  In this paper, we consider positioning with
observed-time-difference-of-arrival (OTDOA) for a device deployed in
long-term-evolution (LTE) based narrow-band Internet-of-things (NB-IoT)
systems. We propose an iterative expectation-maximization based successive
interference cancellation (EM-SIC) algorithm to jointly consider estimations of
residual frequency-offset (FO), fading-channel taps and time-of-arrival (ToA)
of the first arrival-path for each of the detected cells. In order to design a
low complexity ToA detector and also due to the limits of low-cost analog
circuits, we assume an NB-IoT device working at a low-sampling rate such as
1.92 MHz or lower. The proposed EM-SIC algorithm comprises two stages to detect
ToA, based on which OTDOA can be calculated. In a first stage, after running
the EM-SIC block a predefined number of iterations, a coarse ToA is estimated
for each of the detected cells. Then in a second stage, to improve the ToA
resolution, a low-pass filter is utilized to interpolate the correlations of
time-domain PRS signal evaluated at a low sampling-rate to a high sampling-rate
such as 30.72 MHz. To keep low-complexity, only the correlations inside a small
search window centered at the coarse ToA estimates are upsampled. Then, the
refined ToAs are estimated based on upsampled correlations. If at least three
cells are detected, with OTDOA and the locations of detected cell sites, the
position of the NB-IoT device can be estimated. We show through numerical
simulations that, the proposed EM-SIC based ToA detector is robust against
impairments introduced by inter-cell interference, fading-channel and residual
FO. Thus significant signal-to-noise (SNR) gains are obtained over traditional
ToA detectors that do not consider these impairments when positioning a device.
