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In order to mitigate the effect of additive noises and reduce the computational burden, we propose a new computationally efficient cross-correlation based two-dimensional (2-D) direction-of-arrivals (DOAs) estimation (CODE) method for noncoherent narrowband signals impinging on the L-shaped sensor array structured by two uniform linear arrays (ULAs). By estimating the azimuth and elevation angles independently with a one-dimensional (1-D) subspace-based estimation technique without eigendecomposition, where the null spaces are obtained through a linear operation of the matrices formed from the cross-correlation matrix between the received data of two ULAs, then the pair-matching of estimated azimuth and elevation angles is accomplished by searching the minimums of a cost function of the azimuth and elevation angles, where the computationally intensive and time-consuming eigendecomposition process is avoided. Further the asymptotic mean-square-error (MSE) expressions of the azimuth and elevation estimates are derived. The effectiveness of proposed method and the theoretical analysis are verified through numerical examples, and it is shown that the proposed CODE method performs well at low signal-to-noise ratio (SNR) and with a small number of snapshots.