Minimum Mean Square Error Equalizer Research Articles

Iterative Sparse Channel Estimation and Decoding for Underwater MIMO-OFDM

We propose a block-by-block iterative receiver for underwater MIMO-OFDM that couples channel estimation with multiple-input multiple-output (MIMO) detection and low-density parity-check (LDPC) channel decoding. In particular, the channel estimator is based on a compressive sensing technique to exploit the channel sparsity, the MIMO detector consists of a hybrid use of successive interference cancellation and soft minimum mean-square error (MMSE) equalization, and channel coding uses nonbinary LDPC codes. Various feedback strategies from the channel decoder to the channel estimator are studied, including full feedback of hard or soft symbol decisions, as well as their threshold-controlled versions. We study the receiver performance using numerical simulation and experimental data collected from the RACE08 and SPACE08 experiments. We find that iterative receiver processing including sparse channel estimation leads to impressive performance gains. These gains are more pronounced when the number of available pilots to estimate the channel is decreased, for example, when a fixed number of pilots is split between an increasing number of parallel data streams in MIMO transmission. For the various feedback strategies for iterative channel estimation, we observe that soft decision feedback slightly outperforms hard decision feedback.

Managing the interference structure of MIMO HSDPA: A multi-user interference aware MMSE receiver with moderate complexity

It is known that Wideband Code-Division Multiple Access (W-CDMA) networks are limited by interference more than by any other single effect. Due to the frequency selectivity of the wireless channel, intra-cell interference composed of selfand other-user interference occurs. The intra-cell interference as a result of Transmit Antenna Array (TxAA) HSDPA multi-user transmissions, however, shows a special structure that can be exploited to allow for an efficient interference suppression. The contributions of this article are the following: we (a) propose a suitable system model to derive an intra-cell interference aware Minimum Mean Squared Error (MMSE) equalizer with moderate complexity and investigate its capabilities to suppress the multi-user intra-cell interference, (b) propose solutions to estimate the pre-coding state of the cell both with and without available training, and (c) investigate the resulting throughput performance with physical layer as well as system-level simulations. Our proposed solution can be interpreted as a multi-user extension of the classical MMSE equalizer for HSDPA systems without decoding the undesired users, resulting in only slightly increased complexity.

BER Degradation of MC-CDMA at High SNR with MMSE Equalization and Residual Frequency Offset

Multicarrier Code Division Multiple Access (MC-CDMA) is an attractive technique for high speed wireless data transmission in view of its advantages over orthogonal frequency division multiplexing. In this paper, we analyze the performance of fully loaded downlink MC-CDMA systems with minimum mean square error (MMSE) equalizer in the presence of residual frequency offset (RFO) in multipath Rayleigh fading channels. We first show that as the SNR is increased beyond a value, referred as threshold SNR, the performance degrades. We then analyze the cause for this behavior and propose a remedy to prevent the degradation by regularizing the coefficient(s) of the equalizer, and use the regularized equalizer for SNRs beyond the threshold value. We suggest two methods for estimating this SNR, one gives close to the true value but requires the knowledge of RFO and the channel state information (CSI), while the other gives an approximate value but requires only CSI. We show that the regularization based on the approximate value also prevents the degradation, but the performance at higher SNRs is slightly poorer compared to that with the better estimate. Numerical and simulation results are provided to support the analysis.

Asynchronous CDMA Under Single-Carrier Block Transmission—Architectures and Signal Models

Single-carrier (SC) block transmission with frequency-domain equalization (FDE) is an efficient scheme that avoids complex time-domain equalization in multipath channels. There are also several systems that are proposed that apply SC-FDE in code-division multiple access (CDMA). However, the present CDMA systems with FDE may not be suitable for asynchronous users for lack of a signal model that can suitably express the despread signal in the frequency domain. In this paper, we first propose circularly sliding (CS) despreading that can attain preliminary separation of interference among asynchronous users. Then, we derive a signal model that represents spreading, channel effect, and despreading as a series of circular convolutions. This signal model helps to derive a new FD minimum mean-square error (MMSE) equalization algorithm for SC block transmission asynchronous CDMA. We further extend the signal model by including equalization as another circular convolution. The extended signal model indicates several equivalent architectures of the receiver. For these architectures, despreading and equalization can be implemented in either the time or frequency domain, and the order is exchangeable. Based on the proposed signal model, we also derive a RAKE combiner that can be implemented in the frequency domain. Our architectures and signal model can be applied for further development of multiuser-detection algorithms.

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.

Interference Coordination for E-MBMS Transmissions in LTE-Advanced

Interference coordination methods for Evolved-Multimedia Broadcast/Multicast Service (E-MBMS) in Long-Term Evolution Advanced (LTE-A) are presented. In addition, we consider signal space diversity based on Rotation Matrices (RM) known to provide good performance gains over uncorrelated Rayleigh fading channels. OFDM/OFDMA systems can make the use of RM very attractive both for single and multiple antenna transmissions. In this paper, OFDM/OFDMA signals based on LTE parameters are combined with RM, MIMO, Turbo, or LDPC codes. We have considered different types of receivers, namely, we used an MMSE (Minimum Mean Squared Error) equalizer and a Maximum Likelihood Soft Output criterion (MLSO). Frequency, signal, and space diversity gains are evaluated for different spatial channel models (SCM) based on ITU multipath propagation channels. Different adaptive frequency reuse and schedulers are considered to evaluate the E-MBMS spectral efficiency at the cell borders.

Performance analysis of a flexible subsampling receiver for pulsed UWB signals

This paper presents a flexible digital receiver for pulsed Ultra-Wideband (UWB) communications which is sampling below Nyquist rate. This receiver can trade demodulation performance for sampling rate, i.e. power consumption. The bit error rate for pulse amplitude and pulse position modulations is evaluated in AWGN and typical UWB channels. The performance of several types of equalizer is compared, taking into account their implementation complexity. A suboptimal but implementation efficient Minimum Mean-Square Error (MMSE) equalizer which reaches performances similar to the ideal MMSE equalizer is proposed. The impact of imperfect knowledge of the propagation channel and signal-to-noise ratio, due to the limited number of training symbols, on the performance of the receiver is assessed. Finally, the receiver architecture and implementation cost are discussed. The proposed subsampling receiver provides an attractive alternative to classical architectures based on correlation with a template.

Space–Time-Coded MIMO ZP-OFDM Systems: Semiblind Channel Estimation and Equalization

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> The space–time-block-code (STBC) multiple-input–multiple-output (MIMO) zero-padding orthogonal frequency-division multiplexing (ZP-OFDM) has been widely investigated in recent years. It provides a good performance for the multiuser scenario with a small number of pilots. However, it would fail in the face of complex symmetric signals. In this paper, novel channel estimation and equalization for complex input signals are investigated. With the Alamouti-like STBC scheme, the channel impulse responses of the space–time-coded MIMO ZP-OFDM system are shown to be identifiable up to two ambiguity matrices by subspace channel estimation. The frequency domain minimum mean-square error (MMSE) equalizer is then employed to detect the OFDM symbols. Furthermore, we propose a forward–backward averaging technique to enhance the performances of blind channel estimation. The weight analysis for the MMSE equalizer is also conducted to reduce the complexity of system design. Computer simulations demonstrate the effectiveness and correctness of channel estimation and weight analysis for the space–time-coded MIMO ZP-OFDM systems. </para>

Low-complexity linear frequency domain equalization for continuous phase modulation

In this paper, we develop a new low-complexity linear frequency domain equalization (FDE) approach for continuous phase modulated (CPM) signals. As a CPM signal is highly correlated, calculating a linear minimum mean square error (MMSE) channel equalizer requires the inversion of a nondiagonal matrix, even in the frequency domain. In order to regain the FDE advantage of reduced computational complexity, we show that this matrix can be approximated by a block-diagonal matrix without performance loss. Moreover, our MMSE equalizer can be simplified to a low-complexity zero-forcing equalizer. The proposed techniques can be applied to any CPM scheme. To support this theory we present a new polyphase matrix model, valid for any block-based CPM system. Simulation results in a 60 GHz environment show that our reduced-complexity MMSE equalizer significantly outperforms the state of the art linear MMSE receiver for large modulation indices, while it performs only slightly worse for small ones.

Low complexity iterative detection for OFDMA uplink with frequency offsets

In this work, we propose an iterative algorithm for the detection of transmitted symbols at the uplink of an orthogonal frequency-division multiple access (OFDMA) system. The algorithm allows distinct frequency-offsets (FO)s from each user that cause multiple-access and self interference. The proposed algorithm squeezes the interference of subcarrier k into 2D + 1 nearby subcarriers by preprocessing the received signal and yields a banded structure interference matrix. Here, the value of D depends on the FO and determines the squeezing depth. The proposed algorithm exploits this banded structure and realizes a low complexity iterative soft-interference-cancellation minimum mean-squared error (SIC-MMSE) equalizer that can be used in Turbo equalization. Simulation results show that the bit-error-rate (BER) performance of the proposed algorithm outperforms existing detection algorithms and is very much close to the zero-FO frequency-domain-equalization (zero-FO-FDE).

Double Turbo Equalization of Continuous Phase Modulation with Frequency Domain Processing

In this paper, a doubly-iterative linear receiver, equipped with a soft-information aided frequency domain minimum mean-squared error (MMSE) equalizer, is proposed for the combined equalization and decoding of coded continuous phase modulation (CPM) signals over long multipath fading channels. In the proposed receiver architecture, the front-end frequency domain equalizer (FDE) is followed by the soft-input, softoutput (SISO) CPM demodulator and channel decoder modules. The receiver employs double turbo processing by performing back-end demodulation/decoding iterations per each equalization iteration to improve the a priori information for the front-end FDE. As presented by the computational complexity analysis and simulations, this process provides not only a significant reduction in the overall computational complexity, but also a performance improvement over the previously proposed iterative and noniterative MMSE receivers.

Diversity–Multiplexing Tradeoff in ISI Channels

The optimal diversity-multiplexing tradeoff curve for the intersymbol interference (ISI) channel is computed and various equalizers are analyzed using this performance metric. Maximum-likelihood signal decoding (MLSD) and decision feedback equalization (DFE) equalizers achieve the optimal tradeoff without coding, but zero forcing (ZF) and minimum mean-square-error (MMSE) equalizers do not. However if each transmission block is ended with a period of silence lasting the coherence time of the channel, both ZF and MMSE equalizers become diversity-multiplexing optimal. This suggests that the bulk of the performance gain obtained by replacing linear decoders with computationally intensive ones such as orthogonal frequency-division multiplexing (OFDM) or Viterbi, can be realized in much simpler fashion-with a small modification to the transmit scheme.

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.

Blind Channel Equalization with Colored Source Based on Constrained Optimization Methods

Tsatsanis and Xu have applied the constrained minimum output variance (CMOV) principle to directly blind equalize a linear channel—a technique that has proven effective with white inputs. It is generally assumed in the literature that their CMOV method can also effectively equalize a linear channel with a colored source. In this paper, we prove that colored inputs will cause the equalizer to incorrectly converge due to inadequate constraints. We also introduce a new blind channel equalizer algorithm that is based on the CMOV principle, but with a different constraint that will correctly handle colored sources. Our proposed algorithm works for channels with either white or colored inputs and performs equivalently to the trained minimum mean-square error (MMSE) equalizer under high SNR. Thus, our proposed algorithm may be regarded as an extension of the CMOV algorithm proposed by Tsatsanis and Xu. We also introduce several methods to improve the performance of our introduced algorithm in the low SNR condition. Simulation results show the superior performance of our proposed methods.

Minimum Mean-Square Error Equalization for Second-Order Volterra Systems

In this paper, a novel nonlinear Volterra equalizer is presented. We define a framework for nonlinear second-order Volterra models, which is applicable to different applications in engineering. We use this framework to define the channel and to model the equalizer. We then solve the minimum mean-square error (MMSE) problem explicitly for the tandem connection of the two second-order Volterra systems. Optimal solutions for a simplified, linear version of the MMSE equalizer are also presented. The novel equalizer was tested when applied to a nonlinear ultra-wideband transmitted reference receiver front end. As a comparison, a least mean squares (LMS) equalizer with a training sequence has been used to verify the performance of the newly proposed equalizer. The simulation results show that the LMS equalizer is only able to attain the proposed MMSE equalizer after very long training, which might not be desirable in a communication system.

A Detection Algorithm for Multi-Input Multi-Output (MIMO) Transmission using Poly-Diagonalization and Trellis Decoding

A MIMO detection algorithm utilizing poly- diagonalization and tail-biting trellis is proposed. Linear MIMO detection, such as zero-forcing or minimum mean squared error (MMSE) equalization, is basically a channel diagonalization technique, where interferences from other data streams are decoupled for the separate decoding. It is well known, however, that such decoders suffer from noise enhancement, which causes considerable performance degradation. In this paper, we propose poly-diagonalization of the channel matrix in zero-forcing and MMSE senses. The idea behind poly-diagonalization is to allow interferences partially in order to alleviate the noise enhancement and, then, to use post trellis decoding for the joint detection utilizing the poly-diagonal structure of the effective channel. Under the proposed framework, the zero-forcing and the MMSE equalizer can be regarded as special cases of poly-diagonalization, i.e., of the first order. The proposed scheme can provide a tradeoff between the complexity and performance by choosing an appropriate order of poly-diagonalization. According to the simulation results, considerable gain can be obtained even with the second order, i.e., bi-diagonalization, for which the decoding complexity is far less than that of the maximum likelihood decoding.

A Low-Complexity Bock Linear Smoothing Channel Estimation for SIMO-OFDM Systems without Cyclic Prefix

Orthogonal frequency-division multiplexing (OFDM) systems often use a cyclic prefix (CP) to simplify the equalization design at the cost of bandwidth efficiency. To increase the bandwidth efficiency, we study the blind equalization with linear smoothing [1] for single-input multiple-output (SIMO) OFDM systems without CP insertion in this paper. Due to the block Toeplitz structure of channel matrix, the block matrix scheme is applied to the linear smoothing channel estimation, which equivalently increases the number of sample vectors and thus reduces the perturbation of sample autocorrelation matrix. Compared with the linear smoothing and subspace methods, the proposed block linear smoothing requires the lowest computational complexity. Computer simulations show that the block linear smoothing yields a channel estimation error smaller than that from linear smoothing, and close to that of the subspace method. Evaluating by the minimum mean-square error (MMSE) equalizer, the block linear smoothing and subspace methods have nearly the same bit-error-rates (BERs).

A Low Complexity MMSE Equalizer for OFDM Systems over Time-Varying Channels

A low complexity minimum mean squared error (MMSE) equalizer for orthogonal frequency division multiplexing (OFDM) systems over time-varying channels is presented. It uses a small matrix of dominant partial channel information and recursive calculation of matrix inverse to significantly reduce the complexity. Theoretical analysis and simulations results are provided to validate its significant performance or complexity advantages over the previously published MMSE equalizers.

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.

Performance of SC-FDE system in UWB communications with imperfect channel estimation

Single carrier block transmission with frequency domain equalization (SC-FDE) has been shown to be a promising candidate in ultra-wideband (UWB) communications. In this paper, we analyze the performance of SC-FDE over UWB communications with channel estimation error. The probability density functions of the frequency domain minimum mean-squared error (MMSE) equalizer taps are derived in closed form. The error probabilities of single carrier block transmission with frequency domain MMSE equalization under imperfect channel estimation are presented and evaluated numerically. Compared with the simulation results, our semi-analytical analysis yields fairly accurate bit error rate performance, thus validating the use of the Gaussian approximation method in the performance analysis of the SC-FDE system with channel estimation error.