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Abstract Broadband Power Line Communication (BB-PLC) technology enables data transmission for smart grid applications. Nevertheless, channel equalizers are required in the receiver to estimate and compensate for the nonlinear time-variant impulse response and noise interference effects introduced by the BB-PLC channel. In this paper, we append the Particle Swarm Optimization (PSO) algorithm and its proposed improved version to the commonly used Least-Square (LS) and Linear Minimum Mean Square Error (LMMSE) algorithms to advance four new blocktype pilot-aided hybrid channel estimation algorithms for low-voltage Orthogonal Frequency Division Multiplexing (OFDM)-based BB-PLC systems. Extensive numerical simulation results for four different M-QAM formats (M = 8, 16, 32, 64) show that the proposed algorithms significantly improve the performance of the traditional LS and LMMSE estimators, at least for the parameters of the BB-PLC system studied in this work. In addition, the computational load complexity of the PSO-inspired LMMSE algorithm is lower compared to the conventional LMMSE estimator.

The large number of estimated parameters in a reconfigurable intelligent surface (RIS) makes it difficult to achieve accurate channel estimation accuracy in 6G. Therefore, we suggest a novel two-phase channel estimation framework for uplink multiuser communication. In this context, we propose an orthogonal matching pursuit (OMP)-based linear minimum mean square error (LMMSE) channel estimation approach. The OMP algorithm is used in the proposed algorithm to update the support set and pick the columns of the sensing matrix that are most correlated with the residual signal, which successfully reduces pilot overhead by removing redundancy. Here, we use LMMSE’s advantages for handling noise to address the problem of inadequate channel estimation accuracy when the signal-to-noise ratio (SNR) is low. Simulation findings demonstrate that the proposed approach outperforms least-squares (LS), traditional OMP, and other OMP-based algorithms in terms of estimate accuracy.

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.

The linear minimum mean square error (LMMSE) channel estimation technique is often employed in orthogonal frequency division multiplexing (OFDM) systems because of its optimal performance in the mean square error (MSE) performance. However, the LMMSE method requires cubic complexity of order O(N 3 p ), where Np is the number of pilot subcarriers. To reduce the computational complexity, a discrete Fourier transform (DFT) based LMMSE method is proposed in this paper for OFDM systems in the frequency selective channel. To validate the proposed method, the closed form mean square error (MSE) expression is also derived. Finally, a computer simulation is carried out to compare the performance of the proposed LMMSE method with the classical LS and LMMSE methods in terms of bit error rate (BER) and computational complexity. Results of the simulation show that the proposed LMMSE method achieves exactly the same performance as the conventional LMMSE method, with much lower computational complexity.

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.

In recent years, multispectral imaging systems are considerably expanding with a variety of multispectral demosaicking algorithms. The most crucial task is setting up an optimal multispectral demosaicking algorithm in order to reconstruct the image with less error from the raw image of a single sensor. In this paper, we presented a four-band multispectral filter array (MSFA) with the dominant blue band and a multispectral demosaicking algorithm that combines the linear minimum mean square error (LMMSE) and the adaptive kernel regression methods. To estimate the missing blue bands, we used the LMMSE algorithm and for the other spectral bands, the directional gradient method, which relies on the estimated blue bands. The adaptive kernel regression is then applied to each spectral band for their update without persistent artifacts. The experiment results demonstrate that our proposed method outperforms other existing approaches both visually and quantitatively in terms of peak signal-to-noise-ratio (PSNR), structural similarity index (SSIM) and root mean square error (RMSE).

A high transmission rate can be obtained using Multi Input Multi Output (MIMO) Orthogonal Frequency Division Multiplexing (OFDM) model. The most commonly used 3D-pilot aided channel estimation (PACE) techniques are Least Square (LS) and Least Minimum Mean Square (LMMSE) error. Both of the methods suffer from high mean square error and computational complexity. The LS is quite simple and LMMSE being superior in performance to LS providing low Bit Error Rate (BER) at high Signal to Noise ratio (SNR). Artificial Intelligence when combined with these two methods produces remarkable results by reducing the error between transmission and reception of data signal. The essence of LS and LMMSE is used priory to estimate the channel parameters. The bit error so obtained is compared and the least bit error value is fine-tuned using particle swarm optimization (PSO) to obtained better channel parameters and improved BER. The channel parameter corresponding to the low value of bit error rate obtained from LS/LMMSE is also used for particle initialization. Thus, the particles advance from the obtained channel parameters and are processed to find a better solution against the lowest bit error value obtained by LS/LMMSE. If the particles fail to do so, then the bit error value obtained by LS/LMMSE is finally considered. It has emerged from the simulated results that the performance of the proposed system is better than the LS/LMMSE estimations. The performance of OFDM systems using proposed technique can be observed from the imitation and relative results.

A low-complexity iterative channel estimation and Reed-Solomon (RS) decoding receiver is developed. The joint channel estimation and decoding receiver is based on the linear minimum mean square error (LMMSE) channel estimation technique and the recently proposed RS parity-check transformation algorithm (PTA). A key feature of this joint receiver is the simple symbol remapping process used to refine the initial LMMSE estimate of the channel after each iterative RS-PTA decoding. The performance of the joint iterative receiver is compiled through computer simulation assuming a rectangular M-ary quadrature amplitude modulation as the underlying modulation scheme. Simulation results show significant symbol error rate (SER) improvement in the iterative receiver in comparison with the receiver without iterative feedback. Besides, the RS-PTA iterative receiver outperforms the recently proposed RS Koetter and Vardy (RS-KV) iterative receiver structure both in terms of the SER performance and the computational time complexity. Of particular interest, results verify that the computational time complexity of the RS-PTA iterative receiver can be reduced without compromising the SER performance of the receiver.

A novel hybrid channel estimator is proposed for multiple-input multiple-output orthogonal frequency- division multiplexing (MIMO-OFDM) system with per-subcarrier transmit antenna selection having optimal power allocation among subcarriers. In practice, antenna selection information is transmitted through a binary symmetric control channel with a crossover probability. Linear minimum mean-square error (LMMSE) technique is optimal technique for channel estimation in MIMO-OFDM system. Though LMMSE estimator performs well at low signal to noise ratio (SNR), in the presence of antenna-to-subcarrier-assignment error (ATSA), it introduces irreducible error at high SNR. We have proved that relaxed MMSE (RMMSE) estimator overcomes the performance degradation at high SNR. The proposed hybrid estimator combines the benefits of LMMSE at low SNR and RMMSE estimator at high SNR. The vector mean square error (MSE) expression is modified as scalar expression so that an optimal power allocation can be performed. The convex optimization problem is formulated and solved to allocate optimal power to subcarriers minimizing the MSE, subject to transmit sum power constraint. Further, an analytical expression for SNR threshold at which the hybrid estimator is to be switched from LMMSE to RMMSE is derived. The simulation results show that the proposed hybrid estimator gives robust performance, irrespective of ATSA error.

In order to reduce the equalization delay induced by iteration, two parallel methods were proposed respectively based on maximum a-posteriori probability （MAP） and linear minimum mean-squared error （LMMSE） equalization algo-rithm in Turbo equalization. Through theoretical analysis, simulation and hardware complexity discussion, it is concluded that the proposed two parallel equalization schemes can fully reduced the equalization delay with small hardware com-plexity and excellent performance.