Efficient Maximum Likelihood Joint Estimation of Angles and Times of Arrival of Multiple Paths

This paper presents and analyses two computationally attractive Maximum Likelihood (ML) estimators for joint Angle of Arrival (AoA) and Time of Arrival (ToA) of a Single Input Multiple Output (SIMO) link in an OFDM communication setting. We consider a rich multipath channel, which is the case of an indoor environment, where the received signal is a sum of scaled and delayed versions of the original transmitted OFDM symbol. The first algorithm is a modification of the two dimensional Iterative Quadratic ML (2D-IQML) algorithm, where an additional constraint is added for joint ToA and AoA estimation. We show that 2D-IQML gives biased estimates of ToAs/AoAs and performs poorly at low SNR due to noise induced bias. The 2D-IQML cost function can be "denoised" by eliminating the noise contribution: the resulting algorithm, two dimensional Denoised IQML (2D-DIQML), gives consistent estimates and outperforms 2D-IQML. Furthermore, 2D-DIQML is asymptotically globally convergent and hence insensitive to the initialisation. Also, we show that the 2D-DIQML algorithm behaves asymptotically at any SNR as the 2D-IQML algorithm behaves at high SNR. A simulation example is presented to show the asymptotic behaviour of both algorithms at low SNR. Finally, joint AoA/ToA estimates could bring very useful information for localisation purposes, especially in a rich multipath channel, that could allow single anchor based localisation.