Development of a Single-Channel Direction Finding Algorithm
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- Điều hướng trang này:
- List of Tables
- List of Acronyms
- Symbol Glossary
- Chapter 1 Introduction
- Project Equipment Description
- Thesis Description
- Chapter 2 Introduction to DF Concepts
- Direction Finding Fundamentals
| List of Figures
1.1Project Equipment Description 3 1.1.1Software Introduction 3 1.1.2Hardware Introduction 3 1.2Thesis Description 3 Chapter 2 4 2.1Direction Finding Fundamentals 5 2.1.1Basic Assumptions 5 2.1.2The Received Signal Model 6 2.2Classical DF Algorithms 10 2.2.1Watson-Watt Algorithm 10 Figure 4.14. Example plot of error in frequency offset estimate per array sweep index... 37 Figure 4.15. PLL output and first difference curve amplitudes relative to antenna array 1.1Project Equipment Description 3 1.1.1Software Introduction 3 1.1.2Hardware Introduction 3 1.2Thesis Description 3 Chapter 2 4 2.1Direction Finding Fundamentals 5 2.1.1Basic Assumptions 5 2.1.2The Received Signal Model 6 2.2Classical DF Algorithms 10 2.2.1Watson-Watt Algorithm 10 List of Tables 1.1Project Equipment Description 3 1.1.1Software Introduction 3 1.1.2Hardware Introduction 3 1.2Thesis Description 3 Chapter 2 4 2.1Direction Finding Fundamentals 5 2.1.1Basic Assumptions 5 2.1.2The Received Signal Model 6 2.2Classical DF Algorithms 10 2.2.1Watson-Watt Algorithm 10 Table 6.3. Tabular description of manual switching circuit state control via DIP switches. 8. 8 List of Acronyms
Symbol Glossary
a Wavelength p Phase propagation factor, p = 2 'n/ a M Number of elements in an antenna array m Index of elements in an antenna array, m = 0,1, ..., M — 1 D Number of signals incident upon the antenna array d Index of incident signals, d = 0,1, ... ,D—1 K Number of samples taken per array element r Array radius Chapter 1 Introduction Radio direction finding (DF) systems use a multiple-antenna array with one or more receivers to produce an estimate of the bearing angle or geographical coordinates of an intercepted signal of interest (SOI). The primary function of a DF system is to produce a direction-of-arrival (DOA). DF systems have numerous applications from amateur use in HAM radio “foxhunting” contests to emergency service to military defense and intelligence operations. These systems can be categorized into two main types, n-channel DF systems using typically one receiver channel per antenna, and single-channel DF systems which use a single receiver with a multiple-antenna array along with some form of switching among the elements or combining them to present the receiver with a single signal. Single-channel DF systems offer obvious advantages over n-channel systems in terms of size, weight, power, and portability requirements but in general pay for these advantages with reduced processing power, accuracy, and robustness in adverse channel conditions. The challenges inherent in developing a single-channel DF system are precisely what make it an attractive field of study as the utility of a system that can offer performance characteristics that approach those of n-channel systems is undisputed. This thesis is concerned with a specific single-channel DF algorithm known as the Phase Locked Loop Algorithm [1],[2],[3],[4]. It is the continuation of work started at MPRG by a previous student, John Keaveny, along with his advisor Dr. Michael Buehrer and fellow student Swaroop Venkatesh. His work focused on the initial development, simulation, and implementation of the algorithm. In short, the algorithm uses an 8 element circular array connected to a single-channel software defined radio (SDR) receiver through a digitally controlled 8-to-1 switching circuit that switches sequentially around the elements. This time divided signal is then fed into a bank of eight parallel phase locked loops (PLLs) which then track the phase of the signal at each antenna. This collected phase data is then differentiated and fed through a signal processing block to produce a single DOA estimate for one full array sweep (i.e. the time required to switch from the first antenna element to the last). This work extends the original algorithm development and implementation in a few ways. First, the initial implementation of the PLL model, while perfectly functional, was overly processor intensive. In order to add further enhancements to the algorithm implementation it was necessary to produce a more efficient implementation of the PLL model. Second, it was discovered during the initial implementation that a slight frequency offset occurs between the test signal generated by the transmitter and the receiver's local oscillator (LO). Since the DOA estimations process of the PLL algorithm is based on the phase of the received SOI, this frequency offset can wreak havoc with the estimate if it is of significant magnitude. This work provides a means of removing the frequency offset. Third, a method for improving the error performance of the system was developed. This consists of producing a quality metric to accompany each DOA estimate as well as filtering the output DOA estimates over time. Finally, a method for scaling the algorithm to work with a 16 element array was also considered. This involved a new approach to dealing with the phase data generated by the PLLs as the original signal processing block would be computationally infeasible when the number of antenna elements is increased. Project Equipment Description Software Introduction Practically all algorithm development was performed in Matlab. Matlab provides an excellent environment for quick evaluation of algorithms through its combination of built in functions and ease of development. For implementation purposes, the majority of the code was simply translated from Matlab into C. Only certain functions, such as the DFT implementation and switch control were prototyped in C before integration into the larger implementation. The C program was compiled using TI Code Composer Studio and downloaded to the SDR using proprietary software developed by DRS-SS. Hardware Introduction The SDR used in this project, as well as the funding, was provided by DRS Signal Solutions, Inc. of Gaithersburg, MD. This work is part of the Sunrise University project, which was established to fund implementation-based research at the graduate level at both Virginia Tech and Carnegie Mellon University. The radio used is the WJ-8629a software-definable surveillance receiver. The 8629a has a frequency range of 20MHz to 2.7GHz, 22 selectable IF bandwidths from 200Hz to 1.23MHz, and 5 user-definable bandwidth slots. It also contains a floating point Texas Instruments C67 DSP capable of 1GFLOPS. DRS-SS also furnished their proprietary software for program development and download as well as radio control. As far as algorithm development is concerned, the actual specifications of the hardware used for implementation is unimportant as long as it conforms to certain basic assumptions, mainly that it provides a digital baseband version of the targeted RF signal relatively free of spurious signals generated by the receiver itself. Thesis Description Chapter 2 will provide a brief overview of direction finding techniques and will give a few examples of both single-channel and n-channel algorithms. Chapter 3 continues the discussion of DF algorithms by describing in detail the PLL Algorithm for single-channel DF. In Chapter 4, we will discuss the various enhancements to algorithm that encompass the bulk of the work. These enhancements include modification of the PLL model used for both more efficient implementation and robustness in the presence of a frequency shift on the signal of interest; modification of the curve-fitting algorithm to reduce computational complexity when used with antenna arrays consisting of a large number of elements; and the development of a quality metric to aid in the determination of estimation errors. Chapter 5 presents simulations of the PLL algorithm and its enhancements discussed in Chapters 3 and 4. The simulation results were generated using Matlab and focus on the statistical performance of the algorithm in an AWGN channel with various operating parameters. The chapter will also investigate the operation of the algorithm with a moving target and simple multipath channel model. Chapter 6 will describe the implementation of the enhancements to the algorithm. The chapter will also present limited performance results of the algorithm operating under controlled laboratory conditions. The final chapter will present our conclusions on the work. It will discuss the main contributions of this work to the PLL algorithm as well as a summary of the implementation successes and failures and lessons learned during the research. Finally, it will describe possible future directions for research. Chapter 2 Introduction to DF Concepts When one searches for DF literature, they will most likely find a vast assortment of algorithms and corresponding systems. However, much of this literature presupposes a familiarity on the part of the reader with fundamental knowledge of DF topics. In this chapter we will briefly discuss some of the basic concepts encountered in practically any DF discussion as well as introduce a few well-known DF algorithms in order to illustrate the basic concepts. Two of the algorithms discussed, the Watson-Watt and Doppler/Pseudo-Doppler methods, are single-channel techniques that . The third algorithm, Correlative Vector DF, is an n-channel method based on simple delay- and-sum beamforming. The fourth and final algorithm discussed, MUSIC, is a high-performance algorithm capable of operating in a multipath environment. We will revisit this algorithm in Chapter 7. Direction Finding Fundamentals Basic Assumptions DF algorithms, apart from being classified by the number of receiver channels used, can also be classified by the manner in which they treat the signal received at an antenna array. Central to this is the response of the antenna array over DOA (in azimuth and possibly elevation) as well as frequency. Approaches can be categorized as amplitude-based, phase-based, or a combination of the two. Amplitude-based systems compare the received amplitude among the various elements in the antenna array to locate a point in an plane about the array that the signal originates. Phase-based systems determine DOA information from either the absolute or differential phase of the wavefront as it crosses the array. Systems that use a combination of amplitude and phase information tend to be more complex but also result in higher performance. Beamforming and superresolution systems fall into this category. The basic antenna array can be envisioned as an arbitrary array of isotropic antennas arranged about an arbitrarily defined origin point as in Figure 2.1. For our purposes, we need to make a few basic assumptions about the antenna array [5]: • The difference in amplitude of a received SOI between antenna elements is negligible. • There is a finite number of incident SOIs, each of which can be described by a plane wave. • The SOIs are narrowband signals. These assumptions follow the basic requirements for narrowband beamforming systems. The first point essentially means that the antenna array is small relative to the distance of propagation such that any measured path loss from one antenna to another is insignificant. This implies that the primary response of the antenna array to a signal is by modifying the phase of the signal. The second point allows for simplified modeling of the antenna array — the multipath environment can be described as the linear sum of a finite number of signals. Finally, the narrowband assumption implies that the phase response of the array is flat across the signal's bandwidth. The Received Signal Model Referring to the array in Figure 2.1 the phase difference between any antenna and a reference point at the origin of the coordinate system is given as A^m =fi( Xm cos ộ sin £+y m sin ộ sin £ + Zm cos z I (2.1) where b=2p/l is called the phase propagation factor, ộ is the DOA in azimuth, £ is the DOA in elevation, and the three-dimensional coordinates of the m-th antenna element are given as xm , ym , and zm . In all analysis in this paper, the antenna arrays of interest are two-dimensional, meaning Figure 2.1. Example of an arbitrary antenna array for modeling purposes. that the term relating to the z-coordinate of the array can be ignored. When modeling the signal received at the antenna element, the phase response of that element relative to a reference point along with the antenna's amplitude gain are seen as a complex scaling factor given by: am (ộ. 5)=g„e - a,'-=g,jm ộ""5+y-•" ộsin 5 (2.2) where gm is the gain for the m-th antenna, and the complex baseband output of the m-th antenna is given by: (t) = 5(t)am(ộ. 5) =5(t)gme -j p (x m cos ộ sin 5+ym sinộ sin 5) (2.3) where s(t) is the SOI and xm (t) is the signal at the output of the m--th antenna. If we are concerned only with signals arriving on the same plane of the array then the elevation angle q is equal to 90°, resulting in: xm (t ) = 5 (t) g me - jp(Xmcos ộ +ymsin ộ) (2.4) The collection of scaling factors into an Mx1 vector a is known as the array manifold vector or as the array steering vector in beamforming contexts: a = [a0 (ộ. 5) ai (ộ. 5) ••• «M-1 (ộ. 5)]T (2-5) The received signal at the output of the array can then be expressed in matrix notation as tải về 2.23 Mb. Chia sẻ với bạn bè của bạn:
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