Underdetermined-order recursive least-squares adaptive filtering: The concept and algorithms

Published versio

Subspace Tracking and Least Squares Approaches to Channel Estimation in Millimeter Wave Multiuser MIMO

The problem of MIMO channel estimation at millimeter wave frequencies, both in a single-user and in a multi-user setting, is tackled in this paper. Using a subspace approach, we develop a protocol enabling the estimation of the right (resp. left) singular vectors at the transmitter (resp. receiver) side; then, we adapt the projection approximation subspace tracking with deflation and the orthogonal Oja algorithms to our framework and obtain two channel estimation algorithms. We also present an alternative algorithm based on the least squares approach. The hybrid analog/digital nature of the beamformer is also explicitly taken into account at the algorithm design stage. In order to limit the system complexity, a fixed analog beamformer is used at both sides of the communication links. The obtained numerical results, showing the accuracy in the estimation of the channel matrix dominant singular vectors, the system achievable spectral efficiency, and the system bit-error-rate, prove that the proposed algorithms are effective, and that they compare favorably, in terms of the performance-complexity trade-off, with respect to several competing alternatives.Comment: To appear on the IEEE Transactions on Communication

Robust adaptive filtering algorithms for system identification and array signal processing in non-Gaussian environment

This dissertation proposes four new algorithms based on fractionally lower order statistics for adaptive filtering in a non-Gaussian interference environment. One is the affine projection sign algorithm (APSA) based on L₁ norm minimization, which combines the ability of decorrelating colored input and suppressing divergence when an outlier occurs. The second one is the variable-step-size normalized sign algorithm (VSS-NSA), which adjusts its step size automatically by matching the L₁ norm of the a posteriori error to that of noise. The third one adopts the same variable-step-size scheme but extends L₁ minimization to Lp minimization and the variable step-size normalized fractionally lower-order moment (VSS-NFLOM) algorithms are generalized. Instead of variable step size, the variable order is another trial to facilitate adaptive algorithms where no a priori statistics are available, which leads to the variable-order least mean pth norm (VO-LMP) algorithm, as the fourth one. These algorithms are applied to system identification for impulsive interference suppression, echo cancelation, and noise reduction. They are also applied to a phased array radar system with space-time adaptive processing (beamforming) to combat heavy-tailed non-Gaussian clutters. The proposed algorithms are tested by extensive computer simulations. The results demonstrate significant performance improvements in terms of convergence rate, steady-state error, computational simplicity, and robustness against impulsive noise and interference --Abstract, page iv

On the variance of the Least Mean Square squared-error sample curve

Most studies of adaptive algorithm behavior consider performance measures based on mean values such as the mean-square error. The derived models are useful for understanding the algorithm behavior under different environments and can be used for design. Nevertheless, from a practical point of view, the adaptive filter user has only one realization of the algorithm to obtain the desired result. This letter derives a model for the variance of the squared-error sample curve of the least-mean-square (LMS) adaptive algorithm, so that the achievable cancellation level can be predicted based on the properties of the steady-state squared error. The derived results provide the user with useful design guidelines

Efficient time delay estimation and compensation applied to the cancellation of acoustic echo

The system identification problem is notably dealt with using adaptive filtering approaches. In many applications the unknown system response consists of an initial sequence of zero-valued coefficients that precedes the active part of the response. The presence of these coefficients introduces a flat delay in the incoming signals which can take significantly large values. When most adaptive approaches attempt to model such a system, the presence of flat delay impairs their operation and performance. The approach introduced in this thesis aims to model the flat delay and active part of the unknown system separately. An efficient system for time delay estimation (TDE) is introduced to estimate the flat delay of an unknown system. The estimated delay is then compensated within the adaptive system thus allowing the latter to cover the active part ofthe unknown system. The proposed system is applied to the Acoustic Echo Cancellation (ABC) problem

Microgrid state estimation and control using Kalman filter and semidefinite programming technique

The design of environment-friendly microgrids at the smart distribution level requires a stable behaviour for multiple state operations. This paper develops a Kalman filter based optimal feedback control method for the microgrid state estimation and stabilization. First, the microgrid is modelled by a discrete-time state space equation. Then the cost-effective smart sensors are deployed in order to obtain the required system information. From the communication point of view, the recursive systematic convolution code is adopted to add the redundancy in the system. At the end, the soft output Viterbi decoder is used to recover the system information from the noisy measurements and transmission uncertainties. Thereafter, the Kalman filter is utilized to estimate the system states, which acts as a precursor for applying the control algorithm. Finally, this paper proposes an optimal feedback control method to stabilize the microgrid based on semidefinite programming. The performance of the proposed approach is demonstrated by extensive numerical simulations

A subband Kalman filter for echo cancellation

This thesis involves the implementation of a Kalman filter for the application of echo cancellation. This particular Kalman filter is implemented in the frequency domain, in subbands, so as to make it faster and of lesser calculational complexity for real time applications. To evaluate the functioning of this subband Kalman filter, comparison of the performance of the subband Kalman filter is done with respect to the original time domain Kalman filter, and also with other subband adaptive filters for echo cancellation such as the NLMS filter. Additionally, since background noise affects the working of any adaptive filter, the newly developed subband Kalman filter\u27s performance at different noise conditions is compared, and an attempt to keep track of and predict this noise is also performed --Abstract, page iii

Signal processing topics in multicarrier modulation : frequency offset correction for OFDM and multiuser interference cancellation for MC-CDMA

Orthogonal frequency division multiplexing (OFDM) is discussed as a special form of multi-carrier modulation (MCM). One major problem of the OFDM system is the sensitivity to an unknown frequency offset at the receiver. To improve the performance of the OFDM system, correction of the frequency offset is required before decision making. An adaptive method of frequency offset correction is presented. The adaptation algorithm used here is based on the LMS and the estimation is proven unbiased. A multiuser communications system having similar signal structure to the OFDM system, termed as multi-carrier code division multiple access (MC-CDMA), is discussed. The MC-CDMA system is susceptible to multiuser interference. Although orthogonal multiuser codes are used, the frequency selective fading might destroy the orthogonality between different codes and result in multiuser interference. The conventional decorrelator can be used to cancel such interference completely but has the disadvantage of enhancing noise power. An adaptive decorrelation algorithm, known as the Bootstrap algorithm, is implemented to separate interference from the desired user\u27s signal. Such algorithm is shown to perform better than the conventional decorrelator particularly in the low interference region