Samir Attallah

Fast algorithms for subspace tracking

We present two normalized versions of Ojas (1992) algorithm (NOja and NOOja), which can be used for the estimation of minor and principal subspaces of a vector sequence. The new algorithms offer, as compared to Oja, a faster convergence, orthogonality, and a better numerical stability with a slight increase in computational complexity.

Orthogonal Oja algorithm

In this letter, we propose an orthogonalized version of the Oja algorithm (OOja) that can be used for the estimation of minor and principal subspaces of a vector sequence. The new algorithm offers, as compared to Oja, such advantages as orthogonality of the weight matrix, which is ensured at each iteration, numerical stability, and a quite similar computational complexity.

The wavelet transform-domain LMS adaptive filter with partial subband-coefficient updating

In this paper, we propose and analyze the wavelet transform-domain LMS (WTDLMS) algorithm where only a subset of the adaptive filter coefficients are updated at each iteration. The use of wavelets or subband filterbanks can lead to several novel schemes whose combinations can lead to other sub-schemes as well. In the proposed scheme, the coefficients can be selected altogether as a block and not just individually as done earlier in the literature. This algorithm is then tested in the context of system identification and equalization

Blind estimation of residual carrier offset in OFDM systems

In orthogonal frequency division multiplexing (OFDM) systems, the loss of orthogonality between the subcarriers due to carrier offset can degrade the performance of the system. In the literature, Liu and Tureli proposed a blind, music-like method to solve such a problem. The latter has a good performance as compared to the Cramer-Rao bound, but can have a very high computational complexity. In this letter, based on practical considerations, we present a new implementation of the previous method that reduces significantly the cost without sacrificing the performance.

The wavelet transform-domain LMS algorithm: a more practical approach

The wavelet transform-domain least-mean square (WTDLMS) algorithm is known to have, in general, a faster convergence rate than the time-domain LMS algorithm, and can find many applications in signal processing and communications areas. However, the computational complexity of the wavelet filter bank is relatively high. In this work, we show how to exploit the redundancy which exists in the computation of the wavelet coefficients between successive iterations so as to significantly reduce the computational load of the algorithm.

Non-Data-Aided Joint Carrier Frequency Offset and Channel Estimator for Uplink MC-CDMA Systems

This paper addresses the problem of joint estimation of carrier frequency offset (CFO) and channel impulse response (CIR) in the uplink transmission of multicarrier code-division multiple-access (MC-CDMA) systems. A subspace-based blind estimator is proposed, which only uses the received signal and the desired users spreading code to estimate the CFO and CIR. The CFO is estimated using a one-dimensional linear search where the objective of the search is to minimize the determinant of a low dimensional matrix and the CIR is estimated as the unit-norm eigenvector corresponding to the minimum eigenvalue of this matrix. The identifiability of the CFO and CIR estimates is investigated by imposing asymptotic constraints on the spreading codes. Although the cost function used by the proposed estimator is nonlinear and nonconvex, it is locally convex in the neighborhood of the true CFO value. This property is used to formulate a simple two-stage CFO estimator. In the first stage, a coarse search is performed to lock into the local convexity region. Then, an adaptive algorithm is used in the second stage to finetune the CFO estimate. The ldquolinearizedrdquo proposed estimator is shown to be unbiased. The simulation results show that the proposed estimators performance is close to the Cramer-Rao lower bound (CRLB).

The generalized Rayleigh's quotient adaptive noise subspace algorithm: a householder transformation-based implementation

Recently, we proposed a low-cost adaptive algorithm for noise (or minor) subspace estimation based on the generalized Rayleighs quotient. In this paper, we show how to numerically stabilize this algorithm using Householder transformation without incurring any significant increase in its computational complexity. Simulation results are given to validate this new algorithm

Joint channel and carrier offset estimation in a multiuser CDMA system

We investigate the problem of CDMA multiuser detection in the presence of a small residual carrier offset. We propose, in particular, a method based on the generalized eigenvalue problem for efficiently estimating the channel response and the carrier offset blindly. Simulation results are given to verify the validity of the proposed method.

On a Class of Orthonormal Algorithms for Principal and Minor Subspace Tracking

This paper elaborates on a new class of orthonormal power-based algorithms for fast estimation and tracking of the principal or minor subspace of a vector sequence. The proposed algorithms are closely related to the natural power method that has the fastest convergence rate among many power-based methods such as the Oja method, the projection approximation subspace tracking (PAST) method, and the novel information criterion (NIC) method. A common feature of the proposed algorithms is the exact orthonormality of the weight matrix at each iteration. The orthonormality is implemented in a most efficient way. Besides the property of orthonormality, the new algorithms offer, as compared to other power based algorithms, a better numerical stability and a linear computational complexity.

Analysis of DCTLMS algorithm with a selective coefficient updating

Recently, a fast version of LMS algorithm where only a small subset of the coefficients is updated at each iteration has been published in the literature. In this work, we analyze the effects of this technique on the discrete cosine transform domain LMS (DCTLMS) algorithm, and highlight its advantages and drawbacks. It is shown, in particular, that a reduction in the computational complexity can be achieved without causing any degradation to the steady state error of the algorithm. The analytical results are then confirmed by simulations where real speech and first-order Markov signals are used.