  We consider channel estimation (CE) in narrowband Internet-of-Things (NB-IoT)
systems. Due to the fluctuations in phase within receiver and transmitter
oscillators, and also the residual frequency offset (FO) caused by
discontinuous receiving of repetition coded transmit data-blocks, random phase
noises are presented in received signals. Although the coherent-time of fading
channel can be assumed fairly long due to the low-mobility of NB-IoT
user-equipments (UEs), such phase noises have to be considered before combining
the the channel estimates over repetition copies to improve their accuracies.
In this paper, we derive a sequential minimum-mean-square-error (MMSE) channel
estimator in the presence of random phase noise that refines the CE
sequentially with each received repetition copy, which has a low-complexity and
a small data storage. Further, we show through simulations that, the proposed
sequential MMSE estimator improves the mean-square-error (MSE) of CE by 1 dB in
the low signal-to-noise ratio (SNR) regime, compared to a traditional
sequential MMSE estimator that does not thoroughly consider the impact of
random phase noises.
