Design of a Grating Lobes-Free Architecture for Distributed Sensor System with Arbitrary Element Spacing

Two main difficulties for the accurate direction of arrival (DOA) estimation in a distributed sensor system are grating lobes and system synchronization. Different from the traditional phased array system based on single carrier frequency, this paper designs a novel architecture for distributed sensor system using dual carrier frequency measurements. Both two carrier frequencies are combined and transmitted simultaneously in the proposed architecture. Instead of single carrier frequency $f_1$ in the traditional method, the frequency separation $f_2-f_1$ is used in the proposed algorithm to determine a maximum unambiguous DOA estimate. Since $f_2-f_1$ is much less than $f_1$ and the choice of $f_2-f_1$ is more flexible, the proposed method can provide an unambiguous DOA estimate in the whole field of view (FOV) for arbitrary element spacing and a looser requirement on system synchronization than the traditional method based on single carrier frequency. For a case with $f_1=3$ Ghz, $f_2-f_1=150$ Mhz and 10 times element spacing, there is no grating lobe for the proposed method in the whole FOV $[-\pi /2,\pi /2]$, whereas the traditional method has many grating lobes and the FOV of the traditional method without grating lobes is only ${5.73}^{\circ }$. To obtain the same combining efficiency in this case, the requirement on the positioning error of the proposed method is 0.4 m and the location error of the traditional method must be smaller than 0.02 m. Hence, the proposed method can greatly reduce hardware requirements. The performances of the proposed architecture for the cases with perfect and imperfect system synchronizations are evaluated in terms of the average beampattern and combining efficiency, respectively. Some characteristics of the derived beampattern and combining efficiency are also presented in the paper.