An antenna array of directional sensors offers more degrees-of-freedom to improve the source localization accuracy. The originally sophisticated expression of the CRB turns into a factorized one at high SNR, perfectly suitable to derive an objective function that depends on the array geometry and the source direction PDF. Analytically untractable, optimization is conducted by systematic search for a two-sensor array. The so-optimized array has a finite accuracy in all directions, contrarily to fixed-geometry linear arrays, and a performance comparable to larger-sized fixed-geometry circular arrays, and so at all SNR levels.

Arrays of sensors freely located along an axis are considered in this paper that are used to localize a near-field emitting source. Using Taylor expansion and a suitable coordinate system, simple, yet rich to interpret, Cramer-Rao bounds relative to the direction and range parameters are derived. Our analysis allows in particular to unveil a family of non-uniform linear arrays with better near field estimation capabilities, compared to the well-established uniform linear arrays.

This paper is devoted to the Cramer Rao bound (CRB) on the azimuth, elevation and range of a narrow-band near-field source localized by means of a uniform circular array (UCA), using the exact expression of the time delay parameter. After proving that the conditional and unconditional CRB are generally proportional for constant modulus steering vectors, we specify conditions of isotropy w.r.t. the distance and the number of sensors. Then we derive very simple, yet very accurate non-matrix closed-form expressions of different approximations of the CRBs.

In this paper, we address the problem of the sensor placement for estimating the direction of a narrow-band source, randomly located in the far-field of a planar antenna array. Estimation performance is evaluated by means of the expectation of the conditional Cramer Rao bound (ECRB), which depends on the prior probabilistic distribution of the DOA angles. We study the particular, but practical, case where the azimuth angle is uniformly distributed. Surprisingly, it turns out that the optimal arrays are not isotropic, i.e. they do not have the same accuracy in all possible look directions. In fact, optimal arrays computed here increase performance by about 10% compared to optimal isotropic arrays computed in a previous work.

Based on the CRB of the 2D-DOA estimation problem, we prove a condition on the sensor coordinates of a planar array to be ambiguity-free and isotropic. A systematic search of such antenna arrays is conducted leading to the identification of all possible ambiguity-free isotropic arrays. In particular, we select the arrays that outperform the popular uniform circular array (UCA). It is shown that these arrays allow to enhance the DOA estimation by as much as 25%, in comparison with UCA. As the number of sensors increases, the best isotropic array tends towards the non-intuitive V-shape.

A new SOS-expressed blind channel shortening algorithm is proposed. It is based on a necessary and sufficient condition that guarantees detection of all possible shortening equalizers before the best one is selected. The unique existing SOS-based blind channel shortening algorithm meets the same objective but has a much higher complexity

The error rate of a coded multi-carrier system can be controlled by adjusting the modulation parameters (signal constellation and level) per sub-carrier, while at the same time, minimizing the transmission power. We modify existing techniques to allow for efficient error rate control and to take the encoder/decoder into account. In particular, we study the soft decision receiver for which no adaptive allocation technique has been proposed to-date.

The linear prediction (LP) algorithm can be regarded as one that leads to the estimation of a set of zero-forcing equalizers. A final step in the LP algorithm consists in (linearly) combining these equalizers to form one that restores the transmitted symbols ISI-free, unattenuated and not delayed. We show that the way they were originally combined is not justified. We propose and justify a different combination of the original LP equalizers. The modified LP algorithm shows enhanced performances for both equalization and identification tests. We also comment on the often questioned robustness of the LP algorithm to channel order over estimation. We argue here that the LP algorithm is truly robust to order over estimation and we give a formal proof to this.

We address the estimation of the direction(s) of arrivals (DOA) of emitting sources. In a number of applications, a priori knowledge about the source location is available so that the possible DOA values can be restricted to a limited angular sector. In addition to a subsequent complexity reduction of the DOA estimation algorithm (especially that of the MUSIC algorithm), this relieves from the need to use antenna arrays (often circular arrays) with uniform accuracy. After developing a simplified Cramer-Rao bound, alternative array configurations are proposed. While these do not provide a uniform error in all directions, they improve the performance within a given sector, the width of which can be chosen as large as desired.

We propose a new blind algorithm to estimate Zero-Forcing equalizers with arbitrarily chosen length and delay using second order statistics. We justify, theoretically, the interest in mid-delay equalization and show, through simulations, that those estimated by the proposed algorithm outperform those estimated by existing algorithms, such as the linear prediction algorithm or the GRDA algorithm. The linear prediction and the Outer Product Decomposition algorithms tum to be two special cases of the proposed algorithm. Hence, a formal connection is established between these two algorithms, often observed to have very close performances.

We study the asymptotic behavior of the smallest singular value of the single input multiple output (SIMO) channel filtering matrix. We prove that this can be expressed in terms of the sub-channel transfer functions. We apply this result to study the identifiability of bandlimited channels from their (estimated) second order statistics (SOS). We prove, and verify through examples, that SOS based algorithms are unable to identify frequency selective channels regardless of the assumed channel order.

Szego's (1984) theorem states that the asymptotic behavior of the eigenvalues of a Hermitian Toeplitz matrix is linked to the Fourier transform of its entries. This result was later extended to block Toeplitz matrices, i.e., covariance matrices of multivariate stationary processes. The present work gives a new proof of Szego's theorem applied to block Toeplitz matrices. We focus on a particular class of Toeplitz matrices, those corresponding to covariance matrices of single-input multiple-output (SIMO) channels. They satisfy some factorization properties that lead to a simpler form of Szego's theorem and allow one to deduce results on the asymptotic behavior of the lowest nonzero eigenvalue for which an upper bound is developed and expressed in terms of the subchannels frequency responses. This bound is interpreted in the context of blind channel identification using second-order algorithms, and more particularly in the case of band-limited channels.

Active research in blind identification of single input multiple output (SIMO) channels has led to a variety of second order statistics based algorithms, mainly the subspace and the linear prediction approaches. The subspace algorithm shows good performance, although it requires exact knowledge of the channel order, which is not guaranteed by current order detection algorithms. The linear prediction algorithm is sensitive to observation noise while its robustness to channel order over estimation is only theoretical. We propose a new second order statistics based blind channel identification algorithm using a shifted version of the channel output covariance matrix. It proves to be truly robust to channel order over estimation i.e., able to estimate the channel impulse response when the assumed channel order is greater than the exact order and when channel output is corrupted by additive noise and observed over finite time duration. Moreover, the proposed algorithm shows clearly better performance than the linear prediction algorithm.