The authors propose the use of a generalised array manifold for parameterised spatial signature estimation in wireless communication channels with local scattering. The array manifold commonly used for point sources is generalised to include linear combinations of the nominal array response vectors and their derivatives. The motivation behind this idea is to obtain better estimates of the spatial signatures for direction of arrival (DOA) based signal waveform estimation. The estimators proposed exploit the orthogonality between the so-called noise and signal subspaces, leading to a separable solution for the derivative coefficients. As a result, a search is required for the DOAs only. For uniform linear arrays, the spatial signatures are shown to be approximately Vandermonde vectors with damped modes, and a closed-form estimator such as ESPRIT may be used in this case. Simulation examples are included to compare the signal estimation performance obtained using the proposed generalised manifold and the conventional array manifold.