Minimum Mean Square Error Equalizer Research Articles

Low Complexity Equalization of HCM Systems with DPFFT Demodulation over Doubly-Selective Channels

To mitigate the inter-carrier interference (ICI) of doubly-selective (DS) fading channels, we consider a hybrid carrier modulation (HCM) system employing the discrete partial fast Fourier transform (DPFFT) demodulation and the banded minimum mean square error (MMSE) equalization in this letter. We first provide the discrete form of partial FFT demodulation, then apply the banded MMSE equalization to suppress the residual interference at the receiver. The proposed algorithm has been demonstrated, via numerical simulations, to be its superior over the single carrier modulation (SCM) system and circularly prefixed orthogonal frequency division multiplexing (OFDM) system over a typical DS channel. Moreover, it represents a good trade-off between computational complexity and performance.

CMA Channel Equalization Through An Adaptive MMSE Equalizer Based RLS Algorithm

The adaptive algorithm has been widely used in the digital signal processing like channel estimation, channel equalization, echo cancellation, and so on. One of the most important adaptive algorithms is the RLS algorithm. We present in this paper n multiple objective optimization approach to fast blind channel equalization. By investigating first the performance (mean-square error) of the standard fractionally spaced CMA (constant modulus algorithm) equalizer in the presence of noise, we show that CMA local minima exist near the minimum mean-square error (MMSE) equalizers. Consequently, CMA may converge to a local minimum corresponding to a poorly designed MMSE receiver with considerable large mean-square error. The step size in the RLS algorithm decides both the convergence speed and the residual error level, the highest speed of convergence and residual error level.

An adaptive algorithm for blind MMSE equalization of SIMO channels

In this paper, a new adaptive method is proposed to estimate blind minimum mean-square error equalizer with arbitrary delay of single-input-multiple-output channel. By using a recursive least-square-similar algorithm to recursively update a correlation matrix and its pseudo-inverse, the proposed algorithm ensures convergence and is not sensitive to the initialization of its parameters. Compared with other batch-type approaches, the new adaptive method does not require to compute the pseudo-inverse or singular value decomposition directly, consequently does not need rank estimation nor channel order estimation. Furthermore, the fast convergence enables the proposed method to be used in real time communication applications. Simulation results are provided to demonstrate the performance of the proposed method.

Beamforming for Energy Efficient Multiuser MIMO SC-FDMA Transmission with QoS Requirements

In this letter we consider beamforming (BF) with per user Quality of Service (QoS) requirements for a single-carrier frequency-division multiple-access (SC-FDMA) transmission employing a linear equalizer at the receiver. A virtual multiple-input multiple-output (V-MIMO) uplink transmission with user pairing is studied. The problem of finding the optimum BF filter coefficients that minimize the transmit power is addressed. It is shown that the optimum solution for a given data rate requirement can be analytically determined for zero-forcing (ZF) equalization, which results in an expression related to the solution available for optimum transmitter-receiver design assuming conventional linear modulation. The transmit power savings of BF compared to constant power allocation (CPA) for all subcarriers are analyzed for user pairing in the uplink of LTE. Additionally, BF for minimum mean-squared error (MMSE) equalization is investigated, for which it turns out that a numerical search algorithm has to be used for coefficient optimization. Numerical results show that the transmit power can be significantly reduced with the proposed BF scheme.

Receiver Design for Molecular Communication

In the Molecular Communication (MC), molecules are utilized to encode, transmit, and receive information. Transmission of the information is achieved by means of diffusion of molecules and the information is recovered based on the molecule concentration variations at the receiver location. The MC is very prone to intersymbol interference (ISI) due to residual molecules emitted previously. Furthermore, the stochastic nature of the molecule movements adds noise to the MC. For the first time, we propose four methods for a receiver in the MC to recover the transmitted information distorted by both ISI and noise. We introduce sequence detection methods based on maximum a posteriori (MAP) and maximum likelihood (ML) criterions, a linear equalizer based on minimum mean-square error (MMSE) criterion, and a decision-feedback equalizer (DFE) which is a nonlinear equalizer. We present a channel estimator to estimate time varying MC channel at the receiver. The performances of the proposed methods based on bit error rates are evaluated. The sequence detection methods reveal the best performance at the expense of computational complexity. However, the MMSE equalizer has the lowest performance with the lowest computational complexity. The results show that using these methods significantly increases the information transmission rate in the MC.

Continuous Phase Modulation for Digital Video Broadcasting

ABSTRACT In this paper, we study the performance of the Digital Video Broadcasting- Terrestrial (DVB-T) system with Continuous Phase Modulation Orthogonal Frequency Division Multiplexing (CPM-OFDM). The proposed structure combines the advantage of mitigating the Peak-to-Average Power Ratio (PAPR) problem in the Power Amplifier (PA)in addition to exploiting the channel frequency diversity and power efficiency of CPM. The proposed CPM-OFDM DVB-T system is implemented with Frequency-Domain Equalization (FDE) to avoid the complexity of the equalization. Two types of frequency domain equalizers are considered and compared for performance evaluation of the system; the Zero-Forcing (ZF) equalizer and the Minimum Mean Square Error (MMSE) equalizer. Simulation results show that the performance of the CPM-OFDM DVB-T system with multi-path fading is better than its performance with single-path fading. Keywords DVB-T; OFDM; CPM; ZF Equalizer; MMSE Equalizer; PAPR.

A Novel Subblock-Based Frequency-Domain Equalizer over Doubly-Selective Channels

A novel frequency-domain equalizer (FDE) is proposed for single-carrier block transmission over a doubly-selective channel. The proposed FDE partitions a received block into multiple subblocks in order to reduce the effect of the time variation of the channel. The nonuniformity in the error statistics of a subblock-based FDE is analyzed, when a one-tap minimum mean-squared error (MMSE) equalizer is employed. The nonuniformity is exploited to remove the drawback of subblock processing so that the performance of a subblock-based FDE is significantly improved. Numerical results show that the proposed FDE has much better performance than other known subblock-based FDEs. Furthermore, it has robust performance over high Doppler environments.

Performance of Linear Receivers in Frequency-Selective MIMO Channels

This paper investigates the performance of the zero-forcing (ZF) and minimum mean-square error (MMSE) equalizers in MIMO frequency selective channels under zero-padding (ZP) transmission. It was previously known that the SISO zero-forcing ZP receiver achieves full diversity; this paper shows that the MIMO version of this receiver is suboptimal in diversity. The MMSE ZP is also investigated, showing that it exhibits an intricate error behavior that depends not only on channel memory and antenna configuration, but also on transmission rate. This behavior is fully characterized in closed form, revealing that the MMSE ZP receiver attains the (optimal) diversity of a ML receiver but only at small spectral efficiencies. Thus MMSE ZP works better than ZF ZP, but not quite as well as ML. To further improve the performance, lattice-reduction aided equalization in the frequency-selective channel is investigated. It is shown that lattice-reduction-aided zero forcing equalizer as well as MMSE equalizer achieve the maximum spatial and temporal diversity at all spectral efficiencies.

Maximum-Likelihood Detection in Few-Mode Fiber Transmission With Mode-Dependent Loss

In this letter, the performance of maximum-likelihood (ML) detection is evaluated and compared with the zero-forcing (ZF) and minimum mean square error (MMSE) equalizers for a 3 × 158-Gb/s mode-division multiplexed dual-polarization quadrature phase shift keying orthogonal frequency division multiplexing transmission impaired by mode-dependent loss. The receiver schemes are compared in terms of performance and complexity. The simulations show that the ML approach outperforms both ZF and MMSE equalization for strongly coupled modes. However, the complexity of the ML detection is significantly higher and increases faster with the number of modes used for transmission and the modulation format order.

Complexity reduced detection for MIMO–OFDMA uplink with distinct frequency offsets from each user

In this work, we propose a relatively low-complexity iterative algorithm for the detection of transmitted symbols at the uplink of a multiple-input multiple-output (MIMO) orthogonal frequency-division multiple-access (OFDMA) system. The algorithm allows distinct frequency-offsets (FO)s between each user and the base-station (BS). FOs cause inter-carrier-interference (ICI), which degrades the performance of the receiver and increases the computational-complexity to decode the transmitted symbols. In order to decrease the computational-complexity at each receive antenna the proposed algorithm accounts for the interference of subcarrier k onto only ±D nearby subcarriers and ignores the interference on remaining subcarriers. This yields a banded structured ICI matrix, which is exploited to design a low-complexity soft-interference-cancelation minimum mean-squared error (SIC-MMSE) equalizer. The effects of ignoring the subcarriers are compensated for by increasing the number of receive antennas. Simulation results show that for an uncoded system the bit-error-rate (BER) performance of the proposed algorithm outperforms the MMSE equalization and is very close to the no FO scenario. Moreover, when convolution encoding is incorporated, the proposed algorithm outperforms the coded MMSE equalizer only after the first iteration.

음영 지역을 위한 3-슬롯 기반의 AF 방식 중계기 네트워크에서의 단일 반송파 주파수 대역 등화 기법

셀 커버리지 확대 및 음영 지역 해소를 위하여 중계기를 활용하는 이동 통신 시스템이 널리 연구되고 있다. 본 논문에서는 음영 지역 성능 개선을 위하여 AF(amplify-and-forward) 방식 중계기를 활용하여 다중 경로가 확보된 네트워크에서의 SC-FDE(single carrier-frequency domain equalizer)를 위한 등화 기법을 제안한다. 3-슬롯 기반 다중 경로 상황에서 중계기를 통해 수신된 신호를 MRC (maximum ratio combining) 방식으로 합쳐 MMSE (minimum mean square error) 등화 기법을 적용하면 다이버시티 이득을 획득하여 SC-FDE 시스템의 수신 성능을 크게 향상시킬 수 있다. 이를 위하여, AF 방식 중계기 기반의 다중 경로 네트워크에서 SC-FDE를 위한 MRC 계수 및 MMSE 등화 탭의 수식을 정확히 도출하여 제시하고, 실험 결과를 통해 성능 향상을 확인한다. In order to extend cell coverage and to cope with shadow areas, a relay-assisted wireless communications system has been widely studied. In this paper, we propose new equalization method for single carrier (SC) frequency domain equalizer (FDE) in amplify-and-forward (AF) relaying multi-path networks to improve the performance at shadow areas. The performance of SC-FDE system in 3-slot based multi-path networks can be improved considerably with the diversity gain which we obtain by equalizing the combined signal from relays by means of the minimum mean square error (MMSE) criteria. We find the weighting coefficients of maximum ratio combining (MRC) and the tap coefficients of MMSE equalizer for SC-FDE in AF relaying multi-path networks. Simulation results show that the proposed system considerably outperforms the conventional SC-FDE system.

A Cyclic Shift Relaying Scheme for Asynchronous Two-way Relay Networks

Perfect time synchronization among multiple relay nodes is quite difficult to realize in distributed relay networks. In this paper, we proposed a cyclic prefix (CP) assisted cyclic shift relaying (CFR) scheme for asynchronous two-way amplify-and-forward (AF) relay networks over flat fading channels. In the proposed scheme, a CP is inserted at the two source nodes to combat the asynchronous delays. Each relay amplifies the received mixed asynchronous signals after CP removal, and a cyclic delay is introduced to further improve the system performance. With the CP and the cyclic delay, the multiple flat fading relay channels are transformed into a multipath fading channel. As a result, low complexity frequency domain equalizers, such as zero-forcing and minimum mean square error (MMSE) equalizer, can be used to recover the transmit signal. Furthermore, the performance of the proposed CFR scheme with MMSE equalizer is analyzed and closed-form expression for the lower bound of uncoded bit error rate (BER) performance is derived. Based upon this lower bound, we also investigate the power allocation among the sources and the relays to improve the system performance. Finally, extensive numerical results are provided to show the BER and frame error rate performance of the proposed CFR scheme.

Mitigation of channel estimation error in TR–UWB system based on a novel MMSE equalizer

The time reversal (TR) technique combined with the ultra-wideband (UWB) system offers a new potential for decreasing the cost and complexity of the UWB receivers. In spite of TR–UWB's good performance in perfect channel state information (CSI), it is very sensitive to the channel estimation error. The effect of channel imperfection on the TR–UWB system is considered in this paper. At first, based on a minimum mean square error (MMSE) equalizer receiver, a prefilter is calculated in closed form to improve the performance of the TR–UWB system in an imperfect CSI scenario. Furthermore, for comparison purposes, a similar calculation for prefilter is carried out based on a simple matched filter (MF) receiver. Then, in order to improve the MF receiver performance, a two-stage iteration-based algorithm is developed. The initial value for this iteration-based improved algorithm is considered to be a prefilter which is calculated in the TR–UWB system with MMSE equalizer. This optimized algorithm causes the channel estimation error in the TR–UWB system to become zero in some steps. Finally, exhaustive simulations are done to demonstrate the performance advantage attained by the improved algorithm.

Efficient MIMO DS-UWB Downlink Chip-Level MMSE Equalization Using Subband Adaptive Interference Mitigation Techniques

An adaptive subband chip-level equalizer is investigated for downlink multiple-input-multiple-output (MIMO) direct-sequence (DS) ultrawideband (UWB) systems to cope with intersymbol interference (ISI) and multiple-access interference (MAI) in multipath fading channels. The subband decomposition technique with multiple analysis and synthesis filter banks (FBs) is employed to substantially improve the downlink reception of mobile-terminal (MT) receivers. This chip equalizer utilizes subband adaptive interference suppression techniques based on the minimum mean square error (MMSE) criterion. A reduced-complexity chip-level MMSE equalization scheme is proposed by making full use of the reduced-rank (RR) multistage matrix Wiener filter (MMWF) and the matrix conjugate gradient (MCG) architectures in subbands. Simulations are conducted to provide a comparative evaluation of the proposed subband chip equalizer with other existing full-band and subband chip equalizers.

Performance Analysis of a Frequency-Domain Equal-Gain-Combining Time-Reversal Scheme for Distributed Antenna Systems

Time-reversal (TR) precoding focuses the energy of the effective channel in time and improves receive performance of a single tap receiver or a minimum mean square error (MMSE) receiver with distributed antenna systems (DAS). Frequency-domain equal-gain-combining (FD-EGC) scheme is proposed as a new TR scheme, which works in linear block precoding (LBP) fashion and has better temporal focusing performance than the traditional TR. Extending the FD-EGC as LBP in DAS, the mean square error is analyzed for the MMSE equalizer at receiver. We show that the FD-EGC with a few antennas, which is a more realistic case than that with many antennas, has better performance than the traditional TR.

Adaptive MMSE Equalizer for Optical Multipath Dispersion in Indoor Visible Light Communication

Multipath dispersion results from optical signals passing through more than one path. In this paper, we investigate a non-directed line of sight (LOS) model using white light emitting diode illumination. Typically in such a link, the optical signals are modeled as a reflection component and a directed LOS component over optical wireless (OW) channels. However, inter-symbol interference (ISI) induced by multipath dispersion critically influences the performance of OW communications. In this paper, we propose the adaptive minimum mean squared error (MMSE) equalizer scheme to suppress the multipath ISI, since this scheme can minimize the mean square error (MSE) between the desired equalizer output and the actual equalizer output. We compared the following two algorithms: Least mean square and recursive least square. Our computer simulations demonstrated that visible light communication using an adaptive MMSE equalizer can alleviate the serious effects of optical multipath dispersion.

A Simplified MMSE Equalizer for Distributed TR-STBC Systems with Multiple CFOs

In distributed wireless systems, the traditional carrier frequency offset (CFO) compensation methods may not be applied due to the existence of multiple CFOs. In this paper, we address the equalization issue for distributed time-reversal space-time block coded (TR-STBC) systems when multiple CFOs are presented. A simplified minimum mean-square error (MMSE) equalizer is proposed, which exploits the nearly-banded structure of the channel matrices and utilizes the {LDL}^H factorization to reduce the computational complexity. Simulation results show that the proposed equalizer can achieve the similar performance as the traditional MMSE equalizer while possessing much less complexity.

Performance Analysis of Hybrid Carrier System with MMSE Equalization over Doubly-Dispersive Channels

A hybrid carrier (HC) system employing a frequency domain linear equalization based on minimum mean square error (MMSE) criterion is analyzed in this letter. The analytical studies prove that HC modulation scheme achieves a trade-off between circularly prefixed orthogonal frequency division multiplexing (OFDM) and single-carrier (SC) systems in terms of resisting doubly-selective fading. By dispersing the aggregated residual interference effectively, the HC system with particular modulation orders outperform OFDM and SC systems within a specific signal noise ratio (SNR) interval. Both analysis and simulation results over a typical double selective fading channel verify the superiority of HC modulation in suppressing residual interferences.

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.

Robust Fast Time-Varying Multipath Fading Channel Estimation and Equalization for MIMO-OFDM Systems via a Fuzzy Method

Channel estimation is an important issue for wireless communication systems. A channel estimation scheme using a Takagi-Sugeno (T-S) fuzzy-based Kalman filter under the time-varying velocity of the mobile station in a multiple-input multiple-output orthogonal frequency-division multiplexing (MIMO-OFDM) system is proposed in this paper. The fuzzy technique is used to interpolate several linear models to approximate the nonlinear estimation system. A MIMO system with the orthogonal space-time block coding (OSTBC) scheme is considered, where the radio channel is modeled as an autoregressive (AR) random process. The parameters of the AR process and the channel gain are simultaneously estimated by the proposed method. One-step-ahead prediction can be obtained during this estimation procedure. This is useful for the decision-directed channel-tracking design, particularly in the fast-fading channel. Furthermore, the robust minimum mean-square error (MMSE) equalization design can be achieved by considering the channel prediction error to improve the performance of symbol detection. To validate the performance of our proposed method, several simulation results are given and compared with those of other methods. When considering the time-varying velocity of the mobile station communication in the MIMO-OFDM system, the enhanced equalizer based on the T-S fuzzy-based Kalman filter performs better than those based on the conventional channel estimators in terms of symbol error rate.