This paper presents an efficient framework for estimating the direction-of-arrival (DOA) of wideband sound sources. The proposed framework provides an efficient way to construct a wideband cross-correlation matrix from multiple narrowband cross-correlation matrices for all frequency bins. In addition, the proposed framework is inspired by the coherent signal subspace technique with further improvement of linear transformation procedure, and the new procedure no longer requires any process of DOA preliminary estimation by exploiting unique cross-correlation matrices between the received signal and itself on distinct frequencies, along with the higher-order generalized singular value decomposition of the array of this unique matrix. Wideband DOAs are estimated by employing any subspace-based technique for estimating narrowband DOAs, but using the proposed wideband correlation instead of the narrowband correlation matrix. It implies that the proposed framework enables cutting-edge studies in the recent narrowband subspace methods to estimate DOAs of the wideband sources directly, which result in reducing computational complexity and facilitating the estimation algorithm. Practical examples are presented to showcase its applicability and effectiveness, and the results show that the performance of fusion methods perform better than others over a range of signal-to-noise ratios with just a few sensors, which make it suitable for practical use.