWave channel of any locations of interests. To be specific, the CPM is used to extract the neighborhood propagation path data, and an autonomous determination algorithm is used to find the number of path clusters at the location of interest. The recorded propagation path information is processed by the Equivalent Base Station (EBS) scheme, and the path clustering is accomplished by using the AGglomerative NESting (AGENS) algorithm. In each path cluster, Inverse Distance Weighted (IDW) algorithm is developed to forecast the path information at the user location. With all path information at user location are forecast, the channel can be reconstructed. The anticipated overhead is substantially lower than that of conventional methods because the computational cost of the procedure only depends on the total number of paths at the nearby locations. Ray-tracing based simulations are carried out to demonstrate the performance of the proposed algorithm. The results show that, when applied to a CPM with a spatial location precision of 5 m, the Normalized Mean Squared Error (NMSE) of the proposed algorithm is nearly identical to that of Linear Minimum Mean Square Error (LMMSE) estimation. The actual achievable date rate can match the needs of upcoming wireless communications and is superior over the conventional LMMSE.

Low-Complexity BFGS-Based Soft-Output MMSE Detector for Massive MIMO Uplink

For the massive multiple-input multiple-output (MIMO) uplink, the linear minimum mean square error (MMSE) detector is near-optimal but involves undesirable matrix inversion. In this paper, we propose a low-complexity soft-output detector based on the simplified Broyden–Fletcher–Goldfarb–Shanno method to realize the matrix-inversion-free MMSE detection iteratively. To accelerate convergence with minimal computational overhead, an appropriate initial solution is presented leveraging the channel-hardening property of massive MIMO. Moreover, we employ a low-complexity approximated approach to calculating the log-likelihood ratios with negligible performance losses. Simulation results finally verify that the proposed detector can achieve the near-MMSE performance with a few iterations and outperforms the recently reported linear detectors in terms of lower complexity and faster convergence for the realistic massive MIMO systems.

Expectation-maximization vector approximate message passing-based frequency-domain turbo equalization for underwater acoustic communications.

Channel equalization plays a crucial role in single-carrier underwater acoustic (UWA) communications. Recently, a frequency-domain turbo equalization (FDTE) scheme enabled by the vector approximate message passing (VAMP) algorithm, was proposed, and it outperformed classic linear minimum mean square error FDTE at acceptable complexity cost. The operation of the VAMP-FDTE requires knowledge of noise power, which is predetermined before the equalization starts. In practice, however, it is difficult to obtain prior knowledge of noise power due to factors of unknown channel estimation errors and dynamic underwater environments. Motivated by this fact, we propose an enhanced VAMP-FDTE scheme, which learns the noise power knowledge during the equalization process via the expectation-maximization (EM) algorithm. The EM-based noise power estimation makes use of intermediate results of the VAMP-FDTE and, thus, only incurs a small extra computational overhead. The improved VAMP-FDTE, named EM-VAMP-FDTE, was tested by experimental data collected in shallow-sea horizontal UWA communication trials with MIMO configuration. It showed better performance than the existing VAMP-FDTE scheme, attributed to the online noise power learning.

Low-complex channel estimation in extra-large scale MIMO with the spherical wave properties

This paper investigates the low-complex linear minimum mean squared error (LMMSE) channel estimation in an extra-large scale MIMO system with the spherical wave model (SWM). We model the extra-large scale MIMO channels using the SWM in the terahertz (THz) line-of-sight propagation, in which the transceiver is a uniform circular antenna array. On this basis, for the known channel covariance matrix (CCM), a low-complex LMMSE channel estimation algorithm is proposed by exploiting the spherical wave properties (SWP). Meanwhile, for the unknown CCM, a similar low-complex LMMSE channel estimation algorithm is also proposed. Both theoretical and simulation results show that the proposed algorithm has lower complexity without reducing the accuracy of channel estimation.

Enhanced MIMO-DCT-OFDM system using cosine domain equaliser

ABSTRACT The Discrete Cosine Transform (DCT) can be used instead of the conventional Discrete Fourier Transform (DFT) for the Orthogonal Frequency Division Multiplexing (OFDM) construction, which offers many advantages. In this paper, the Multiple-Input-Multiple-Output (MIMO) DCT-OFDM is enhanced using a proposed Cosine Domain Equaliser (CDE) instead of a Frequency Domain Equaliser (FDE). The results are evaluated through the Rayleigh fading channel with Co-Carrier Frequency Offset (Co-CFO) of different MIMO configurations. The average bit error probability and the simulated time of the proposed scheme and the conventional one are compared, which indicates the importance of the proposed scheme. Also, a closed formula for the number of arithmetic operations of the proposed equaliser is developed. The proposed equaliser gives a simulation time reduction of about 81.21%, 83.74% compared to that of the conventional Linear Zero Forcing (LZF)-FDE and Linear Minimum Mean Square Error (LMMSE)-FDE, respectively, for the case of a 4 × 4 configuration.

Achievable Rate Analysis of the STAR-RIS-Aided NOMA Uplink in the Face of Imperfect CSI and Hardware Impairments

Reconfigurable intelligent surfaces (RIS) are capable of beneficially ameliorating the propagation environment by appropriately controlling the passive reflecting elements. To extend the coverage area, the concept of simultaneous transmitting and reflecting reconfigurable intelligent surfaces (STAR-RIS) has been proposed, yielding supporting 360° coverage user equipment (UE) located on both sides of the RIS. In this paper, we theoretically formulate the ergodic sum-rate of the STAR-RIS assisted non-orthogonal multiple access (NOMA) uplink in the face of channel estimation errors and hardware impairments (HWI). Specifically, the STAR-RIS phase shift is configured based on the statistical channel state information (CSI), followed by linear minimum mean square error (LMMSE) channel estimation of the equivalent channel spanning from the UEs to the access point (AP). Afterwards, successive interference cancellation (SIC) is employed at the AP using the estimated instantaneous CSI, and we derive the theoretical ergodic sum-rate upper bound for both perfect and imperfect SIC decoding algorithm. The theoretical analysis and the simulation results show that both the channel estimation and the ergodic sum-rate have performance floor at high transmit power region caused by transceiver hardware impairments.

Nonlinear Equalization for Performance Enhancement of FBMC Systems Using Walsh Transform

The Filter Bank Multi-Carrier (FBMC) is an interesting recent technology for next-generation wireless radio communication systems. Equalization is a fundamental technique for enhancing Bit Error Rate (BER) performance. The traditional Linear Zero Forcing (LZF) and Linear Minimum Mean Square Error (LMMSE) equalizers have large noise amplification and high complexity, respectively. As the estimated error of the Signal-to-Noise Ratio (SNR) grows, the BER performance of the LMMSE equalizer degrades. In this paper, we present a Joint Low Complexity Optimized ZF-Successive Interference Cancellation (JLCOZF-SIC) equalizer for FBMC communication systems that are based on the Walsh–Hadamard Transform (WHT) rather than the Fast Fourier Transform (FFT). As in the MMSE-Successive Interference Cancellation (MMSE-SIC) equalizer, the proposed equalizer avoids the estimating error induced by average power per symbol estimation. The simulation results show that the proposed algorithm improves the system performance more than the existing algorithms. Furthermore, the proposed equalization provides stability in the BER performance at high levels of the co-Carrier Frequency Offset (co-CFO). In terms of computational complexity, the proposed scheme has a lower computational complexity than traditional schemes.

Autoencoder assisted subcarrier optimization for nonlinear frequency division multiplexing.

Nonlinear frequency division multiplexing (NFDM) is a novel optical communication technique that can achieve nonlinear free transmission. However, current design of NFDM is analogous to orthogonal frequency division multiplexing (OFDM), where sinc function is utilized as subcarriers, which may not be optimal for nonlinear spectrums. In this paper, we propose an auto-encoder (AE) assisted subcarrier optimization scheme for dual-polarized (DP) NFDM systems. Numerical verifications show that our scheme can improve the Q-factor by 1.54 dB and 0.62 dB compared to sinc subcarrier and linear minimum mean square error (LMMSE) equalization, respectively, in a 960 km transmission scenario. We also analyze the characteristics of the optimized subcarriers and discuss how they enhance the performance. Furthermore, we demonstrate the robustness of the optimized subcarriers to different modulation formats, transmission distances and bandwidth. Our work provides a new idea in subcarrier design for NFDM.