Cramer–Rao Bound for Noncoherent Direction of Arrival Estimation in the Presence of Sensor Location Errors

In previous work, we have shown that the noncoherent direction of arrival (DOA) estimation by an array of sensors is insensitive to sensor phase errors. Here, we analyze the effects of sensor location errors on noncoherent DOA estimation. In the presence of additive white Gaussian noise, we show that the distribution of magnitude-only measurements collected by a sensor array may be approximated by a Gaussian distribution. Further, if one of the sources is received with high signal-to-noise ratio, the mean of the Gaussian distribution is a function of location errors while the variance of the Gaussian distribution is invariant with location errors. We derive a closed-form analytical expression for the hybrid Cramer-Rao bound of the spatial frequency difference between two sources. Numerical results illustrate that, unlike phase errors that have no effect on noncoherent DOA estimation, both noncoherent and coherent DOA estimation are affected by location errors.