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Spatial spectrum estimation direction finding system design

Abstract: spatial spectrum estimation direction finding is a new direction finding technology based on multi antenna array combined with modern digital signal processing. Aiming at the typical algorithm MUSIC algorithm in spatial spectrum estimation, based on the study of the composition, working principle and hardware implementation scheme of super-resolution direction finding system, a parallel processing scheme for realizing mu-sic algorithm is proposed

Keywords: spatial spectrum estimation; Multiple antenna array; MUSIC algorithm; Super resolution direction finding; Parallel processing

1 introduction

with the development of electronic technology, electronic countermeasure plays an important role in weapon systems, and electronic countermeasure systems are developing to diversification, such as electronic countermeasure methods that directly interfere with the normal work of each other's electronic systems by using electronic jamming equipment; Use weapons and ammunition systems to attack each other's electronic equipment. No matter which method is adopted to win the battlefield initiative, the prerequisite is to know the location of the other party's communication equipment, radio communication and other electronic equipment transmitting radio signals. In addition, in order to implement the interference to multiple sources (such as multiple fuzes, multiple communication machines or jammers), it is necessary to effectively use our power resources of the jammer driven by the downstream lithium battery demand to determine the direction of the transmitting source, and the angle of rotating the receiving antenna can be used to determine the direction of the transmitting source. However, this method has the contradiction between angle measurement accuracy and measurement speed, and it is difficult to meet the requirements of determining the orientation of each target when there are multiple moving targets in space. The spatial spectrum estimation direction finding technology can achieve the simultaneous super-resolution direction finding of multiple targets in the airspace. Therefore, the design scheme of spatial spectrum estimation direction finding system is given here

2 spatial spectrum estimation direction finding principle

spatial spectrum estimation direction finding is a super-resolution spectrum estimation method based on the spatial correlation characteristics of antenna array output signals. MUSIC algorithm is a spatial spectrum estimation method based on eigenstructure analysis. Its direction finding principle is to decompose the array output covariance matrix according to the matrix eigendecomposition theory, decompose the signal space into noise subspace enh and signal subspace EHS, and use the property that the noise subspace enh is orthogonal to the column vector of the array direction matrix to construct the spatial spectral function p () and search the spectral peak, Thus, only the computer with LabVIEW can meet the requirements of simulation teaching and estimate the direction of arrival information. Figure 1 shows the signal source direction messages simulated and measured by using music algorithm for spatial spectrum estimation technology. The signal source directions are 45, 30, 18 and 25 respectively. According to the simulation results of music algorithm in Figure 1, the algorithm can accurately determine the direction information of signal source

3 design of spatial spectrum estimation DF system

the realization of spatial spectrum estimation DF system requires physical support (antenna array and digital receiver) and software system support. The two complement each other. The high performance and consistency of its hardware will reduce the error of sampling data in the next step, so as to fully demonstrate the super-resolution performance of spectrum estimation software; The high speed and high stability of spectrum estimation algorithm reduce the hardware cost requirements

3.1 composition of spatial spectrum estimation DF system

the basic composition block diagram of spatial spectrum estimation DF system is shown in Figure 2. It can be seen from the figure that the DF system is composed of a multi-element antenna array, a multi-channel receiver, a converter and a signal processing terminal. In order to make the excellent performance of spatial spectrum estimation algorithm well reflected in direction finding, it is necessary to solve the technical problems of the corresponding group in addition to the conventional adjustment

3.1.1 multiple antenna array

multiple antenna array is a sensor for spatial signal acquisition. The amplitude and phase of the signal received by each antenna array element are related to the relationship between the signal and the direction of signal arrival. In principle, the antenna array can be arranged in any form, and the characteristics of each antenna array element are also different. In spatial spectrum estimation and direction finding, all array elements with the same characteristics are set as omni-directional antenna array elements, which are evenly and equidistantly distributed on a straight line, and the spacing of array elements is generally taken as one-half of the working wavelength. This array is usually called uniform linear array. Each array element of the multi-element antenna array requires high mechanical positioning accuracy, the pattern of each array element should be consistent as much as possible, and the mutual coupling between each array element should be as small as possible

3.1.2 multi channel receiver

the output of each antenna element is sent to its respective receiver input. For example, if there are N antenna elements, there are n identical receivers. The receiver amplifies and converts the signal to a frequency suitable for a/D conversion, so as to output the intermediate frequency signal. The A/D converter can also be integrated with the receiver to directly output digital signals. In order to completely save the signal amplitude and phase information received by each antenna array element, the I and Q channel method is generally adopted, that is, orthogonal mixing is adopted in the final stage of the intermediate amplifier, and two local oscillator signals with a phase difference of 90 are sent to two mixers, whose output low-pass signals are I and Q channel signals. I and Q channels are respectively connected with an A/D converter, and its output is the real part and imaginary part of the digitized complex signal. The receiver model of each array element is shown in Figure 3

in communication reconnaissance and direction finding, the receiver can adopt the heterodyne receiver with multiple frequency conversion, while in radar reconnaissance and direction finding, it is a broadband microwave digital receiver. Spatial spectrum estimation algorithm requires high consistency of each channel. Although the consistency of channels can be improved by adding correction sources, it is also required to ensure good consistency of each channel of multi-channel receiver in practical application

3.1.3 MD converter

the output of each receiver needs to be converted into a digital signal through a/D conversion. The selection of bits of a/D converter should consider factors such as the dynamic range of the signal, quantization noise, influence on direction finding performance, and price. Generally, it should not be less than 8 bits

in addition to using I and O channels to save signal amplitude and phase information, digital orthogonal channels can also be used. At this time, only one a/D converter is needed for the output of each receiver, but the sampling frequency should exceed 2 times the signal bandwidth (usually 4 times the signal bandwidth), and then the real and imaginary parts of the signal (Digital Hilbert filter) are formed by digital method. The data receiving part requires the converter to have high sampling accuracy, more effective word length and more sampling times per unit time. This is conducive to capturing sudden and transient signals in space

3.1.4 digital signal processing terminal

the digital signals output by the multi-channel receiver after a/D conversion are sent to the digital signal terminal for processing at the same time, so as to realize the estimation of the number of spatial signals, the direction of signal arrival and other parameters of the signal. The excellent performance of spatial spectrum estimation direction finding method is mainly through the excellent direction finding algorithm and its implementation on the signal processing terminal. Different from the direction finding methods such as amplitude and phase comparison, the direction of arrival of the signal to be measured can be obtained by the spatial spectrum estimation direction finding method through more complex calculations. Therefore, the efficient direction finding algorithm and high-speed digital signal processing terminal with excellent performance have become the core of this direction finding technology. In principle, a general-purpose microcomputer can be used for signal processing terminal. When the direction finding process is required to be real-time or accurate, a high-speed digital signal processor should be used to complete the task of the signal processing terminal

3.2 hardware implementation scheme of spatial spectrum estimation algorithm

modern digital signal processing schemes mostly adopt the hybrid design of FPGA and general DSP, that is, the design scheme of dsp+fpga. FPGA is used to design the coprocessor to deal with a large number of regular calculations, and the flexibility of DSP is used to deal with complex and irregular calculations, so that the performance of the whole system can be optimized

according to the analysis of music algorithm in spatial spectrum estimation direction finding, music algorithm can be divided into: solving covariance matrix, eigendecomposition of covariance matrix and spectral peak search. Among them, solving the covariance matrix is an algorithm that contains a large number of regular calculations, and the calculated data is directly obtained from the output of the A/D converter of the receiver. It can be calculated in fixed-point mode, which is suitable for FPGA implementation. FPGA has the characteristics of programmability and field configuration. It uses the CAD software corresponding to the device to realize various specific functions specified by users, and has high flexibility. Designers can regard it as an array composed of several NAND gates, which are connected in a certain way to achieve specific functions

Jacobian algorithm can be used to realize the characteristic decomposition of covariance matrix. In this algorithm. The dynamic range of data is very large, and the overflow will occur when using fixed-point calculation, and it can not meet the accuracy requirements, so only floating-point calculation can be used; Jacobian algorithm includes not only a large number of multiplication and addition, but also irregular calculations such as square root and division. Therefore, the Jacobian algorithm for feature decomposition should not be implemented by FPGA, but by DSP. DSP is similar to general microprocessor CPU, but it has its characteristics for digital signal processing. It is different from the general microprocessor in that it adopts Harvard structure, and the program and data are stored separately; Adopt a series of measures to ensure the processing speed of digital signals, such as special optimization of FFT. Therefore, the digital signal processing ability of DSP is much better than that of general-purpose microprocessor. At the same time, it also has the characteristics of high flexibility of general-purpose microprocessor system and programmable computing control, which can be applied to all kinds of complex signal processing

therefore, the hardware implementation of music algorithm can be realized by dsp+fpga, that is, the scheme of mixed fixed-point calculation and floating-point calculation. FPGA can solve the covariance matrix by using fixed-point calculation method, and then send the obtained data to DSP, convert its fixed-point to floating-point, and use floating-point calculation method to calculate feature decomposition and spectral peak search

there are two schemes for solving covariance matrix: serial and parallel. Serial scheme is mainly a scheme that takes saving resources as a priority, which can be used in applications that do not have strict requirements for real-time performance; Parallel solution is mainly a solution that gives priority to processing speed, and can be used in applications that require high real-time performance. Figure 4 shows the principle block diagram of the parallel processing scheme

the difference between the parallel scheme and the serial scheme is that the parallel scheme uses multiple parallel multiplication accumulators for calculation. This can effectively improve the processing speed of the whole system. The parallel processing scheme should balance the load of each processor. For the DF system with 8 array elements, it is necessary to calculate the values of 36 elements, so different parallel processing schemes of 2, 3, 4, 6, 12, 18, 36 multiplication accumulators can be selected. Obviously, the more multiply accumulators, the faster the processing speed, but its cost is also high

4 conclusion

based on the composition, working principle, some key technologies and hardware implementation of spatial spectrum estimation direction finding system, this paper introduces the principle of music algorithm based on correlation matrix eigendecomposition and its hardware implementation scheme. Spatial spectrum estimation technology has a good prospect for radar signal reconnaissance and direction finding, and has research value

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