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.

The localization of sensors in wireless sensor networks has recently gained considerable attention. The existing location methods are based on a one-spot measurement model. It is difficult to further improve the positioning accuracy of existing location methods based on single-spot measurements. This paper proposes two location methods based on multi-spot measurements to reduce location errors. Because the multi-spot measurements model has more measurement equations than the single-spot measurements model, the proposed methods provide better performance than the traditional location methods using one-spot measurement in terms of the root mean square error (RMSE) and Cramer–Rao lower bound (CRLB). Both closed-form and iterative algorithms are proposed in this paper. The former performs suboptimally with less computational burden, whereas the latter has the highest positioning accuracy in attaining the CRLB. Moreover, a novel CRLB for the proposed multi-spot measurements model is also derived in this paper. A theoretical proof shows that the traditional CRLB in the case of single-spot measurements performs worse than the proposed CRLB in the case of multi-spot measurements. The simulation results show that the proposed methods have a lower RMSE than the traditional location methods.