Sichun Wang

Direction of Arrival Estimation Using Directive Antennas in Uniform Circular Arrays

The effect of directional antenna elements in uniform circular arrays (UCAs) for direction of arrival (DOA) estimation is studied in this paper. While the vast majority of previous work assumes isotropic antenna elements or omnidirectional dipoles, this work demonstrates that improved DOA estimation accuracy and increased bandwidth is achievable with appropriately-designed directional antennas. The Cramer-Rao Lower Bound (CRLB) is derived for UCAs with directional antennas and is compared to isotropic antennas for 4- and 8-element arrays using a theoretical radiation pattern. The directivity that minimizes the CRLB is identified and microstrip patch antennas approximating the optimal theoretical gain pattern are designed to compare the resulting DOA estimation accuracy with a UCA using dipole antenna elements. Simulation results show improved DOA estimation accuracy and robustness using microstrip patch antennas as opposed to conventional dipoles. Additionally, it is shown that the bandwidth of a UCA for DOA estimation is limited only by the broadband characteristics of the directional antenna elements and not by the electrical size of the array as is the case with omnidirectional antennas.

Efficient approximations for the arctangent function

1053-5888/06/

Hybrid RSS/AOA emitter location estimation based on least squares and maximum likelihood criteria

20.00©2006IEEE T his article provides several efficient approximations for the arctangent function using Lagrange interpolation and minimax optimization techniques. These approximations are particularly useful when processing power, memory, and power consumption are important issues. In addition to comparing the errors and the computational workload of these approximations, we also extend them to all four quadrants.

Upper and Lower Bounds for the Threshold of the FFT Filter Bank-Based Summation CFAR Detector

Linear least squares (LS) and maximum likelihood (ML) estimators are derived for emitter geolocation using both received signal strength (RSS) and angle of arrival (AOA) information obtained from an heterogeneous sensor array. The results of simulation experiments provide useful insights into the behavior of these hybrid approaches and demonstrate that the use of simple RSS sensors to augment traditional AOA sensors can significantly improve the attainable geolocation accuracy.

A near-optimal least squares solution to received signal strength difference based geolocation

The reliable computation of detection threshold T given a desired probability of false alarm Pfa a is an important issue in the design of the FFT filter bank-based summation CFAR (constant false alarm rate) detector. The computation of detection threshold T is based on numerical procedures such as the Newton-Ralphson algorithm and a priori knowledge of lower and upper bounds for T for a given Pfa. Current approaches used in the initialization stage of the computation of threshold T are largely ad hoc as there are no theoretical upper and lower bounds for T reported in the literature. In this article, several theoretical upper and lower bounds for T for overlapped and non-overlapped signal data are derived. These results enable a proper design of the FFT filter bank-based summation CFAR detector

The Multiple Antenna Induced EMF Method for the Precise Calculation of the Coupling Matrix in a Receiving Antenna Array

A simple geometric interpretation for received signal strength (RSS) difference based geolocation can be illustrated by considering a plane containing a single pair of receivers and a transmitter. If the path loss follows a simple inverse power law, the RSS difference (in decibels) between the two receivers can be shown to define a circle on which the transmitter must lie. With additional receivers, the position of the transmitter can be solved by finding the common intersection of the circles corresponding to the different pairs of receivers. In practice, the solution of this problem is complicated by the errors contributed by environmental noise, measurement errors and the deviation of the actual path losses from the model. The optimal nonlinear least squares solution can be obtained by performing a search on a planar grid. However, the computational cost becomes an issue when the number of receivers is large. This paper presents an efficient least squares solution whose performance approaches that of the optimal nonlinear least squares solution.

Computation of the Normalized Detection Threshold for the FFT Filter Bank-Based Summation CFAR Detector

Practical antenna array designs generally require that the elements are separated by electrically short distances. The resultant mutual coupling often adversely afiects the achievable performance. Various methods are available to quantify the efiects of mutual coupling in arrays and improve performance through mutual coupling compensation. Mutual coupling is often described by a coupling matrix that relates the coupled and uncoupled quantities. Unfortunately, the accuracy with which the coupling matrix can be calculated is highly dependent on both the method selected and the frequency. This is a signiflcant limitation for wideband analysis where the coupling matrix needs to be calculated accurately at all frequencies of interest. This paper introduces a novel method for the precise calculation of the coupling matrix at any frequency of interest. It is an extension of the induced EMF method to multiple array elements. The method has the important practical advantage of being independent of the numerical technique used in the analysis. Since the coupling matrix is calculated by exciting the elements in the transmission mode, the method resembles well-known network analysis. However, as outlined in the paper, there are subtle difierences between the two approaches, which lead to more accurate results with the new proposed method. It is also demonstrated that antennas with arbitrary geometries and illuminations are handled accurately by the method.

Relationship between the maximum likelihood emitter location estimators based on received signal strength (RSS) and received signal strength difference (RSSD)

The FFT filter bank-based summation CFAR detector is widely used for the detection of narrowband signals embedded in wideband noise. The simulation and implementation of this detector involves some problems concerning the reliable computation of the normalized detection threshold for a given probability of false alarm. This paper presents a comprehensive theoretical treatment of major aspects of the numerical computation of the normalized detection threshold for an AWGN channel model. Equations are derived for the probability of false alarm, Pfa, for both non-overlapped and overlapped input data and then used to compute theoretical upper and lower bounds for the detection threshold T. A very useful transformation is introduced that guarantees the global quadratic convergence of the Newton-Ralphson algorithm in the computation of T for overlapped data with an overlap ratio not exceeding 50%. It is shown that if the product of the number of FFT bins assigned to a channel for signal power estimation and the number of input data blocks is relatively small, e.g., less than 60, the theoretical normalized detection threshold can be accurately computed without numerical problems. To handle other cases, good approximations are derived.

Detection of Narrow-Band Signals Through the FFT and Polyphase FFT Filter Banks: Noncoherent Versus Coherent Integration

Under the assumption of a log-normal path loss model, maximum likelihood (ML) emitter location estimators are derived for both received signal strength (RSS) and received signal strength difference (RSSD) information. It is then shown that these ML estimators are identical, contrary to the seemingly common perception that the RSS-based ML location estimator should outperform the RSSD-based ML location estimator. The Cramer-Rao lower bounds (CRLB) for the average miss distance are also shown to be identical. Using the least squares estimation criterion, a non-linear least squares (NLS) emitter location estimator is also formulated in this paper for comparison. These theoretical developments are illustrated by computer simulation experiments.

FFT filter bank based majority and summation CFAR detectors: a comparative study

Formulas are derived for computing performance gain that is achieved by coherent integration over noncoherent integration in detection schemes based on polyphase fast Fourier transform (FFT) and FFT filter banks. Numerical computation of the processing gain is then discussed. The crucial role that is played by window energy normalization in detection performance comparisons, which has never been recognized in the literature, is emphasized and analyzed. The numerical results provided for typical implementation parameters are useful for making appropriate tradeoffs in the design of solutions for practical signal detection problems.