An Off-Grid Turbo Channel Estimation Algorithm for Millimeter Wave Communications.

Channel estimation (CE) is a challenging problem and one of the key technologies in Orthogonal Frequency Division Multiplexing (OFDM) systems. The Linear Minimum Mean Square Error (LMMSE) proposed for OFDM systems has excellent Mean Square Error (MSE) performance. However, the conventional method requires the statistical knowledge of the channel information in advance and the complicated inverse operation of large dimension matrices. In this case, an enhanced fast LMMSE channel estimation using Fast Fourier Transform (FFT) operation and the most significant taps (MST) algorithm for OFDM systems is proposed. This method has the advantage of low computational complexity and no requirement on the detailed channel information. In addition, simulation results demonstrate that the proposed algorithm outperforms other LMMSE methods in terms of bit error rate (BER) without the loss of MSE performance.

A decision-directed (DD) channel estimation based on iterative linear minimum mean square error (LMMSE) is proposed for orthogonal frequency division multiplexing systems. Existing DD channel estimation is well known to have the problem of error propagation because of symbol-by-symbol detection. The proposed algorithm can estimate the correction term of current channel state information (CSI) according to the error vector of previous CSI by applying the orthogonality principle, and corrects the current CSI with this correction term. Analysis and simulation results have shown that this method has no error propagation problem. The performance of the proposed algorithm is much better than the conventional DD channel estimation, and close to the optimal LMMSE estimator, but with much less computational complexity compared with the optimal LMMSE estimator.

Generalized frequency division multiplexing (GFDM) is a promising candidate waveform for next-generation wireless communication systems. However, GFDM channel estimation is still challenging due to the inherent interference. In this paper, we formulate a pilot design framework with linear minimum mean square error (LMMSE) channel estimation for GFDM, and propose a novel pilot design to achieve interference precancellation during pilot generation with the fixed transmit sample values at selected frequency bins. Numerical results demonstrate that the proposed method reduces the channel estimation mean square error and the symbol error rate (SER) in high signal-to-noise ratio (SNR) regions, compared with the conventional methods.

This paper proposes a cognitive radio approach for WiMAX (CogMAX). The proposed system has all the capabilities of cognitive radio from monitoring to action, decision and learning. We use fuzzy logic (FL) reasoning as the core of the reasoning engine. The reasoning engine is used to determine different parameters that will be used by the WiMAX system. This work will focus on one of the main functions of the reasoning engine i.e. determination of the channel type and the number of pilots used for channel estimation. The number of pilots will depend on the type of channel which is determined by the cognitive engine. We examine two channel estimators, the Least Square (LS) and the Linear Minimum Mean Square Error (LMMSE) along with 2D-Linear, averaging and constant coefficients interpolators. Evaluation is done using the minimum square error with the SNR of the channel. Numerical results reveal that changing the number of pilots can lead to better channel estimation.

SummaryThis paper introduces the concept of spatial and media‐based modulated (SMBM) orthogonal frequency division multiplexing (OFDM) as a potential candidate for highly mobile next generation beyond 5G (B5G) wireless communications. The proposed SMBM‐OFDM technique utilizes not only the transmit antenna and channel state indices but also OFDM subcarriers to improve the system performance under high mobility. In addition, this study sheds light on challenging fast time‐varying channel estimation problem of MBM‐based systems by using the linear minimum mean square error (LMMSE) approach due to its optimality to investigate the achievable system performance with the aid of basis expansion modeling. The minimum lower bound on the channel estimation error (Bayesian Cramer–Rao bound) is derived theoretically and shown to be attainable by the considered LMMSE estimator. Moreover, symbol detection performance is provided for different modulation types and higher mobile velocities. Simulation results demonstrate that SMBM‐OFDM system under high mobility is able to provide around 12‐dB performance gains in terms of both channel estimation and symbol detection error compared to conventional spatial modulation (SM)‐OFDM systems without MBM. The presented framework is important due to addressing the high mobility support of SMBM‐OFDM systems for B5G wireless communications in terms of achievable channel estimation and data detection performance.

We consider a wirelessly powered Internet of Things (IoT) based on cell-free massive MIMO with energy harvesting. In such a system, during the downlink phase, the sensors harvest radio-frequency (RF) energy emitted by the distributed access points (APs). During the uplink phase, sensors transmit data to the APs using the harvested energy. We assume that single antenna sensors send uplink pilots in order to allow APs to detect active users and estimate their channel coefficients. We assume that each AP is equipped with N$\geq$1 antennas and uses the linear minimum mean square error (LMMSE) channel estimation. Through an asymptotic analysis, we derive closedform approximations for the variance of the LMMSE channel coefficient estimates, the amount of harvested energy, and the achievable rates for the uplink data transmission. We next use these expressions to jointly optimize the charging duration and uplink and downlink power control coefficients to minimize the total transmit energy consumptions of APs and sensors, which is crucially important for IoT sensors. Simulation results verify the accuracy of the obtained expressions, and shows that significant gains in energy efficiency can be achieved by the proposed optimization algorithms.

Channel estimation is a critical component in orthogonal frequency division multiplexing (OFDM) systems for ensuring reliable wireless communication. In this study, we propose a fast super-resolution convolutional neural network (FSRCNN) model for channel estimation, designed to reduce computational complexity while maintaining high estimation accuracy. The proposed FSRCNN model incorporates modifications such as replacing linear interpolation with zero padding and leveraging a new fast CNN architecture to estimate channel coefficients. Our numerical experiments and simulations demonstrate that the FSRCNN model significantly outperforms traditional methods, such as least square (LS) and linear minimum mean square error (LMMSE), in terms of mean square error (MSE) across various signal-to-noise ratios (SNRs). Specifically, the FSRCNN model achieves MSE values comparable to MMSE estimation, particularly at higher SNRs, while maintaining lower computational complexity. At an SNR of 20 dB, the FSRCNN model shows a notable improvement in MSE performance compared to the ChannelNet and LS methods. The proposed model also demonstrates robust performance across different SNR levels, with optimal results observed when the training SNR is close to the operating SNR. These findings validate the effectiveness of the FSRCNN model in providing a low-complexity, high-accuracy alternative for channel estimation, making it suitable for real-time applications and devices with limited computational resources. This advancement holds significant promise for enhancing the reliability and efficiency of current and future wireless communication networks.

Pair-wise error probability (PEP) is analyzed in the presence of channel estimation error (CEE) for orthogonal frequency division multiplexing (OFDM) in a quasi-static Rayleigh fading channel. Subcarriers in OFDM are grouped in an equi-spaced manner with the number of subcarriers in a group equal to the number of channel taps. One group is dedicated for training and the rest are for data transmission. A linear minimum mean square error (LMMSE) based channel estimation for coherent detection is considered in this paper. This enables the signal dependent CEE to be uncorrelated to the data. Since ML decoding employed with perfect CSI becomes suboptimal in the presence of CEE, an optimal ML decoding is derived. It is observed from our training-based PEP expression that the CEE does not reduce the diversity order but contributes to a loss of coding gain. Moreover, a code design criterion is established. To reduce the loss of coding gain, an optimal training scheme is developed, based on the PEP expression. Loss of performance due to an imperfect channel estimate is quantified in terms of bounds on bit error probability (BEP) for high SNR. Our analytical findings are corroborated by simulation examples.

Orthogonal frequency division multiplexing (OFDM) is multi carrier modulation scheme. The channel estimation is a process of characterizing the effect of the transmission channel on the input signal. In this paper we compare the performance of Least Square (LS) and Linear Minimum Mean Square Error (LMMSE) channel estimation technique for Wavelet based OFDM system. The channel estimation based on block type pilot arrangement is performed by sending pilots at every sub-channel and using this estimation for a specific number of following symbols. In this paper we used wavelet transform instead of fast Fourier transform (FFT), which have more bandwidth efficiency, less prone to Doppler shift and also complexity of order O(N) as opposed to the FFTs O(N log <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> N).

In this paper, we propose a joint channel estimation and symbol detection (JCESD) algorithm relying on message-passing algorithms (MPA) for orthogonal frequency division multiple access (OFDMA) systems. The channel estimation and symbol detection leverage the framework of expectation propagation (EP) and belief propagation (BP) with the aid of Gaussian approximation, respectively. Furthermore, to reduce the computation complexity involved in channel estimation, the matrix inversion is transformed into a series of diagonal matrix inversions through the Sherman-Morrison formula. Simulation experiments show that the proposed algorithm can reduce the pilot overhead by about 50%, compared with the traditional linear minimum mean square error (LMMSE) algorithm, and can approach to the bit error rate (BER) performance bound of perfectly known channel state information within 0.1 dB.

In orthogonal frequency division multiplexing (OFDM) systems, the least square (LS) in addition to the technique of linear minimum mean square error (LMMSE) channel estimation are compared using frequency as well as time domain in this paper. A constant LMMSE channel estimation has been proposed in time domain where the channel is not intimated before. It is presented by the Simulation outcomes that the channel estimation execution can be improved by the techniques of time domain but not using the techniques of frequency domain. Additionally, using the technique of LMMSE, higher accuracy is achieved by the proposed method which is presented in the outputs of the simulation.

In recent years, there has been an increased need for digital wireless applications to use high rate data transmission. OFDM (Orthogonal Frequency Division Multiplexing) offers an interesting solution that allows for the exploitation of the 60 GHz band with optimal spectral efficiency, a robustness to frequency selective fading, and a resistance to inter-symbol interference (ISI) that is a major problem in high speed data communications. Transmitted data in an OFDM system is divided on different subcarriers, after applying PSK (phase shift keying) or QAM (Quadrature Amplitude Modulation) modulation. The bandwidth of the obtained signal is converted to the time domain by using an IFFT (Inverse Fast Fourier Transform) in order to transmit it through a wireless channel. To recover the distorted data at the receiver, the effects of the channel must be estimated and compensated by the receiving system [1, 2]. In this paper, the 60 GHz channel estimation methods for OFDM systems based on comb-type pilot arrangement are investigated, as the algorithm of channel estimation based on comb-type is divided into pilot signal estimation and channel interpolation. The pilot signal estimation based on LS (Least Squares) or LMMSE (Linear Minimum Mean Square Error) criteria is studied along with the channel interpolation based on LI (linear interpolation). The performances of various estimation algorithms are evaluated and compared by measuring the Bit Error rate (BER) and Mean Square Error (MSE) where 16-QAM modulation scheme is applied.

Backscatter communication (BC) has emerged as a promising paradigm for enabling energy-efficient and low-cost Internet of Things (IoT) systems. However, one practical constraint that is often neglected in BC studies is the circuit sensitivity of the backscatter device (BD), which sets the minimum signal strength required to activate it for signal reflection. In this paper, we address the channel estimation (CE) problem in the BC system with a circuit sensitivity constraint. Specifically, we propose three channel estimators for the receiver in the BC system that is unaware of the activation states of the BD, namely the maximum likelihood (ML), linear minimum mean square error (LMMSE), and maximum a posteriori (MAP) estimators. We derive both the Cramér-Rao bound (CRB) and Bayesian Cramér-Rao bound (BCRB) to evaluate the performance of the proposed estimators. Finally, we provide simulations to validate our analysis. Our results demonstrate that the proposed LMMSE and MAP estimators outperform traditional estimators that neglect the circuit sensitivity constraint.

With the increasing rate of wireless devices and high bandwidth operations, wireless networking and communications are becoming over crowded. To cope with such crowded and messy situation, massive MIMO is designed to work with hundreds of low-cost serving antennas at a time as well as improve the spectral efficiency at the same time. Time Division Duplexing (TDD) has been used for gaining beamforming which is a major part of massive MIMO, to gain its best improvement to transmit and receive pilot sequences. All the benefits are only possible if the channel state information or channel estimation is gained properly. Least Square (LS), Minimum Mean Square Error (MMSE) and Linear Minimum Mean Square Error (LMMSE) are the estimators commonly used for estimating channel matrices. We have optimized these methods using genetic algorithm to minimize the mean squared error and finding the best channel matrix from existing algorithms with less computational complexity. Our simulation result has shown that the use of Genetic Algorithm (GA) worked well on existing algorithms in a Rayleigh slow fading channel and existence of Additive White Gaussian Noise. We found that the GA optimized LS is better than existing algorithms. GA provides optimal result in some few iterations in terms of Mean Square Error (MSE) with respect to SNRand computational complexity.

We generalize the multiuser (CDMA spread spectrum) communication systems to the fading environments. We first extend Verdu's (1986) conventional optimum receiver to Rayleigh-fading environments and then evaluate its performance. Having no knowledge of the received power at the receiving end, we therefore need an estimator to efficiently estimate the received signal strength of each user in fading environments. A linear minimum mean square error (LMMSE) unbiased estimator is proposed to attain this goal. By using the minimum mean square error (MMSE) Bayesian estimation, we further propose the LMMSE bit estimator for efficient demodulation. Its performance is close to the optimum multiuser receiver but with a much simpler polynomial complexity. To further reduce the complexity, we extend the LMMSE estimator to the sequential LMMSE estimator. In sequential estimation, we do not need to implement the matched filter banks and to perform the matrix inversion when estimating. In addition, it converges after approximately 2k iterations, where k is the number of users. With this fast convergence property and the simple structure, the sequential LMMSE estimator provides an attractive alternative to the implementation of a multiuser system.