Narrowband and wideband DOA estimation with unknown number of sources
Vinod Veera Reddy
Date of Issue2013
School of Electrical and Electronic Engineering
Array processing has been an active research area for several decades. The advent of new signal processing techniques has maintained this topic afresh in the research community with new challenging problems. The estimation of direction-of-arrival (DOA) for instance has evolved from high-resolution to superresolution techniques, and of-late, is heading towards increasing the available degrees of freedom. Excited by these developments and the awaiting potential applications, we have considered the study of DOA estimation for narrowband and wideband sources in this thesis under various conditions. Within an array processing system, the inter-dependence between the model-order estimation, DOA estimation and beamforming tasks reﬂects the sensitivity of one task to the outcome of the other. In view of this, beamformers have been designed in the past to incorporate robustness against look direction mismatch and array manifold errors. However, existing DOA estimation techniques are sensitive to the accuracy of estimated number of sources. In order to overcome this limitation, we propose a new narrowband DOA estimation technique which substitutes the noise subspace eigenvectors with a weight vector matrix. This allows one to obtain the spatial spectrum with unknown number of sources. Any error in model order estimation will therefore have no impact on the accuracy of DOA estimates. Estimating the number of sources in the presence of wideband sources is a very challenging task considering the fact that existing techniques retrieve the model order either from a coherently-averaged covariance matrix or by the maximum likelihood approach. While the estimated model-order from the former method is susceptible to the initial estimates, the latter technique is computationally expensive. We therefore present a time-domain DOA estimation technique which provides distinct peaks along the source directions in its spatial spectrum without estimating the number of sources. The underlying idea relies on the array manifold approximation using Taylor series expansion across the signal bandwidth. The undesired derivative components are then suppressed by the proposed optimization problem. The eﬀectiveness of this technique is veriﬁed with a detailed mathematical analysis and simulations. With ﬁnite-ordered Taylor series expansion, the array manifold approximation is accurate for sources with a percentage bandwidth less than 30%. For larger source bandwidth, the estimation accuracy of the time-domain technique decreases. We therefore transform the problem to frequency domain and perform DOA estimation on a regulated signal bandwidth. Environmental factors such as multipath, dispersion and scattering adversely aﬀect the performance of existing DOA estimation techniques in many applications such as radio wave communication, seismic and underwater acoustic applications. Existing techniques such as matched-ﬁeld processing incorporate the speed proﬁle and introduce robustness to random perturbations in speed. However, the estimation of speed proﬁle is itself challenging and inaccurate many times. We therefore consider redeﬁning array manifold approximation such that robustness can be incorporated to dispersion. The optimization problem introduces derivative compensation with respect to the wavenumber which absorbs the eﬀect of dispersion in the signal model. With this approach, one requires to only estimate the propagation speed at only a reference frequency instead of the entire source bandwidth.
DRNTU::Engineering::Electrical and electronic engineering