Linear Minimum Mean Square Error Channel Estimation Research Articles

Iterative Joint Estimation Procedure of Channel and PDP for OFDM Systems.

The power-delay profile (PDP) estimation of wireless channels is an important step to generate a channel correlation matrix for channel linear minimum mean square error (LMMSE) estimation. Estimated channel frequency response can be used to obtain time dispersion characteristics that can be exploited by adaptive orthogonal frequency division multiplexing (OFDM) systems. In this paper, a joint estimator for PDP and LMMSE channel estimation is proposed. For LMMSE channel estimation, we apply a candidate set of frequency-domain channel correlation functions (CCF) and select the one that best matches the current channel to construct the channel correlation matrix. The initial candidate set is generated based on the traditional CCF calculation method for different scenarios. Then, the result of channel estimation is used as an input for the PDP estimation whereas the estimated PDP is further used to update the candidate channel correlation matrix. The enhancement of LMMSE channel estimation and PDP estimation can be achieved by the iterative joint estimation procedure. Analysis and simulation results show that in different communication scenarios, the PDP estimation error of the proposed method can approach the Cramér-Rao lower bound (CRLB) after a finite number of iterations. Moreover, the mean square error of channel estimation is close to the performance of accurate PDP-assisted LMMSE.

Joint Pilot Design and Channel Estimation Using Deep Residual Learning for Multi-Cell Massive MIMO Under Hardware Impairments

In multi-cell massive multiple-input multiple-output (MIMO) systems, channel estimation is deteriorated by pilot contamination and the effects of pilot contamination become more severe due to hardware impairments. In this paper, we propose a joint pilot design and channel estimation based on deep residual learning in order to mitigate the effects of pilot contamination under the consideration of hardware impairments. We first investigate a conventional linear minimum mean square error (LMMSE) based channel estimator to suppress the interference caused by pilot contamination. After that, a deep learning based pilot design is proposed to minimize the mean square error (MSE) of LMMSE channel estimation, which is utilized to the joint pilot design and channel estimator for transfer learning approach. For the channel estimator, we use a deep residual learning which extracts the features of interference caused by pilot contamination and eliminates them to estimate the channel information. Simulation results demonstrate that the proposed joint pilot design and channel estimation method can effectively reduce the effect of pilot contamination as well as outperforms the conventional approach in multi-cell massive MIMO scenarios. Moreover, the joint pilot design and channel estimation method using transfer learning further enhances the estimation performance when the prior knowledge of pilot contamination cannot be exploited.

A DFT-based Low Complexity LMMSE Channel Estimation Technique for OFDM 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.

LMMSE channel estimation for OFDM systems with channel correlation function selection

In the linear minimum mean square error (LMMSE) estimation for orthogonal frequency division multiplexing (OFDM) systems, the problem about the determination of the algorithm's parameters, especially those related with channel frequency response (CFR) correlation, has not been readily solved yet. Although many approaches have been proposed to determine the statistic parameters, it is hard to choose the best one within those approaches in the design phase, since every approach has its own most suitable application conditions and the real channel condition is unpredictable. In this paper, we propose an enhance LMMSE estimation capable of selecting parameters by itself. To this end, sampled noise MSE is first proposed to evaluate the practical performance of interpolation. Based on this evaluation index, a novel parameter comparison scheme is proposed to determine the parameters which can endow LMMSE estimation best performance within a parameter set. After that, the structure of the enhanced LMMSE is illustrated, and it is applied in OFDM systems. Besides, the issues about theoretical analysis on accuracy of the parameter comparison scheme, the parameter set design and algorithm complexity are explained in detail. At last, our analyses and performance of the proposed estimation method are demonstrated by simulation experiments.

On Channel Estimation in LTE-Based Downlink Narrowband Internet of Things Systems

Narrowband Internet of Things (NB-IoT) systems were specified by 3GPP in release 13 as a low power wide area network (LPWAN) technology to operate with a very narrow bandwidth of 180 kHz only. Due to fragile radio signal operating conditions (where a signal is weaker than noise), NB-IoT channel status becomes highly complex. Therefore, an effective and low complexity channel estimation will perform a significant role in the receiver operation. The linear minimum mean square error (LMMSE) scheme is very effective in estimating the channel but introduces massive complexity because of having complex matrix inversion. In this paper, we first derive the analytical model of the signal for long-term evolution (LTE)-based NB-IoT downlink systems and propose a reduced complexity LMMSE channel estimation for the downlink NB-IoT systems by applying singular value decomposition (SVD) technique along with partitioning the whole channel matrix into small submatrices. Furthermore, we apply the overlap banded technique to optimize the performance of the proposed channel estimator. As a result of exploiting several submatrices instead of a larger channel matrix, the operational complexity is significantly optimized. Lastly, we propose a polyphase filter structure for implementing the interpolation procedure instead of the conventional interpolation method to further optimize the performance and complexity of the proposed channel estimator further. The performance of the proposed technique has been justified by the mean square error (MSE), bit error rate (BER), and instantaneous throughput for the related signal-to-noise ratio (SNR). The system complexity is verified by the number of complex multiplications used. Simulation evaluations indicate that with the sacrifice of negligible performance, the proposed modified LMMSE technique along with the proposed interpolation possesses a good balance between the performance and the system complexity that could help the proposed techniques to be applied successfully in the low complexity NB-IoT systems.

LMMSE Channel Estimation in OFDM Systems: A Vector Quantization Approach

The linear minimum mean square error (LMMSE) channel estimation yields the optimal performance in terms of the mean square error (MSE). However, the high computational complexity limits its application in practical systems. To overcome this issue, this letter proposes a vector quantization approach to the LMMSE channel estimation. The LMMSE filtering matrices corresponding to some typical wireless channels are calculated off-line. When performing the LMMSE channel estimation on-line, an appropriate LMMSE filtering matrix is selected according to the MSE criterion. At the expense of a negligible performance degradation, the computational complexity of the LMMSE channel estimation is reduced.

A Low Complexity Optimal LMMSE Channel Estimator for OFDM System

Linear minimum mean square error (LMMSE) is the optimal channel estimator in the mean square error (MSE) perspective, however, it requires matrix inversion with cubic complexity. In this paper, by exploiting the circulant property of the channel frequency autocorrelation matrix RHH, an efficient LMMSE channel estimation method has been proposed for orthogonal frequency division multiplexing (OFDM) based on fast Fourier transformation (FFT) and circular convolution theorem. Finally, the computer simulation is carried out to compare the proposed LMMSE method with the classical LS and LMMSE methods in terms of performance measure and computational complexity. The simulation results show that the proposed LMMSE estimator achieves exactly same performance as conventional LMMSE estimator with much lower computational complexity.

Pilot Length and Channel Estimation for Massive MIMO IoT Systems

Massive capacity gain in Massive MIMO (multiple-input and multiple-output) depends on uplink pilots sent by the users to provide up-to-date CSI (channel state information) for closed-loop precision beamforming. To support a huge number of IoT (Internet of Things) devices, a set of orthogonal pilots with possible reuse or random non-orthogonal pilots can be assigned to IoT devices for this purpose. We investigate the performance differences between a simple channel estimation and LMMSE (linear minimum mean square error) channel estimation, combined with orthogonal pilot reuse and random pilot schemes, and the impact of pilot length. We develop simple algorithms to estimate optimal pilot length that can support the most IoT devices simultaneously.

Compression-Based LMMSE Channel Estimation With Adaptive Sparsity for Massive MIMO in 5G Systems

Massive multi-input multi-output (MIMO) has been regarded as one of the key technologies for fifth generation (5G) mobile communication systems, as it can significantly enhance the system capacity with high spectrum and energy efficiency. For massive MIMO systems, accurate channel estimation is a challenging problem, especially when the number of parameters to be estimated is large and the number of pilots is limited. In this paper, a compression-based linear minimum mean square error (CLMMSE) channel estimation algorithm is proposed for massive MIMO in 5G systems. Compared with the traditional linear minimum mean square error (LMMSE) algorithm, the proposed approach calculates the channel autocorrelation matrix by investigating the channel prior information based on compressive sensing (CS) theory, utilizing the block sparsity of massive MIMO channels, to reduce the complexity for obtaining autocorrelation matrix. Then it substitutes matrix inverse operation by singular value decomposition to further reduce the computational complexity. In addition, a block sparsity adaptive matching pursuit (BSAMP) method is also proposed to adaptively estimate the block sparsity of the channel in the first step of the proposed CLMMSE algorithm, which can make it more efficient. The sparsity-adaptive processing is achieved by setting a threshold and finding the position of the maximum backward difference, then using the regularized method to solve channel estimation as a convex optimization problem. Analyses and simulations indicate that with slight performance degradation, the proposed algorithm reduces the computational complexity significantly compared with the traditional LMMSE algorithm. And compared with pure CS methods, CLMMSE has an obviously better performance, which is beneficial to solve the pilot pollution problem of massive MIMO in 5G systems. Furthermore, the BSAMP-based CLMMSE algorithm has better performance and lower time complexity than the algorithm based on other CS methods, which further improves the system performance.

LMMSE channel estimation for wireless energy harvesting AF relaying

Wireless energy harvesting can be adopted in relaying systems to solve the energy issue at the relay node. Channel estimation is an important aspect of its system design. Thus, in this paper, we study channel estimation for wireless energy harvesting relaying. In the study, we use the linear minimum mean squared error (LMMSE) estimators to estimate the source-to-relay link and the relay-to-destination link separately in an amplify-and-forward relaying system. Time-varying Rayleigh fading channels using the Jakes model are considered. Both time-switching (TS) and power-splitting (PS) energy harvesting strategies are examined. Fixed-gain relaying is compared with variable-gain relaying. The signal-to-noise ratios and the bit error rates are calculated. Numerical results are used to show that the system suffers from an error floor due to the use of LMMSE estimators and that its performance depends on several important system parameters. In particular, it is found that PS outperforms TS, variable-gain relaying is better than fixed-gain relaying, and a stationary relay can lead to better performance than a mobile relay. For PS, the choice of the PS factor is important. On the other hand, the symbol position has little effect on the BER.

Implementation of Massive MIMO Uplink Receiver on RaPro Prototyping Platform

The updated physical layer standard of the fifth generation wireless communication suggests the necessity of a rapid prototyping platform. To this end, we develop 5G rapid prototyping system architecture (RaPro), a multi-core general purpose processor-based massive multiple-input-multiple-output (MIMO) prototyping platform. To enhance RaPro, high performance detection and beamforming are needed, whereas both of them request for accurate channel state information (CSI). In this paper, linear minimum mean square error (LMMSE)-based channel estimator is adopted and encapsulated inside RaPro to gain more accurate CSI. Considering the high complexity and unknown of channel statistics, we design low-complexity LMMSE channel estimator to alleviate the rising complexity along with increasing antenna number and set more computational resource aside for massive MIMO uplink detection and downlink beamforming. Simulation results indicate the high mean square error performance and robustness of designed low-complexity method. Indoor and corridor scenario tests show prominent improvement in bit error rate performance. Time cost analysis proves the practical use and real-time transmission ability of the implemented uplink receiver on RaPro.

LMMSE channel estimation in OFDM context: a review

Linear minimum mean square error (LMMSE) is by definition the optimal channel estimator in the sense of mean square error criterion, but its practical application is limited by its high complexity. Furthermore, the LMMSE estimation method requires the knowledge of both the channel and the noise statistics, which are a priori unknown at the receiver. A wide range of techniques are proposed in the literature in order to overcome these two drawbacks. In this study, the authors give an overview of the LMMSE-based channel estimation in an orthogonal frequency division multiplexing (OFDM) context. A didactic reminder concerning the basics of LMMSE estimation and its performance is provided, and a survey of techniques of the literature, which enable the practical application of LMMSE and the reduction of its complexity, is presented in both single-input single-output and multiple-input multiple-output contexts. Finally, some perspectives are provided, in particular the application of the LMMSE estimator to flexible waveforms beyond OFDM.

Neumann Series Expansion Based LMMSE Channel Estimation for OFDM Systems

In an orthogonal frequency division multiplexing (OFDM) system, the linear-minimum-mean-square-error (LMMSE)-based channel estimator often requires a matrix inversion with cubic complexity. In this letter, by employing a $K$ terms Neumann series expansion to approximate the matrix inversion, the computational complexity is reduced to $\mathcal{O}(N \log L) $ per channel realization, where $N$ is the number of subcarriers and $L$ is the number of non-zero time domain channel taps. Extensive simulation results show that even with small $K$ ( $K \leq 2$ ), the performance loss caused by the proposed approximation is marginal.

Low-Rank Channel Estimation for MIMO MB-OFDM UWB System Over Spatially Correlated Channel

In this letter, we derive a low-complexity channel estimation scheme for multiple-input multiple-output multiband orthogonal frequency division multiplexing ultrawideband (MIMO MB-OFDM UWB) system over spatially correlated channel. More precisely, we drive a linear minimum mean-squared-error (LMMSE) channel estimation algorithm. Then, an optimal low-rank LMMSE channel estimation method based on low-rank approximation is deduced from the LMMSE one. Through simulation results, we show that the proposed LMMSE channel estimator provides significant performance gain over least square (LS) one. We also show that the low-rank LMMSE channel estimator reduces significantly the computational complexity while maintaining comparable performance with LMMSE one for low signal-to-noise ratio (SNR) and minor performance degradation for high SNR.

Network Coded Multihop Wireless Communication Networks: Channel Estimation and Training Design

User-cooperation-based multihop wireless communication networks (MH-WCNs) as the key communication technological component of mobile social networks (MSNs) can be exploited to enhance data rates and extend coverage. As one of the most promising and efficient user cooperation techniques, network coding can increase the potential cooperation performance gains among selfishly driven users in MSNs. To take full advantages of network coding in MH-WCNs, a network coding transmission strategy and its corresponding channel estimation technique are studied in this paper. Particularly, a four-hop network coding transmission is presented first, followed by an extension strategy for the arbitrary $2N$ -hop scenario $(N\geq 2)$ . The linear minimum mean square error (LMMSE) and maximum-likelihood (ML) channel estimation methods are designed to improve the transmission quality in MH-WCNs. Closed-form expressions in terms of the mean square error (MSE) for the LMMSE channel estimation method are derived, which allows the design of the optimal training sequence. Unlike the LMMSE method, it is difficult to obtain closed-form MSE expressions for the nonlinear ML channel estimation method. In order to accomplish optimal training sequence design for the ML method, the Cramer–Rao lower bound is employed. Numerical results are provided to corroborate the proposed analysis, and the results demonstrate that the analysis is accurate and the proposed methods are effective.

Pilot-Symbol Assisted Power Delay Profile Estimation for MIMO-OFDM Systems

This letter proposes a power delay profile (PDP) estimation technique for linear minimum mean square error (LMMSE) channel estimator of multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) sys-tems. For practical applications, only the pilot symbols of all transmit antenna ports are used in estimating the PDP. The distortions caused by null subcarriers and an insufficient number of samples for PDP estimation are also considered. The proposed technique effectively reduces the distortions for accurate PDP estimation. Simulation results show that the performance of LMMSE channel estimation using the proposed PDP estimate approaches that of Wiener filtering due to the mitigation of distortion effects. Index Terms: Channel estimation, power delay profile, MIMO, OFDM, 3GPP-LTE

Optimal Training Signal Design for Estimation of Correlated MIMO Channels in Two-Way Amplify-and-Forward Relay Systems

In this study, we design a training signal for a correlated two-way amplify-and-forward (AF) relay channel, where the relay system consists of two sources and one relay, and each terminal is equipped with multiple antennas. In the system, given that a mean square error (MSE) exists at each source, we minimize the sum of the two MSEs. In particular, we first derive a linear minimum MSE channel estimator with an arbitrary training signal. Second, we formulate the training signal design problem to minimize the sum of the MSEs of the two sources. Finally, we present the optimal structure of the training signal. The optimal training signal is obtained numerically, and a suboptimal training signal is obtained in a closed form. The simulation results show that the MSE performance of the closed-form training signal is almost the same as that of the optimal training signal.

Iterative LMMSE Channel Estimation and Decoding Based on Probabilistic Bias

Iterative channel estimation and decoding based on probabilistic bias is investigated. In order to control the occurrence probability of transmitted symbols, biased convolutional codes (CCs) are proposed. A biased CC is obtained by puncturing the parity bit of a conventional (unbiased) CC and by inserting a fixed bit at the punctured position when the state is contained in a certain subset of all possible states. A priori information about the imposed bias is utilized for the initial linear minimum mean-squared error (LMMSE) channel estimation. This paper focuses on biased turbo codes that are constructed as the parallel concatenation of two biased CCs with interleaving, and proposes an iterative LMMSE channel estimation and decoding scheme based on approximate belief propagation. The convergence property of the iterative LMMSE channel estimation and decoding scheme is analyzed via density evolution (DE). The DE analysis allows one to design the magnitude of the bias according to the coherence time, in terms of the decoding threshold. The proposed scheme is numerically shown to outperform conventional pilot-based schemes in the moderate signal-to-noise ratio (SNR) regime, at the expense of a performance degradation in the high SNR regime.

Low-Complexity Channel Estimation For The UHF MIMO-RFID Systems With Optimal Training

The issue of channel estimation is investigated for the UHF MIMO-RFID systems over pinhole channel. A training sequences aided linear minimum mean square error (LMMSE) channel estimation is proposed for the whole pinhole channel at the reader. Based on the mean square error (MSE) criterion, the MSE bound and the optimal training scheme with this bound are derived. By exploiting the optimal training scheme, an optimal low-rank LMMSE channel estimator is proposed to reduce the computational complexity via singular value decomposition (SVD). Furthermore, the Chu sequence is employed as the optimal training sequence to implement with easy realization and reduce computational complexity at the reader. Simulation results demonstated the effectiveness of the proposed low-complexity channel estimation method and the superiority of the derived optimal training scheme for the MIMO-RFID systems.

Large-System Analysis of Joint Channel and Data Estimation for MIMO DS-CDMA Systems

This paper presents a large-system analysis of the performance of joint channel estimation, multiuser detection, and per-user decoding (CE-MUDD) for randomly-spread multiple-input multiple-output (MIMO) direct-sequence code-division multiple-access (DS-CDMA) systems. A suboptimal receiver based on successive decoding in conjunction with linear minimum mean-squared error (LMMSE) channel estimation is investigated. The replica method, developed in statistical mechanics, is used to evaluate the performance in the large-system limit, where the number of users and the spreading factor tend to infinity while their ratio and the number of transmit and receive antennas are kept constant. The performance of the joint CE-MUDD based on LMMSE channel estimation is compared to the spectral efficiencies of several receivers based on one-shot LMMSE channel estimation, in which the decoded data symbols are not utilized to refine the initial channel estimates. The results imply that the use of joint CE-MUDD significantly reduces rate loss due to transmission of pilot signals, especially for multiple-antenna systems. As a result, joint CE-MUDD can provide significant performance gains, compared to the receivers based on one-shot channel estimation.