Kwok-Chiang Ho

Linear independence of steering vectors of an electromagnetic vector sensor

We investigate linear independence of steering vectors of one electromagnetic vector sensor. We show that every three steering vectors with distinct directions of arrival (DOAs) are linearly independent. We also show that four steering vectors with distinct DOAs are linearly independent if the ellipticity angles of the signals associated with any two of the four steering vectors are distinct. Moreover, every four steering vectors corresponding to circularly polarized signals with the same spin direction are linearly dependent. We then establish that five steering vectors are linearly independent if exactly two or three of them correspond to circularly polarized signals with the same spin direction. Finally, we demonstrate that given any five steering vectors, then for any DOA there exists a steering vector that is linearly dependent on the five steering vectors.

Minimum-noise-variance beamformer with an electromagnetic vector sensor

We study the performance of the minimum-noise-variance beamformer employing a single electromagnetic (EM) vector sensor that is capable of measuring the complete electric and magnetic fields induced by EM signals at one point. Two types of signals are considered: one carries a single message, and the other carries two independent messages simultaneously. The state of polarization of the interference under consideration ranges from completely polarized to unpolarized. We first obtain explicit expressions for the signal to interference-plus-noise ratio (SINR) in terms of the parameters of the signal, interference, and noise. Then, we discuss some physical implications associated with the SINR expressions. These expressions provide a basis for effective interference suppression as well as generation of dual-message signals of which the two message signals have minimum interference effect on one another. We also analyze the characteristics of the main-lobe and side-lobe of the beampattern of an EM vector sensor and compare them with other types of sensor arrays.

Estimating directions of arrival of completely and incompletely polarized signals with electromagnetic vector sensors

We are concerned with direction-of-arrival estimation and signal classification with electromagnetic vector sensors for scenarios where completely and incompletely polarized signals may co-exist. We propose an efficient ESPRIT-based method, address the identifiability of the proposed method, and compare its performance against CRB.

Efficient method for estimating directions-of-arrival of partially polarized signals with electromagnetic vector sensors

We have developed a high-resolution ESPRIT-based method for estimating the directions-of-arrival of partially polarized signals with electromagnetic vector sensors, each of which provides measurements of the complete electric and magnetic fields induced by electromagnetic signals. The method is computationally efficient since unlike many high-resolution methods, it does not involve searching across a multidimensional array manifold. In addition, the method has two variants, of which one is applicable to scenarios where a priori information about the array system, such as the sensor positions, is unavailable.

Linear dependence of steering vectors associated with tripole arrays

We are concerned with the linear independence of steering vectors associated with tripoles, each of which provides measurements of the three components of electric field induced by electromagnetic signals. We first establish that for a single tripole, any steering vector is linearly dependent on at least one other steering vector corresponding to a different direction-of-arrival (DOA) for a general problem where signals may arrive from anywhere in a three-dimensional (3-D) space, but every two steering vectors with distinct DOAs are linearly independent if the signals are nonlinearly polarized and arrive from a strictly hemispherical space. We then obtain a series of upper bounds for the number of linearly independent steering vectors associated with a tripole array with general sensor configurations. We also show that for applications where signals are known to be linearly polarized in the same direction, the ability to estimate DOAs using a tripole array is identical to that using a scalar-sensor array if both of them have identical sensor configurations.

Estimation of directions-of-arrival of partially polarized signals with electromagnetic vector sensors

We develop a high-resolution method for estimating the directions-of-arrival of partially polarised signals with electromagnetic (EM) vector sensors, of which each provides measurements of the complete electric and magnetic fields induced by EM signals. The method is computationally efficient since unlike many high-resolution methods, it does not involve searching across a multi-dimensional array manifold. In addition, it does not require a priori information about the array system such as sensor positions.

Estimating Directions-of-Arrival of Completely and Incompletely Polarized Signals with Electromagnetic Vector Sensors

Abstract We develop two high-resolution methods for direction-of-arrival estimation with electromagnetic vector sensors (i.e., sensors which provide measurements of the complete electric and magnetic fields at one point). Both methods, of which the first is ESPRIT-based and the second MUSIC-based, are applicable to scenarios where completely polarized and incompletely polarized signals co-exist. The ESPRITbased method is computationally efficient, but there must be 3 vector sensors with a specific sensor arrangement in order to apply the algorithm. On the other hand, the MUSIC-based method, although involving more computations, can work without the constraint that the ESPRIT-based method faces.

Uniqueness study of measurements obtainable with an electromagnetic vector sensor

We investigate the linear dependence of the steering vectors of one electromagnetic vector sensor. We show that every 3 steering vectors with distinct DOAs are linearly independent. We also show that 4 steering vectors with distinct DOAs are linearly independent if the ellipticity angles of the signals associated with any 2 of the 4 steering vectors are distinct. We then establish that 5 steering vectors are linearly independent if exactly 2 or 3 of them correspond to circularly polarized signals with the same spin direction. Finally, we demonstrate that given any 5 steering vectors, then for any DOA there exists a steering vector which is linearly dependent on the 5 steering vectors.