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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 around 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.

Sequential channel estimation in the presence of random phase noise in NB-IoT systems