Hakan A. Cirpan

Stochastic maximum likelihood methods for semi-blind channel estimation

A blind stochastic maximum likelihood (ML) channel estimation algorithm is adapted to incorporate a known training sequence as part of the transmitted frame. A hidden Markov model (HMM) formulation of the problem is introduced, and the Baum-Welch (1970) algorithm is modified to provide a computationally efficient solution to the resulting optimization problem. The proposed method provides a unified framework for semi-blind channel estimation, which exploits information from both the training and the blind part of the received data record. The performance of the ML estimator is studied, based on the evaluation of Cramer-Rao bounds (CRBs). Finally, some preliminary simulation results are presented.

Maximum likelihood blind channel estimation in the presence of Doppler shifts

Transmitter/receiver motion in mobile radio channels may cause frequency shifts in each received path due to Doppler effects. Most blind equalization methods, however, assume time-invariant channels and may not be applicable to fading channels with severe Doppler spread. We address the problem of simultaneously estimating the Doppler shift and channel parameters in a blind setup. Both deterministic and stochastic maximum likelihood methods are developed and iterative solutions proposed. The stochastic maximum likelihood solution is based on the modified version of the Baum-Welch (1970) algorithm, which originated in the study of hidden Markov models. The proposed methods are well suited for short data records appearing in TDMA systems. Identifiability and performance analysis issues are discussed, and Cramer-Rao bounds are derived. In addition, some illustrative simulations are presented.

Nondata-aided channel estimation for OFDM systems with space-frequency transmit diversity

This paper proposes a computationally efficient nondata-aided maximum a posteriori (MAP) channel-estimation algorithm focusing on the space-frequency (SF) transmit diversity orthogonal frequency division multiplexing (OFDM) transmission through frequency-selective channels. The proposed algorithm properly averages out the data sequence and requires a convenient representation of the discrete multipath fading channel based on the Karhunen-Loeve (KL) orthogonal expansion and estimates the complex channel parameters of each subcarrier iteratively, using the expectation maximization (EM) method. To further reduce the computational complexity of the proposed MAP algorithm, the optimal truncation property of the KL expansion is exploited. The performance of the MAP channel estimator is studied based on the evaluation of the modified Cramer-Rao bound (CRB). Simulation results confirm the proposed theoretical analysis and illustrate that the proposed algorithm is capable of tracking fast fading and improving overall performance.

Iterative Channel Estimation and Decoding of Turbo Coded SFBC-OFDM Systems

We consider the design of turbo receiver structures for space-frequency block coded orthogonal frequency division multiplexing (SFBC-OFDM) systems in the presence of unknown frequency and time selective fading channels. The turbo receiver structures for SFBC-OFDM systems under consideration consists of an iterative MAP expectation/maximization (EM) channel estimation algorithm, soft MMSE-SFBC decoder and a soft MAP outer-channel-code decoder. MAP-EM employs iterative channel estimation and it improves receiver performance by re-estimating the channel after each decoder iteration. Moreover, the MAP-EM approach considers the channel variations as random processes and applies the Karhunen-Loeve (KL) orthogonal series expansion. The optimal truncation property of the KL expansion can reduce computational load on the iterative estimation approach. The performance of the proposed approaches are studied in terms of mean square error and bit-error rate. Through computer simulations, the effect of a pilot spacing on the channel estimator performance and sensitivity of turbo receiver structures on channel estimation error are studied. Simulation results illustrate that receivers with turbo coding are very sensitive to channel estimation errors compared to receivers with convolutional codes. Moreover, superiority of the turbo coded SFBC-OFDM systems over the turbo coded STBC-OFDM systems is observed especially for high Doppler frequencies.

A set of new Chebyshev kernel functions for support vector machine pattern classification

In this study, we introduce a set of new kernel functions derived from the generalized Chebyshev polynomials. The proposed generalized Chebyshev polynomials allow us to derive different kernel functions. By using these polynomial functions, we generalize recently introduced Chebyshev kernel function for vector inputs and, as a result, we obtain a robust set of kernel functions for Support Vector Machine (SVM) classification. Thus in this study, besides clarifying how to apply the Chebyshev kernel functions on vector inputs, we also increase the generalization capability of the previously proposed Chebyshev kernels and show how to derive new kernel functions by using the generalized Chebyshev polynomials. The proposed set of kernel functions provides competitive performance when compared to all other common kernel functions on average for the simulation datasets. The results indicate that they can be used as a good alternative to other common kernel functions for SVM classification in order to obtain better accuracy. Moreover, test results show that the generalized Chebyshev kernel approaches to the minimum support vector number for classification in general.

An adaptive channel interpolator based on Kalman filter for LTE uplink in high Doppler spread environments

Long-Term Evolution (LTE) systems will employ single carrier frequency division multiple access (SC-FDMA) for the uplink. Similar to the Orthogonal frequency-division multiple access (OFDMA) technology, SC-FDMA is sensitive to frequency offsets leading to intercarrier interference (ICI). In this paper, we propose a Kalman filter-based approach in order to mitigate ICI under high Doppler spread scenarios by tracking the variation of channel taps jointly in time domain for LTE uplink systems. Upon acquiring the estimates of channel taps from the Kalman tracker, we employ an interpolation algorithm based on polynomial fitting whose order is changed adaptively. The proposed method is evaluated under four different scenarios with different settings in order to reflect the impact of various critical parameters on the performance such as propagation environment, speed, and size of resource block (RB) assignments. Results are given along with discussions.

Unconditional maximum likelihood approach for localization of near-field sources: Algorithm and performance analysis

Abstract Localization of near-field sources requires sophisticated estimation algorithms. In this paper, we propose an unconditional maximum likelihood method for estimating direction of arrival and angle parameters of near-field sources. However, the calculation of maximum likelihood estimation from the corresponding likelihood function results in difficult nonlinear constraint optimization problems. We therefore employed an Expectation/Maximization (EM) iterative method for obtaining maximum likelihood estimates. The most important feature of the EM algorithm is that it decomposes the observed data into its components and then estimates the parameters of each signal component separately providing computationally efficient solution to resulting optimization problem. The performance of the unconditional maximum likelihood location estimator for the near-field sources is studied based on the concentrated likelihood approach to obtain Cramer-Rao bounds. Some insights into the achievable performance of the conditional maximum likelihood algorithm is obtained by numerical evaluation of the Cramer-Rao bounds for different test cases.

Chip interleaving in direct sequence CDMA systems

Direct sequence code division multiple access (CDMA) systems are considered, in a multipath environment. We address the problem of estimating each users signature waveform without requiring training sequences. We show that the problem is considerably simplified if a novel transmission strategy is adopted, which combines spreading and interleaving. In this setup, chip sequences corresponding to successive bits are interleaved before transmission. Novel channel estimation algorithms are developed in this chip interleaving framework and their performance is analyzed. Adaptive implementations are derived and some illustrative simulations are presented.

Deterministic maximum likelihood approach for 3-D near field source localization

Summary In this paper, maximum likelihood estimator is proposed for passive localization of narrowband sources in the spherical coordinates (azimuth, elevation, and range). We adapt Expectation/Maximization iterative method to solve the complicated multi-parameter optimization problem appearing on the 3-D localization problem. The proposed algorithm is based on maximum likelihood criterion which employs the source signals recorded by 2-D array under near-field assumption. Expectation/Maximization algorithm decomposes the observed data into its components and then estimates the parameters of each signal component separately providing computationally efficient solution to the resulting optimization problem. Performance analysis of the proposed algorithm is then carried out through the evaluation of Cramer-Rao bounds. Finally, the applicability and effectiveness of the proposed algorithm is illustrated by some numerical simulations.

A low-complexity KL expansion-based channel estimator for OFDM systems

This paper first proposes a computationally efficient, pilot-aided linear minimum mean square error (MMSE) batch channel estimation algorithm for OFDM systems in unknown wireless fading channels. The proposed approach employs a convenient representation of the discrete multipath fading channel based on the Karhunen-Loeve (KL) orthogonal expansion and finds MMSE estimates of the uncorrelated KL series expansion coefficients. Based on such an expansion, no matrix inversion is required in the proposed MMSE estimator. Moreover, optimal rank reduction is achieved by exploiting the optimal truncation property of the KL expansion resulting in a smaller computational load on the estimation algorithm. The performance of the proposed approach is studied through analytical and experimental results. We then consider the stochastic Cramér-Rao bound and derive the closed-form expression for the random KL coefficients and consequently exploit the performance of the MMSE channel estimator based on the evaluation of minimum Bayesian MSE. We also analyze the effect of a modelling mismatch on the estimator performance. To further reduce the complexity, we extend the batch linear MMSE to the sequential linear MMSE estimator. With the fast convergence property and the simple structure, the sequential linear MMSE estimator provides an attractive alternative to the implementation of channel estimator.