Minimum Mean Square Error Algorithm Research Articles

Semi-blind simplified mean value channel estimator for MC-IDMA systems

The Multi-Carrier Interleave Division Multiple Access (MC-IDMA) scheme combines Orthogonal Frequency Division Multiplexing and IDMA. The scheme combats both Inter-Symbol Interference (ISI) and Multiple Access Interference (MAI). For coherent detection of the transmitted signals at the receiver, Channel State Information (CSI) is crucial. There are several schemes that can be used to obtain CSI at the receiver, such as pilot-based schemes and decision directed scheme, semi-blind and as blind channel estimation schemes. This paper focuses on developing semi-blind channel estimation scheme for the MC-IDMA systems. The developed scheme is based on Minimum Mean Square Error (MMSE) algorithm. The estimator employs applications of the eigenvalue and eigenvector decomposition (EVD) techniques to simplify the MMSE algorithm, and is named Simplified Mean Value Estimator (SMVE). Simulation results show that the proposed SMVE-based estimator outperforms Least Mean Square (LMS) algorithm-based estimator, Modified Minimized Mean Value Estimator (MMMVE), and the Minimized Mean Value-MMSE Estimator (MMVE).

An Improved Soft-Input Soft-Output Detector for Generalized Spatial Modulation

Generalized spatial modulation (GSM) is a recently proposed appealing multi-input multi-output (MIMO) transmission technique, which is capable of striking a tradeoff between the achievable transmission rate and the cost of radio frequency (RF) chains. In this letter, a novel low-complexity near-optimal soft decision (SoD)-aided detector is proposed for GSM, which considerably reduces the search space by employing a block minimum mean-squared error (B-MMSE) algorithm. Our simulation results show that the proposed detector is capable of achieving a better tradeoff between bit-error-rate (BER) performance and computational complexity compared with the existing matched filter (MF)-based SoD algorithms.

Low-complexity signal detection based on relaxation iteration method in massive MIMO systems

Minimum mean square error (MMSE) detection algorithm can achieve nearly optimal performance when the number of antennas at the base station (BS) is large enough compared to the number of users. But the traditional MMSE involves complicated matrix inversion. In this paper, we propose a modified MMSE algorithm which exploits the channel characteristics occurring in massive multiple-input multiple-output (MIMO) channels and the relaxation iteration (RI) method to avoid the matrix inversion. A proper initial solution is given to accelerate the convergence speed. In addition, we point out that the channel estimation scheme used in channel hardening-exploiting message passing (CHEMP) receiver is very appropriate for our proposed detection algorithm. Simulation results verify that the proposed algorithm can achieve very close performance of the traditional MMSE algorithm with a small number of iterations.

Design and Implementation of Flexible Dual-Mode Soft-Output MIMO Detector With Channel Preprocessing

This paper proposes a flexible dual-mode soft-output multiple-input multiple-output (MIMO) detector to support open-loop and closed-loop in Chinese enhanced ultra high throughput (EUHT) wireless local area network (LAN) standard. The proposed detector uses minimum mean square error (MMSE) sorted QR decomposition (MMSE-SQRD) to produce channel preprocessing result, which is realized by a modified systolic array architecture with concurrent sorting. Moreover, the adopted square-root MMSE algorithm for closed-loop reuses MMSE-SQRD preprocessing to largely save hardware overhead. In addition, an optimized K-Best detection algorithm is proposed for open-loop, which increases throughput by odd-even parallel sorting and produces high quality soft-output with discarded paths (DPs). A flexible VLSI architecture is designed for the proposed dual-mode detector, which supports $1\times 1\sim 4\times 4$ antennas and BPSK $\sim$ 64-QAM modulation configuration. Implemented in SMIC 65 nm CMOS technology, the detector is capable of running at 550 MHz, which has a maximum throughput of 2.64 Gb/s for K-Best detection and 3.3 Gb/s for linear MMSE detection. The proposed detector is competitive to recent published works and meets the data-rate requirement of the EUHT standard.

Low-Complexity Soft-Output Signal Detection Based on Gauss–Seidel Method for Uplink Multiuser Large-Scale MIMO Systems

For uplink large-scale multiple-input–multiple-output (MIMO) systems, the minimum mean square error (MMSE) algorithm is near optimal but involves matrix inversion with high complexity. In this paper, we propose to exploit the Gauss–Seidel (GS) method to iteratively realize the MMSE algorithm without the complicated matrix inversion. To further accelerate the convergence rate and reduce the complexity, we propose a diagonal-approximate initial solution to the GS method, which is much closer to the final solution than the traditional zero-vector initial solution. We also propose an approximated method to compute log-likelihood ratios for soft channel decoding with a negligible performance loss. The analysis shows that the proposed GS-based algorithm can reduce the computational complexity from ${{\mathcal O}({K^3})}$ to ${{\mathcal O}({K^2})}$ , where ${K}$ is the number of users. Simulation results verify that the proposed algorithm outperforms the recently proposed Neumann series approximation algorithm and achieves the near-optimal performance of the classical MMSE algorithm with a small number of iterations.

Low-Complexity Signal Detection for Large-Scale MIMO in Optical Wireless Communications

Optical wireless communication (OWC) has been a rapidly growing research area in recent years. Applying multiple-input multiple-output (MIMO), particularly large-scale MIMO, into OWC is very promising to substantially increase spectrum efficiency. However, one challenging problem to realize such an attractive goal is the practical signal detection algorithm for optical MIMO systems, whereby the linear signal detection algorithm like minimum mean square error (MMSE) can achieve satisfying performance but involves complicated matrix inversion of large size. In this paper, we first prove a special property that the filtering matrix of the linear MMSE algorithm is symmetric positive definite for indoor optical MIMO systems. Based on this property, a low-complexity signal detection algorithm based on the successive overrelaxation (SOR) method is proposed to reduce the overall complexity by one order of magnitude with a negligible performance loss. The performance guarantee of the proposed SOR-based algorithm is analyzed from the following three aspects. First, we prove that the SOR-based algorithm is convergent for indoor large-scale optical MIMO systems. Second, we prove that the SOR-based algorithm with the optimal relaxation parameter can achieve a faster convergence rate than the recently proposed Neumann-based algorithm. Finally, a simple quantified relaxation parameter, which is independent of the receiver location and signal-to-noise ratio, is proposed to guarantee the performance of the SOR-based algorithm in practice. Simulation results verify that the proposed SOR-based algorithm can achieve the exact performance of the classical MMSE algorithm with a small number of iterations.

Channel Estimation Using Radial Basis Function Neural Network in OFDM–IDMA System

In this paper, channel estimation based on Radial Basis Function Neural Network (RBFNN) is proposed to estimate channel frequency responses in orthogonal frequency division multiplexing---interleave division multiple access (OFDM---IDMA) systems. Several channel estimation techniques including least squares (LS) and minimum mean square error (MMSE) known as conventional pilot based channel estimation algorithms and multilayered perceptron (MLP) with two different training algorithms like Levenberg---Marquardt (LM) and resilient backpropagation (RBP) are also utilized to be able to make comparisons with our proposed method with the help of bit error rate and mean square errror (MSE) graphs. It is demonstrated with computer simulations that the method in which RBFNN is used for channel estimation shows better performance than LS, multilayered perceptron---Resilient backpropagation (MLP---RBP) and multilayered perceptron---Levenberg---Marquardt (MLP---LM) without the requirement of channel statistics and noise information that are essential for MMSE algorithm to estimate the channel coefficients. Even though MMSE algorithm still shows the best performance, our proposed channel estimator has the advantage of being less complex and easy to apply which makes it a serious candidate for channel estimation in OFDM---IDMA system.

Channel estimation in OFDM systems using neural network technology combined with a genetic algorithm

Orthogonal frequency division multiplexing (OFDM) is a multicarrier modulation used in a variety of broadband systems, such as asymmetric digital subscriber lines, very-high-speed digital subscriber lines, digital video and audio broadcasting, and wide local area network standards. OFDM is a promising solution achieving high data rates in a mobile environment. In wireless communication systems, signal distortion and attenuation in transmission caused by multipath effects makes it necessary to obtain knowledge related to the channel impulse response using channel estimation to provide compensation. This study combined a back propagation neural network for the estimation of channel and compensation signals with a genetic algorithm to improve performance and the convergence rate. We compared bit error rates and the mean square error of the proposed neural network with that of the conventional neural network, the least square (LS) algorithm, and the minimum mean square error (MMSE) algorithm in existing OFDM channel environments. Our results demonstrate that the proposed algorithm outperforms the LS algorithm and is on par with the MMSE algorithm.

Minimizing the Symbol-Error-Rate for Amplify-and-Forward Relaying Systems Using Evolutionary Algorithms

In this paper, a new detector is proposed for an amplify-and-forward (AF) relaying system. The detector is designed to minimize the symbol-error-rate (SER) of the system. The SER surface is non-linear and may have multiple minimas, therefore, designing an SER detector for cooperative communications becomes an optimization problem. Evolutionary based algorithms have the capability to find the global minima, therefore, evolutionary algorithms such as particle swarm optimization (PSO) and differential evolution (DE) are exploited to solve this optimization problem. The performance of proposed detectors is compared with the conventional detectors such as maximum likelihood (ML) and minimum mean square error (MMSE) detector. In the simulation results, it can be observed that the SER performance of the proposed detectors is less than 2 dB away from the ML detector. Significant improvement in SER performance is also observed when comparing with the MMSE detector. The computational complexity of the proposed detector is much less than the ML and MMSE algorithms. Moreover, in contrast to ML and MMSE detectors, the computational complexity of the proposed detectors increases linearly with respect to the number of relays.

Efficient Scheme for Channel Estimation in OFDM System

The choice of channel estimation is of fundamental importance in OFDM receiver designs, which further involves a trade-off between complexity and estimation accuracy. In pilot-symbol-aided OFDM system, the Least Square (LS) estimator suffers from inherent additive Gaussian noise and Inter Carrier Interference (ICI), although the estimator exhibits lower complexity and requires implicit knowledge of the channel. In comparison, the Minimum Mean-Square-Error (MMSE) estimator shows much better performance than the LS. However, a major drawback of the MMSE is its higher computational overhead, which further grows with increasing the number of pilots. Accordingly, the optimal design of channel estimators has remained an area of ongoing research. This study performs modifications to both existing LS and MMSE algorithms, followed by proposing two new channel estimators, namely Simplified Least Square (SLS) and Simplified Minimum Mean Square Error (SMMSE). Mathematical analyses and simulation results show that the proposed SLS method is more robust against the additive Gaussian noise and outperforms the original LS estimator. Moreover, this method can perform almost similar to the MMSE for a range of SNRs. Meanwhile, in our study the proposed SMMSE method requires only a minimum knowledge of the Channel Impulse Response (CIR) to efficiently estimate the channel. Additionally, the SMMSE exhibits computational complexity to be significantly lower than that of the original MMSE estimator

Minimizing performance loss of MMSE algorithm for CDMA-based O-MIMO-OFDM

This paper presents an algorithm to minimize the performance loss (PL) of minimum mean square error (MMSE) in code division multiple access (CDMA) based optical multiple input multiple output orthogonal frequency division multiplexing (O-MIMO-OFDM) systems over 1200km of standard single mode fiber (SSMF). The performance of the system using proposed algorithm scheme is compared to MMSE scheme by simulation results. It shows the superior performance of proposed algorithm.

Low‐complexity near‐optimal signal detection for uplink large‐scale MIMO systems

The minimum mean square error (MMSE) signal detection algorithm is near-optimal for uplink multi-user large-scale multiple-input-multiple-output (MIMO) systems, but involves matrix inversion with high complexity. It is firstly proved that the MMSE filtering matrix for large-scale MIMO is symmetric positive definite, based on which a low-complexity near-optimal signal detection algorithm by exploiting the Richardson method to avoid the matrix inversion is proposed. The complexity can be reduced from O(K 3 ) to O(K 2 ), where K is the number of users. The convergence proof of the proposed algorithm is also provided. Simulation results show that the proposed signal detection algorithm converges fast, and achieves the near-optimal performance of the classical MMSE algorithm.

Distributed Pricing-Based User Association for Downlink Heterogeneous Cellular Networks

This paper considers optimization of the user and base-station (BS) association in a wireless downlink heterogeneous cellular network under the proportional fairness criterion. We first consider the case where each BS has a single antenna and transmits at fixed power and propose a distributed price update strategy for a pricing-based user association scheme, in which the users are assigned to the BS based on the value of a utility function minus a price. The proposed price update algorithm is based on a coordinate descent method for solving the dual of the network utility maximization problem and it has a rigorous performance guarantee. The main advantage of the proposed algorithm as compared to an existing subgradient method for price update is that the proposed algorithm is independent of parameter choices and can be implemented asynchronously. Further, this paper considers the joint user association and BS power control problem and proposes an iterative dual coordinate descent and the power optimization algorithm that significantly outperforms existing approaches. Finally, this paper considers the joint user association and BS beamforming problem for the case where the BSs are equipped with multiple antennas and spatially multiplex multiple users. We incorporate dual coordinate descent with the weighted minimum mean-squared error (WMMSE) algorithm and show that it achieves nearly the same performance as a computationally more complex benchmark algorithm (which applies the WMMSE algorithm on the entire network for BS association) while avoiding excessive BS handover.

MMSE Space-Time Multi-User Detection in OFDM Systems Based on a Variety of Modulation

MIMO-OFDM is considered as candidates for future 3G/B3G broadband wireless services. High quality mobile services have to eliminate multiple-access interference (MAI) that affects multi-user receiver performance in MIMO-OFDM system. In this paper, we analyze the effect of MAI on MIMO-OFDM system and adapt a successive interference cancellation (SIC) multi-user detection algorithm which based on minimum mean square error (MMSE) algorithm for MIMO-OFDM system. This algorithm by optimizing the sorting structure enables the receiver algorithm has better performance. The simulation results show that the algorithm can obtain rate is better than the conventional linear MMSE algorithm performance in the error, and constellation mapping point spacing also affect the detection performance. As the spacing is reducing, the bit error probability will rise.

The Simulation Analysis of Channel Estimation Based on LS and MMSE Alrorithms

Due to the complex propagation caused by the multipath effect, the time-varying characteristics, the frequency selective fading and other factors of the wireless communication, consequently, the channel estimation is an important component in the receiving system with high performance. In this paper, comparisons with regard to the mean-square error and bit error rate are made in the WPDM-CDMA system based on two typical channel estimation algorithms, including the least squares error (LS) algorithm and the minimum mean-square error (MMSE) algorithm.

Block-Diagonal MIMO Equalization for Polarization-Multiplexed OFDM Transmission With Direct Detection

We propose a novel digital signal processing (DSP)-based multiple-input-multiple-output (MIMO) equalization algorithm set for polarization-multiplexed orthogonal frequency-division multiplexing transmission with direct detection (POLMUX-OFDM-DD), based on block-diagonal matrix processing. The new methodology significantly reduces legacy zero forcing (ZF)-based equalization complexity, and enables performance gains via efficient minimum mean square error (MMSE) and maximum likelihood (ML) detection. The new block-diagonal MMSE and ML algorithms are experimentally shown to extend transmission distance from 870 to 900 km and beyond 960 km, respectively, in 20-Gb/s standard single-mode fiber (SSMF) POLMUX OFDM quadrature-phase-shift-keying (QPSK)-DD transmission. The new algorithms are highly attractive for future cost-efficient, DSP-based optical metro/access systems.

Channel Estimation Based on Adaptive Neuro-Fuzzy Inference System in OFDM

In this letter we purpose adaptive neuro-fuzzy inference system (ANFIS) for channel estimation in orthogonal frequency division multiplexing (OFDM) systems. To evaluate the performance of this estimator, we compare the ANFIS with least square (LS) algorithm, minimum mean square error (MMSE) algorithm by using bit error rate (BER) and mean square error (MSE) criterias. According to computer simulations the performance of ANFIS has better performance than LS algorithm and close to MMSE algorithm. Besides there is unnecessity to send pilot when used the ANFIS.

Suboptimal Algorithm of MLD Using Gradient Signal Search in Direction of Noise Enhancement for MIMO Channels

This paper proposes a suboptimal algorithm for the maximum likelihood detection (MLD) in multiple-input multiple-output (MIMO) communications. The proposed algorithm regards transmitted signals as continuous variables in the same way as a common method for the discrete optimization problem, and then searches for candidates of the transmitted signals in the direction of a modified gradient vector of the metric. The vector is almost proportional to the direction of the noise enhancement, from which zero-forcing (ZF) or minimum mean square error (MMSE) algorithms suffer. This method sets the initial guess to the solution by ZF or MMSE algorithms, which can be recursively calculated. Also, the proposed algorithm has the same complexity order as that of conventional suboptimal algorithms. Computer simulations demonstrate that it is much superior in BER performance to the conventional ones.

Adaptive MMSE Algorithm Used in Turbo Iterative SoIC of V-Blast System

Based on the minimum mean square error (MMSE) detection with iterative soft interference cancellation (SoIC), we propose an adaptive MMSE (A-MMSE) algorithm which acts as an MMSE operator at the beginning of iteration and a maximum ratio combination (MRC) when the interference is nearly cancelled. In our algorithm, a modified metric matrix based on the reliability of soft information from the decoder output is multiplied by the interference part of channel correlation matrix to update the detection operator. The simulation results have shown that this A-MMSE iterative SoIC algorithm can achieve significant performance advantage over the traditional MMSE iterative SoIC algorithm.

Multiple antenna options for high data rate CDMA systems

1xEV-DO (1xEVolution-Data Only) is a method for transmission of wireless packet data at high rates which is based on code division multiple access (CDMA) technology. Adaptive modulation and coding is used together with proportional fairness scheduling to take full advantage of the channels between the base stations and mobile stations when they are at their best. Methods such as receive antenna diversity and multiple input multiple output (MIMO) have the potential to improve the performance of such a system. A model which simulates an 1xEV-DO network with multiple transmit and receive antennas has been developed to investigate this. Results are given showing how the throughput varies with the number of users per cell for different numbers of transmit and receive antennas. The performance of MMSE (minimum mean square error) and MRC (maximal ratio combining) algorithms are also investigated. The effects of introducing multiple paths and Rayleigh and Rician fading are compared. Simulation results for multiple transmit and receive antennas are compared with the channel capacity predicted by the Shannon capacity equation.