Maximum Likelihood Time Delay Estimation From Single- and Multi-Carrier DSSS Multipath MIMO Transmissions for Future 5G Networks

In this paper, we address the problem of time delay estimation (TDE) from single-carrier (SC) or multi-carrier (MC) direct-sequence spread spectrum (DSSS) multipath transmissions in the presence of multiple transmit and/or receive antennas that will characterize future 5G radio interface technologies (RITs), such as coded-domain nonorthogonal multiple access. We derive for the first time a closed-form expression for the Cramer-Rao lower bound (CRLB) and develop two maximum likelihood (ML) multipath TDEs for SC DSSS single-input multiple-output (SIMO) in the non-data-aided (NDA) case. The first TDE, based on iterative expectation maximization (EM), provides accurate estimates whenever a good initial guess of the parameters is available at the receiver. The second TDE implements the ML criterion in a non-iterative way and finds the global maximum of the compressed likelihood function using the importance sampling (IS) technique without requiring any initialization. We also extend both the SC DSSS SIMO CRLB and the two new SC DSSS SIMO ML NDA TDEs to MC DSSS RITs and to multiple-input multiple-output structures with any diversity versus multiplexing pre-coding type before generalizing them all to the data-aided (DA) case. Simulations suggest that the EM TDE is suitable for large observation in space, time, and/or frequency, whereas the IS TDE is preferred in the opposite case of very short data records. Moreover, we show in the NDA case, both analytically and by simulations, that spatial (transmit and receive), temporal, and frequency samples interchangeably have the same impact on estimation accuracy and performance bound regardless of the channel correlation type and amount present in each dimension. Furthermore, we are able to properly cope with such channel correlations that do indeed arise in practice and, hence, become very challenging both in estimation and CRLB derivation in the DA case, but that have been so far overlooked in previous works.