Estimation and Minimization of the Cramer-Rao lower bound for radio direction-finding on the azimuth and elevation of planar antenna arrays

In this paper an approach of obtaining optimal planar antenna arrays consisting of omnidirectional sensors is proposed. The novelty of the proposed approach is to apply an exact expression of the Cramer-Rao lower bound for an arbitrary planar antenna array consisting of a number of omnidirectional elements which has been presented in the further chapters of the paper. The obtained formula describes the influence of antenna elements locations on the direction-of-arrival estimation accuracy. It has been shown that the direction-of-arrival accuracy via planar antenna arrays is determined as the sum of squares of differences between all omnidirectional elements coordinates along x- and y-axis. Thus knowing an expected area or sector of signal source it is very easy to calculate optimal arrangement of antenna elements in order to reduce direction-finding errors, because obtained by that way positions gives the best match according to the maximum likelihood criterion. It is worth nothing that such antenna arrays are useful in the way that they allow estimating the coordinates of radio emission sources in the three-dimensional coordinate space, i.e. in azimuth and elevation. In order to confirm the proposed methodology optimal antenna arrays constructed after minimization of the new formulas are researched. It is found out that the new shapes of antenna arrays based on the analytical expressions have better direction-of-arrival accuracy in comparison with the circular ones

Multisource Self-calibration for Sensor Arrays

Calibration of a sensor array is more involved if the antennas have direction dependent gains and multiple calibrator sources are simultaneously present. We study this case for a sensor array with arbitrary geometry but identical elements, i.e. elements with the same direction dependent gain pattern. A weighted alternating least squares (WALS) algorithm is derived that iteratively solves for the direction independent complex gains of the array elements, their noise powers and their gains in the direction of the calibrator sources. An extension of the problem is the case where the apparent calibrator source locations are unknown, e.g., due to refractive propagation paths. For this case, the WALS method is supplemented with weighted subspace fitting (WSF) direction finding techniques. Using Monte Carlo simulations we demonstrate that both methods are asymptotically statistically efficient and converge within two iterations even in cases of low SNR.Comment: 11 pages, 8 figure

A Cramér-Rao bounds based analysis of 3D antenna array geometries made from ULA branches

International audienceIn the context of passive sources localization using antenna array, the estimation accuracy of elevation, and azimuth are related not only to the kind of estimator which is used, but also to the geometry of the considered antenna array. Although there are several available results on the linear array, and also for planar arrays, other geometries existing in the literature, such as 3D arrays, have been less studied. In this paper, we study the impact of the geometry of a family of 3D models of antenna array on the estimation performance of elevation, and azimuth. The Cramer-Rao Bound (CRB), which is widely spread in signal processing to characterize the estimation performance will be used here as a useful tool to find the optimal configuration. In particular, we give closed-form expressions of CRB for a 3D antenna array under both conditional, and unconditional observation models. Thanks to these explicit expressions, the impact of the third dimension to the estimation performance is analyzed. Particularly, we give criterions to design an isotropic 3D array depending on the considered observation model. Several 3D particular geometry antennas made from uniform linear array (ULA) are analyzed, and compared with 2D antenna arrays. The isotropy condition of such arrays is analyzed. The presented framework can be used for further studies of other types of arrays

3D conformal antennas for radar applications

Embedded below the radome of a missile, existing RF-seekers use a mechanical rotating antenna to steer the radiating beam in the direction of a target. Latest research is looking at replacing the mechanical antenna components of the RF seeker with a novel 3D conformal antenna array that can steer the beam electronically. 3D antennas may oer signicant advantages, such as faster beamsteering and better coverage but, at the same time, introduce new challenges resulting from a much more complex radiation pattern than that of 2D antennas. Thanks to the mechanical system removal, the new RF-seeker has a wider available space for the design of a new 3D conformal antenna. To take best benets of this space, dierent array shapes are studied, hence the impact of the position, orientation and conformation of the elements is assessed on the antenna performance in terms of directivity, ellipticity and polarisation. To facilitate this study of 3D conformal arrays, a Matlab program has been developed to compute the polarisation pattern of a given array in all directions. One of the task of the RF-seeker consists in estimating the position of a given target to correct the missile trajectory accordingly. Thus, the impact of the array shape on the error between the measured direction of arrival of the target echo and its true value is addressed. The Cramer-Rao lower bound is used to evaluate the theoretical minimum error. The model assumes that each element receives independently and allows therefore to analyse the potential of active 3D conformal arrays. Finally, the phase monopulse estimator is studied for 3D conformal arrays whose quadrants do not have the same characteristics. A new estimator more adapted to non-identical quadrants is also proposed

Wideband reconfigurable vector antenna for 3-D direction finding application

Direction finding plays a crucial role in various civilian and military applications, related to either radionavigation or radiolocation. Most of the direction finding antennas operate over a wide frequency band, but only a minority of them enable the direction of arrival estimation of an incoming electromagnetic field over a 3-D angular coverage (i.e., estimation of both azimuth and elevation angles). An original approach to obtain a 3-D angular coverage consists in measuring the six components of the incident electromagnetic field through a so-called vector antenna. The aim of this Ph.D. is to design a passive, compact and wideband vector antenna in order to cover a maximum of applications. Two vector antennas have been designed, manufactured and experimentally characterized. Unlike conventional topology, they enable the measurement of the components of an incoming electromagnetic field thanks to the radiation pattern reconfigurability of an original arrangement of Vivaldi antennas. The first prototype is mounted over a finite metallic support and enables the direction of arrival estimation of vertically-polarized electromagnetic fields over a 1.69:1 bandwidth while the second one can be used regardless of the polarization of the incoming electromagnetic fields over a 8:1 bandwidth. Moreover, the direction finding performances of these vector antennas have been improved in terms of estimation accuracy, sensitivity, robustness to angular ambiguity and polarization mismatch by synthesizing new radiation patterns in the estimation process. A method based on the Cramer-Rao lower bound has been proposed to select efficiently and rapidly the additional radiation pattern

Spatio-Temporal processing for Optimum Uplink-Downlink WCDMA Systems

The capacity of a cellular system is limited by two different phenomena, namely multipath fading and multiple access interference (MAl). A Two Dimensional (2-D) receiver combats both of these by processing the signal both in the spatial and temporal domain. An ideal 2-D receiver would perform joint space-time processing, but at the price of high computational complexity. In this research we investigate computationally simpler technique termed as a Beamfom1er-Rake. In a Beamformer-Rake, the output of a beamfom1er is fed into a succeeding temporal processor to take advantage of both the beamformer and Rake receiver. Wireless service providers throughout the world are working to introduce the third generation (3G) and beyond (3G) cellular service that will provide higher data rates and better spectral efficiency. Wideband COMA (WCDMA) has been widely accepted as one of the air interfaces for 3G. A Beamformer-Rake receiver can be an effective solution to provide the receivers enhanced capabilities needed to achieve the required performance of a WCDMA system. We consider three different Pilot Symbol Assisted (PSA) beamforming techniques, Direct Matrix Inversion (DMI), Least-Mean Square (LMS) and Recursive Least Square (RLS) adaptive algorithms. Geometrically Based Single Bounce (GBSB) statistical Circular channel model is considered, which is more suitable for array processing, and conductive to RAKE combining. The performances of the Beam former-Rake receiver are evaluated in this channel model as a function of the number of antenna elements and RAKE fingers, in which are evaluated for the uplink WCDMA system. It is shown that, the Beamformer-Rake receiver outperforms the conventional RAKE receiver and the conventional beamformer by a significant margin. Also, we optimize and develop a mathematical formulation for the output Signal to Interference plus Noise Ratio (SINR) of a Beam former-Rake receiver. In this research, also, we develop, simulate and evaluate the SINR and Signal to Noise Ratio (Et!Nol performances of an adaptive beamforming technique in the WCDMA system for downlink. The performance is then compared with an omnidirectional antenna system. Simulation shows that the best perfom1ance can be achieved when all the mobiles with same Angle-of-Arrival (AOA) and different distance from base station are formed in one beam

Optimal Precoders for Tracking the AoD and AoA of a mm-Wave Path

In millimeter-wave channels, most of the received energy is carried by a few paths. Traditional precoders sweep the angle-of-departure (AoD) and angle-of-arrival (AoA) space with directional precoders to identify directions with largest power. Such precoders are heuristic and lead to sub-optimal AoD/AoA estimation. We derive optimal precoders, minimizing the Cram\'{e}r-Rao bound (CRB) of the AoD/AoA, assuming a fully digital architecture at the transmitter and spatial filtering of a single path. The precoders are found by solving a suitable convex optimization problem. We demonstrate that the accuracy can be improved by at least a factor of two over traditional precoders, and show that there is an optimal number of distinct precoders beyond which the CRB does not improve.Comment: Resubmission to IEEE Trans. on Signal Processing. 12 pages and 9 figure

Spatio-Temporal processing for Optimum Uplink-Downlink WCDMA Systems

The capacity of a cellular system is limited by two different phenomena, namely multipath fading and multiple access interference (MAl). A Two Dimensional (2-D) receiver combats both of these by processing the signal both in the spatial and temporal domain. An ideal 2-D receiver would perform joint space-time processing, but at the price of high computational complexity. In this research we investigate computationally simpler technique termed as a Beamfom1er-Rake. In a Beamformer-Rake, the output of a beamfom1er is fed into a succeeding temporal processor to take advantage of both the beamformer and Rake receiver. Wireless service providers throughout the world are working to introduce the third generation (3G) and beyond (3G) cellular service that will provide higher data rates and better spectral efficiency. Wideband COMA (WCDMA) has been widely accepted as one of the air interfaces for 3G. A Beamformer-Rake receiver can be an effective solution to provide the receivers enhanced capabilities needed to achieve the required performance of a WCDMA system. We consider three different Pilot Symbol Assisted (PSA) beamforming techniques, Direct Matrix Inversion (DMI), Least-Mean Square (LMS) and Recursive Least Square (RLS) adaptive algorithms. Geometrically Based Single Bounce (GBSB) statistical Circular channel model is considered, which is more suitable for array processing, and conductive to RAKE combining. The performances of the Beam former-Rake receiver are evaluated in this channel model as a function of the number of antenna elements and RAKE fingers, in which are evaluated for the uplink WCDMA system. It is shown that, the Beamformer-Rake receiver outperforms the conventional RAKE receiver and the conventional beamformer by a significant margin. Also, we optimize and develop a mathematical formulation for the output Signal to Interference plus Noise Ratio (SINR) of a Beam former-Rake receiver. In this research, also, we develop, simulate and evaluate the SINR and Signal to Noise Ratio (Et!Nol performances of an adaptive beamforming technique in the WCDMA system for downlink. The performance is then compared with an omnidirectional antenna system. Simulation shows that the best perfom1ance can be achieved when all the mobiles with same Angle-of-Arrival (AOA) and different distance from base station are formed in one beam

Experimental evaluation of synchronization errors on the performance of smart antenna algorithms for CDMA

The CDMA and smart antennas are two promising approaches to increase system capacity and spectrum efficiency for mobile communication services. In a CDMA system, frequency offset between local oscillator and the carrier of impinging signal, timing offset between local generated PN sequence and received PN sequence, imperfect power control may exist and this degrades the performance of the smartantenna algorithms. In this thesis, the effects of frequency and timing offsets on smart antenna performance is presented. A smart antenna system has been set up to implement blind adaptive algorithms for W-CDMA in a laboratory environment. The blind adaptive algorithms implemented on the smart antenna system are Least- Squares Despread-Respread Multi Target Array (LS-DRMTA) and Least- Squares Despread-Respread Multi Target Constant Modulus Algorithm (LSDRMTCMA). Since both LS-DRMTA and LS-DRMTCMA algorithms utilize users PN sequence, they have several advantages compared to other blind adaptive algorithms for CDMA. BER and beamforming performances of LS-DRMTA and LSDRMTCMA algorithms in a two-user and two- element-antenna array system is evaluated for systems with timing offset and frequency offset. Experimental results show that frequency and timing offset degrades the performance, however they still give reasonable BER. In all test conditions LS-DRMTA and LS-DRMTCMA outperforms conventional receiver, moreover LS - DRMTCMA can generate deeper nulls and outperforms LS-DRMTA