When the ultra-low power mm-scale sensor node does not have a crystal oscillator and phase-lock loop, it inevitably exhibits significant carrier frequency offset (CFO) and sampling frequency offset (SFO) with respect to the reference frequencies in the gateway. This disclosure enables efficient real-time calculation of accurate SFO and CFO at the gateway, thus the ultra-low power mm-scale sensor node can be realized without a costly and bulky clock reference crystal and also power-hungry phase lock loop. In the proposed system, the crystal-less sensor starts transmission with repetitive RF pulses with a constant interval, followed by the data payload using pulse-position modulation (PPM). A proposed algorithm uses a two-dimensional (2D) fast Fourier transform (FFT) based process that identifies the SFO and CFO at the same time to establish successful wireless communication between the gateway and crystal-less sensor nodes.

Methods and system for carrier frequency offset (CFO) estimation are described. The method includes determining correlation values between a plurality of samples from a received signal and a plurality of reference signals corresponding to a plurality of CFO candidates. A set of correlation values which exceeds a threshold is determined and a corresponding CFO candidate for each correlation value in the set is selected. A CFO estimate based on an interpolation of selected CFO candidates is then calculated.

A digital radio receiver is adapted to receive radio signals modulated using continuous phase modulation. The receiver includes components for receiving analogue radio signals having various carrier frequencies and a plurality of correlators corresponding to different bit sequences. Each of the plurality of correlators share a common estimator for estimating a frequency offset between the radio signals carrier frequencies and nominal carrier frequencies. The receiver further includes components allowing the estimator to determine which of the correlators produce the most optimal output signal.

When the ultra-low power mm-scale sensor node does not have a crystal oscillator and phase-lock loop, it inevitably exhibits significant carrier frequency offset (CFO) and sampling frequency offset (SFO) with respect to the reference frequencies in the gateway. This disclosure enables efficient real-time calculation of accurate SFO and CFO at the gateway, thus the ultra-low power mm-scale sensor node can be realized without a costly and bulky clock reference crystal and also power-hungry phase lock loop. In the proposed system, the crystal-less sensor starts transmission with repetitive RF pulses with a constant interval, followed by the data payload using pulse-position modulation (PPM). A proposed algorithm uses a two-dimensional (2D) fast Fourier transform (FFT) based process that identifies the SFO and CFO at the same time to establish successful wireless communication between the gateway and crystal-less sensor nodes.

The present disclosure provides a method implemented in a wireless communication device for estimating a frequency offset between a carrier frequency of a received signal and a frequency of a local oscillator as well as the wireless communication device. The method comprises determining a plurality of phase change candidates for a phase change between a data symbol and a first reference symbol in the signal. The method further comprises generating a collection of constellation symbols from the data symbol and rotating the collection of constellation symbols by the plurality of phase change candidates. Then, one of the phase change candidates corresponding to one of the rotated collections of constellation symbols is selected in such a manner that said one of the rotated collections of constellation symbols matches a set of constellation points best. Next, the frequency offset is determined based on the selected phase change candidate.

Some aspects of the present disclosure relate to detection of a Phase Hit and, upon detecting the Phase Hit, determining the magnitude and location of the Phase Hit. Detecting the Phase Hit may involve comparing a phase offset difference for successive pilot symbol to a detection threshold. Determination of the detection threshold may involve a Neyman-Pearson binary hypothesis testing (NP-BHT) approach. Once the magnitude and location of the Phase Hit are known, data symbols received after the location may be processed to remove the magnitude of the Phase Hit.

Some aspects of the present disclosure relate to detection of a Phase Hit and, upon detecting the Phase Hit, determining the magnitude and location of the Phase Hit. Detecting the Phase Hit may involve comparing a phase offset difference for successive pilot symbol to a detection threshold. Determination of the detection threshold may involve a Neyman-Pearson binary hypothesis testing (NP-BHT) approach. Once the magnitude and location of the Phase Hit are known, data symbols received after the location may be processed to remove the magnitude of the Phase Hit.

A method for determining coarse carrier phase and frequency offsets of an initial block of received M-QAM symbols includes creating a grid of discrete candidate phase offset values and for each candidate value: applying the candidate value to each symbol, applying a respective hard decision to each applied symbol, and computing a figure of merit based thereon. The candidate value having the best figure of merit is selected as an initial phase offset estimate. An initial frequency offset estimate is computed using the symbols updated with the initial phase offset estimate, their respective hard decisions, and an approximation of the complex exponential function. To track carrier phase and frequency offsets associated with a series of symbol blocks, for each symbol of a current block, set a binary trust weight based on comparison of a computed parameter with a threshold and use the binary trust weights to compute a phase offset error and a frequency offset error for the current block.

A method (50) for estimating a frequency shift and a frequency drift affecting a useful signal including a code word formed by a channel encoder, including an analysis phase (51) including: for two analysis frequency drifts: a compensation (52) of the analysis frequency drift on the useful signal, an estimation (53) of the frequency shift on each useful signal obtained after compensation, a selection (54) of frequency hypotheses, and an estimation phase (55) including: for each frequency hypothesis: a frequency recalibration (56) of the useful signal depending on the frequency hypothesis, in order to obtain sample sequences, an evaluation (57) of the probability of each sample sequence to be a code word of said channel encoder, an estimation (58) of the frequency shift and of the frequency drift depending on the most probable frequency hypothesis.

A method (50) for estimating a frequency shift and a frequency drift affecting a useful signal including a code word formed by a channel encoder, including an analysis phase (51) including: for two analysis frequency drifts: a compensation (52) of the analysis frequency drift on the useful signal, an estimation (53) of the frequency shift on each useful signal obtained after compensation, a selection (54) of frequency hypotheses, and an estimation phase (55) including: for each frequency hypothesis: a frequency recalibration (56) of the useful signal depending on the frequency hypothesis, in order to obtain sample sequences, an evaluation (57) of the probability of each sample sequence to be a code word of said channel encoder, an estimation (58) of the frequency shift and of the frequency drift depending on the most probable frequency hypothesis.