text: abstract—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 lowmobility 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.