Least Square Channel Estimation Research Articles

Modified DDFTN Algorithm for Band-Limited Short-Reach Optical Interconnects

Inter symbol interference (ISI) degrades the performance of intensity modulation and direct detection (IM/DD) transmission systems due to various transceiver and channel impairments. To overcome the ISI of IM/DD transmission systems, the direct detection faster than Nyquist (DDFTN) algorithm has been widely used. However, when a system is subjected to severe ISI, the performance of the conventional DDFTN algorithm is suboptimal. To further improve the performance of IM/DD transmission systems, a modified DDFTN algorithm is proposed. We add least squares (LS) channel estimation after the postfilter. The coefficients of maximum likelihood sequence estimation (MLSE) are close to the initial channel response with LS channel estimation. The performance of the conventional and modified DDFTN algorithms is compared for 112, 140, and 160 Gbit/s PAM4 signals over 2 km, 1 km, and 500 m standard single-mode fibers (SSMFs) in a 3 dB bandwidth, 19 GHz IM/DD system in the C band. For 140 Gbit/s signal transmission over 1 km, the modified DDFTN algorithm achieves the optimal receiver sensitivity of -1.5 dBm at a 7% forward error correction (FEC) threshold of 3.8E-3, which is better than the receiver sensitivity of -0.5 dBm achieved with the conventional DDFTN algorithm. Furthermore, for 160 Gbit/s signal transmission over 500 m, the modified DDFTN algorithm achieves the optimal receiver sensitivity of 1 dBm at 3.8E-3, which is also a superior result compared to the conventional DDFTN algorithm.

Spectral decomposition-based optimization for MMSE receiver design in an uplink MU-MIMO cooperative communication system with imperfect CSI

The receiver’s architecture is always a critical issue in multiple-input multiple-output (MIMO) systems, as it has a great impact on the system’s performance and complexity. Accordingly, in this paper, a spectral decomposition-based minimum mean squared error (MMSE) receiver is proposed in an uplink multi-user MIMO (MU-MIMO) system with a full-duplex decode and forward relay. Imperfect channel state information is assumed at the relay and base station where, least-squares channel estimation technique is applied due to its simplicity and low complexity. An equivalent relay is applied for self-interference cancellation. While, multi-user interference is mitigated by using the block diagonalization concept. A closed-form expression for the mean squared error (MSE) of the estimated data symbol is derived in the presence of channel estimation error. Moreover, an optimization problem is solved to derive an expression for the proposed MMSE receiver’s matrix. Finally, the performance of the proposed receiver is compared to that of the conventional receiver and Zero-forcing (ZF) receiver. Results show the superiority of the proposed receiver over both receivers.

Modified entropy based least square channel estimation technique for 5G massive multiple input multiple output universal filtered multicarrier systems

These days’ Massive multiple input multiple output (mMIMO) systems have become popular because of their enhanced data transmission rates, robustness against multipath fading, enhanced spectral efficacy, and ability to communicate with a more significant number of users with immense coverage. The critical challenge of the mMIMO systems is precisely replenishing the channel state information (CSI), along with the synchronization between receiver and transmitter. The CSI has recovered with the help of various channel estimation (CE) techniques. This paper presents a modified entropy-based least square CE technique for 5G mMIMO-UFMC systems. The proposed CE technique performance is novel and better than the Least Square (LS) and minimum mean square error (MMSE) CE techniques. The proposed CE technique was evaluated using MATLAB, and its performance results are shown in the simulation. The performance results of the proposed CE are evaluated based on the mean square error (MSE) and bit error rate (BER) of the obtained signal. The executed results prove that the proposed CE is efficient compared to conventional CE methods. The performance of the MCM techniques with respect to the proposed CE is also presented in this paper. This paper also explains the analytical assessment of the LS, MMSE, and MELS CE techniques. The results show that at high values of SNR, the proposed algorithm outperforms the LS and MMSE for both BER and MSE.

BER Reduction Using Partial-Elements Selection in IRS-UAV Communications With Imperfect Phase Compensation

This article considers minimizing the communications bit error rate (BER) of unmanned aerial vehicles when assisted by intelligent reflecting surfaces. By noting that increasing the number of IRS elements in the presence of phase errors does not necessarily improve the system’s BER, it is crucial to use only the elements that contribute to reducing such a parameter. To this end, we propose an efficient algorithm to select the elements that can improve BER. The proposed algorithm has lower complexity and comparable BER to the optimum selection process, which is an NP-hard problem. The accuracy of the estimated phase is evaluated by deriving the probability distribution function (PDF) of the least-square channel estimator, and showing that the PDF can be closely approximated by the von Mises distribution at high signal-to-noise ratios. The obtained analytical and simulation results show that using all the available reflectors can significantly deteriorate the BER, and thus, partial element selection is necessary. It is shown that, in some scenarios, using about 26% of the reflectors provides more than tenfold BER reduction. The number of selected reflectors may drop to only 10% of the total elements. As such, the unassigned 90% of the elements can be allocated to serve other users, and the overhead associated with phase information is significantly reduced.

An improved least squares (LS) channel estimation method based on CNN for OFDM systems

<abstract><p>Least squares (LS) is a commonly used pilot-based channel estimation algorithm in orthogonal frequency division multiplexing (OFDM) systems. This algorithm is simple and easy to implement because of its low computation complexity. However, it has poor performance, especially at low signal-to-noise ratio (SNR). To solve this problem, an improved LS channel estimation method based on convolutional neural network (CNN) is proposed on the basis of analyzing the traditional LS channel estimation methods. A channel estimation compensated network is designed based on CNN, which can solve the problem of performance degradation of the mean square error (MSE) through the online and offline modules. By designing the input-output relations, training data set, and testing data set, a CNN network is iteratively trained to learn the relevant features of the channels, so that the traditional LS estimation value can be corrected to improve the accuracy. Simulation results show that the proposed method can achieve better performance in bit error rate (BER) and MSE, compared with the traditional channel estimation methods.</p></abstract>

Estimation of Channel for Millimeter-Wave Hybrid Massive MIMO Systems using Orthogonal Matching Pursuit (OMP)

In a millimeter-wave (mm-Wave) large MIMO system, hybrid precoding is a critical component for lowering radio-frequency hardware costs as compared to the traditional full-digital precoding strategy. Knowledge of channels is required for hybrid precoding. Though, estimation of the channel is problematic for the mm-Wave system because of the usage of a massive array of antenna and hybrid architecture with analog precoding. Due to the extremely directed nature of wireless propagation, wireless channels have spatial sparsity. In this paper, we exploit this spatial sparsity nature of wireless channels to develop orthogonal matching pursuit technique-based estimation of channels for hybrid millimeter-wave (mm-Wave) wireless systems. Genie (Ideal) channel estimation is also performed in which we presume that actual angle of departures (AoD) and angle of arrivals (AoA) are known to us. Finally, the simulation results reveal that suggested OMP algorithm-based channel estimation has a significant advantage over conventional approaches like least-squares channel estimation.

Impacts of channel fluctuations on least-squares channel estimation in underwater acoustic communications.

The time-varying multipath introduces major distortions to transmissions in the underwater acoustic communication channel. Channel estimation is often used as one of the central steps to address such distortions in high-rate communication receivers. The focus of this paper is to quantify the impacts of the channel fluctuations on the performance of the least-squares channel estimator. A metric, channel variation ratio (CVR), is defined to describe the rate of fluctuations in the channel impulse responses. Equations are derived to reveal the direct relationships between the CVR and channel estimation performance, which is measured by the channel estimation mean squared error (MSE) and signal prediction error (SPE). The equations show that both the MSE and SPE increase linearly with the CVR. The MSE and SPE metrics both have an error floor for time-varying impulse responses, even with zero ambient noise. It is confirmed that an optimum estimated channel length, achieving the minimum estimation error, exists for time-varying impulse responses. The truncation effects in the channel estimation are also investigated. Experimental data are used to validate the findings.

Performance Evaluation of GFDM Channel Estimation Using DFT for Tactile Internet Application

In this work, discrete Fourier transform (DFT)-based channel estimation is proposed in generalized frequency division multiplexing (GFDM) system. In the GFDM system, the subcarriers are non-orthogonal; therefore, the pilot symbols cannot be easily observed due to the interference from data symbols and noise. The proposed method can improve the channel estimation of least square (LS) method by eliminating channel impulse response outside the number of actual impulse response. First, the received signal is demodulated using zero forcing demodulator. Then, it is divided with transmitted pilot symbols to obtain channel response. Interpolation in frequency and time domains is conducted to acquire channel response for all GFDM blocks. Finally, the channel estimation algorithm using DFT is performed. The parameters of the system are adjusted so that they are suitable for tactile internet application. The channel model used is NYUSIM, which utilizes mmWave. Three scenarios in NYUSIM such as urban microcell, urban macro cell and rural macro cell are used and power delay profiles generated from NYUSIM simulator are employed in this system. The results show that mean square error (MSE) from DFT-based channel estimation gives substantial improvement for all scenarios. In addition, symbol error rate (SER) of DFT-based channel estimation provides a slight improvement of ~1.5 dB than LS channel estimation.

Large Intelligent Surfaces With Channel Estimation Overhead: Achievable Rate and Optimal Configuration

Large intelligent surfaces (LIS) present a promising new technology for enhancing the performance of wireless communication systems. Realizing the gains of LIS requires accurate channel knowledge, and in practice the channel estimation overhead can be large due to the passive nature of LIS. Here, we study the achievable rate of a LIS-assisted single-input single-output communication system, accounting for the pilot overhead of a least-squares channel estimator. We demonstrate that there exists an optimal $K^{*}$, which maximizes achievable rate by balancing the power gains offered by LIS and the channel estimation overhead. We present analytical approximations for $K^{*}$, based on maximizing an analytical upper bound on average achievable rate that we derive, and study the dependencies of $K^*$ on statistical channel and system parameters.

Joint Semi-Blind Channel Estimation and Finite Alphabet Signal Recovery Detection for Large-Scale MIMO Systems

In this paper, we consider large-scale MIMO systems and we address the channel estimation problem. We propose an iterative receiver consisting of the cascade of a semi-blind least-squares channel estimation algorithm with a simplicity-based detection algorithm for finite-alphabet signals (FAS and FAS-SAC). A minimum number of pilot sequences is used to get an initial channel estimation. The detection algorithm outputs are then used to refine it gradually. Two feeding methods are studied. The first one uses raw detection outputs. The second one is based on hard decisions and enables better performance. Theoretical MSEs are calculated in both cases. Simulations assess the efficiency of the proposed iterative procedure compared to the state-of-the-art methods and show that it performs very close to the ideal scenario where all the communication frame sequences are known.

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.

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.

ZF and MMSE Detectors Performances of a Massive MIMO System Combined with OFDM and M-QAM Modulation

This paper presents a least squares channel estimation (LSCE) in the UpLink transmission for a Massive MIMO systems in 5G wireless communications, combined with Orthogonal Frequency Division Multiplexing and higher-order M-QAM modulation. The Mean Square Error (MSE) of the LSCE is computed, and the performance of ZF, MMSE and V-BLAST detectors is also evaluated. Using 128-QAM modulation (i.e., increasing the noise system sensibility) with 1024 subcarriers and increasing the Base Station antennas array decreases more the Bit Error Rate (BER) for the ZF, MMSE and V-BLAST detectors with respect to the MSE. The performance degradation both ZF and MMSE compared to V-BLAST is negligible in a high receive antennas; hence, faster data rates and higher spectral efficiency levels for the communication systems. Consequently, the ZF, MMSE and V-BLAST detectors achieve a better BER with respect to channel estimation.

Frequency-domain equalization with interference rejection combining for single carrier multiple-input multiple-output underwater acoustic communications.

This paper describes a three-step frequency-domain equalization scheme for multiple-input multiple-output (MIMO) underwater acoustic communication. First, an iterative least-squares channel estimation method is developed to enhance the accuracy of channel estimation in MIMO communication. The interference rejection combining method is then adopted to suppress co-channel interference based on the estimated MIMO channels. This technique exploits the correlation between the interference received through different channels. Finally, a decision feedback equalizer embedded with a digital phase-lock loop is cascaded before the final determination of equalized symbols to compensate the phase rotation. Experimental results show that the bit error rates of the proposed scheme can be several orders of magnitude lower than those of conventional frequency-domain equalization schemes.

Reference Signal Reconstruction Under Oversampling for DTMB-Based Passive Radar

The robust reconstruction of the reference signal is one of the key technologies in passive radars. This paper investigates the reference signal reconstruction problem for digital television terrestrial multimedia broadcasting (DTMB)-based passive radar. The conventional digital signal processing for the DTMB signal is usually based on the assumption of the equal bandwidth sampling (EBS) in which the sampling rate is equal to the nominal bandwidth 7.56 MHz defined in the DTMB standard. But we reveal that the high-frequency subcarriers of the DTMB signal are aliased under the EBS, which will degrade the reconstruction performance. Thus we suggest the oversampling approach for the DTMB-based passive radar. The least squares (LS) channel estimation under oversampling is thoroughly analyzed. Moreover to solve the problem that the LS algorithm cannot estimate the time-domain response of the channel under oversampling, we propose two modified LS channel estimation algorithms, namely the Tikhonov regularization LS and reduced rank approximation LS. The advantages of the reference signal reconstruction under oversampling over that under EBS are validated by both the simulation and field experimental data.

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.

Interference Mitigation Using Angular Diversity Receiver With Efficient Channel Estimation in MIMO VLC

Visible Light Communication (VLC) is a promising solution to meet the ever increasing demand for indoor data connectivity with high bit rates. VLC uses the license-free bands and provides high-speed connections unlike RF wireless communication. However; indoor VLC suffers from performance degradation due to either co-channel interference (CCI) or inter-symbol interference (ISI). In this paper, an interference management scheme is proposed for VLC Multi-Input Multi-Output (MIMO) based systems. The scheme reduces the number of interfered signals by using a constrained field-of-view angular diversity receiver CFOV-ADR and then uses least-square (LS) channel estimation with maximum-likelihood (ML) equalizer to resolve the interfered signals. The proposed interference mitigation scheme using constrained-FOV-ADR with channel estimation IM-CFOV-CE enables frequency reuse of one. The bit-error-rate (BER) is calculated at various room positions with different receiver’s heights and rotation angles. The performance evaluation results reveal that the proposed system can achieve a higher number of downlink channels and superior BER performance than that of without CCI management. Also, the proposed scheme has been compared with Time Division Multiple Access (TDMA) technique, and achieves enhanced performance at all positions and orientations of the ADR.

Detection of pilot spoofing attack in massive MIMO systems based on channel estimation

In coherent massive MIMO systems, the training phase provides opportunity for an active eavesdropper to attack legitimate communication, which is known as pilot spoofing attack. Hence, this paper proposes an algorithm to detect this attack based on channel estimate. Concretely, the user sends pilots to the base station (BS), where channel estimation is carried out using least square (LS) method. According to the likelihood ratio test principle, three detectors based on LS channel estimate are proposed. Moreover, performance analysis concerning the probability of detection (Pd) is presented, particularly the impact of key parameters on it. From the perspective of legitimate user, deploying more antennas is effective in improving Pd, whereas an eavesdropper needs to tunes its transmit power to strike a balance between eavesdropping and hidden abilities.

Linear Minimum Error Probability Detection for Massive MU-MIMO With Imperfect CSI in URLLC

It is challenging to realize ultra-reliable and low latency communications (URLLC) under severe shadow fading and imperfect channel state information (CSI). However, reliability can be increased by exploiting space diversity from multiple receive antennas rather than retransmission with limited latency. Massive multi-user multiple-input-multiple-output (MU-MIMO) is studied to enable URLLC with imperfect CSI from least-square channel estimation. The linear minimum error probability (MEP) detector with a given length of pilots (LoP) is derived. Further, the LoP is optimized to minimize the error probability of the uplink with a limited number of channel uses, using the finite blocklength information theory and one-dimensional search methods. Numerical results verify that the proposed linear MEP detection incorporated in massive MU-MIMO improves reliability with limited latency and imperfect CSI.

Application Analysis of LS Channel Estimation for Transform Domain Communication System

To reduce the influence of wireless transmission channel on transform domain communication system (TDCS) and improve the channel estimation accuracy, a system model of Least Square (LS) channel estimation on TDCS is established. In this paper, the influence of the unavailable frequency existing in basic function is analysed for the LS channel estimation, then the expression of mean square error (MSE) is derived. After that, the frequency pilot insertion pattern and the interpolation algorithm suitable for TDCS is proposed. The simulation results verify the paper’s theoretical analysis, and the effectiveness of the proposed algorithm is proved by the comparison of the MSE and BER performance.