#### Abstract

Insect radar is an important tool for studying the ecological behaviors of insects. Due to the harsh environment, radar is susceptible to interference from ground echoes, which makes it difficult to monitor insects in low altitude. To study the flying insects at low altitude in radar entomology, the research of ultra-wideband (UWB) insect radar based on log-periodic antenna array was proposed. This method uses a conical conformal array to receive signals and an improved multiple signal classification (MUSIC) algorithm to process the signals. This array is capable of monitoring insects of different sizes in the ultra-wideband range, adjusting the angle of the cone tip to change the position and polarization information, and obtaining information on various insects flying at low altitude. The problem of two-dimensional angle of arrival estimation of insect cone conformal array was analyzed by computer simulation, which are low-altitude flying targets with different cone apex angles. In addition, a modified multiple signal classification algorithm was implemented to make the radar search and catch multiple targets faster and more accurate. The algorithm greatly reduces computational complexity while maintaining the accuracy of estimation. There is a linear relationship between the time calculation and the accuracy with the modified algorithm, compared with the relationship between exponential growth and the generalized MUSIC algorithm. Finally, the experimental simulation has proved the superiority of the proposed algorithm.

#### 1. Introduction

Insect radar is a relatively advanced technology for observing insect ecological behavior, and it detects the migration or spread of insects in the air using electromagnetic wave [1, 2]. At present, insect radars are mainly pulse radars, such as scanning radars and vertical beam radars [3]. They use the difference in time between the pulse transceiver switches and can monitor the speed, number, and position of insects over long distance [4–6]. However, there is a detection blind zone at low altitude within 100 meters above the ground. The deficiencies of pulse radar limit the monitoring of low-altitude flying insects. Low altitude is an important activity area for most insects, where they catch food and thrive. Flying insects at low altitude mainly move from the crop canopy above to dozens of meters below [7, 8]. Harmonic radar tracks and detects low-altitude insects by the electronic marking on them and is suitable for larger insects such as Lepidoptera, Hymenoptera, Coleoptera, Orthoptera, and Diptera, but it also has major limitations [9–12]. Doppler radar adopts a dual antenna structure to transmit and receive radar signals with separate technology, which can monitor flying insects at a height of 100 meters or lower [13]. However, this kind of radar has a narrow working frequency band and is difficult to monitor insects of different sizes. As a result, fewer types of insects can be monitored in practical applications.

The ultra-wideband insect radar uses a logarithmic periodic antenna of a circular array [14]. Logarithmic periodic antennas are frequency-independent with ultra-wideband characteristics of the array. Although the logarithmic periodic antenna circular array can adjust the physical aperture of the array, it is limited to the planar array design, which is not conducive to the multidimensional acquisition of target flight speed and direction parameter information by the UWB insect radar. Using multiple signal classification (MUSIC) algorithm to obtain insect location information has a huge amount of calculation, which will take long time, and the real-time performance of the algorithm cannot be realized. Therefore, improvements to the MUSIC algorithm are necessary. The new ultra-wideband insect radar adopts a conical conformal array design, and by adjusting the height of the control lever, a planar array of different diameters and a three-dimensional array can be formed, to achieve rapid low-altitude flight monitoring and azimuth estimation of insects of different sizes on a fixed base.

The major results of the work are summarized as follows:(1)Designed a conical conformal array based on a log-periodic antenna. This array monitors insects of various sizes in the ultra-wideband range by changing the angle of the apex of the cone to transform the position and polarization information of the antenna oscillators. (2)Proposed the improved MUSIC algorithm with adjustable step length for spectral peak search. The algorithm can reduce computation time by adjusting the step size to narrow the peak search, enabling the real-time performance of the algorithm.

#### 2. Principle of Ultra-Wideband Insect Radar

##### 2.1. The Structure of Log-Periodic Antenna

The log-periodic antenna is composed of symmetrical elements arranged in proportion. The upper limit of the working frequency band of log-periodic antenna is determined by the length of the shortest element, and the lower limit is determined by the length of the longest element. The origin of the coordinates is the virtual apex of the element [15]. The schematic diagram is shown in Figure 1.

In a log-periodic antenna structure consisting of *N* arrays, the relationship is as follows:

In the formula, is the distance between the − 1th to the th oscillator, is the length of the th oscillator, and is the linear distance from the th oscillator to the virtual apex *O*. The structure of the log-periodic antenna is determined by the virtual apex *O*, opening angle 2*α* of the structure, and the scale factor *τ*, as shown in Figure 1.

##### 2.2. The Design of Conical Conformal Array

The structure of conical conformal array (Figure 2) mainly consists of log-periodic antennas, control rod, support rod, base, and chute. The apex of the support rod is connected with the logarithmic periodic antennas through the control rod, and the bottom of the support rod is connected with the base. The control rod can adjust the size of the apex angle of the conical conformal array, and the sliding slot can adjust the position of the conical conformal array on the base.

The ultra-wideband insect radar controls the rod of the conical conformal array to adjust the size of the cone apex angle, which can obtain more dimension azimuth information about the target insect. Since the conical conformal array can form a three-dimensional array consisting of a circular array of different diameters on the fixed base, it has the characteristics of small footprint and strong adjustability.

##### 2.3. Mathematical Model of Conical Conformal Array

The circular array of log-periodic antenna is located under the apex of the cone. In Figure 3, the cone is made up of several circular arrays, which contain *n* array elements. The busbar of the cone surface consists of several straight lines distributed along the cone surface. In the three-dimensional coordinate system, the azimuth angle of the signal incident direction is , the pitch angle is , and the apex of the cone conformal array is the origin of the coordinate system [16, 17].

The conical conformal array can be considered as consisting of *Q* circular arrays from the apex downwards. There are *n* elements in each circular array, where *Q* is the sequence number of the circular array from apex to bottom (when , , *d* is the distance between each layer of ring array, is the number of apex angles of the conical conformal array, and *u* is the serial number of the oscillator in each layer of the circular array in anticlockwise order. For the conical conformal array antenna of Figure 3, the coordinates of each element are set in the global rectangular coordinate system, and then, the coordinates of each element are [18]as follows:

It is assumed that *m* far-field broadband signal sources are incident on a conical conformal array composed of *n* array elements, where is the pitch angle of the broadband signal source incident signal and is the azimuth angle of the broadband signal source incident signal, and then, the signal received by the array is [19–21]as follows:

In the formula (3), is the received signal of the *m*th source, is the noise signal, and is the manifold matrix of the array:

In the manifold matrix, is the steering vector of the th source, and the expression is as follows:

In the formula, is the unit pattern of the th signal of the array element in the global coordinate system. is the delay expression between the elements obtained from the geometric relationship. In the conical conformal antenna array, since the orientation of each element is different, the corresponding element pattern is also different, and the element pattern of each element is referenced to the global coordinates of the element. Therefore, in the conical conformal antenna array, the element pattern of the oscillator is transformed into the element pattern of the array.

The conical conformal antenna array uses the Euler rotation transformation to realize the global rotation transformation of the polarization pattern of the oscillator unit, and finally, the following is obtained:

By utilizing the polarization diversity of the conical conformal array, the insect targets are monitored. The conical conformal array can adjust the opening angle of the apex angle of the conical array, to realize the variable distance zoom on the fixed base for more dimensional monitoring targets. In addition, the MUSIC algorithm is needed to estimate the position information of insects.

##### 2.4. MUSIC Algorithm with Adjustable Step Length

In the MUSIC algorithm, the spatial spectrum function is composed of the signal subspace and the noise subspace of the covariance matrix. The orthogonality of two subspaces obtains the parameter information of insect target signals in the two-dimensional direction of arrival (DOA) estimation. According to the target range of the monitored insects, the peak is searched by the formula [13]. The direction of the incident signal is obtained by finding the extreme points of the spatial spectrum function. Among them, the abscissa and ordinate of the maximum point correspond to the azimuth and pitch angle information of the insect target [22, 23], and the spectral peak search formula is as follows:

When the computer realizes the generalized MUSIC, the search step length is set to *J* (0 < *J* < 90), the search azimuth angle range is set to [0°–360°], and the pitch angle range is set to [0°–90°]. The time complexity of the generalized MUSIC algorithm is [24, 25]as follows:

Suppose the number of array elements is *N*, the number of incident signal sources is *M*, the number of buses is *L,* and the number of snapshots is *P*. The amount of calculation for multiplying two complex numbers is (4*m* + 2*a*) (*m* means multiplication and a means addition). The computational complexity of generalized MUSIC algorithm is 90 × 360 × 90 × 360 × ((*N* − *M*) × (*N* + 1) × (4*m* + 4*a*)). The recursive equation analyzes the time complexity of the MUSIC algorithm. The problem can be divided into *k* subproblems using the partition recursive method, while the time spent on calculation is *n*/*m*. Assume that the time spent on the calculation interval of the computer is *τ*. Suppose that it takes *f*(*n*) time intervals to divide the original problem into *k* subproblems and merge the solutions to the *k* subproblems into the original problem. *T*(*n*) represents the time required to work out the problem *n*, so the recursive equation is as follows:

The spectral values obtained from the accurate estimation of the arrival direction are related to the step size at the modified search stage. To obtain the better effect of real-time search and improve the accuracy of search step size, the MUSIC algorithm with freely adjustable step size search (adjustable step size MUSIC algorithm) is proposed. The position where the search signal is located can be known by setting the searching area of the target, selecting the range, determining the steps for searching target, and roughly searching for all but one limit value. If the accuracy of calculating at this level does not fully meet the requirements of the superior, the angle near the accuracy peak based on the results of this level will continue to be searched till the peak is found. That is to search for the specific direction of a step till it fully meets the requirements for search accuracy of DOA estimation. Through such a precise and adjustable linear search, we can effectively avoid unnecessary precision in the linear search algorithm, while low precision is related to high calculation precision. Due to the high accuracy, the linear search can meet the angle requirements in different arrival directions at the same time, which greatly shortens the execution time of angle operation using spatial spectral peak linear search and ensures the angle accuracy of spatial filter evaluation algorithm and other angle value evaluation algorithms. Thus, the spatial spectral peak linear search can greatly shorten the execution time of angle operation and guarantee the angle accuracy of spatial filter evaluation algorithm and the accuracy of other angle value evaluation algorithms.

*Step 1. *Suppose that a signal’s pitch angle is 0∼90°, the range of the azimuth pitch angle can be defined as 0∼360°, and the search step is , and let and , so the spectral function is defined as the matrix:The minimum value in the local search matrix *G*_{1} × *K*_{1} is found. It is judged whether the obtained azimuth and pitch angles meet the required accuracy requirements. If the angle accuracy is obtained, the final value will be output. If the output angle accuracy needs to be less accurate, step 2is proceeded.

*Step 2. *According to step 1, the output azimuth and pitch angle degrees are , the search step is , let and , and the spectral function is matrix :The minimum value in the local search matrix *G*_{2} × *K*_{2} is found. It is judged whether the obtained azimuth and pitch angles meet the required accuracy requirements. If the angle accuracy is obtained, the final value will be output. If the output angle accuracy needs to be less accurate, the operation of step 2 is repeated. Among them, . The flow chart of the proposed algorithm is shown in Figure 4.

#### 3. Simulation Analysis

The simulation experiment system is built on the Windows 10 professional edition system, and the programming platform is MATLAB R2019b. The receiving antenna adopts a 12-element × 8-element conical conformal array, the distance between the array elements is , the central operating frequency of the antenna is 10.5 GHz, sampling number is 1024, and sampling rate is 0.02 GHz. The Gaussian noise signal with average value of 0 and standard deviation of 1 is randomly generated by MATLAB software and then radar signals are simulated in MATLAB software.(1)Suppose the azimuth and pitch angles of the insects within the radar monitoring range are (100°, 30°), the signal-to-noise ratio (SNR) is 25 dB, and the apex angles of the conical conformal array are set to 30°, 92°, 105°, and 160°. The insect parameter information is substituted into MATLAB software to simulate the signal, obtaining the target spatial location information by the MUSIC algorithm, as shown in Figure 5. The signal-to-noise ratio of the above results is 25 dB: when the apex angle of the conical conformal array is 30°, multiple signal peaks appear in the two-dimensional MUSIC spectrum, and the monitoring effect is poor. When the apex angle of the conical conformal array is 105°, the insect target is submerged in the noise signal, and the insect target signal cannot be distinguished. When the apex angle of the conical conformal array is 92°, there are fewer false peaks in the MUSIC spectrum, and the signal monitoring effect of insect target is better. When the apex angle of the conical conformal array is 160°, the signal peak is obvious in the MUSIC spectrum, and the insect target information can be monitored easily.(2)Suppose the azimuth and pitch angles of the insects within the radar monitoring range are (212°, 65°), and the other parameter settings are the same as in simulation experiment 1. The insect parameter information is substituted into MATLAB software to simulate the signal and is searched according to the MUSIC algorithm to obtain the spatial information about. The apex angle of cone conformal array in experiment 2 is the same as in experiment 1, to compare the influence of a different azimuth and pitch angle on the monitoring target. In Figure 6, when the apex angle of the conical conformal array is 92°, the monitoring effect is poor. When the apex angle of the conical conformal array is 105°, the noise signal is too high to distinguish the target signal. When the apex angles of the conical conformal array are 30° and 160°, the signal peak in the two-dimensional MUSIC spectrum is obvious, so the insect target signal can be monitored. Comparing experiment 1 with experiment 2, when the number of apex angles of the conical conformal array is the same, the monitoring effects are different for incident signals of different azimuth and pitch angles. Therefore, the conical conformal array can monitor different insect targets in more dimensions by adjusting the apex angle of the conical array.(3)Suppose there are two insects with very close azimuth and pitch angles within the radar monitoring range are (108.56°, 31.22°) and (108.86°, 31.52°), and the other parameter settings are the same as in simulation experiment 1. The insect parameter information is substituted into MATLAB software to simulate the signal and is searched according to the MUSIC algorithm with adjustable step length to obtain the spatial information about. Suppose the search step length is *L*. The algorithm search results are shown in Figure 7. Suppose the two insects have closer azimuth and pitch angles within the radar monitoring range are (108.512°, 31.242°) and (108.515°, 31.245°) and further is searched according to the MUSIC algorithm with adjustable step length to obtain the spatial information about insect. The algorithm search results are shown in Figure 8. The algorithm will iterate continuously according to the distance between the two targets until the two targets are clearly distinguished or until it is difficult to distinguish them. The experiment 3 shows the high accuracy of the adjustable step length MUSIC algorithm, even if the azimuth and pitch angles of the two targets differ by only 0.001°. When the distance between the two targets is less than 0.001, the signal peak is not obvious. The algorithm can effectively distinguish multiple targets with a difference in azimuth and pitch angle of about 0.001.(4)Under different signal-to-noise ratios, simulation experiments are performed on insects flying at low altitudes with azimuth and pitch angles within the radar monitoring range. According to experiment 1 and experiment 2, when the apex angle of the conical conformal array is 160°, both the azimuth angle and the pitch angle have achieved better monitoring results. Therefore, the azimuth angles are 100° and 212°, the pitch angles are 30° and 65°, and the apex angle of the conical conformal array is 160°. The signal-to-noise ratio is simulated in the range of −18 dB to 28 dB. The results are shown in Figure 9: when the SNR is higher, the simulation effect of the conical conformal array is better. When SNR is 8 dB, the RMSE of the azimuth angle and the pitch angle is gradually approaching 0. The results show that the conical conformal array has very stable monitoring effect when the SNR is higher; however, it also has a relatively stable monitoring effect when the SNR is lower.(5)In the simulation, simulation conditions are set as the same for experiment 4 except for the change in SNR, and the SNR ratio is simulated from −10 dB to 20 dB. Figure 10 shows the root-mean-square error (RMSE) of the pitch angle estimation of the generalized MUSIC, the steering vector synthesis reduced dimension (SVS-RD) MUSIC algorithm [26] and the MUSIC algorithm with adjustable step length (ASL-MUSIC). It can be seen from Figure 10 that the estimation results of the ASL-MUSIC algorithm are superior to those of the SVS-RD-MUSIC algorithm and generalized MUSIC at low SNR. When SNR is equal to 10 dB, the RMSE of the three algorithms is approximately equal. When SNR is greater than 10 dB, the RMSE of the ASL-MUSIC algorithm will be lower than the generalized MUSIC algorithm, but slightly greater than the SVS-RD algorithm value. However, there exists a trend that with the increase in SNR, there is a convergence between the RMSE of ASL-MUSIC algorithm and the RMSE of SVS-RD-MUSIC algorithm, which shows the superiority of the ASL-MUSIC algorithm.(6)According to the simulation situation of experiment 1 and experiment 2, assuming that the azimuth and pitch angles of the insects within the radar monitoring range are (212°, 65°), the SNR is 25 dB, and the apex angles of the conical conformal array are set to 160°. The insect parameter information is substituted into MATLAB software to simulate the signal. The insect target search algorithm uses the generalized MUSIC algorithm and the MUSIC algorithm with adjustable step length, respectively.

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Table 1 lists the running time of the two algorithms in 100 random experiments under different accuracy conditions. In addition, Figure 11 displays the running time of the generalized MUSIC algorithm compared with the MUSIC algorithm with adjustable step length. The running time of the generalized MUSIC algorithm increases exponentially as the accuracy requirements increase. The running time of the MUSIC algorithm with adjustable step length does not increase significantly with the increase in accuracy requirements. The time complexity of the improved algorithm is greatly reduced, and it has better real-time performance. At the same time, the multiple target signals can be obtained for different accuracy requirements.

#### 4. Conclusion

The research on the ultra-wideband insect radar monitoring method based on the conical conformal array has the following characteristics:(1)The conical conformal array forms a planar array and a three-dimensional array of different diameters by adjusting the height of the control rod. It has the characteristics of small footprint and high adjustability.(2)The conical conformal array is compatible with the advantages of the log-periodic antenna array. Under the condition of appropriate signal-to-noise ratio, the angular resolution of the antenna array is more accurate by adjusting the physical aperture of the conical conformal array.(3)The conical conformal array introduces polarization information parameters, improves the corresponding ultra-wideband signal spatial spectrum estimation algorithm, and obtains target information on insect. The advantages of MUSIC algorithm with adjustable step length can be listed as follows:(1)The improved algorithm owns much lower time complexity than the generalized MUSIC algorithm.(2)The improved algorithm reduces the search time and gives different precision DOA estimations according to the demand.(3)The improved algorithm can effectively distinguish multiple targets with a difference in azimuth and pitch angle of about 0.001.

By adjusting the apex on a conical conformal array, the monitoring of low-altitude flying targets has been simulated. In the case of the corresponding signal-to-noise ratio, the monitoring of the insect target signal is improved by adjusting the cone apex angle. The improved MUSIC algorithm with adjustable step length greatly shortens the search time, and the results for simulation prove the correctness of the theory. The improved MUSIC algorithm with adjustable step length used in the study shows the advantages of homologous signal resolution, enabling rapid monitoring of multiple targets, rather than single target.

#### Data Availability

The relevant data are already in the article.

#### Conflicts of Interest

The authors declare that they have no conflicts of interest.

#### Acknowledgments

This work was supported by the National Natural Science Foundation of China under grant no. 31860500.