Blind equalization/detection for OFDM signals overfrequency-selective channels

A novel equalization/detection algorithm for orthogonal frequency division multiplexing (OFDM) signals transmitted over frequency-selective channels is introduced and investigated. The algorithm stems from the recognition that the Fourier transform processing inherent in OFDM turns a single wideband frequency-selective channel into a set of correlated narrowband frequency-flat fading channels. This suggests that sequence detection techniques, such as those discussed by Vitetta et al. (see IEEE Trans. Commun., vol.43, p.2750-8, 1995, IEEE Trans. Commun., vol.43, pt.II, p.1256-9, 1995, and Proc. IEEE Commun. Theory Mini-Conf (Globecom '96), London, UK, p.153-7, 1996), for time-selective flat-fading channels, can be also profitably utilized for joint equalization and decoding of OFDM signals in the frequency domain. Simulation results show that the proposed detection strategy, implemented via a standard Viterbi algorithm, provides improved performance over differential detection, with a moderate increase in receiver complexity and without requiring the periodic transmission of training blocks     

Blind channel equalization using chirp modulating signals

This paper addresses the problem of blind channel equalization in the context of digital communications. Recent results have shown that certain operations applied to the source signal at the transmitter help in the blind identification and equalization of the channel at the receiver. In this paper, the baseband data signal is multiplied with a chirp sequence. Exploiting certain structural properties arising from this operation, a batch-type algorithm is obtained for calculating the equalizer's coefficients. Conditions on the chirp sequence parameters are obtained that guarantee an equalization solution. A low-complexity adaptive algorithm is also proposed. Finally, extensive simulations, and comparisons with other well-known blind techniques, illustrate the excellent performance of this algorithm.     

Classification of LPI radar signals using spectral correlation and support vector machines

In modern radar systems, low probability of intercept (LPI) waveforms are used to make detection by a potential adversary difficult. This is accomplished using wideband waveforms, frequency hopping, and continuous waveforms (FMCW) to reduce the signal profile. The low signal profile of the LPI signal enables the radar to perform detection and or target tracking while the target remains unaware. Several modulation techniques such as polytime codes, polyphase codes, FSK, and FMCW are used to produce LPI signals for transmission. This paper looks at the ability of spectral correlation along with a support vector machine in order to automatically classify the different LPI signal types in a non-cooperative environment.     

Blind equalization for short burst wireless communications

In this paper, we propose a dual mode blind equalizer based on the constant modulus algorithm (CMA). The blind equalizer is devised for short burst transmission formats used in many current wireless TDMA systems as well as future wireless packet data systems. Blind equalization is useful for such short burst formats, since the overhead associated with training can be significant when only a small number of bits are transmitted at a time. The proposed equalizer overcomes the common problems associated with classic blind algorithms, i.e., slow convergence and ill-convergence, which are detrimental to applying blind equalization to short burst formats. Thus, it can eliminate the overhead associated with training sequences. Also, the blind equalizer is extended to a two branch diversity combining blind equalizer. A new initialization for fractionally spaced CMA equalizers is introduced. This greatly improves the symbol timing recovery performance of fractionally spaced CMA equalizers with or without diversity, when applied to short bursts. Through simulations with quasi-static or time-varying frequency selective wireless channels, the performance of the proposed equalizer is compared to selection diversity and conventional equalizers with training sequences. The results indicate that its performance is far superior to that of selection diversity alone and comparable to the performance of equalizers with short training sequences. Thus, training overhead can be removed with no performance degradation for fast time-varying channels, and with slight performance degradation for static channels     

Blind equalization of constant modulus signals using an adaptiveobserver approach

The paper addresses the problem of blind equalization of constant modulus signals which are degraded by frequency selective multipath propagation and additive white noise. An adaptive observer is used to update the weights of an FIR equalizer in order to restore the signal's constant modulus property. The observer gain is selected using fake algebraic Riccati methods in order to guarantee local stability. The performance of this method is compared to the constant modulus algorithm for simulated FM-FDM signals and exhibits significantly better convergence properties, particularly for heavy-tailed noise     

Novel semi-blind ICI equalization algorithm for wireless OFDM systems

Intercarrier interference is deemed as one of the crucial problems in the wireless orthogonal frequency division multiplexing (OFDM) systems. The conventional ICI mitigation schemes involve the frequency-domain channel estimation or the additional coding, both of which require the spectral overhead and hence lead to the significant throughput reduction. Besides, the OFDM receivers using the ICI estimation rely on a large-dimensional matrix inverter with high computational complexity especially for many subcarriers such as digital video broadcasting (DVB) systems and wireless metropolitan-area networks (WMAN). To the best of our knowledge, no semi-blind ICI equalization has been addressed in the existing literature. Thus, in this paper, we propose a novel semi-blind ICI equalization scheme using the joint multiple matrix diagonalization (JMMD) algorithm to greatly reduce the intercarrier interference in OFDM. However, the well-known phase and permutation indeterminacies emerge in all blind equalization schemes. Hence we also design a few OFDM pilot blocks and propose an iterative identification method to determine the corresponding phase and permutation variants in our semi-blind scheme. Our semi-blind ICI equalization algorithm integrating the JMMD with the additional pilot-based iterative identification is very promising for the future high-throughput OFDM systems. Through Monte Carlo simulations, the QPSK-OFDM system with our proposed semi-blind ICI equalizer can achieve significantly better performance with symbol error rate reduction in several orders-of-magnitude. For the 16QAM-OFDM system, our scheme can also improve the performance over the plain OFDM system to some extent.     

Blind detection of equalization errors in communication systems

In adaptive channel equalization, transmitted symbol estimates at the equalizer output may be in error because of excessive channel noise, convergence of the equalizer to a “closed-eye” local minimum, or error propagation if the equalizer has a decision feedback structure. This paper is concerned with the detection of equalization errors (i.e., errors in transmitted symbol estimates) in a blindfolded manner whereby no direct access to the channel input is required. The detection problem is cast into a binary hypothesis testing framework. Assuming a linear communication channel that is time-invariant during the test interval, a relationship between the presence of equalization errors and time variations in the underlying linear model taking the transmitted symbol estimates to the equalizer input is established. Based on this relationship, a uniformly most powerful test is constructed to detect the presence of equalization errors in finite-length observations. Finite sample size and asymptotic detection performance of the test is studied. A method for estimating the equalization delay without direct access to the channel input is developed. The effectiveness of the test is illustrated by way of computer simulations     

Adaptive equalization for high-speed indoor wireless data communication

The performance of a 4-QAM indoor wireless data communication system with adaptive equalizer is investigated. The effectiveness of using linear and decision-feedback equalizer for Rayleigh and Rician frequency-selective indoor channels is evaluated, and contrasted to the performance of a 4-QAM modem without equalizer. The effects of some important channel and system parameters (multipath spreads up to 200 ns, data rates up to 25 Mbit/s, signaling pulse rolloff factor between 0.5 and 1.0, and additive, white Gaussian noise) on the indoor communication system performance are examined and presented in the paper. The indoor propagation measurements, carried out in a research laboratory, provided data to be used for BER performance assessments of the system with and without equalizer. The performance results based on computer generated channels are then compared with those obtained for measured channel impulse responses.     

Decision feedback equaliser design using support vector machines

The conventional decision feedback equaliser (DFE) that employs a linear combination of channel observations and past decisions is considered. The design of this class of DFE is to construct a hyperplane that separates the different signal classes. It is well known that the popular minimum mean square error (MMSE) design is generally not the optimal minimum bit error rate (MBER) solution. A strategy is proposed for designing the DFE based on support vector machines (SVMs). The SVM design achieves asymptotically the MBER solution and is superior in performance to the usual MMSE solution. Unlike the exact MBER solution, this SVM solution can be computed very efficiently     

Alzheimer's diagnosis using eigenbrains and support vector machines

An accurate and early diagnosis of the Alzheimer's disease (AD) is of fundamental importance for the patient's medical treatment. Single photon emission computed tomography (SPECT) images are commonly used by physicians to assist the diagnosis. Presented is a computer-assisted diagnosis tool based in a principal component analysis (PCA) dimensional reduction of the feature space approach and a support vector machine (SVM) classification method for improving the AD diagnosis accuracy by means of SPECT images. The most relevant image features were selected under a PCA compression, which diagonalises the covariance matrix, and the extracted information was used to train an SVM classifier, which could classify new subjects in an unsupervised manner.     

Estimation of highly selective channels for OFDM system by complex least squares support vector machines

A channel estimator using complex least squares support vector machines (LS-SVM) is proposed for pilot-aided OFDM system and applied to Long Term Evolution (LTE) downlink. This channel estimation algorithm use knowledge of the pilot signals to estimate the total frequency response of the channel. Thus, the algorithm maps trained data into a high dimensional feature space and uses the structural risk minimization (SRM) principle, which minimizes an upper bound on the generalization error, to carry out the regression estimation for the frequency response function of the highly selective channel. Simulation results show that the proposed method has better performance compared to the conventional LS and Decision Feedback methods and it is more robust at high speed mobility.     

Covering numbers for support vector machines

Support vector (SV) machines are linear classifiers that use the maximum margin hyperplane in a feature space defined by a kernel function. Previously, the only bounds on the generalization performance of SV machines (within Valiant's probably approximately correct framework) took no account of the kernel used except in its effect on the margin and radius. It has been shown that one can bound the relevant covering numbers using tools from functional analysis. In this paper, we show that the resulting bound can be greatly simplified. The new bound involves the eigenvalues of the integral operator induced by the kernel. It shows that the effective dimension depends on the rate of decay of these eigenvalues. We present an explicit calculation of covering numbers for an SV machine using a Gaussian kernel, which is significantly better than that implied by previous results     

Supervised classification of marble textures using support vector machines

A novel approach is described for the supervised classification of marble textures in different classes according to visual appearance, using sum and difference histograms for texture analysis and feature extraction, and support vector machines for classification. Results show very good discrimination between classes.     

Linear and decision-feedback per tone equalization for DMT-based transmission over IIR channels

The per-tone equalizer (PTEQ) has been presented as an attractive alternative for the classical time-domain equalizer (TEQ) in discrete multitone (DMT) based systems, such as ADSL systems. The PTEQ is based on a linear minimum mean-square-error (L-MMSE) equalizer design for each separate tone. In this paper, we reconsider DMT modulation and equalization in the ADSL context under the realistic assumption of an infinite impulse response (IIR) model for the wireline channel. First, optimum linear zero-forcing (L-ZF) block equalizers for arbitrary IIR model orders and cyclic prefix (CP) lengths are developed. It is shown that these L-ZF block equalizers can be decoupled per tone, hence they lead to an L-ZF PTEQ. Then, based on the L-ZF PTEQ, low-complexity L-MMSE PTEQ extensions are developed: the linear PTEQ extension exploits frequency-domain transmit redundancy from pilot and unused tones; alternatively, a closely related decision-feedback PTEQ extension can be applied. The PTEQ extensions then add flexibility to a DMT-based system design: the CP overhead can be reduced by exploiting frequency-domain transmit redundancy instead, so that a similar bitrate as with the original PTEQ is achieved at a lower memory and computational cost or, alternatively, a higher bitrate is achieved without a considerable cost increase. Both PTEQ extensions are also shown to improve the receiver's robustness to narrow-band interference.     

Computational load reduction in decision functions using support vector machines

A new method of reducing the computational load in decision functions provided by a support vector classification machine is studied. The method exploits the geometrical relations when the kernels used are based on distances to obtain bounds of the remaining decision function and avoids to continue calculating kernel operations when there is no chance to change the decision. The method proposed achieves savings in operations of 25–90% whilst keeping the same accuracy. Although the method is explained for support vector machines, it can be applied to any kernel binary classifier that provides a similar evaluation function.     

Image tamper detection and classification using support vector machines

The use of robust watermarks for attack characterisation is an area of considerable potential which has been largely overlooked to date. The authors extend their earlier work on accurate attack characterisation using a double watermarking technique to include a larger library of attacks. It is shown that the complexity of the double watermarking technique can be reduced with only a very small performance penalty. A further reduction in the algorithm complexity can be achieved by removing the thresholding process from the watermark estimation procedure. Analysis of the nature and location of the characterisation errors for the above methods is also presented.     

Design methodology for configurable analog to digital conversion using support vector machines

We apply a support vector machine (SVM) classifier to the design of analog to digital converters. Each output bit of the converter is the output of a binary classifier, which is a nonlinear SVM. The classifier effectively learns a folding characteristic for each bit, which is realized as the weighted sum of a set of kernel functions. In our proposal, the kernel does not need to be symmetric or positive definite, unlike in the case of a conventional SVM. This makes the approach more amenable to VLSI design, where such constraints are hard to satisfy. The SVM uses a set of binary weights, which allows the folding characteristics to be digitally corrected after fabrication. This facility is of considerable value in analog design in a deep sub micron era, where simulation models do not adequately capture the behavior of devices, or their variations. The proposed methodology reduces design time, can be automated and calibrated for process variations and ageing, by changing a set of digital scaling coefficients.     

Blind and semiblind detections of OFDM signals in fading channels

This paper considers the problem of blind joint channel estimation and data detection for orthogonal frequency-division multiplexing (OFDM) systems in a fading environment. Employing a regression model for a time-varying channel, we convert the problem into one that finds the data sequence x whose associated least-squares (LS) channel estimate z(x) is closest to the space of some regression curves (surfaces). We apply the branch-and-bound principle to solve the nonlinear integer programming problem associated with finding the curve that fits a subchannel in the LS sense. A recursive formula for fast metric update is obtained by exploiting the intrinsic characteristic of our objective function. The impacts of reordering the data sequence and selective detection are addressed. By employing a preferred order along with a selective detection method, we greatly reduce the detector complexity while giving up little performance loss. Both the complete and the reduced-complexity algorithms can be used for blind and semiblind detections of OFDM signals in a subchannel-by-subchannel manner. To further reduce the complexity and exploit the frequency-domain channel correlation, we suggest a two-stage approach that detects a few selected positions in some subchannels first, and then, treating the detected symbols as pilots, determines the remaining symbols within a properly chosen time-frequency block by a two-dimensional model-based pilot-assisted algorithm. The proposed methods do not require the information of the channel statistics like signal-to-noise ratio or channel correlation function. Performance of differential modulations like differential quaternary phase-shift keying and STAR 16-ary quadrature amplitude modulation are provided. Both blind and semiblind schemes yield satisfactory performance.     

高速无线通信中的正交多载波调制技术OFDM

本文介绍了无线信道的特征,进而引出多载波调制技术,着重介绍了正交频分复用(OFDM)的原理,优缺点及其在无线通信中的广泛应用。     

A hybrid adaptive blind equalization algorithm for QAM signals in wireless communications

A hybrid adaptive channel equalization technique for quadrature amplitude modulation (QAM) signals is proposed. The proposed algorithm, which is referred to as the modified constant modulus algorithm (MCMA), minimizes an error cost function that includes both amplitude and phase of the equalizer output. In addition to the amplitude-dependent term that is provided by the conventional constant modulus algorithm (CMA), the cost function includes an additive signal constellation matched error (CME) term. This term can be designed to satisfy a set of desirable properties. The MCMA is compared with the CMA for blind equalization. The performance is measured for wireless channels using both transient and steady-state behavior of the mean square error (MSE). It is shown that MCMA is superior and more robust in low signal-to-noise ratio (SNR) environments. Simulation results demonstrate that using MCMA improves adaptive channel equalization by increasing the convergence rate and decreasing the steady-state mean square error.