Stochastic Cramer-Rao Bound for DOA Estimation With a Mixture of Circular and Noncircular Signals

Abstract

The Cramer-Rao bound (CRB) offers insights into the inherent performance benchmark of any unbiased estimator developed for a specific parametric model, which is an important tool to evaluate the performance of direction-of-arrival (DOA) estimation algorithms. In this paper, a closed-form stochastic CRB for a mixture of circular and noncircular uncorrelated Gaussian signals is derived. As a general one, it can be transformed into some existing representative results. The existence condition of the CRB is also analysed based on sparse arrays, which allows the number of signals to be more than the number of physical sensors. Finally, numerical comparisons are conducted in various scenarios to demonstrate the validity of the derived CRB. INDEX TERMS Cramer-Rao bound, direction of arrival, circular and noncircular, sparse arrays.

A low-complexity two-dimensional DOA estimation algorithm based on an L-shaped sensor array

“…As a special case, for the situation with circular signals only, the DM-MUSIC algorithm is developed as in our earlier published conference paper [26]. As the Cramer-Rao bound (CRB) provides an important benchmark for assessing the performance of various 2D DOA estimation algorithms [27], [28], the CRB for 2D DOA estimation for a mixture of circular and noncircular signals is derived following the approach in [29], which can handle the general underdetermined problem. As demonstrated by computer simulations, the DB-MUSIC-M and DB-MUSIC algorithms have outperformed some existing corresponding L-shaped array based 2D DOA estimation algorithms.…”

“…Moreover, significantly reduced computation time was achieved by the proposed solution in comparison with a direct 2D search method based on I-MUSIC.APPENDIX AIn order to assess the performance of the proposed algorithms, the CRB for 2D DOA estimation for a mixture of circular and noncircular signals is derived in this part. According to the result of 1D CRB in[29], the 2D CRB result is CRB e (α, β)r e = vec (R e ) ,(44)where S nap is the number of snapshots, ⊗ is the Kronecker product operator, and vec(•) is the vectorization operation.The matrices C and D in the proposed CRB e (α, β) can be further represented asdif = E[z(t)z H (t)], R sum = E[z(t)z T (t)], r d = vec (R dif ) = T d (α, β) η + σ 2 vec (I N +M ) , r s = vec (R sum ) = T s (α nc , β nc ) diag{η nc } diag{ρ}ψ e , T d (α, β) = A * (α, β) ⊙ A (α, β) , T s (α nc , β nc ) = A (α nc , β nc ) ⊙ A (α nc , β nc ) , ψ e = [ e jψ1 , e jψ2 , . .…”