Minimum Mean Square Error Algorithm Research Articles

Evaluating Performance: A Study of Encrypted vs. Unencoded Signals in SISO-OFDM with LS and MMSE Estimations

The continuous progress in digital communication has played a crucial role in meeting the increasing need for faster data rates. Orthogonal Frequency Division Multiplexing (OFDM), a pivotal methodology in this progression, attains improved data rates through the efficient utilisation of densely packed carriers within a specified channel bandwidth. This article focuses on the investigation of channel estimation in OFDM systems. the study of search lies in its examination of the performance consequences associated with the incorporation or lack thereof of a convolutional encoder in OFDM systems and looks at how well two well-known channel estimation algorithms, Least Square (LS) and Minimum Mean Square Error (MMSE), work in 4-Quadrature amplitude modulation (4-QAM) OFDM systems with and without a convolutional encoder with a comprehensive evaluation of the efficacy of the OFDM system across various channel conditions. It uses MATLAB implementations as its main tool. The findings of the study indicate that the MMSE algorithm, despite its higher complexity, exhibits superior performance in comparison to the LS algorithm when combined with a convolutional encoder. The gain in terms of bit error rate (BER) improvement approximately 12 dB. This represents the logarithmic scale improvement in BER from BER1(uncoded) to BER2(coded) at the same the energy per bit to noise power spectral density ratio (Eb/N0) of 40 dB.

Iterative algorithms and architectures in massive MIMO detection

Massive multiple-input multiple-output (MIMO) wireless systems play an important role in the 5G networks. The complexity of signal detection in massive MIMO is increasing rapidly due to the growth of the number of transmitting antennas. In this paper, we introduced different iterative algorithms to decrease the computational cost of the approximate minimum mean-square error (MMSE) algorithm, including the Neumann Series algorithm, Jacobi method, Gauss-Seidel method, Successive Over Relaxation method and the Conjugate Gradient method. In addition, the VLSI architecture implementations of algorithms mentioned above are also discussed in the article.

5G Channel Estimation Based on Whale Optimization Algorithm

This paper presents a novel approach, based on the whale optimization algorithm (WOA), for channel estimation in wireless communication systems. The proposed method provides a means to accurately estimate the wireless channel, while not requiring the statistical characteristics of the channel. This method uses the WOA to search for the best channel statistical characteristics toward the ultimate goal of having the smallest bit error rate (BER). The proposed approach is aimed at enhancing the efficiency of pilot-based OFDM systems under frequency-selective fading channels used in the performance testing of 5G New Radio gNodeB. In terms of BER and mean square error (MSE), the performance of the proposed WOA-based channel estimation algorithm is evaluated and compared with the conventional least square (LS) and minimum mean square error (MMSE) algorithms. The simulation results demonstrate that the proposed algorithm provides highly competitive performance over the MMSE algorithm and significantly outperforms the LS algorithm in a variety of system configurations. Since the requirement on prior channel statistics information makes the MMSE algorithm impractical or extremely complex, the proposed WOA-based channel estimation algorithm should be a suitable and promising candidate for dealing with channel estimation problems. The simulation framework is implemented in MATLAB and available upon request.

Novel Zero Circular Convolution Sequences for Detection and Channel Estimations

Multiuser communication systems or multiple access scheme systems favor sequences possessing the ideal periodic cross-correlation function (PCCF) property. In comparison, channel estimation, equalization, and synchronization applications favor sequences possessing the ideal periodic auto-correlation function (PACF) property. However, there is no set of sequences possessing both the ideal PCCF and PACF properties simultaneously, where auto-correlation and cross-correlation balance each other. In this work, sequences possessing the ideal PACF property are used as the base sequences. Then, a modulation technique is applied upon these base sequences to construct a set of zero circular convolution (ZCC) sequences within which an arbitrary pair of two sequences possesses the ideal PCCF property. Compared with least squares (LS) and minimum mean squared error (MMSE) algorithm, the simulation results show that the channel estimation performance of ZCC is better than MMSE and LS algorithms, and the computational complexity of the algorithm is the same as LS algorithm, but far lower than MMSE algorithm. This is the first study on ZCC sequences reported in the literature, in which their fundamental theorems, properties, construction, and applications are investigated. The advantage of possessing the desired PACF and the ideal PCCF properties allows the ZCC sequences to be used in a broader range of applications than other sets of sequences.

Rethinking WMMSE: Can Its Complexity Scale Linearly With the Number of BS Antennas?

Precoding design for maximizing weighted sum-rate (WSR) is a fundamental problem for downlink of massive multi-user multiple-input multiple-output (MU-MIMO) systems. It is well-known that this problem is generally NP-hard due to the presence of multi-user interference. The weighted minimum mean-square error (WMMSE) algorithm is a popular approach for WSR maximization. However, its computational complexity is cubic in the number of base station (BS) antennas, which is unaffordable when the BS is equipped with a large antenna array. In this paper, we consider the WSR maximization problem with either a sum-power constraint (SPC) or per-antenna power constraints (PAPCs). For the former, we prove that any nontrivial stationary point must have a low-dimensional subspace structure, and then propose a reduced-WMMSE (R-WMMSE) with linear complexity by exploiting the solution structure. For the latter, we propose a linear-complexity WMMSE approach, named PAPC-WMMSE, by using a novel recursive design of the algorithm. Both R-WMMSE and PAPC-WMMSE have simple closed-form updates and guaranteed convergence to stationary points. Simulation results verify the efficacy of the proposed designs, especially the much lower complexity as compared to the state-of-the-art approaches for massive MU-MIMO systems.

Research on Computational Intelligence Algorithm in LTE Channel Estimation

Because data traffic is growing at a rapid pace thanks to advancements in the Internet of Things, precise modelling and precisely anticipating Long-Term Evolution (LTE) Channel is critical for a variety of applications like as video streaming, effective bandwidth consumption, and power management. In this research, we propose a model based on a Computational Intelligence (CI) Algorithm that may enhance Channel Estimation based on received signal. Two Algorithms are considered. In contrast to previous work that focused solely on designing models to estimate channel using traditional Minimum Mean Square Error (MMSE) and Least Square (LS) algorithms, we used 1) GA (Genetic Algorithm) and 2) PSO (Particle Swarm Optimization Algorithm) to work on Discrete and Continuous Long-Term Evolution (LTE) drive test data. We're looking at LTE in the 5.8 GHz band in particular. By lowering the mean square error of LS and the complexity of MMSE, the design model attempts to improve channel estimation. Pilots are put at random and sent with data to gather channel information, which aids the receiver in decoding and estimating the channel using LS, MMSE, Taguchi GA, and PSO. The Bit Error Rate (BER), Signal to Noise Ratio, and Mean Square Error of a CI-based model have all been estimated. In comparison to the MMSE and LS algorithms, the proposed model BER achieves the target gain of 2.4 dB and 5.4 dB.

Efficient Hybrid Iterative Method for Signal Detection in Massive MIMO Uplink System over AWGN Channel

Massive multiple input multiple output (massive MIMO) is a key technology in fifth-generation (5G) and beyond fifth-generation (B5G) networks. It improves performance metrics such as gain, energy efficiency, spectral efficiency, and bit error rate (BER). Because of the large number of users and antennas, sophisticated processing is required to detect the transmitted message signal. One of the challenges in massive MIMO systems is transmitted message signal detection. To respond to these challenges, several detection algorithms have been developed, including minimum mean squared error (MMSE), zero forcing (ZF), matched filter (MF), conjugate-gradient (CG), gauss-seidel (GS), and optimized coordinate descent (OCD). Although the ZF and MMSE algorithms perform well, their computational complexity is high due to direct matrix inversion. When the number of users is much lower than the number of antennas, the MF algorithm performs well. However, as the number of users increases, the performance of the MF algorithm degrades. Although the OCD, CG, and GS algorithms have less computational complexity than the MMSE algorithm, they perform poorly in comparison. To address and resolve the shortcomings of existing methods, an efficient iterative algorithm has been proposed in this manuscript, which is a hybrid method possessing the combination of MMSE with the alternating direction method of multipliers (ADMM) technique and Gauss-Seidel method. The initial vector has a large influence on the performance, complexity, and convergence rate of such iterative algorithms. The proposed detector’s initial solution is determined using the diagonal matrix and MMSE with the ADMM technique. The proposed algorithm’s performance and complexity are compared with existing algorithms based on BER and the real number of multiplications, respectively. The numerical results revealed that the proposed algorithm achieves the desired performance with a small number of iterations and a significant reduction in computational complexity. At 8QAM, SNR = 20 dB, 80 × 120 massive MIMO antenna configuration, and n = 2, the percentage performance improvement of the proposed detector from the GS detector is 99.82%. At 32QAM, SNR = 25 dB, 120 × 180 antenna configuration, and n = 5, performance improvement of the proposed detector is 99.89%. At 64QAM, SNR = 28 dB, 80 × 120 antenna configuration, and n = 3, performance improvement of the proposed detector is 99.93%.

Design of 7 × 2.5 Gbps decision feedback equalization scheme for mode division multiplexing over free-space optics under diverse atmospheric turbulence

Free-space optics (FSO) systems use the atmosphere as a medium to propagate data in the form of an optical signal. Using mode division multiplexing (MDM) over FSO systems increases the capacity of the FSO link. However, atmospheric turbulence is one of the main problems that seriously limit the data transmission rate in FSO systems. This causes signal distortion during transmission that leads to data loss at the receiver side totally or partially. To address this problem, a decision feedback equalization (DFE) scheme with minimum mean square error (MMSE) in MDM for FSO systems was developed in OptSim 5.2 software to mitigate the adverse effects of atmospheric turbulence. The MMSE algorithm was used to optimize both the feed-forward and feedback filter coefficients of the DFE. The proposed DFE scheme in MDM for the FSO system comprises seven parallel 2.5 Gbps MDM channels using Hermite–Gaussian modes at the transmitter to transmit 17.5 Gbps and seven DFE schemes at the receiver to mitigate the effects of atmospheric turbulence. The simulation results demonstrate that the DFE scheme can transmit 17.5 Gbps over 40 m, 800 m, 1400 m, and 2 km under medium fog, medium rain, medium haze, and clear weather, respectively. We show that the DFE scheme improves the MDM over FSO system immunity to distortion in medium fog, medium rain, medium haze, and clear weather while maintaining high throughput and desired low bit error rate.

A comparative analysis of computational intelligence algorithms for estimation of LTE channels

Precise modelling and accurate estimation of long-term evolution (LTE) channels are essential for numerous applications like video streaming, efficient use of bandwidth and utilization of power. This deals with the fact that data traffic is increasing continuously with advances in Internet of things. Previous works were focused mainly on designing models to estimate channel using traditional minimum mean square error (MMSE) and least squares (LS) algorithms. The proposed model enhances LTE channel estimation. The designed model combines LS and MMSE methods using Taguchi genetic (GE) and Particle Swarm Intelligence (PSO) algorithms. We consider LTE operating in 5.8 GHz range. Pilot signals are sent randomly along with data to obtain information about the channel. They help to decode a signal in a receiver and estimate LS and MMSE combined with Taguchi GA and PSO, respectively. CI-based model performance was calculated according to the bit error rate (BER), signal-to-noise ratio and mean square error. The proposed model achieved the desired gain of 2.4 dB and 5.4 dB according to BER as compared to MMSE and LS algorithms, respectively.

Proposed Different Signal Processing Tools for Efficient Optical Wireless Communications

Optical Wireless Communication (OWC) is a new trend in communication systems to achieve large bandwidth, high bit rate, high security, fast deployment, and low cost. The basic idea of the OWC is to transmit data on unguided media with light. This system requires multi-carrier modulation such as Orthogonal Frequency Division Multiplexing (OFDM). This paper studies optical OFDM performance based on Intensity Modulation with Direct Detection (IM/DD) system. This system requires a non-negativity constraint. The paper presents a framework for wireless optical OFDM system that comprises (IM/DD) with different forms, Direct Current biased Optical OFDM (DCO-OFDM), Asymmetrically Clipped Optical OFDM (ACO-OFDM), Asymmetrically DC-biased Optical OFDM (ADO-OFDM), and Flip-OFDM. It also considers channel coding as a tool for error control, channel equalization for reducing deterioration due to channel effects, and investigation of the turbulence effects. The evaluation results of the proposed framework reveal enhancement of performance. The performance of the IM/DD-OFDM system is investigated over different channel models such as AWGN, log-normal turbulence channel model, and ceiling bounce channel model. The simulation results show that the BER performance of the IM/DD-OFDM communication system is enhanced while the fading strength is decreased. The results reveal also that Hamming codes, BCH codes, and convolutional codes achieve better BER performance. Also, two algorithms of channel estimation and equalization are considered and compared. These algorithms include the Least Squares (LS) and the Minimum Mean Square Error (MMSE). The simulation results show that the MMSE algorithm gives better BER performance than the LS algorithm.

Interference Mitigation by Adaptive Analog Spatial Filtering for MIMO Receivers

Exposed to strong cochannel/adjacent-channel interference, digital multiple-input–multiple-output (MIMO) receivers require high-dynamic-range analog-to-digital converters (ADCs). Hybrid beamforming featuring spatial filtering before the ADCs can adaptively mitigate interference in both the analog and digital domains; hence relaxing the required dynamic ranges of the ADCs. This article demonstrates the effectiveness of hybrid beamforming in this mitigation utilizing adaptive minimum mean square error (MMSE) and error vector magnitude (EVM) as an optimization criterion. Extensive EVM measurements are carried out with a conductive setup using a four-element 22-nm FD-SOI CMOS prototype MIMO receiver chip to verify the performance of the adaptive MMSE algorithm. Over-the-air (OTA) measurements with a linear four-element dipole antenna array with half-wavelength spacing in the 2.4-GHz industrial scientific and medical (ISM) band quantify the improvement for real-world scenarios, e.g., having a multipath propagation channel and mutual coupling between the antenna array elements. OTA results show that a rejection of 22.5 and 24.5 dB can be achieved on average in an in-door laboratory environment utilizing vector modulator (VM) constellations with 16 and 64 points, respectively.

Joint Deep Reinforcement Learning and Unfolding: Beam Selection and Precoding for mmWave Multiuser MIMO With Lens Arrays

The millimeter wave (mmWave) multiuser multiple-input multiple-output (MU-MIMO) systems with discrete lens arrays (DLA) have received great attention due to their simple hardware implementation and excellent performance. In this work, we investigate the joint design of beam selection and digital precoding matrices for mmWave MU-MIMO systems with DLA to maximize the sum-rate subject to the transmit power constraint and the constraints of the selection matrix structure. The investigated non-convex problem with discrete variables and coupled constraints is challenging to solve and an efficient framework of joint neural network (NN) design is proposed to tackle it. Specifically, the proposed framework consists of a deep reinforcement learning (DRL)-based NN and a deep-unfolding NN, which are employed to optimize the beam selection and digital precoding matrices, respectively. As for the DRL-based NN, we formulate the beam selection problem as a Markov decision process and a double deep Q-network algorithm is developed to solve it. The base station is considered to be an agent, where the state, action, and reward function are carefully designed. Regarding the design of the digital precoding matrix, we develop an iterative weighted minimum mean-square error algorithm induced deep-unfolding NN, which unfolds this algorithm into a layer-wise structure with introduced trainable parameters. Simulation results verify that this jointly trained NN remarkably outperforms the existing iterative algorithms with reduced complexity and stronger robustness.

Damped Jacobi Methods Based on Two Different Matrices for Signal Detection in Massive MIMO Uplink

Abstract For massive multiple-input multiple-output (m-MIMO) uplink, the performances of the linear minimum mean-square error (MMSE) detector are considered near optimal, and they occupy benchmark place for most linear iterative detectors. However, the MMSE algorithm is known by its load computational complexity due to the implication of large-scale matrix inversions, and in other hand, iterative methods are often preferred in signal detection because of its low complexity. In this paper, we propose a New Damped Jacobi (NDJ) detector in order to improve the performance of the classical Jacobi linear algorithm. Starting from the classical Jacobi technique to our new proposal, we go through the development of two variants; one uses a damping factor and the other uses a stair-matrix. However, the NDJ incorporates a damping factor in its construction and basing also on stair matrix instead of diagonal matrix. The performances in terms of convergence and low complexity of each Jacobi variant studied in this paper are analyzed. Finally, some simulation examples are given to illustrate the advantages of the new proposed algorithm.

Soft Output Signal Detection for Massive MIMO Systems Based on Chebyshev Trace Iteration

Minimum Mean Square Error (MMSE) algorithm can achieve near-optimal detection performance for multi-user massive Multiple Input Multiple Output (MIMO) systems. However, the calculation of the high-dimensional matrix inversion required in MMSE algorithm causes excessively high computational complexity, which makes it difficult to implement quickly and effectively in practical applications. At the same time, for the Higher Quadrature Amplitude Modulation (HQAM), the direct use of hard decision to realize the symbol-to-bit demapper will result in an obvious performance loss. Therefore, a low-complexity soft output signal detection algorithm based on Chebyshev-Trace Iteration (CTI) is proposed for Gray-coded HQAM in this paper. The algorithm not only effectively avoids the calculation of the high dimensional matrix inversion, but also gives a simplified calculation method with the trident list searching to compute the bit Log-Likelihood Ratio (LLR) by using the bit flip property of Gray-coded modulation and binary tree architecture. The simulation results show that the proposed soft output detection algorithm needs at most 3 iterations to converge and achieve detection performance close to MMSE, which achieves a good tradeoff between the complexity and the detection performance.

The Art of Piecewise Linear Approximation in MMSE Estimator for Most Accurate and Fast Frequency Extraction in DIFM Receivers

Detection of wideband passive radar signals, accomplished by instantaneous frequency measurement (IFM) systems, is crucial for gaining a profound knowledge of environmental circumstances. The need for fast pulse detection has hindered the investigation of frequency extraction with higher accuracy in IFM receivers. A noteworthy research in recent years shows that fast and reliable frequency extraction in high bit-count (HBC) IFMs while attaining a better frequency accuracy [called intelligent, reliable, and design-independent (InReDI)] is feasible. In addition, some investigated process-intensive algorithms like the minimum mean squared error (MMSE) estimator promise excellent frequency accuracy. In this work, we present a new method of MMSE algorithm modified by a piecewise linear approximation [named linear approximation of MMSE (LAMMSE)]. By utilizing the InReDI methodology and the novel LAMMSE algorithm, we propose a new architecture for a fast, accurate, and reliable frequency extraction (FAREx) in HBC digital IFMs (DIFM) receivers. The proposed FAREx architecture resolves the compromise challenge between frequency accuracy and extraction speed that has been long lingered in DIFM receivers. We have implemented the new architecture using Xilinx field-programmable gate array (FPGA) on a fabricated 15 bit, 2–4 GHz, and 70 dB dynamic range IFM receiver. The measurement results show an average frequency rms error of 1.43 MHz for a CW signal, 2.49 MHz average rms error for a 50 ns pulsed input signal, and 2.7 MP/s detection speed, representing a state-of-the-art receiver and a breakthrough compared to the latest works.

Wire-Mesh Sensor Super-Resolution Based on Statistical Reconstruction

A wire-mesh sensor (WMS) is a widely used instrument to visualize and estimate derived parameters of multiphase flows, e.g., gas void fraction or liquid hold-up. The spatial resolution of obtained flow images is associated with the number of crossing points formed by the transmitter and receiver wires of a given sensor. This may be a limitation for applications that require high spatial resolution since WMS is an intrusive device and the increase of electrodes may increase pressure drop and deform/fragment bubbles. In order to minimize such undesirable effects and maximize the sensor resolution, we employed a reconstruction algorithm based on the minimum mean-square error (MMSE) estimator to increase image resolution of WMS with fewer wires than commonly reported in the literature, i.e., here, we apply <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$8\times 8$ </tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$6\times 6$ </tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$4\times 4$ </tex-math></inline-formula> , and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2\times 2$ </tex-math></inline-formula> sensors for 1-in pipe. Since standard regularization approaches may provide incorrect solutions for such configurations, a new methodology to obtain the prior model is presented. In our approach, the prior is assumed as a multivariate Gaussian model, which is extracted from experimental flow data of a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$16\times 16$ </tex-math></inline-formula> WMS (the most common resolution for 1-in pipe). Finally, the sensitivity matrix obtained by electric field simulation and the experimental prior model is incorporated into the MMSE algorithm to restore experimental flow data of the low-resolution sensors. The experiments were performed in a flow loop operating at slug flow. The experimental results suggest that the MMSE estimator combined with the experimental prior model has a high potential not only to improve image resolution but also to correct the average void fraction estimation.

Mitigation of Atmospheric Turbulences Using Mode Division Multiplexing based on Decision Feedback Equalizer for Free Space Optics

AbstractIn mode division multiplexing (MDM) free space optical (FSO) communication system, the atmospheric turbulences such as fog, rain, and haze cause adverse effects on system performance. This paper investigates the mitigation of atmospheric turbulences of FSO using MDM and decision feedback equalizer (DFE) with minimum mean square error (MMSE) algorithm. The implementation of the MMSE algorithm is used to optimize both the feedforward and the feedback filter coefficients of DFE. The proposed system comprises three parallel 2.5Gbit/s channels using Hermite–Gaussian modes. A data rate of 7.5Gbit/s over 40 m, 800 m, 1400 m, and 2km under medium fog, rain, haze, and clear weather, respectively, has been achieved. In addition, it is noticed that the link distance is reduced while increasing the attenuation. The simulation results revealed that a DFE improves the performance MDM FSO system while maintaining high throughput and desired low bit error rate.

Low-Complexity Soft-Output Signal Detection Based on Improved Kaczmarz Iteration Algorithm for Uplink Massive MIMO System.

For multi-user uplink massive multiple input multiple output (MIMO) systems, minimum mean square error (MMSE) criterion-based linear signal detection algorithm achieves nearly optimal performance, on condition that the number of antennas at the base station is asymptotically large. However, it involves prohibitively high complexity in matrix inversion when the number of users is getting large. A low-complexity soft-output signal detection algorithm based on improved Kaczmarz method is proposed in this paper, which circumvents the matrix inversion operation and thus reduces the complexity by an order of magnitude. Meanwhile, an optimal relaxation parameter is introduced to further accelerate the convergence speed of the proposed algorithm and two approximate methods of calculating the log-likelihood ratios (LLRs) for channel decoding are obtained as well. Analysis and simulations verify that the proposed algorithm outperforms various typical low-complexity signal detection algorithms. The proposed algorithm converges rapidly and achieves its performance quite close to that of the MMSE algorithm with only a small number of iterations.

Low Complexity MMSE-SQRD Signal Detection Based on Iteration

Aiming at the problem of high computational complexity of Vertical-BLAST (V-BLAST) algorithm in Multiple-Input Multiple-Output-Orthogonal Frequency Division Multiplexing (MIMO-OFDM) system signal detection, this paper first uses Sorted QR Decomposition (SQRD) iterative operation instead of matrix inversion to reduce the computational complexity of the algorithm, and then considering that the algorithm is greatly affected by noise, Minimum Mean Square Error (MMSE) criterion is used to weaken the noise effect. At the same time, in order to reduce the noise and computational complexity, MMSE and SQRD are combined, which can not only reduce the noise and computational complexity, but also obtain the sub-optimal detection order, thus improving the detection performance of the MIMO-OFDM system. Finally, the numerical simulation of the MMSE-SQRD detection algorithm is carried out. The results show that the Eb/No of MMSE-SQRD algorithm is 2 dB greater than that of the MMSE algorithm and the computational complexity is O(N T 3 ) under the conditions that NT = NR = 2 and the BER is 10−2. The detection algorithm satisfies the demand of short wave and wideband wireless communication.

Low-complexity joint channel estimation and symbol detection for OFDMA systems

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.