Minimum Mean Square Error Method Research Articles

Channel Estimation Aware Performance Analysis for Massive MIMO With Rician Fading

In this paper, by considering the average mean squared error (AMSE) of channel estimation, we primarily obtain the closed-from expressions of the probability density function (PDF) and cumulative distribution function of AMSE for the least squares (LS)/minimum mean squared error (MMSE) estimation method as the line-of-sight (LOS) component is known, where the asymptotic analysis is executed in Rayleigh fading and strong LOS conditions. Secondly, the closed-form expressions for the expectation of AMSE ( Exp <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">amse</sub> ) and variance of AMSE ( Var <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">amse</sub> ) are acquired, where Var <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">amse</sub> is inversely proportional to the number of antennas ( M). As M becomes infinite, the PDF of AMSE at Exp <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">amse</sub> has an order of root M. When the pilot power decreases with M in a power law, the LS case keeps deteriorating while the MMSE case converges to a constant which basically depends on the Rician K-factor. Next, the spectral efficiency is investigated by considering AMSE. When Exp <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">amse</sub> accelerates, the spectral efficiency of the LS method keeps dropping and that of the MMSE method firstly is degraded and then is improved to a constant except Rayleigh fading. Finally, all results are validated via simulations.

Secure beamforming design in MIMO NOMA networks for Internet of Things with perfect and imperfect CSI

In this paper, we investigate the secure beamforming design in multiple-input multiple-output (MIMO) nonorthogonal multiple access (NOMA) en-abled Internet of Things (IoT) networks, where a controller transmits confidential messages to multiple actuators and a cooperative controller acts as a jammer to prevent a potential eavesdropper from wiretapping the information. Our goal is to maximize achievable secrecy sum rate subject to the successful successive interference cancellation constraint and transmit power constraints of the controller and jammer. When channel state information (CSI) is perfect, we design the secure beamforming by developing an iterative optimization algorithm based on minimum mean square error (MMSE) method. When perfect CSI is not available, we model the channel errors as deterministically-bounded, and propose a robust secure beamforming design algorithm based on weighted MMSE and cutting-set method. The effectiveness of the proposed algorithms is verified by the simulation results.

Adaptive Beamforming Using Steering Vector Correction for Phased-Array Weather Radar

In December 2017, a dual-polarized (DP) phased-array weather radar (PAWR) was deployed to observe precipitation in Tokyo, Japan. The DP-PAWR has the following characteristics: high-temporal-resolution observations for a volume scan of 30 s in a 60 km range, high-density observations below a 15 km altitude, improved rain rate estimation using dual-polarimetric observations, and hydrometer classification abilities. To achieve high-temporal-resolution observations, wide transmitted waves with a beam width up to 5° are used for elevation angles. Although Fourier-domain digital beamforming can be used for receiving waves, the high sidelobe level of the antenna pattern using this type of beamforming results in substantial errors (e.g., overestimation of received power) because of ground clutter echoes. To solve this problem, an adaptive beamforming method based on the minimum mean square error (MMSE) was developed for a single-polarization phased-array radar. In this study, signal processing procedures, including the steering vector correction of real measurement data, are developed to apply the MMSE method to the DP-PAWR. The effect of phase errors and ground clutter on the dual-polarimetric parameters is evaluated via numerical simulations. Subsequently, the proposed method is applied to real measurement data of the DP-PAWR. Consequently, it is found that the clutter suppression achieved using the proposed method is clearly superior to that achieved using Fourier-domain digital beamforming.

MIMO Channel Estimation in an SDR Platform for Evaluation of D&amp;F Relay Nodes

Relay Nodes (RNs) have received special attention as a radio access technology which can overcome channel fading and improve the channel capacity in high-speed and dense vehicle environments. RNs have been the object of standardization by the 3GPP; however, this process has not been accompanied by the development of hardware that allows for evaluation of the advantages of RNs. Software Defined Radio (SDR) has emerged as a promising technology to implement the concept of RNs at low cost. In this paper, a detailed study of the MIMO wireless channel between an evolved Node-B (eNB) and an RN is carried out. The developed algorithms are implemented in an SDR platform for Decode-and-Forward (D&amp;F) relay node evaluation, resulting in significant improvements of its capabilities on the MIMO channel. A pilot symbol-assisted channel estimation algorithm based on combinations of the Least-Squares (LS) technique and Bi-Cubic (BCI), Bi-Linear (BLI), and Bi-Nearest Neighbors (BNNI) interpolation methods is considered. Furthermore, the Minimum Mean Square Error (MMSE) and Zero-Forcing (ZF) equalization schemes are studied. In the tests conducted, Line-of-Sight (LOS) and Non-Line-of-Sight (NLOS) scenarios are considered, demonstrating the capabilities of the developed platform. The performance measurements using different modulation schemes are compared under the same conditions. The simulation results show that the LS technique together with the BCI and MMSE methods performed the best among all evaluated channel estimation and equalization algorithms, in terms of the Error Vector Magnitude (EVM) performance of the received Resource Grid (RG). Furthermore, we show that the Bit Error Rate (BER) and throughput of the core network increase when using the 2 × 2 MIMO technique.

Speech Intelligibility for Cochlear Implant Users with the MMSE Noise-Reduction Time-Frequency Mask

Cochlear implants (CI) are the most successful electronic prostheses for human beings. They almost completely restore the communication capability in profound-to-severe hearing losses under quiet conditions. However, noisy scenarios still impose critical intelligibility limitations. Time-frequency masks have been widely used to improve signal to noise conditions (SNR) and, as a consequence, increase the speech intelligibility. The most studied methods in the literature are the Binary mask (BM) and the Wiener filter (WF), which were not originally designed for this application. This work analyzes the performance of the minimum mean square error (MMSE) magnitude estimator for increasing intelligibility in CI applications. Objective measures and psychoacoustic experiments with normal hearing volunteers and vocoded signals, as well as CI users indicate that the MMSE method outperfoms the intelligibility performance obtained by both BM and WF time-frequency masks, especially in low SNR conditions (SNR < 8 dB). This observation can be explained by the fact that CIs do not provide speech temporal-fine-structure information to the CI user, and that hard masks may suppress important speech information under low SNR. As a result, we provide strong indications that the MMSE magnitude-based time-frequency mask is more suitable to CI noise reduction applications, as compared to WF and BM, whenever the additional computation burden is tolerable by the CI processor.

Massive MIMO Detection Algorithms Based on MMSE-SIC, ZF-MIC, Neumann Series Expansion, Gauss-Seidel, and Jacobi Method

The massive multiple-input multiple-output (MIMO) systems is an important technology in the fifth generation of mobile communication. To get the result of a MIMO system require some algorithm to approximate the precise result as the computation complexity is too large. There are several methods that have been advanced in the fitting, like zero forcing (ZF) method or minimum mean-square error (MMSE) method. However, in massive MIMO system, these methods require further simplify because of the increasing complexity of matrix inversion. In the papers, many methods were presented to get the approximation matrix: like MMSE-SIC, ZF-MIC, Gauss-Seidel, Jacobi and Neumann series expansion. The Jacobi’s iterative method and Newton’s iterative method both use iteration to approach the MMSE estimation. Their BER performance can outperform current methods and require less computational complexity. Almost every method can get a nearly ideal fit when the number of users or antennas is large enough. But when the number is small, the approximation will not be very accurate.

Advanced Channel Estimation Method for IEEE 802.11p/WAVE System

In this paper, we propose an advanced Minimum Mean Square Error (MMSE) channel estimation method for IEEE 802.11p/Wireless Access in Vehicular Environments (WAVE) systems. To improve the performance of MMSE method, we apply the Weighted Sum using Update Matrix (WSUM) scheme to the step of calculating the instantaneously estimated channel and then, a time domain selectively averaging method is applied after the WSUM scheme. Based on that, the accuracy of instantaneously estimated channel increases and then, the accuracy of auto covariance matrix also increases. Consequently, we can achieve the performance gain over the conventional MMSE method. Through simulations based on the IEEE 802.11p standard, it is confirmed that the proposed scheme can outperform the existing channel estimation schemes.

Lossless Dimension Reduction for Integer Least Squares With Application to Sphere Decoding

Minimum achievable complexity (MAC) for a maximum likelihood (ML) performance-achieving detection algorithm is derived. Using the derived MAC, we prove that the conventional sphere decoding (SD) algorithms suffer from an inherent weakness at low SNRs. To find a solution for the low SNR deficiency, we analyze the effect of zero-forcing (ZF) and minimum mean square error (MMSE) detected symbols on the MAC and demonstrate that although they both improve the SD algorithm in terms of the computational complexity, the MMSE point has a vital difference at low SNRs. By exploiting the information provided by the MMSE method, we prove the existence of a lossless size reduction which can be interpreted as the feasibility of a detection method which is capable of detecting the ML symbol without visiting any nodes at low and high SNRs. We also propose a lossless size reduction-aided detection method which achieves the promised complexity bounds marginally and reduces the overall computational complexity significantly, while obtaining the ML performance. The theoretical analysis is corroborated with numerical simulations.

Singular Value Decomposition Channel Estimation in STBC MIMO-OFDM System

The multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) technology is the combination of the OFDM and MIMO technologies, which could improve the system capacity and make efficient utilization of the frequency spectrum. This paper utilizes space-time block coding (STBC) to achieve diversity gains and combat the channel fading. However, channel estimation is an essential block for space-time block decoding (STBD). Many channel estimation methods are utilized for the single antenna OFDM system, but they cannot be directly applied to the multiple antennas system due to the interference from other antennas. In this paper, orthogonal pilot sequences are designed to suppress the interference of pilot symbols from other transmit antennas. This paper also derives a minimum mean square error (MMSE) channel estimation method in MIMO-OFDM systems. The MMSE method involves the inverse operation of the channel autocorrelation matrix, which has a large calculation complexity. To further reduce the complexity of the MMSE method, the singular value decomposition (SVD) is used to decompose the channel autocorrelation matrix, which avoids the inverse operation. Simulation results verify that the SVD channel estimation method with comb-type pilots and STBC can be effectively adapted to multipath propagation conditions.

Evaluating the Implications of Varying Bluetooth Low Energy (BLE) Transmission Power Levels on Wireless Indoor Localization Accuracy and Precision.

Bluetooth Low Energy (BLE) based Wireless Indoor Localization System (WILS) with high localization accuracy and high localization precision is a key requirement in enabling the Internet of Things (IoT) in today’s applications. In this paper, we investigated the effect of BLE signal variations on indoor localization caused by the change in BLE transmission power levels. This issue is not often discussed as most of the works on localization algorithms use the highest power levels but has important practical implications for energy efficiency, e.g., if a designer would like to trade-off localization performance and node lifetime. To analyze the impact, we used the established trilateration based localization model with two methods i.e., Centroid Approximation (CA) and Minimum Mean Square Error (MMSE). We observed that trilateration based localization with MMSE method outperforms the CA method. We further investigated the use of two filters i.e., Low Pass Filter (LPF) and Kalman Filter (KF) and evaluated their effects in terms of mitigating the random variations from BLE signal. In comparison to non-filter based approach, we observed a great improvement in localization accuracy and localization precision with a filter-based approach. Furthermore, in comparison to LPF based trilateration localization with CA, the performance of a KF based trilateration localization with MMSE is far better. An average of 1 m improvement in localization accuracy and approximately 50% improvement in localization precision is observed by using KF in trilateration based localization model with the MMSE method. In conclusion, with KF in trilateration based localization model with MMSE method effectively eliminates random variations in BLE RSS with multiple transmission power levels and thus results in a BLE based WILS with high accuracy and high precision.

Evaluation of MMSE-Based Iterative Soft Detection Schemes for Coded Massive MIMO System

There have been a number of researches on soft iterative detection and decoding scheme for coded multiple-input-multiple-output (MIMO) systems. Minimum mean square error (MMSE)-based detection schemes were often considered for massive MIMO systems, due to their reasonable complexity and performance tradeoff. This paper evaluates a number of MMSE-based soft iterative detection schemes for massive MIMO systems, with new proposals to improve the performances and to reduce the complexity. We consider joint iterative detection and decoding schemes for a coded massive MIMO system, and various kinds of MMSE-based soft detection methods proposed in the literatures are investigated. By utilizing the diagonal approximation of the channel matrix, we propose efficient soft MMSE filtering methods in combination with soft interference cancellation techniques and a compact soft bit estimation method. In addition, new matrix inversion-less soft MMSE methods are proposed for joint iterative detections. The simulation results demonstrate that the proposed methods clearly contribute to the reduction of the complexity of the conventional methods, and performance enhancement.

ComNet: Combination of Deep Learning and Expert Knowledge in OFDM Receivers

In this article, we propose a model-driven deep learning (DL) approach that combines DL with the expert knowledge to replace the existing orthogonal frequency-division multiplexing (OFDM) receiver in wireless communications. Different from the data-driven fully connected deep neural network (FC-DNN) method, we adopt the block-by-block signal processing method that divides the receiver into channel estimation subnet and signal detection subnet. Each subnet is constructed by a DNN and uses the existing simple and traditional solution as initialization. The proposed model-driven DL receiver offers more accurate channel estimation comparing with the linear minimum mean-squared error (LMMSE) method and exhibits higher data recovery accuracy comparing with the existing methods and FC-DNN. Simulation results further demonstrate the robustness of the proposed approach in terms of signal-to-noise ratio and its superiority to the FC-DNN approach in the computational complexities or the memory usage.

Comparative performance evaluation of MMSE-based speech enhancement techniques through simulation and real-time implementation

In this article, a generic model of minimum mean square error (MMSE) based speech enhancement technique has been presented and implemented on the hardware. Models for different MMSE-based methods were obtained by changing the gain function in the generic model. In all the methods, modified cascaded median-based noise estimation method has been used for noise estimation. Performances of all these MMSE-based methods were compared, among themselves and also with the spectral subtraction method for speech enhancement. The results have been evaluated using objective measures, subjective measure and composite objective measures for different noisy speech files. Results, in terms of objective evaluation parameters, indicated that the adaptive β-order MMSE method yielded better performance than the other methods. In subjective quality test (according to MOS listening test), β-order MMSE and adaptive β-order MMSE method yielded high scores. Real-time implementation has been carried out using TMS320C6416T DSP starter kit and code composer studio software. Estimation of memory consumption and execution time has been done for all the methods.

Speech enhancement for cochlear implant recipients.

In this study, a single microphone speech enhancement algorithm is proposed to improve speech intelligibility for cochlear implant recipients. The proposed algorithm combines harmonic structure estimation with a subsequent statistical based speech enhancement stage. Traditional minimum mean square error (MMSE) based speech enhancement methods typically focus on statistical characteristics of the noise and track the noise variance along time dimension. The MMSE method is usually effective for stationary noise, but not as useful for non-stationary noise. To address both stationary and non-stationary noise, the current proposed method not only tracks noise over time, but also estimates the noise structure along the frequency dimension by exploiting the harmonic structure of the target speech. Next, the estimated noise is employed in the traditional MMSE framework for speech enhancement. To evaluate the proposed speech enhancement solution, a formal listener evaluation was performed with 6 cochlear implant recipients. The results suggest that a substantial improvement in speech intelligibility performance can be gained for cochlear implant recipients in noisy environments.

Channel Estimation and Peak‐to‐Average Power Ratio Analysis of Narrowband Internet of Things Uplink Systems

Narrowband Internet of Things (NB‐IoT) is a cellular based promising low‐power wide‐area network (LPWN) technology standardized by the 3rd Generation Partnership Project (3GPP) in release‐13 as a part of the future 5th Generation (5G) wireless communication systems. The main design target of NB‐IoT was to enhance radio coverage by repeating signal over an additional period of time for the ultralow‐end IoT devices that would be operated in extreme coverage environments. But the power efficiency of the low‐cost NB‐IoT user equipment (NB‐IoT UE) in the uplink is the major concern. Coverage improvement from signal repetitions depends on the channel estimation quality at extremely bad radio conditions. The typical operating signal‐to‐noise ratio (SNR) for NB‐IoT is expected to be much lower than the zero. In this paper, we have proposed two efficient narrowband demodulation reference signal (NDMRS)‐assisted channel estimation algorithms based on the conventional least squares (LS) and minimum mean square error (MMSE) estimation methods. The theoretical analysis and the link‐level performance of our proposed estimation methods are presented. Simulation results exhibit that the proposed methods provide better estimation precision compared to the traditional LS and MMSE methods at the low SNR situations. Furthermore, we have analyzed the raised‐cosine (RC) and square‐root‐raised cosine (RRC) pulse shaping to reduce peak‐to‐average power ratio (PAPR) as an uplink transmit filter. The PAPR values are evaluated through extensive computer simulations for both single‐tone and multi‐tone transmissions. Our evaluation results vindicate that the RRC pulse shaping with lower PAPR values is feasible to design of practical NB‐IoT uplink transmitter and increases power efficiency.

Disjoint Pilot Power and Data Power Allocation in Multi-Cell Multi-User Massive MIMO Systems

In this paper, we consider pilot and data power allocation in multi-cell multi-user massive multiple-input multiple-output (MIMO) systems to maximize the summation of spectral efficiency (sum SE). In conventional massive MIMO systems, equal pilot and data power is assigned to all users so the sum SE is not good. A common way to maximize sum SE is forming a maximization problem with the sum SE objective function containing both pilot and data power as variables. However, pilots are only used for channel estimation so pilot power should be allocated based on channel estimation quality instead of sum SE. Moreover, improving significantly channel estimation quality also helps to indirectly improve the sum SE. This motivated us to propose a disjoint pilot and data power allocation where pilot powers are optimized based on the sum normalized mean squared error (sum NMSE) channel estimation minimization problem and data powers are optimized based on sum SE maximization problem. We consider least squares (LS) and minimum mean squared error (MMSE) estimation methods which are commonly used in massive MIMO. In the first step, we formulate a minimization problem to minimize the summation of NMSE of the system under maximum pilot power per user constraint. Minimization problem for MMSE method is non-deterministic polynomial-time (NP) hard so we propose an algorithm to find the local optimum point. First step is only related to pilot powers and indirectly improves the sum SE by improving channel estimation quality. In second step, we further improve the sum SE by formulating a sum SE maximization problem with data powers as variables under maximum data power per user constraint. Since this problem is NP-hard, we derive a lower bound on the sum SE and maximize this bound instead Numerical results show the advantages of our proposed approach in comparison with existing schemes.

Multi-segmental OFDM signals equalization with piecewise linear channel model over rapidly time-varying channels

For rapidly time-varying channels, the performance of (orthogonal frequency division multiplexing) OFDM systems with the conventional one tap equalizer will be significantly degraded. Because the orthogonality between subcarriers is destroyed, the conventional way to combat the inter-carrier interference (ICI) is employing the banded minimum mean square error (MMSE) equalizer, which can save computational efforts introduced by a large number of subcarriers. However, the width of the banded channel matrix is mainly determined by the normalized Doppler frequency in the sense that with the high Doppler frequency the complexity of equalization for one OFDM block will significantly increase with the band width D. In order to reduce the equalization complexity, the authors proposed multi-segmental OFDM signal equalization method with piecewise linear model (PLM) to approximate the time variations and mitigate the corresponding ICI. Its complexity is significantly reduced with the small segments. Furthermore, an alternative MMSE method with the iterative rank-1 matrix updates is proposed to further reduce the complexity. We also derive the theoretical pre-equalized and equalized signal to interference ratio (SIR) for different normalized Doppler frequencies and segment numbers, which implies that the larger segment number can achieve the better performance. Simulation results demonstrate that the proposed method outperforms the conventional banded MMSE equalizer and the partial fast Fourier transform (FFT) method in terms of bit error rate (BER) with almost the same complexity.

Adaptive Pulse Compression Technique for X-Band Phased Array Weather Radar

Weather radar commonly uses a matched filter (MF) method to improve the range resolution and signal-to-noise ratio. A X-band phased array weather radar (PAWR), which is capable of 3-D precipitation observations in less than 30 s, is in operation at the Osaka University. The PAWR uses the MF method. In weather radar systems, the magnitude of the range sidelobes is an important topic because it can cause overestimation of the received power from a target, such as precipitation or ground clutter echoes. We propose a minimum mean square error (MMSE)-based pulse compression method to reduce the range sidelobes of the PAWR. We evaluated an MF, an MF with a raised-cosine window, and MMSE methods using numerical simulations and actual measurement data obtained from the PAWR. The results show that the MMSE method is clearly superior to the MF and MF with a raised-cosine filter methods when considering the reduction in the range sidelobes.

Performance of Minimum Mean-Square Error Beam Forming for Polarimetric Phased Array Weather Radar

In this paper, the development of a polarimetric phased array weather radar, which consists of a dual-polarized antenna with 2-D circular planar phase-array elements, is discussed. The radar is capable of measuring the 3-D rainfall distribution in less than several tens of seconds. Digital beamforming (DBF) is an important component in the development process of the phased array radar. In this paper, precipitation radar signal simulations are performed taking into consideration radar concepts in order to discuss the estimation accuracy of polarimetric precipitation profiles (differential reflectivity, specific differential phase, and copolar correlation coefficient) with two DBF methods that are based on Fourier and minimum mean-square error (MMSE) methods. A comparison of the performance of the two methods indicates that MMSE is superior in accuracy because of the effect of a stable and a robust main lobe and adaptively suppressed side lobes. MMSE also provides precipitation measurements eliminating the directional dependence of a beam pattern for improving the accuracy of measurements. It is also shown that the estimated accuracies of the precipitation profiles are almost independent of the number of pulses.

Interference Coordination Using Precoding Schemes for Indoor Hotspots

This paper investigates an interference coordination method for indoor hotspot deployment which includes cooperative communication between access points. Coordination between indoor hotspots access point with a method of coordination strategy is used by using of multiple-input multiple-output (MIMO) antennas technique. In order to achieve the capacity, some preceding technique is implemented in MIMO such as Minimum Mean Square Error (MMSE) and Block Diagonalization (BD). MMSE and BD precoding is used to coordinate the transmissions across multiple antenna in transmitter and receiver in case of multiple antenna transmissions. Water-Filling (WF) power allocation is also implemented in this scheme. This schemes is proposed to mitigate inter user interference. Based on the simulation, the results show that coordination scheme in indoor hotspots deployment using BD pre-coding demonstrates a higher data rate than MMSE. The achievable sum rate of hotspot with coordination three access points using BD better around 5 Bps/Hz compared to MMSE method in the same cases.