Spread spectrum receiver and testing method
A method of characterizing a LoRa modulated signal or any such signals with a plurality of chirps as symbols. It foresees sampling and storing the signal, determining a phase of at least one chirp in the signal, and determining a timing error and/or a frequency error based on the phase, The timing error is extracted by the height of a discontinuous step in the phase at the position of the cyclical shift, while the frequency error is obtained by the slope of the phase. The method can be applied to a dedicated receiver for the characterization of LoRa transmitters.
1. A method of characterizing a modulated signal that includes a plurality of chirps, each chirps being limited to a finite interval of time and an finite bandwidth, wherein the chirps include base chirps in which the frequencies follow a monotonic function from the beginning to the end of the interval of time and modulated chirps that are cyclical shifts of a base chirp, the method comprising sampling and storing the signal, determining a phase of at least one chirp in the signal, and determining a timing error and/or a frequency error based on the phase, the timing error being a deviation between a timing of the chirp and a nominal predetermined timing, the frequency error being a deviation between a frequency of the chirp and a nominal predetermined frequency, the at least one chirp being a modulated chirp or a recomposed modulated chirp obtained by applying a window to two consecutive base chirps, and the timing error and/or the frequency error are determined based on a phase error that is the difference between the phase of the at least one chirp and a known phase of a nominal chirp.
2. The method of claim 1 , the signal comprising a preamble of consecutive base chirps followed by a payload of modulated chirps.
3. The method of claim 1 , the timing error being determined as proportional to a height of a step change of the phase error.
4. The method of claim 1 , the frequency error being determined as proportional to a slope of the phase error.
5. The method of claim 1 , wherein the sampling has a sampling frequency that is at least the double of the bandwidth, the method including multiplying sample-by-sample the sampled signal by a vector representing the complex conjugate of a base chirp, applying a Fourier transform on the product of the multiplication, detecting two peaks with a frequency separation equal to the bandwidth in the result of the Fourier transform.
6. The method of claim 1 , wherein the signal is processed repeatedly.
7. The method of claim 1 , including transmitting the signal with a radio-transmitting device, receiving, and sampling the signal in a radio-receiving device, transmitting the sampled signal to a computation server, the time and frequency deviations being determined in the computation server.
8. The method of claim 1 , comprising determining the timing errors of a plurality of chirps received from a given transmitter and determining a sampling timing drift of the transmitter based on the timing errors.
9. The method of claim 8 , comprising determining, for each received chirp a ratio of the sampling timing drift of the transmitter to the frequency offset of the received chirp and using the ratio as a measure of the frequency stability in the transmitter.
10. A method of characterizing the performance of a radio-transmitting device, comprising receiving a signal generated by the radio-transmitting device with a reference radio-receiving device and determining a timing error and/or a frequency error by the method of claim 1 .
11. A method of characterizing the performance of a radio-receiving device, comprising generating a signal with a reference radio-transmitting device, receiving the signal with the radio-receiving device and determining a timing error and/or a frequency error by the method of claim 1 .
12. A radio-receiving device for LoRa signals configured to carry out the method of claim 1 .