Anti-Aliasing Speech DOA Estimation Under Spatial Aliasing Conditions

In wideband DOA estimation scenario, half-wavelength condition for a uniform linear array (ULA) is usually not satisfied in entire frequency bands, which may result in spatial aliasing in higher frequency bands. Especially when the strong and weak sources exist simultaneously, the aliasing components from the strong sources almost always lead to failure detection of weak sources. To handle this issue, the wideband spatial aliasing model for each sub-band in uniform linear arrays (ULAs) is built. By exploiting the Cauchy-Schwarz inequality, we proposed a theorem for determining the lower bound of the time-averaged energy-density spectrum without spatial aliasing. Based on the derived theorem and the similar structure of the spectrum between adjacent sub-bands, three unambiguous wideband DOA estimation schemes are proposed. Firstly, two unambiguous spectra are derived by applying the proposed theorem to conventional beamforming spectrum and Capon spectrum respectively. The former has better aliasing suppression performance than the latter, but with lower resolution. By incorporating the advantages of themselves, a quadratically constrained beamforming (QCB) method is proposed, where an elegant closed form expression for the output power is derived for DOA estimation. Compared to the frequency-difference (FD) approaches and multi-stage approach, the proposed method has higher spatial resolution and detection probability for weak sources. Both simulation and experimental results are provided to demonstrate the effectiveness of the proposed method.