Linear Minimum Mean Square Error Equalizer Research Articles

Nonlinear Equalization for Performance Enhancement of FBMC Systems Using Walsh Transform

The Filter Bank Multi-Carrier (FBMC) is an interesting recent technology for next-generation wireless radio communication systems. Equalization is a fundamental technique for enhancing Bit Error Rate (BER) performance. The traditional Linear Zero Forcing (LZF) and Linear Minimum Mean Square Error (LMMSE) equalizers have large noise amplification and high complexity, respectively. As the estimated error of the Signal-to-Noise Ratio (SNR) grows, the BER performance of the LMMSE equalizer degrades. In this paper, we present a Joint Low Complexity Optimized ZF-Successive Interference Cancellation (JLCOZF-SIC) equalizer for FBMC communication systems that are based on the Walsh–Hadamard Transform (WHT) rather than the Fast Fourier Transform (FFT). As in the MMSE-Successive Interference Cancellation (MMSE-SIC) equalizer, the proposed equalizer avoids the estimating error induced by average power per symbol estimation. The simulation results show that the proposed algorithm improves the system performance more than the existing algorithms. Furthermore, the proposed equalization provides stability in the BER performance at high levels of the co-Carrier Frequency Offset (co-CFO). In terms of computational complexity, the proposed scheme has a lower computational complexity than traditional schemes.

Adaptive Turbo Equalization for Nonlinearity Compensation in WDM Systems

In this paper, the performance of adaptive turbo equalization for nonlinearity compensation (NLC) is investigated. A turbo equalization scheme is proposed where a recursive least-squares (RLS) algorithm is used as an adaptive channel estimator to track the time-varying intersymbol interference (ISI) coefficients associated with inter-channel nonlinear interference (NLI) model. The estimated channel coefficients are used by a MIMO $2\times 2$ soft-input soft-output (SISO) linear minimum mean square error (LMMSE) equalizer to compensate for the time-varying ISI. The SISO LMMSE equalizer and the SISO forward error correction (FEC) decoder exchange extrinsic information in every turbo iteration, allowing the receiver to improve the performance of the channel estimation and the equalization, achieving lower bit-error-rate (BER) values. The proposed scheme is investigated for polarization multiplexed 64QAM and 256QAM, although it applies to any proper modulation format. Extensive numerical results are presented. It is shown that the scheme allows up to 0.7 dB extra gain in effectively received signal-to-noise ratio (SNR) and up to 0.2 bits/symbol/pol in generalized mutual information (GMI), on top of the gain provided by single-channel digital backpropagation.

Performance improvement of data transmission using a hybrid underwater and terrestrial system

AbstractIn this paper, we investigate and enhance the performance of data transmission using a hybrid underwater and terrestrial system with low‐complexity linear equalization. Due to the low speed, salinity, water depth, pH degree, and water temperature variations, underwater acoustic communication has become one of the most challenging technologies in the world. The most common linear equalizers are the Linear Zero Forcing (LZF), and Linear Minimum Mean Square Error (LMMSE) equalizers. The LZF equalizer suffers from the noise enhancement problem, while the LMMSE equalizer requires the value of the operating Signal‐to‐Noise Ratio (SNR) to work, correctly, which increases the computational complexity. In addition, this paper presents a low‐complexity equalization scheme to overcome the drawbacks associated with the LZF, and LMMSE equalizers. The proposed equalizer is called the Joint Low‐Complexity Regularized LZF equalizer, which depends on a fixed regularization parameter to minimize the noise enhancement phenomenon caused by the LZF equalizer. The proposed equalizer does not need the estimation of the SNR, and the computational complexity is reduced due to the utilization of the banded‐matrix approximation. The proposed equalizer is implemented based on the Single‐Input‐Single‐Output configuration for Orthogonal Frequency Division Multiplexing (OFDM) using the Discrete Cosine Transform. The obtained simulation results show that the proposed equalizer outperforms different equalizers for the same channel conditions.

Signal Detection for Underwater IoT Devices With Long and Sparse Channels

Underwater acoustic communication often suffers from extended channel impulse response (CIR) and large Doppler spread such that signals become difficult to detect and decode. For the underwater Internet-of-Things (IoT) applications, the challenges are even bigger, because the IoT devices usually transmit very short messages due to severe power constraints, and the length of pilots are often shorter than that of CIR. Therefore, conventional pilot-assisted channel estimation and equalization approaches are incapable of detecting the information data. Moreover, the existing blind channel equalization algorithms, which do not require pilots, are not able to detect information data either, because the number of transmitted symbols is too small to approximate the expected loss with empirical loss, where the loss refers to as the error of estimated signal envelopes. In this article, a new equalization and decoding algorithm is proposed for the underwater IoT devices under harsh communication environments. Inspired by the recent blind deconvolution and compressive sensing techniques, we construct an optimization problem with the objective function rewarding sparsity of the estimated CIR using l4-norm and convexify the feasible set of the problem while guarantee the same solution. Then, we develop a pruned tree search initialization method and use gradient descent to find an optimal solution efficiently. The new algorithm is first verified by simulations, which show that the proposed algorithm outperforms conventional methods, such as the linear minimum mean square error (LMMSE) equalizer and a constant modulus algorithm (CMA). The proposed algorithm, along with a practical procedure for compensating large Doppler spread and carrier frequency offset, is further employed to process the real-world underwater IoT data collected in a fish-tag project. It shows that the proposed algorithm can equalize and detect the IoT data which were corrupted by channels whose lengths are longer than that of pilots, but the existing algorithms, such as LMMSE equalizer and CMA-based blind equalizer are not able to accomplish. It also shows that the proposed algorithm can provide a very impressive improvement compared to raw detection (no equalization or decoding) and decoding-only approaches.

Iterative Equalizer Based on Kalman Filtering and Smoothing for MIMO-ISI Channels

This paper proposes an iterative equalizer based on Kalman filtering and smoothing (IEKFS) for multiple-input multiple-output inter-symbol interference (MIMO-ISI) channels. A state-space model with a priori information and the corresponding Kalman filtering (KF) and Kalman smoothing (KS) operations are developed. The KF operations perform a linear minimum mean-square error (MMSE) equalization procedure with soft interference cancellation. In addition, the KF and KS operations produce and exchange the updated extrinsic information. During this IEKFS process, the soft estimate of a desired symbol does not participate in the equalization procedures for the desired symbol; only the feedback information of the other transmit symbols is used. Therefore, the proposed IEKFS performs iterative linear MMSE equalization based on the Kalman framework and turbo principle. The complexity of the IEKFS is linear with respect to the number of transmit signal vectors in a transmission block, and simulation results show that the IEKFS can achieve near-optimum bit error rate performances approaching the matched filter bound (MFB) of the channel in various environments.

Iterative estimation of doubly selective underwater acoustic channel using basis expansion models

An iterative channel estimation scheme is proposed for orthogonal frequency division multiplexing (OFDM) systems over doubly selective underwater acoustic channels. The channel estimator is developed based on the basis expansion model (BEM) with two different types of basis functions, complex exponential (CE) basis and discrete prolate spheroidal sequences (DPSS). Considering the different Doppler characteristics for each cluster, we use cluster-specific parameters in the BEM for the most significant taps, such that the number of unknowns during channel estimation can be considerably reduced. The frequency domain received samples are expressed in terms of the model coefficients of the most significant taps. The channel estimator operates in an iterative, decision-directed fashion. At the first iteration, it utilizes only pilot symbols. After the first iteration, the estimator also uses the symbol decisions produced by a linear minimum mean squared error (LMMSE) block equalizer, in addition to the pilot symbols. We verify the bit-error-rate (BER) performance of the OFDM system over a simulated underwater acoustic channel based on Monterey-Miami Parabolic Equation modeling. It is shown that the LMMSE equalizer with the BEM-based channel estimators and the one-tap equalizer with perfect channel state information have similar BER performances. Both the proposed BEM-based channel estimation schemes perform much better than the basic matching pursuit method, a classic sparsity-aware channel estimation technique.

Widely linear MMSE precoding and equalization techniques for SC-FDE systems

Single-carrier systems using frequency-domain equalization (SC-FDE) systems were proposed to overcome the low robustness to carrier frequency offset (CFO) and high peak-to-average-power ratio (PAPR) inherent to regular orthogonal frequency-division multiplexing (OFDM) systems. Usually, linear minimum mean square error (MMSE) equalization is used to compensate the channel effect, since maximum likelihood (ML) detection is computationally impractical. However, if the transmitted signal comes from an improper constellation, widely linear processing can be used to take advantage of all the available second-order statistics from this transmitted signal, obtaining this way a performance gain when compared to the strictly linear case. In this paper, a SC-FDE system employing widely linear MMSE equalization is proposed in its regular and decision-feedback (DFE) versions. A SC-FDE system employing widely linear MMSE Tomlinson-Harashima precoding (THP) and equalization is also proposed. With Tomlinson-Harashima precoding, the error propagation problem observed in systems using a decision-feedback equalizer vanishes, because the feedback processing is done at the transmitter. Simulation results show that together with the error performance gain, these systems have lower sensibility to the feedback filter length in systems using decision-feedback equalizers. In Tomlinson-Harashima precoded systems, the performance gain is observed even with channel estimation/channel state information errors.

Efficient Image Transmission with Multi-Carrier CDMA

This paper presents a new approach for efficient image transmission over Multi-Carrier Code Division Multiple Access (MC-CDMA) systems using chaotic interleaving. The chaotic interleaving scheme based on Baker map is applied on the image data prior to transmission. The proposed approach transmits images over wireless channels, efficiently, without posing significant constraints on the wireless communication system bandwidth and noise. The performance of the proposed approach is further improved by applying Frequency-Domain Equalization (FDE) at the receiver. Two types of frequency-domain equalizers are considered and compared for performance evaluation of the proposed MC-CDMA system; the Zero-Forcing equalizer and the Linear Minimum Mean Square Error (LMMSE) equalizer. Several experiments are carried out to test the performance of the image transmission with different sizes over the proposed MC-CDMA system. Simulation results show that image transmission over wireless channels using the proposed chaotic interleaving approach is much more immune to noise and fading. Moreover this chaotic interleaving process adds a degree of encryption to the transmitted data. The results also show a noticeable performance improvement in terms of the Root Mean Square Error and Peak Signal-to-Noise Ratio values when applying FDE in the proposed approach, especially with the LMMSE equalizer.

Fast Recursive Equalizers for 1D and 2D Linear Equalization

We develop fast recursive equalizers to be used in the one-dimensional (1D) or two-dimensional (2D) linear minimum mean-squared error equalization of a known linear finite-length channel. In particular, these equalization algorithms address the communications scenario in which the channel or the prior information on the transmitted symbols may be time varying. The latter case of time-varying priors is especially pertinent for turbo equalization, on which we focus here. We first consider a 1D sliding-window equalizer based on a Cholesky-factorization update and then generalize this approach to the 2D case. Finally, we develop a 2D equalizer that is based on a recursive matrix-inverse update. We summarize each of these algorithms and describe their computational complexities.

이중 선택적 채널 OFDM 시스템을 위한 블록 선형 MMSE 등화 방식의 성능 분석

본 논문에서는 이중 선택적 채널 OFDM 시스템을 위한 블록 선형 MMSE(Minimum Mean Square Error) 등화 방식의 성능을 컴퓨터 모의실험을 통하여 분석한다. 블록 선형 MMSE 등화 방식의 BER(Bit Error Rate) 성능은 SNR(Signal-to-Noise Ratio)이 증가함에 따라 BER이 처음에는 감소하다가 SNR이 일정 값을 넘어서면 BER이 오히려 증가하는 다소 특이한 현상을 나타낸다. 본 논문에서는 블록 선형 MMSE 등화 과정에 포함된 선형연립방정식 계수 행렬의 상태수(condition number) 분석을 통하여 이러한 블록 선형 MMSE 등화 방식의 BER 특성을 규명하고 높은 SNR 값에서의 BER 성능 저하를 개선하는 새로운 방안을 제시한다. In this paper, we analyze the performance of the block linear MMSE equalization for OFDM systems in doubly selective channels by computer simulations. The block linear MMSE equalization shows somewhat unusual BER characteristics in that the BER curve drops at first as SNR increases but then rises up as SNR increases further beyond some point. In this paper, we investigate the BER characteristics of the block linear MMSE equalization by analyzing the condition number of the coefficient matrix in the linear system involved in the equalization process, and propose a new method to avoid the BER performance degradation at high SNR.

Doubly-selective fading channel equalization: A comparison of the Kalman filter approach with the basis expansion model-based equalizers

In this paper, we exploit the Kalman filter as a time-varying linear minimum mean-square error equalizer for doubly-selective fading channels. We use a basis expansion model (BEM) to approximate the doubly-selective channel impulse response. Several time-varying linear equalizers have been proposed in the literature where both the channel and the equalizer impulse responses are approximated by complex exponential (CE) BEMs. Our proposed Kalman filter formulation does not rely on a specific BEM for the underlying channel, therefore, it can be applied to any BEM, including the CE-BEM and the discrete prolate spheroidal (DPS) BEM. Moreover, the Kalman filter relies solely on the channel model and therefore, does not incur any approximation error inherent in the CE-BEM representation of the equalizer. Through computer simulations, we show that compared to two of the existing algorithms, the proposed Kalman filter formulation yields the same or an improved bit error rate at a much lower computational cost, where the latter is measured in terms of the number of flops needed for the equalizer design and implementation.

A hybrid equalizer/Rake receiver for the Wideband CDMA Downlink in large delay spread channels

Abstract. Signals transmitted over a multi-path propagation channel exhibit Inter-Path Interference (IPI) and fading. The receiver has to employ measures to mitigate these effects or it will incur severe performance degradation. A classic approach in Code Division Multiple Access (CDMA) communications is the Rake receiver. Alternatively, a Linear Minimum Mean Square Error (LMMSE) equalizer can further improve performance. This paper compares performance and computational complexity of these two algorithms. A hybrid solution will be introduced in order to decrease computational complexity while retaining most of the interference suppression capabilities of the LMMSE equalizer.

주파수 선택적 시변 채널 OFDM 시스템에서의 파일럿 심볼을 이용한 채널 예측 및 등화

본 논문에서는 주파수 선택적 시변 채널 OFDM 시스템에서 파일럿 심볼을 이용하는 채널 예측 및 등화 방식의 성능을 분석하고 문제점 및 개선 방안을 제시한다. 주파수 영역 채널 행렬의 대역폭을 제한하기 위하여 시간 영역 윈도우를 도입하며, 채널 예측에 LS(Least Square) 및 선형 MMSE(Minimum Mean Square Error) 예측 방식을 이용한다. 채널 등화에는 채널 예측에 이용되는 파일럿 심볼의 존재가 고려된 선형 MMSE 및 결정 귀환 등화 방식을 이용한다. 계산량을 감소시키기 위하여 채널 등화 알고리즘에 요구되는 선형 연립 방정식의 풀이에 band LU 행렬 분해 알고리즘을 도입하며, 컴퓨터 시뮬레이션을 통하여 기존 방식과의 성능을 비교한다. 결정 귀환 등화 방식에 시간 영역 윈도우를 적용하는 경우, 결정 귀환 관련 행렬의 대역폭이 제한되지 않아 성능이 저하되는 문제점을 분석하였다. In this paper, we analyze the performance of pilot symbol assisted channel estimation and equalization schemes for OFDM systems over frequency-selective time-varying channels and propose methods to improve the system performance. In the least square(LS) and linear minimum mean square error(MMSE) channel estimation, time domain windowing is introduced for banding the frequency domain channel matrix. The linear MMSE and decision feedback equalization schemes are employed with the pilot symbols for channel estimation taken into account in the equalization process. To reduce computational complexity, the band LU matrix factorization algorithm is introduced in solving the linear systems involved in the equalization, and the performances are compared with the known previous results by computer simulations. When time domain windowing is employed in the decision feedback equalization, the matrix related with the decision feedback process is shown to be unhanded and the resultant performance degradation is analyzed.

Space-Time Equalizers for MIMO High Speed WCDMA Downlinks

Multiple-input multiple-output (MIMO) communications based on multiple transmit and receive antennae will be applied to enhance the data rates of the third generation (3G) cellular systems or wideband code division multiple access (WCDMA) and in particular, their high speed downlink packet access (HSDPA) services. This causes both spatial multiplexing interference (SMI) and downlink multiple access interference (MAI). In this paper, we derive an improved linear minimum mean square error (LMMSE) detector approximation suitable for MIMO-WCDMA systems. We also propose a new two-stage receiver architecture to suppress the effects of both MAI and SMI in HSDPA communications. SMI often dominates MAI, since it does not benefit from spreading gain. Therefore, a spatial maximum a posteriori (MAP) detector is used to suppress SMI, and a LMMSE based channel equalizer is applied as its front- end. The performance of the resulting LMMSE-MAP receiver structure is studied via Monte Carlo computer simulations with assumptions very realistically mimicking those of the HSDPA specification. The results show that it clearly outperforms the rake receiver or the improved LMMSE equalizer approximation, which, on the other hand, is also shown to be superior to the more conventional LMMSE equalizers.

Low-Cost Approximate LMMSE Equalizer Based on Krylov Subspace Methods for HSDPA

The throughput of the high speed downlink packet access (HSDPA) sub-system of UMTS suffers significantly from multiple access interference in the wireless channel. A linear minimum mean square error (LMMSE) equalizer at the receiver achieves higher throughput than a conventional RAKE receiver, at the cost of higher complexity. We introduce an iterative algorithm based on Krylov subspace projections, approximating the LMMSE equalizer with negligible loss of performance for the receiver. Slow variations of the channel can be exploited to allow further acceleration of the algorithm. Computational complexity as well as storage requirements are strongly reduced

Reduction of Doppler effects in OFDM systems

This paper observes the inter-carrier interference (ICI) by Doppler effect in time domain in orthogonal frequency division multiplexing systems. This observation allows us to propose a new time domain two-stage equalization scheme that iteratively cancels the ICl. The proposed scheme consists of the following two stages: First, we apply low-complexity linear minimum mean squared error (MMSE) employing partial rank of time impulse response matrix to shorten the ICI components into diagonal region. Second, we propose new parallel interference cancellation with hard decision feedback to remove the residual ICI. Performance evaluations and complexity analyses show that the bit error rate and the signal-to-interference-plus-noise ratio performances of the proposed scheme are very close to those of the classical frequency domain linear MMSE equalization scheme with much reduced complexity

A linear equalizer for high-speed APD-based integrate-and-dump receivers

A linear minimum mean-square error (LMMSE) equalizer for avalanche-photodiode (APD) based integrate-and- dump receivers is designed to compensate for intersymbol- interference (ISI) introduced by the APD's random impulse response. Recent work on the characterization of the joint probability distribution of the APD's gain and buildup-time are adopted and utilized to determine the mean and correlation matrix of the APD-based receiver's random impulse response. This LMMSE equalizer is shown to improve the bit-error- rate dramatically at high transmission rates, resulting in an improvement in the receiver sensitivity by approximately 2.3 dB at 15GHz. Index Terms—Avalanche photodiodes, equalization, random impulse response, bit-error-rate, receiver sensitivity.

Application of linear minimum mean-squared-error equalization for volume holographic data storage

When target densities of volume holographic data storage systems are increased, the systems experience increased interference from adjacent pixels and noise. Here we present a method for designing and applying linear minimum mean-squared-error (LMMSE) equalization to improve the bit error rates (BER's) and hence the storage densities achievable. Numerical results with five defocused data pages indicate that a significant improvement in the BER is possible with LMMSE equalization.