A large-scale fully-digital receive antenna array can provide very high-resolution direction of arrival (DOA) estimation, but resulting in a significantly high RF-chain circuit cost. Thus, a hybrid analog and digital (HAD) structure is preferred. Two phase alignment (PA) methods, HAD PA (HADPA) and hybrid digital and analog PA (HDAPA), are proposed to estimate DOA based on the parametric method. Compared to analog phase alignment (APA), they can significantly reduce the complexity in the PA phases. Subsequently, a fast root multiple signal classification HDAPA (Root-MUSIC-HDAPA) method is proposed specially for this hybrid structure to implement an approximately analytical solution. Due to the HAD structure, there exists the effect of direction-finding ambiguity. A smart strategy of maximizing the average receive power is adopted to delete those spurious solutions and preserve the true optimal solution by linear searching over a set of limited finite candidate directions. This results in a significant reduction in computational complexity. Eventually, the Cramer-Rao lower bound (CRLB) of finding emitter direction using the HAD structure is derived. Simulation results show that our proposed methods, Root-MUSIC-HDAPA and HDAPA, can achieve the hybrid CRLB with their complexities being significantly lower than those of pure linear searching-based methods, such as APA.

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In this paper, we make an investigation of the problem of passive multi-satellite localization based on time differences of arrival (TDOA) with Earth constraint (EC). By utilizing TDOA measurements and EC, the problem of estimating target position is formulated as a quadratically constrained quadratic optimization. Following this, the approximate analytic solution of target position is obtained by using the method of Lagrange multipliers and deleting the infeasible roots of polynomial in the Lagrange multiplier. Simulation results show that the proposed method can achieve the Cramer-Rao lower bound (CRLB) with EC for three typical scenarios, even in the worst case, e.g., in the presence of large TDOA measurement errors with even target being far from the subastral point. However, the existing TDOA localization methods will deviate from the CRLB with EC as the measurement error of TDOA increases. Thus, the proposed method is more robust compared with the existing methods. In addition, the EC has a significant impact on the TDOA localization performance. Compared with the case of no EC, the EC can make a one-ordermagnitude improvement in localization precision. INDEX TERMSPassive multi-satellite localization, time difference of arrival, quadratical optimization, least squares, earth constraint.

Medium-scale or large-scale receive antenna array with digital beamforming can be employed at receiver to make a significant interference reduction, but leads to expensive cost and high complexity of the RF-chain circuit. To deal with this issue, a classic analog-and-digital beamforming (ADB) structure was proposed in the literature for greatly reducing the number of RF-chains. Based on the ADB structure, we in this paper propose a robust hybrid ADB scheme to resist directions of arrival (DOAs) estimation errors. The key idea of our scheme is to employ null space projection (NSP) in analog beamforming domain and diagonal loading (DL) method in digital beamforming domain. Simulation results show that the proposed scheme performs more robustly, and moreover, has a significant improvement on the receive signal to interference plus noise ratio (SINR) compared to NSP ADB scheme and DL method.

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