Efficient Two-Dimensional Direction-of-Arrival Estimation for a Mixture of Circular and Noncircular Sources

In this paper, the two-dimensional (2-D) direction-of-arrival (DOA) estimation problem for a mixture of circular and noncircular sources is considered. In particular, we focus on a 2-D array structure consisting of two parallel uniform linear arrays and build a general array model with mixed circular and noncircular sources. The received array data and its conjugate counterparts are combined together to form a new data vector, based on which a series of 2-D DOA estimators is derived. Compared with existing methods, the proposed one has three main advantages. First, it can give a more accurate estimation in situations, where the number of sources is within the traditional limit of high-resolution methods. Second, it can still work effectively when the number of mixed signals is larger than that of the array elements. Finally, the paired 2-D DOAs of the proposed method can be obtained automatically without the complicated 2-D spectrum peak search and, therefore, has a much lower computational complexity

R-dimensional ESPRIT-type algorithms for strictly second-order non-circular sources and their performance analysis

High-resolution parameter estimation algorithms designed to exploit the prior knowledge about incident signals from strictly second-order (SO) non-circular (NC) sources allow for a lower estimation error and can resolve twice as many sources. In this paper, we derive the R-D NC Standard ESPRIT and the R-D NC Unitary ESPRIT algorithms that provide a significantly better performance compared to their original versions for arbitrary source signals. They are applicable to shift-invariant R-D antenna arrays and do not require a centrosymmetric array structure. Moreover, we present a first-order asymptotic performance analysis of the proposed algorithms, which is based on the error in the signal subspace estimate arising from the noise perturbation. The derived expressions for the resulting parameter estimation error are explicit in the noise realizations and asymptotic in the effective signal-to-noise ratio (SNR), i.e., the results become exact for either high SNRs or a large sample size. We also provide mean squared error (MSE) expressions, where only the assumptions of a zero mean and finite SO moments of the noise are required, but no assumptions about its statistics are necessary. As a main result, we analytically prove that the asymptotic performance of both R-D NC ESPRIT-type algorithms is identical in the high effective SNR regime. Finally, a case study shows that no improvement from strictly non-circular sources can be achieved in the special case of a single source.Comment: accepted at IEEE Transactions on Signal Processing, 15 pages, 6 figure