Minimum Mean Square Error Channel Estimation Research Articles

Performance evaluation of DFT-based channel estimation in MIMO-OFDM system

Multiple input multiple output-orthogonal frequency division multiplexing (MIMO-OFDM) is an emerging multiplexing technique used in modern mobile communication systems. A main challenge to MIMO-OFDM is retrieval of the channel state information (CSI) accurately and synchronisation between the transmitter and receiver. The CSI is retrieved with the help of channel estimation algorithms such as training-based, blind and semi-blind channel estimation by various researchers. The mean square error (MSE) of existing training-based least square (LS) and minimum mean square error (MMSE) estimation are usually high. In order to minimise MSE, discrete Fourier transform (DFT)-based channel estimation is proposed. This paper deals with MIMO-OFDM system and simulation of training-based LS and MMSE channel estimation, performance evaluation of DFT-based channel estimation. The simulation results clearly indicate the drastic minimisation of MSE by the implementation of DFT channel estimation with LS and MMSE estimation.

Channel Estimation for Massive MIMO-OFDM Systems by Tracking the Joint Angle-Delay Subspace

In this paper, we propose joint angle-delay subspace based channel estimation in single cell for broadband massive multiple-input and multiple-output (MIMO) systems employing orthogonal frequency division multiplexing (OFDM) modulation. Based on a parametric channel model, we present a new concept of the joint angle-delay subspace which can be tracked by the low-complexity low-rank adaptive filtering (LORAF) algorithm. Then, we investigate an interference-free transmission condition that the joint angle-delay subspaces of the users reusing the same pilots are non-overlapping. Since the channel statistics are usually unknown, we develop a robust minimum mean square error (MMSE) estimator under the worst precondition of pilot decontamination, considering that the joint angle-delay subspaces of the interfering users fully overlap. Furthermore, motivated by the interference-free transmission criteria, we present a novel low-complexity greedy pilot scheduling algorithm to avoid the problem of initial value sensitivity. Simulation results show that the joint angle-delay subspace can be estimated effectively, and the proposed pilot reuse scheme combined with robust MMSE channel estimation offers significant performance gains.

A Joint MMSE Channel and Noise Variance Estimation for OFDM/OQAM Modulation

This paper deals with the minimum mean square error (MMSE)-based multipath channel and noise variance estimation in the case of a pilot-aided orthogonal frequency division multiplexing/offset quadrature amplitude modulation (OFDM/OQAM) system. The theoretical expression of the LMMSE channel estimation is formulated and a simpler closed-form is derived. The MSE analysis shows that LMMSE inevitably reaches an error floor due to the interference inherent to OFDM/OQAM modulation. Furthermore, an algorithm for the joint MMSE estimation of both the channel and the noise variance (J-MCNE) is proposed and features a reduced complexity thanks to the low-rank approximation method. The noise level estimation represents a challenge as it is concealed in the intrinsic interferences generated by the OFDM/OQAM. Simulations reveal the capability of the proposed J-MCNE method to estimate the noise variance and show that the achieved bit error rate (BER) is close to that of the perfect estimation.

Low-Complexity Bayesian Estimation of Cluster-Sparse Channels

This paper addresses the problem of channel impulse response estimation for cluster-sparse channels under the Bayesian estimation framework. We develop a novel low-complexity minimum mean squared error (MMSE) estimator by exploiting the sparsity of the received signal profile and the structure of the measurement matrix. It is shown that, due to the banded Toeplitz/circulant structure of the measurement matrix, a channel impulse response, such as underwater acoustic channel impulse responses, can be partitioned into a number of orthogonal or approximately orthogonal clusters. The orthogonal clusters, the sparsity of the channel impulse response, and the structure of the measurement matrix, all combined, result in a computationally superior realization of the MMSE channel estimator. The MMSE estimator calculations boil down to simpler in-cluster calculations that can be reused in different clusters. The reduction in computational complexity allows for a more accurate implementation of the MMSE estimator. The proposed approach is tested using synthetic Gaussian channels, as well as simulated underwater acoustic channels. Symbol-error-rate performance and computation time confirm the superiority of the proposed method compared to selected benchmark methods in systems with preamble-based training signals transmitted over cluster-sparse channels.

A MMSE Channel Estimation Method in QC-LDPC Coded OFDM Systems

An orthogonal frequency division multiplexing (OFDM) is one of the effective techniques used in wireless communications. In OFDM systems, channel impairments due to multipath dispersive wireless channels can cause deep fades in wireless channels. The OFDM receiver also requires an accurate and computationally efficient channel state information when coherent detection is involved. Therefore, it needs a good robust estimation method of the channel in wireless communication for OFDM systems. And one of these channel estimation methods is minimum mean square error (MMSE) channel estimation. MMSE channel estimation one most used method in OFDM systems. In this work we enhanced robustness of MMSE channel estimation by using it in base of quasi-cyclic low density parity check (QC-LDPC) coded OFDM system.

Comparative Study of Bit Error Rate with Channel Estimation in OFDM System for M-ary Different Modulation Techniques

In this paper we investigate the bit error rate performance of orthogonal frequency division multiplexing system with channel estimation through least square error (LSE) and minimum mean square error (MMSE) algorithms. In this paper we are implementing the M-ary phase shift keying (M- PSK) and M-ary quadrature amplitude modulation (M-QAM) digital modulation techniques for mapping the signal in OFDM system for bit error rate evaluation with the employment of comb-type pilot symbol-assisted channel estimation algorithm over frequency selective multi-path Rayleigh fading channel. Here the performance of Least Squares method depends on not only on the signal-to-noise ratio (SNR) but also on the pilot ratio. Simulation results show that applying the LSE and MMSE channel estimation algorithm, they produce the best BER performance over the fading channel. We can consider the OFDM system as either a modulation technique or a multiplexing technique. In a single carrier system, a single fade or interferer can cause the entire link to fail, but in a multicarrier system, only a small percentage of the subcarriers will be affected [1]. Here we are using the pilot symbols as a guard band to eliminate the Inter Symbol Interference, and cyclic prefix eliminates the Inter Subcarrier Interference. Keywords Channel estimation, orthogonal frequency division multiplexing (OFDM), least square error (LSE), minimum mean square error (MMSE), pilot symbol, bit error rate (BER).

Channel Estimation of MIMO–OFDM System Using PSO and GA

In wireless communication, multiple input multiple output-orthogonal frequency division multiplexing (MIMO–OFDM) plays a major role because of its high transmission rate. Channel estimation and tracking have many different techniques available in OFDM systems. Among them, the most important techniques are least square (LS) and minimum mean square error (MMSE). In least square channel estimation method, the process is simple but the major drawback is it has very high mean square error. Whereas, the performance of MMSE is superior to LS in low SNR, its main problem is it has high computational complexity. While comparing with LS and MMSE method individually, the combined LS and MMSE method using evolutionary programming can greatly reduce the error. If the error is reduced to a very low value, then an exact signal will be received. Thus, we propose a hybrid technique that includes particle swarm optimization (PSO) and genetic algorithm (GA) for channel estimation in MIMO–OFDM systems. The technique performs the conventional LS and MMSE channel estimation followed by enabling a fine tuning on the obtained channel model. The PSO and GA contribute in fine tuning the obtained channel model so that the channel model is derived further to correlate with the ideal model. The result shows the performance of the proposed method is better than LS and MMSE method in all the mutation and crossover values and also in all the iterations computed. The performance of OFDM systems using proposed technique can be observed from the imitation and relative results.

Minimum mean‐square‐error expression of LMMSE channel estimation in SISO OFDM systems

An expression of the minimum mean square error (MMSE) of the linear MMSE channel estimation is given in the case of a non-invertible channel covariance matrix, as in single-input single-output (SISO) OFDM system. A matrix expression, already proposed for a multi-input multi-output OFDM system in a previous article, is not valid in SISO. A new proof is then proposed, by deriving a scalar expression of the MMSE, which leads to solve an optimisation problem. Furthermore, we show that the proposed solution is the global minimum. Simulations validate the proposed development.

Performance of Channel Estimation in MIMO-OFDM Systems

This paper presented the performance of faded channel estimation method on orthogonal frequency division multiplexing-multiple input multiple outputs (OFDM-MIMO) i.e. least squares (LS) and minimum mean squared error (MMSE). Channel impuls response (CIR) was required to overcome the intersymbol interference (ISI). Channel impuls response information was obtained from channel estimation processing. Iterance simulation used monte-carlo technique to determine the performance of bit error rate (BER) and mean squared error (MSE). Simulation results show that the mean squared error performance on MIMO system was better than the SISO system. On MMSE channel estimation, the MIMO 2Tx-2Rx system provided ± 2 dB improvement that compared to SISO system at value of MSE 10 -2 .Furthermore,MIMO 3Tx-2Rx produce improvement about 1.5 dB, MIMO 4Tx-2Rx improve about 3.5 dB at BER 10-4,respectively.The MIMO 2Tx-2Rx system, MMSE channel estimation produced better performance ± 1 dB than LS channel estimation with sufficient SNR value for MSE 10 -2 .Pilot arrangement, the simulation results show that the block type-pilot arrangement produced better performance than the comb type-pilot arrangement at fast fading channel. Block type-pilot arrangement system produced better ± 10 dB than the comb type-pilot arrangement with MMSE method at value of BER 2 10 -2 .

Performance comparison of Different Pilot Aided Channel Estimation Techniques for OFDM IEEE 802. 11e (Mobile Wimax) Systems

Orthogonal frequency-division multiplexing (OFDM) modulation is a promising technique for achieving the high bit rates required for a wireless multimedia service. In this paper we present different channel estimation algorithms for OFDM mobile communication systems based on the use of pilot subcarriers. Specifically we present LS (Least Square), MMSE (Minimum Mean Square Error) and LMS iterative channel estimation techniques to show the performance comparison of channel estimation techniques supported by n IFFT-based time channel estimation. The channel estimation is based on the principle of pilotsymbol aided channel estimation (PACE), and it has been implemented using block-type pilot subcarrier arrangements. The low complexity of LMS algorithm, has a higher efficiency than conventional methods (without channel estimation, LS& LMMSE) and it can work in lower amount of SNRs. We have compared the performances of all schemes by measuring bit error rate with 16QAM as modulation scheme, and multi-path Rayleigh fading channel as channel model. Simulation results validate that the LMS Iterative channel estimation scheme can achieve tremendous performance as the existing channel estimation methods. Keyword: Channel estimation (CE), OFDM (Orthogonal Frequency Division Multiplexing), QAM (Quadrature Amplitude Modulation).

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.

Low-complexity SAGE-based MMSE channel estimation for CoMP multi-user systems

Coordinated multiple point (CoMP) transmission/reception has been investigated recently as a promising technology to increase the cell-edge user performance of long term evolution-advanced (LTE-A), and channel estimation is a crucial technology for CoMP systems. In this paper, we consider a reduced-complexity minimum mean square error (MMSE) channel estimator for CoMP systems. The estimator uses space alternating generalized expectation maximization (EM) (SAGE) algorithm to avoid the inverse operation of the joint MMSE estimator. In the proposed scheme, the base stations (BSs) in the CoMP system estimate the channels of all the coordinated users serially and iteratively. We derive the SAGE-based estimators and analyze complexity. Simulation results verify that the performance of the proposed algorithm is close to the joint MMSE estimation algorithm while reducing the complexity greatly.

OFDM 시스템을 위한 낮은 복잡도를 갖는 2-D MMSE 채널 추정 기법

OFDM (Orthogonal Frequency Division Multiplexing) 시스템에서 2-D MMSE (2-Dimensional Minimum Mean Square Error) 채널 추정 기법은 주파수/시간 선택적 특성을 가지는 채널에서 우수한 성능을 나타내는 것으로 알려져 있다. 하지만 2-D MMSE 채널 추정 방식은 주파수 축 뿐만 아니라 시간 축 까지 고려하기 때문에 행렬 크기가 커지고, 이로 인해 복잡도가 크게 증가한다는 문제점이 있다. 따라서 본 논문에서는 이러한 문제점을 해결하기 위해 l-D MMSE 채널 추정 구조를 기반으로 가중치 합을 이용하여 기존의 2-D MMSE 채널 추정 방식보다 낮은 복잡도를 갖는 방식을 제안한다. 뿐만 아니라 2-D MMSE 채널 추정을 적용하기 위해 필요한 파라미터인 RMS 지연 확산과 도플러 주파수를 추정하는 기법을 고려한다. 성능 검증 결과 제안하는 방식은 기존의 2-D MMSE 방식에 비해서 복잡도를 크게 줄일 수 있을 뿐만 아니라, 2-D MMSE 채널 추정 방법과 유사한 성능을 나타내는 것을 확인하였다. For OFDM (Orthogonal Frequency Division Multiplexing) systems, 2-D MMSE (2-Dimensional Minimum Mean Square Error) channel estimation provides optimal performance in frequency/time selective fading channel environment. However, the 2-D MMSE channel estimation has high computational complexity due to the large matrix size, because the 2-D MMSE channel estimation considers time as well as frequency axis for channel estimation. To reduce the computational complexity, we propose a modified 2-D MMSE channel estimator which is based on 1-D MMSE channel estimation with weighted sum. Furthermore, we consider RMS delay spread and Doppler frequency estimation for 2-D MMSE channel estimation. We show that the proposed method can significantly reduce computational complexity as well as that it can perform close to 2-D MMSE channel estimation.

Power Allocation between Pilot and Data Symbols for MIMO Systems with MMSE Detection under MMSE Channel Estimation

For multiple-input multiple-output (MIMO) wireless communication system with minimum mean square error (MMSE) detection, a new scheme of power allocation between pilot and data symbols is investigated under MMSE channel estimation in this paper. First, we propose a novel soft-output MMSE MIMO detector by taking into consideration the channel estimation error. Then, through the application of randommatrix theorem, we propose an efficient scheme for power allocation between pilot and data symbols which maximizes the lower bound of postprocessing signal-to-interference-and-noise ratio (SINR) for MIMO systems with equal number of transmitter and receiver antennas. We have proven the existence and uniqueness of the proposed optimal power allocation settings. Furthermore, our analysis shows that the proposed power allocation is also valid and applicable for those MIMO systems with unequal number of transmitter and receiver antennas. Finally, our extensive simulation results have validated this novel power allocation scheme.

OFDM With Iterative Blind Channel Estimation

A new blind channel estimation technique is presented for uncoded orthogonal frequency-division multiplexing (OFDM) systems. Instead of using pilots to sound the channel, a decision algorithm first makes primary estimates of the data symbol for each subcarrier based on a constrained linear minimum mean square error (MMSE) criterion. Then, these estimates are applied to optimal MMSE channel estimation. The technique requires only one value from the time–frequency correlation of the channel transfer function. Performance is evaluated by simulation so that comparison can be made with known optimal coherent/differential detection. Compared with known decision-directed Kalman-based estimation and two pilot-aided OFDM schemes (block pilots and comb pilots), the presented technique performs better for regions with mid to high signal-to-noise ratios (SNRs). Its robustness to the time variation of the channel is also quantified by simulation, showing only small degradation in performance relative to the quasistatic case of wireless local area network (WLAN) systems. Finally, the impact of covariance assumptions in the channel modeling is quantified using simulation, offering a feel for the performance with mismatch between the channel model and the receiver assumptions.

Appropriate Algorithms for Estimating Frequency-Selective Rician Fading MIMO Channels and Channel Rice Factor: Substantial Benefits of Rician Model and Estimator Tradeoffs

The training-based channel estimation (TBCE) scheme in multiple-input multiple-output (MIMO) frequency-selective Rician fading channels is investigated. We propose the new technique of shifted scaled least squares (SSLS) and the minimum mean square error (MMSE) estimator that are suitable to estimate the above-mentioned channel model. Analytical results show that the proposed estimators achieve much better minimum possible Bayesian Cramér-Rao lower bounds (CRLBs) in the frequency-selective Rician MIMO channels compared with those of Rayleigh one. It is seen that the SSLS channel estimator requires less knowledge about the channel and/or has better performance than the conventional least squares (LS) and MMSE estimators. Simulation results confirm the superiority of the proposed channel estimators. Finally, to estimate the channel Rice factor, an algorithm is proposed, and its efficiency is verified using the result in the SSLS and MMSE channel estimators.

BER Analysis of Square OSTBCs with LMMSE Channel Estimation in Arbitrarily Correlated Rayleigh Fading Channels

In this paper, we examine the bit error rate (BER) performance of square orthogonal space-time block codes (OSTBCs) under arbitrarily correlated Rayleigh fading channels. We consider a mismatched maximum-likelihood receiver that obtains the channel state information through pilot-based linear minimum mean-square error channel estimation. For PAM and QAM constellations, a closed-form approximation of the BER is presented, which yields very accurate BER results over a wide range of signal-to-noise ratios.

A Study of the Extreme Effects of Fading Correlation and the Impact of Imperfect MMSE Channel Estimation on the Performance of SIMO Zero-Forcing Receivers and on the Capacity-Maximizing Strategy in SIMO Links

In this paper, we shall consider best- and worst-case fading correlation scenarios, i.e., uncorrelated and fully correlated fading channels and will study the performance of a single-input-multiple-output (SIMO) link that uses a practical imperfect online training-based minimum mean square error (MMSE) channel estimator and a zero-forcing (ZF) receiver under these two conditions. Considering the extremes of correlation and focusing on frequency-nonselective Rayleigh block fading, we will find the probability distribution function (pdf) of the postprocessing signal-to-noise ratio (SNR) in each case and shall provide closed-form expressions for the symbol error probability (SEP) of these systems when using M-ary pulse amplitude modulation (M-ary PAM). Moreover, a lower bound will be provided for the information capacity of fully correlated SIMO links with training-based MMSE channel estimation, which will further be optimized to yield its maximum under different conditions. Monte Carlo simulations perfectly verify the analysis.

On Optimum Regenerative Relaying With Imperfect Channel Knowledge

This correspondence is concerned with the performance of a regenerative relaying protocol on fading wireless channels with imperfect channel knowledge at the receivers. Assuming a single source and a single destination with multiple relay nodes, using binary modulation at the source, we present optimum receiver at the destination on frequency-flat Rayleigh fading channels by taking into account the effects of imperfect channel knowledge at the receivers. Since exact performance analysis of the optimal receiver is complicated due to the non-linear nature of the log-likelihood ratio contribution from the relay, upon using a standard technique in the literature, we present a simple approximate receiver and derive closed-form expression for the average bit error rate (BER) at the destination with a single relay node. We also present a simple analytical technique that allows us to numerically evaluate the average BER for an arbitrary number of relay nodes. Finally, with perfect channel estimation our proposed receiver subsumes the coherent receivers whereas with a minimum mean-square error channel estimation it reduces to the non-coherent receiver in the work of Chen and Laneman (2006).

An Improved MMSE Channel Estimator for Joint Coded-Precoded OFDM

An improved iterative minimum mean-squared error (MMSE) channel estimation method is proposed for joint coding and precoding OFDM systems. Compared with the traditional simplified estimator, the proposed scheme provides higher estimation quality with slight complexity increment at low signal-to-noise ratio (SNR) values. The performance of the iterative receiver including the proposed estimator approaches that of the perfect MMSE estimator without any simplification.