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Keywords = sum and difference co-array

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16 pages, 668 KiB  
Article
Noncircular Distributed Source DOA Estimation with Nested Arrays via Reduced-Dimension MUSIC
by Kaiyuan Chen, Weiyang Chen and Jiaqi Li
Sensors 2024, 24(20), 6653; https://doi.org/10.3390/s24206653 - 15 Oct 2024
Viewed by 603
Abstract
This paper focuses on the direction-of-arrival (DOA) estimation for noncircular coherently distributed (CD) sources with nested arrays. Usually, for point sources, sparse arrays have the potential to improve the estimation performance of algorithms by obtaining more degrees of freedom. However, algorithms have to [...] Read more.
This paper focuses on the direction-of-arrival (DOA) estimation for noncircular coherently distributed (CD) sources with nested arrays. Usually, for point sources, sparse arrays have the potential to improve the estimation performance of algorithms by obtaining more degrees of freedom. However, algorithms have to be reconsidered for CD sources with sparse arrays and many problems arise. One thorny problem is the disappearance of displacement invariance of the virtual array manifold constructed by the virtualization technique. To deal with this issue, a nested array processing method for CD sources transmitting noncircular signals is proposed in this paper. Firstly, we construct the virtual sum-and-difference co-array by leveraging the noncircular quality of signals with a nested array. Then, an approximation is made to degrade CD sources into point sources. In this way, spatial smoothing techniques can be applied to restore the rank. Finally, in order to reduce the complexity, we modify the reduced-dimension MUSIC to estimate DOAs through a one-dimensional peak-searching procedure. The simulation results prove the superiority of our algorithm against other competitors. Full article
(This article belongs to the Section Sensor Networks)
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17 pages, 4165 KiB  
Article
Development and Validation of Low-Cost Indoor Air Quality Monitoring System for Swine Buildings
by Elanchezhian Arulmozhi, Anil Bhujel, Nibas Chandra Deb, Niraj Tamrakar, Myeong Yong Kang, Junghoo Kook, Dae Yeong Kang, Eun Wan Seo and Hyeon Tae Kim
Sensors 2024, 24(11), 3468; https://doi.org/10.3390/s24113468 - 28 May 2024
Viewed by 1183
Abstract
The optimal indoor environment is associated with comfortable temperatures along with favorable indoor air quality. One of the air pollutants, particulate matter (PM), is potentially harmful to animals and humans. Most farms have monitoring systems to identify other hazardous gases rather than PM [...] Read more.
The optimal indoor environment is associated with comfortable temperatures along with favorable indoor air quality. One of the air pollutants, particulate matter (PM), is potentially harmful to animals and humans. Most farms have monitoring systems to identify other hazardous gases rather than PM due to the sensor cost. In recent decades, the application of environmental monitoring systems based on Internet of Things (IoT) devices that incorporate low-cost sensors has elevated extensively. The current study develops a low-cost air quality monitoring system for swine buildings based on Raspberry Pi single-board computers along with a sensor array. The system collects data using 11 types of environmental variables along with temperature, humidity, CO2, light, pressure, and different types of gases, namely PM1, PM2.5, and PM10. The system is designed with a central web server that provides real-time data visualization and data availability through the Internet. It was tested in actual pig barns to ensure stability and functionality. In addition, there was a collocation test conducted by placing the system in two different pig barns to validate the sensor data. The Wilcoxon rank sum test demonstrates that there are no significant differences between the two sensor datasets, as all variables have a p-value greater than 0.05. However, except for carbon monoxide (CO), none of the variables exhibit correlation exceeding 0.5 with PM concentrations. Overall, a scalable, portable, non-complex, low-cost air quality monitoring system was successfully developed within a cost of USD 94. Full article
(This article belongs to the Section Environmental Sensing)
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12 pages, 951 KiB  
Communication
A Nested–Nested Sparse Array Specially for Monostatic Colocated MIMO Radar with Increased Degree of Freedom
by Ye Chen, Meng Yang, Jianfeng Li and Xiaofei Zhang
Sensors 2023, 23(22), 9230; https://doi.org/10.3390/s23229230 - 16 Nov 2023
Cited by 3 | Viewed by 869
Abstract
This paper mainly investigates the problem of direction of arrival (DOA) estimation for a monostatic MIMO radar. Specifically, the proposed array, which is called a nested–nested sparse array (NNSA), is structurally composed of two nested subarrays, a NA with [...] Read more.
This paper mainly investigates the problem of direction of arrival (DOA) estimation for a monostatic MIMO radar. Specifically, the proposed array, which is called a nested–nested sparse array (NNSA), is structurally composed of two nested subarrays, a NA with N1+N2 elements and a sparse NA, respectively, with N3+N4 elements. The design process of NNSA is optimized into two steps and presented in detail. Setting NNSA as transmitter/receiver arrays, we derive the closed-form expression of consecutive DOFs and calculate the mutual coupling coefficient. Eventually, extensive simulations are carried out and the results verify the superiority of the proposed array over the previous arrays in terms of consecutive DOFs, array aperture and mutual coupling effect. Full article
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16 pages, 554 KiB  
Article
Non-Circular Signal DOA Estimation with Nested Array via Off-Grid Sparse Bayesian Learning
by Xudong Dong, Jun Zhao, Meng Sun and Xiaofei Zhang
Sensors 2023, 23(21), 8907; https://doi.org/10.3390/s23218907 - 1 Nov 2023
Cited by 2 | Viewed by 1236
Abstract
For the traditional uniform linear array (ULA) direction of arrival (DOA) estimation method with a limited array aperture, a non-circular signal off-grid sparse Bayesian DOA estimation method based on nested arrays is proposed. Firstly, the extended matrix of the received data is constructed [...] Read more.
For the traditional uniform linear array (ULA) direction of arrival (DOA) estimation method with a limited array aperture, a non-circular signal off-grid sparse Bayesian DOA estimation method based on nested arrays is proposed. Firstly, the extended matrix of the received data is constructed by taking advantage of the fact that the statistical properties of non-circular signals are not rotationally invariant. Secondly, we use the difference and sum co-arrays for the nested array technique, thus increasing the array aperture and improving the estimation accuracy. Finally, we take the noise as part of the interest signal and iteratively update the grid points using the sparse Bayesian learning (SBL) method to eliminate the modeling errors caused by off-grid gaps. The simulation results show that the proposed algorithm can improve the accuracy of DOA estimation compared with the existing algorithms. Full article
(This article belongs to the Section Communications)
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21 pages, 2487 KiB  
Article
Direction of Arrival Estimation of Generalized Nested Array via Difference–Sum Co-Array
by Yule Zhang, Guoping Hu, Hao Zhou, Juan Bai, Chenghong Zhan and Shuhan Guo
Sensors 2023, 23(2), 906; https://doi.org/10.3390/s23020906 - 12 Jan 2023
Cited by 2 | Viewed by 1553
Abstract
To address the weakness that the difference co-array (DCA) only enhances the degrees of freedom (DOFs) to a limited extent, a new configuration called the generalized nested array via difference–sum co-array (GNA-DSCA) is proposed for direction of arrival (DOA) estimation. We consider both [...] Read more.
To address the weakness that the difference co-array (DCA) only enhances the degrees of freedom (DOFs) to a limited extent, a new configuration called the generalized nested array via difference–sum co-array (GNA-DSCA) is proposed for direction of arrival (DOA) estimation. We consider both the temporal and spatial information of the array output to construct the DSCA model, based on which the DCA and sum co-array (SCA) of the GNA are systematically analyzed. The closed-form expression of the DOFs for the GNA-DSCA is derived under the determined dilation factors. The optimal results show that the GNA-DSCA has a more flexible configuration and more DOFs than the GNA-DCA. Moreover, the larger dilation factors yield significantly wider virtual aperture, which indicates that it is more attractive than the reported DSCA-based sparse arrays. Finally, a hole-filling strategy based on atomic norm minimization (ANM) is utilized to overcome the degradation of the estimation performance due to the non-uniform virtual array, thus achieving accurate DOA estimation. The simulation results verify the superiority of the proposed configuration in terms of virtual array properties and estimation performance. Full article
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14 pages, 2651 KiB  
Article
k-Level Extended Sparse Array Design for Direction-of-Arrival Estimation
by Pinjiao Zhao, Qisong Wu, Na Wu, Guobing Hu and Liwei Wang
Electronics 2022, 11(23), 3911; https://doi.org/10.3390/electronics11233911 - 26 Nov 2022
Viewed by 1392
Abstract
Sparse arrays based on the concept of a sum-difference coarray (SDCA) have increased degrees of freedom and enlarged effective array aperture compared to those only considering a difference coarray. Nevertheless, there still exist a number of overlapping virtual sensors between the difference coarray [...] Read more.
Sparse arrays based on the concept of a sum-difference coarray (SDCA) have increased degrees of freedom and enlarged effective array aperture compared to those only considering a difference coarray. Nevertheless, there still exist a number of overlapping virtual sensors between the difference coarray and the sum coarray, yielding high coarray redundancy. In this paper, we propose a k-level extended sparse array configuration consisting of one sparse subarray with k-level expansion and one uniform linear subarray. By systematically analyzing the inherent structure of the k-level extended sparse array, the closed-form expressions for sensor locations, uniform DOF and coarray redundancy ratio (CARR) are derived. Moreover, with the utilization of a k-level extended strategy, the proposed array remains a hole-free property and achieves low coarray redundancy. According to the proposed sparse array, the spatial and temporal information of the incident sources are jointly exploited for underdetermined direction-of-arrival estimation. The theoretical propositions are proven and numerical simulations are performed to demonstrate the superior performance of the proposed array. Full article
(This article belongs to the Special Issue Recent Advances and Applications of Array Signal Processing)
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21 pages, 530 KiB  
Article
Sparsity-Based Two-Dimensional DOA Estimation for Co-Prime Planar Array via Enhanced Matrix Completion
by Donghe Liu, Yongbo Zhao and Tingxiao Zhang
Remote Sens. 2022, 14(19), 4690; https://doi.org/10.3390/rs14194690 - 20 Sep 2022
Cited by 5 | Viewed by 1818
Abstract
In this paper, the two-dimensional (2-D) direction-of-arrival (DOA) estimation problem is explored for the sum-difference co-array (SDCA) generated by the virtual aperture expansion of co-prime planar arrays (CPPA). Since the SDCA has holes, this usually causes the maximum virtual aperture of CPPA to [...] Read more.
In this paper, the two-dimensional (2-D) direction-of-arrival (DOA) estimation problem is explored for the sum-difference co-array (SDCA) generated by the virtual aperture expansion of co-prime planar arrays (CPPA). Since the SDCA has holes, this usually causes the maximum virtual aperture of CPPA to be unavailable. To address this issue, we propose a complex-valued, sparse matrix recovery-based 2-D DOA estimation algorithm for CPPA via enhanced matrix completion. First, we extract the difference co-arrays (DCA) from SDCA and construct the co-array interpolation model via nuclear norm minimization to initialize the virtual uniform rectangular array (URA) that does not contain the entire rows and columns of holes. Then, we utilize the shift-invariance structure of the virtual URA to construct the enhanced matrix with a two-fold Hankel structure to fill the remaining empty elements. More importantly, we apply the alternating direction method of the multipliers (ADMM) framework to solve the enhanced matrix completion model. To reduce the computational complexity of the traditional vector-form, sparse recovery algorithm caused by the Kronecker product operation between dictionary matrices, we derive a complex-valued sparse matrix-recovery model based on the fast iterative shrinkage-thresholding (FISTA) method. Finally, simulation results demonstrate the effectiveness of the proposed algorithm. Full article
(This article belongs to the Special Issue Radar High-Speed Target Detection, Tracking, Imaging and Recognition)
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20 pages, 5498 KiB  
Article
Two-Stage Nested Array Direction of Arrival Estimation for Mixed Signals
by Wanru Li and Ke Deng
Sensors 2022, 22(14), 5435; https://doi.org/10.3390/s22145435 - 21 Jul 2022
Viewed by 1420
Abstract
In this paper, a novel two-stage subspace-based direction of arrival (DOA) estimation algorithm with the nested array is proposed for mixed signals containing circular and non-circular ones. By exploiting the difference between the two types of steering vectors, the DOAs of circular signals [...] Read more.
In this paper, a novel two-stage subspace-based direction of arrival (DOA) estimation algorithm with the nested array is proposed for mixed signals containing circular and non-circular ones. By exploiting the difference between the two types of steering vectors, the DOAs of circular signals are estimated in the first stage. After eliminating the estimated information of circular signals by the covariance matrix reconstruction and oblique projection methods, the dimensions of the noise subspace are increased in estimating the DOAs of non-circular signals in the second stage. Through the two-stage estimation, the DOAs of the circular and non-circular signals are estimated separately and different types of signals with similar or the same DOAs can be distinguished. Furthermore, to avoid the two-dimensional (2-D) search with huge computational burden, a one-dimensional (1-D) search method exploiting the rank deficiency is proposed in the DOA estimation for non-circular signals. The simulation results show that the proposed algorithm can effectively improve the estimation accuracy and resolution probability, especially when circular and non-circular signals have similar DOAs. Full article
(This article belongs to the Section Electronic Sensors)
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19 pages, 1236 KiB  
Article
Coprime Transformed Nested Array with Enhanced DOFs and Reduced Mutual Coupling Based on the Difference and Sum Coarray
by Junchi Ma, Shunan Zhong, Zhe Peng, Wei Gao, Weijiang Wang and Xiaohua Wang
Electronics 2022, 11(5), 823; https://doi.org/10.3390/electronics11050823 - 6 Mar 2022
Cited by 1 | Viewed by 1662
Abstract
Recently, the concept of the difference and sum coarray has attracted increasing interest in the direction of the arrival estimation field because it can generate enhanced degrees of freedom. In this paper, we propose an improved transformed nested array design strategy by relaxing [...] Read more.
Recently, the concept of the difference and sum coarray has attracted increasing interest in the direction of the arrival estimation field because it can generate enhanced degrees of freedom. In this paper, we propose an improved transformed nested array design strategy by relaxing the constraints on the dense subarray of the transformed nested array. Then, three conditions are given for the array design to ensure the continuity of the difference and sum coarray. Based on the strategy, we develop a novel nested configuration named coprime transformed nested array (CTNA) whose dense subarray is a coprime structure, and the closed-form expressions for the sensor positions and the range of consecutive coarray are derived. CTNA can increase the number of degrees of freedom (DOFs) compared to the existing nested arrays, while the mutual coupling effect can be maintained at the same low level as the coprime arrays, which indicates that CTNA has the merits of both nested array and coprime array. Numerical simulations are performed to verify the superiority of the proposed array configuration in terms of the number of DOFs, mutual coupling and direction of arrival (DOA) estimation accuracy. Full article
(This article belongs to the Section Circuit and Signal Processing)
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15 pages, 4775 KiB  
Article
Co-Expression of Nogo-A in Dopaminergic Neurons of the Human Substantia Nigra Pars Compacta Is Reduced in Parkinson’s Disease
by Gian-Carlo Eyer, Stefano Di Santo, Ekkehard Hewer, Lukas Andereggen, Stefanie Seiler and Hans Rudolf Widmer
Cells 2021, 10(12), 3368; https://doi.org/10.3390/cells10123368 - 30 Nov 2021
Cited by 5 | Viewed by 2552
Abstract
Parkinson’s disease is mainly characterized by a progressive loss of dopaminergic neurons in the substantia nigra pars compacta. Together with the small number, the high vulnerability of the dopaminergic neurons is a major pathogenic culprit of Parkinson’s disease. Our previous findings of a [...] Read more.
Parkinson’s disease is mainly characterized by a progressive loss of dopaminergic neurons in the substantia nigra pars compacta. Together with the small number, the high vulnerability of the dopaminergic neurons is a major pathogenic culprit of Parkinson’s disease. Our previous findings of a higher survival of dopaminergic neurons in the substantia nigra co-expressing Nogo-A in an animal model of Parkinson’s disease suggested that Nogo-A may be associated with dopaminergic neurons resilience against Parkinson’s disease neurodegeneration. In the present study, we have addressed the expression of Nogo-A in the dopaminergic neurons in the substantia nigra in postmortem specimens of diseased and non-diseased subjects of different ages. For this purpose, in a collaborative effort we developed a tissue micro array (TMA) that allows for simultaneous staining of many samples in a single run. Interestingly, and in contrast to the observations gathered during normal aging and in the animal model of Parkinson’s disease, increasing age was significantly associated with a lower co-expression of Nogo-A in nigral dopaminergic neurons of patients with Parkinson’s disease. In sum, while Nogo-A expression in dopaminergic neurons is higher with increasing age, the opposite is the case in Parkinson’s disease. These observations suggest that Nogo-A might play a substantial role in the vulnerability of dopaminergic neurons in Parkinson’s disease. Full article
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14 pages, 737 KiB  
Article
A Systolic Accelerator for Neuromorphic Visual Recognition
by Shuo Tian, Lei Wang, Shi Xu, Shasha Guo, Zhijie Yang, Jianfeng Zhang and Weixia Xu
Electronics 2020, 9(10), 1690; https://doi.org/10.3390/electronics9101690 - 15 Oct 2020
Cited by 1 | Viewed by 2112
Abstract
Advances in neuroscience have encouraged researchers to focus on developing computational models that behave like the human brain. HMAX is one of the potential biologically inspired models that mimic the primate visual cortex’s functions and structures. HMAX has shown its effectiveness and versatility [...] Read more.
Advances in neuroscience have encouraged researchers to focus on developing computational models that behave like the human brain. HMAX is one of the potential biologically inspired models that mimic the primate visual cortex’s functions and structures. HMAX has shown its effectiveness and versatility in multi-class object recognition with a simple computational structure. It is still a challenge to implement the HMAX model in embedded systems due to the heaviest computational S2 phase of HMAX. Previous implementations such as CoRe16 have used a reconfigurable two-dimensional processing element (PE) array to speed up the S2 layer for HMAX. However, the adder tree mechanism in CoRe16 used to produce output pixels by accumulating partial sums in different PEs increases the runtime for HMAX. To speed up the execution process of the S2 layer in HMAX, in this paper, we propose SAFA (systolic accelerator for HMAX), a systolic-array based architecture to compute and accelerate the S2 stage of HMAX. Using the output stationary (OS) dataflow, each PE in SAFA not only calculates the output pixel independently without additional accumulation of partial sums in multiple PEs, but also reduces the multiplexers applied in reconfigurable accelerators. Besides, data forwarding for the same input or weight data in OS reduces the memory bandwidth requirements. The simulation results show that the runtime of the heaviest computational S2 stage in HMAX model is decreased by 5.7%, and the bandwidth required for memory is reduced by 3.53 × on average by different kernel sizes (except for kernel = 12) compared with CoRe16. SAFA also obtains lower power and area costs than other reconfigurable accelerators from synthesis on ASIC. Full article
(This article belongs to the Section Computer Science & Engineering)
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25 pages, 1384 KiB  
Article
Improved 2D Coprime Array Structure with the Difference and Sum Coarray Concept
by Guiyu Wang, Zesong Fei, Shiwei Ren and Xiaoran Li
Electronics 2020, 9(2), 273; https://doi.org/10.3390/electronics9020273 - 5 Feb 2020
Cited by 3 | Viewed by 2778
Abstract
Recently, the difference and sum (diff-sum) coarray has attracted much attention in one-dimensional direction-of-arrival estimation for its high degrees-of-freedom (DOFs). In this paper, we utilize both the spatial information and the temporal information to construct the diff-sum coarray for planar sparse arrays. The [...] Read more.
Recently, the difference and sum (diff-sum) coarray has attracted much attention in one-dimensional direction-of-arrival estimation for its high degrees-of-freedom (DOFs). In this paper, we utilize both the spatial information and the temporal information to construct the diff-sum coarray for planar sparse arrays. The diff-sum coarray contains both the difference coarray and the sum coarray, which provides much higher DOFs than the difference coarray alone. We take a planar coprime array consisting of two uniform square subarrays as the array model. To fully use the aperture-extending ability of the diff-sum coarray, we propose two novel configurations to improve the planar coprime array. The first configuration compresses the inter-element spacing of one subarray and results in a larger consecutive area in the coarray. The second configuration rearranges the two subarrays and introduces a proper separation between them, which can significantly reduce the redundancy of the diff-sum coarray and increase the DOFs. Besides, we derive the closed-form expressions of the central consecutive ranges in the coarrays of the proposed array configurations. Simulations verify the superiority of the proposed array configurations. Full article
(This article belongs to the Special Issue Theory and Applications in Digital Signal Processing)
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17 pages, 2245 KiB  
Article
Design of Novel Nested Arrays Based on the Concept of Sum-Difference Coarray
by Weijian Si, Zhanli Peng, Changbo Hou and Fuhong Zeng
Electronics 2020, 9(1), 115; https://doi.org/10.3390/electronics9010115 - 7 Jan 2020
Cited by 2 | Viewed by 2874
Abstract
Nested arrays have recently attracted considerable attention in the field of direction of arrival (DOA) estimation owing to the hole-free property of their virtual arrays. However, such virtual arrays are confined to difference coarrays as only spatial information of the received signals is [...] Read more.
Nested arrays have recently attracted considerable attention in the field of direction of arrival (DOA) estimation owing to the hole-free property of their virtual arrays. However, such virtual arrays are confined to difference coarrays as only spatial information of the received signals is exploited. By exploiting the spatial and temporal information jointly, four kinds of novel nested arrays based on the sum-difference coarray (SDCA) concept are proposed. To increase the degrees of freedom (DOFs) of SDCA, a modified translational nested array (MTNA) is introduced first. Then, by analyzing the relationship among sensors in MTNA, we give the specific positions of redundant sensors and remove them later. Finally, we derive the closed-form expressions for the proposed arrays as well as their SDCAs. Meanwhile, different index sets corresponding to the proposed arrays are also designed for their use in obtaining the desirable SDCAs. Moreover, the properties regarding DOFs of SDCAs and physical apertures for the proposed arrays are analyzed, which prove that both the DOFs and physical apertures are improved. Simulation results are provided to verify the superiority of the proposed arrays. Full article
(This article belongs to the Special Issue Recent Advances in Array Antenna and Array Signal Processing)
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14 pages, 410 KiB  
Article
A MIMO Radar-Based DOA Estimation Structure Using Compressive Measurements
by Tao Chen, Jian Yang and Muran Guo
Sensors 2019, 19(21), 4706; https://doi.org/10.3390/s19214706 - 29 Oct 2019
Cited by 11 | Viewed by 3437
Abstract
In this paper, we propose a novel direction-of-arrival (DOA) estimation structure based on multiple-input multiple-output (MIMO) radar with colocated antennas, referred to as compressive measurement-based MIMO (CM-MIMO) radar, where the compressive sensing (CS) is employed to reduce the number of channels. Therefore, the [...] Read more.
In this paper, we propose a novel direction-of-arrival (DOA) estimation structure based on multiple-input multiple-output (MIMO) radar with colocated antennas, referred to as compressive measurement-based MIMO (CM-MIMO) radar, where the compressive sensing (CS) is employed to reduce the number of channels. Therefore, the system complexity and the computational burden are effectively reduced. It is noted that CS is used after the matched filters and that a measurement matrix with less rows than columns is multiplied with the received signals. As a result, the configurations of the transmit and receive antenna arrays are not affected by the CS and can be determined according to the practical requirements. To study the estimation performance, the Cramér–Rao bound (CRB) with respect to the DOAs of the proposed CM-MIMO radar is analyzed in this paper. The derived CRB expression is also suitable for the conventional MIMO radar by setting the measurement matrix as an identity matrix. Moreover, the CRB expression can work in the under-determined case, since the sum-difference coarray structure is considered. However, the random measurement matrix leads to high information loss, thus compromising the estimation performance. To overcome this problem, we consider that the a prior probability distribution of the DOAs associated with the targets can be obtained in many scenarios and an optimization approach for the measurement matrix is proposed in this paper, where the maximum mutual information criterion is adopted. The superiority of the proposed structure is validated by numerical simulations. Full article
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17 pages, 1555 KiB  
Article
A Novel Nested Configuration Based on the Difference and Sum Co-Array Concept
by Zhenhong Chen, Yingtao Ding, Shiwei Ren and Zhiming Chen
Sensors 2018, 18(9), 2988; https://doi.org/10.3390/s18092988 - 7 Sep 2018
Cited by 31 | Viewed by 3433
Abstract
Recently, the concept of the difference and sum co-array (DSCa) has attracted much attention in array signal processing due to its high degree of freedom (DOF). In this paper, the DSCa of the nested array (NA) is analyzed and then an improved nested [...] Read more.
Recently, the concept of the difference and sum co-array (DSCa) has attracted much attention in array signal processing due to its high degree of freedom (DOF). In this paper, the DSCa of the nested array (NA) is analyzed and then an improved nested configuration known as the diff-sum nested array (DsNA) is proposed. We find and prove that the sum set for the NA contains all the elements in the difference set. Thus, there exists the dual characteristic between the two sets, i.e., for the difference result between any two sensor locations of the NA, one equivalent non-negative/non-positive sum result of two other sensor locations can always be found. In order to reduce the redundancy for further DOF enhancement, we develop a new DsNA configuration by moving nearly half the dense sensors of the NA to the right side of the sparse uniform linear array (ULA) part. These moved sensors together with the original sparse ULA form an extended sparse ULA. For analysis, we provide the closed form expressions of the DsNA locations as well as the DOF. Compared with some novel sparse arrays with large aperture such as the NA, coprime array and augmented nested array, the DsNA can achieve a higher number of DOF. The effectiveness of the proposed array is proved by the simulations. Full article
(This article belongs to the Section Physical Sensors)
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