Sheetal Kalyani

Decision directed channel tracking (DDCT) in OFDM systems can suffer from error propagation at high fade rates, due to the combined effect of rapid variation of the channel, long frame length and frequency selectivity of the channel. Conventional estimators like the 2D-minimum mean square error (MMSE) channel estimator and the expectation maximization (EM) based Kalman channel estimator [3] show poor performance when they are applied to DDCT over large frame lengths, due to the error propagation induced by wrong symbol decisions. The poor symbols decisions usually act like leverage points in the regression matrix, and can be identified using the hat matrix as a leverage diagnostic. We use extreme value theory (EVT) on the hat matrix to define a channel estimator, which, in addition to exploiting time and frequency correlation of the channel, downweighs leverage points before utilizing them in the estimator structure. The proposed EVT-leverage weighted (LW) estimator reduces error propagation in the frame since it downweighs possible wrong decisions before using them in the channel estimator structure. The proposed EVT-LW estimator has a significantly better error rate performance when compared to both the 2D-MMSE estimator [2] and the EM based Kalman estimator [3]. © 2006 IEEE.

Decision feedback equalizers (DFEs) are designed to deal with AWGN noise, and hence, generally perform very poorly in the presence of impulsive noise. Extreme value theory (EVT) is used to modify the DFE structure to handle impulsive noise. The received measurements are modified using EVT based weights before passing it to the equalizer. A modified maximal ratio combining (MRC) scheme which also uses EVT is developed to further improve the error-rate performance in the presence of impulsive interference. The proposed method performs much better than the conventional DFE-MRC technique which uses the simple MRC in conjunction with the DFE at low signal-tointerference (SIR) ratios. © 2007 IEEE.

Decision directed channel tracking (DDCT) at high fade rates in OFDM based systems is addressed in this paper. Channel estimation in DDCT can be formulated as a linear errors-in-variables regression problem. While most of the errors in the regression matrix (equalization errors) are Gaussian in nature, few of the detected symbols can have high error due to the frequency and time selective fading. These poor symbol decisions behave like outliers in the regression matrix and give rise to contaminated Gaussian noise distributions. Classical estimators like total least squares (TLS) and the expectation-maximization (EM) based estimators exhibit poor performance in the presence of such outliers. We propose the Huber's M (HM) estimator and an extreme value theory (EVT) based M estimator for the DDCT problem. The proposed HM and EVT-HM estimators are robust to outliers and have an efficiency greater than 95% in purely Gaussian noise. The error rate performance of the proposed HM and EVT-HM estimators are compared with that of the TLS estimator, and the EM based estimator proposed in [4]. © 2006 IEEE.

Channel estimation in the presence of multitone narrowband interference (MNBI) in OFDM systems is addressed in this paper. While pilot based OFDM channel estimation in the presence of only thermal noise at the receiver is a Gaussian regression problem, the presence of MNBI leads to an outlier contaminated Gaussian regression problem. Since Gaussian probability density function (pdf) based maximum likelihood (ML) estimators are highly sensitive to outliers, we define a M estimator based on the theory of robust regression for channel estimation in the presence of MNBI. The proposed iterative M estimator minimizes the Huber's cost function for p iterations and then minimizes a cost function defined by a redescending M estimator based on extreme value theory in the last few iterations. Simulation results indicate that the proposed estimator outperforms both the Gaussian pdf based ML estimator and a M estimator based only on Huber's cost function. © 2006 IEEE.

M estimators have been widely used for parameter estimation in the presence of outliers or impulsive noise. A number of papers use the iteratively reweighted least squares (IRLS) algorithm for M estimation. The IRLS method tries to iteratively converge to the non-linear M estimate using a weighted least squares algorithm. While the performance of the IRLS algorithm has been demonstrated through simulation, to our knowledge, the MSE of the IRLS based M estimation approach has not been theoretically derived in signal processing literature. In this paper, we derive the theoretical MSE of three M estimators, namely, the Huber's M (HM) estimator, the extreme value theory (EVT) based estimator and the Hampel's 3-part (HP) estimator when they are implemented using the IRLS algorithm. This theoretical MSE is a function of the M estimator cost function, the noise distribution, and the iteration number of the IRLS algorithm. Based on the theoretical analysis in this paper, we show that for both Cauchy and Gaussian impulsive noise, the MSE of the IRLS based M estimator converges to the MSE of the desired M estimator within 3 to 5 iterations. © 2007 IEEE.

The presence of narrowband interference (NBI) and thermal noise leads to a contaminated Gaussian (CG) noise probability density function (pdf) at the OFDM receiver. The Cramér-Rao lower bound for channel estimation in the presence of CG noise is analyzed for two NBI pdfs, namely, the Gaussian and the Cauchy pdfs. We then derive the mean square error (MSE) when the actual NBI pdf differs from the NBI pdf for which the estimator is designed, i.e., when the NBI pdf is misspecified. Based on this theoretical MSE analysis, we show that: (i) Even if the maximum likelihood estimator (MLE) designed for the CG noise pdf assuming Cauchy NBI is used when the actual CG pdf has Gaussian NBI, the degradation in MSE performance is negligible; (ii) However, if the MLE for CG pdf designed assuming Gaussian NBI is used for channel estimation in CG noise where the NBI is actually Cauchy, a very poor MSE performance is obtained. This analysis suggests that it is pragmatic to use the MLE designed assuming Cauchy NBI, as it is robust to misspecification of the NBI pdf. Further, an iteratively reweighted least squares algorithm is proposed for implementing the MLE for the CG model with either Gaussian or Cauchy NBI. © 2007 IEEE.

We look at the performance of turbo coded OFDM systems in the presence of narrowband interference (NBI) and co-channel interference (CCI). In systems employing standards such as the IEEE 802.16d/e, CCI behaves like NBI with the number of affected subcarriers ranging from 10% to 30%. Hence we treat symbol detection in such systems as detection in contaminated Gaussian (CG) noise and propose a robust log-likelihood ratio (LLR) computation for it. The proposed LLR computation method exploits the fact that NBI/CCI has a CG probability density function (pdf) but does not assume knowledge of the NBI power, NBI pdf and the fraction of subcarriers affected by NBI. Simulation results indicate that the proposed method performs very close to the optimal method which would have complete knowledge of the CG pdf parameters. ©2008 IEEE.

A robust cost function for log likelihood ratio (LLR) computation is proposed for turbo coded OFDM systems in the presence of narrowband interference (NBI) and co-channel interference (CCI). In systems employing standards such as the IEEE 802.16d/e, CCI behaves like NBI with the number of affected subcarriers ranging from 10% to 30%. The combined effect of NBI and thermal Gaussian noise leads to a contaminated Gaussian (CG) noise probability density function (pdf). Simulation results indicate that the proposed method performs very close to the optimal method where the optimal method computes the LLR using the CG pdf. While the optimal method requires knowledge of the NBI power, the fraction of subcarriers contaminated by NBI and the NBI pdf, the proposed method does not require knowledge of these parameters. © 2008 IEEE.

A method for the mitigation of the effect of narrowband interference (NBI) on the turbo decoder in OFDM systems is proposed. The presence of NBI leads to a contaminated Gaussian (CG) noise probability density function (pdf) which induces an outlier effect in the data detection problem. The outlier effect leads to significant degradation in the performance of turbo coded OFDM systems which use Gaussian noise pdf based log likelihood ratios (LLRs), with the degradation increasing as a function of the power of NBI and the number of subcarriers affected by NBI. We propose to use outlier detection theory to detect subcarriers affected by NBI, and then downweigh the corresponding LLRs before passing them to the turbo decoder. Extreme value theory (EVT) is used to define the weight function in this weighted-LLR (W-LLR) method. The method is easy to implement, is of modest computational complexity, and shows a significant improvement in the simulated error rate performance when compared with the simple unweighted turbo decoder in the presence of NBI. Furthermore, frequency selectivity and diversity mapping in OFDM systems such as IEEE 802.16 d/e WMAN standard causes the co-channel interference (CCI) to look like NBI within the FEC block. Therefore, the W-LLR method can also be applied for CCI mitigation in these systems. Since reuse-one cellular systems have a CCI limited performance, the proposed method provides a significant improvement over the normal turbo decoder. © 2007 IEEE.

Decision directed channel tracking (DDCT) at high fade rates in OFDM based systems is addressed in this paper. Existing DDCT algorithms like the expectation-maximization (EM) algorithm [1] suffer from error propagation and exhibit poor performance when applied to large frames at high fade rates. We propose a robust EM algorithm which mitigates the effect of error propagation and is able to track the channel in the decision directed mode even over frame durations experiencing 2-3 fade cycles. This EM algorithm uses the Huber's cost function in the maximization step instead of the non-robust least squares or Kalman cost function. Further, the noise variance is estimated using the robust median absolute deviation estimator instead of the standard maximum likelihood estimator. The proposed robust EM based DDCT scheme has a better error rate and MSE performance when compared to Kalman filter based pilot assisted channel tracking scheme with a 6.25% pilot overhead, even at a normalized Doppler of 0.04. ©2007 IEEE.