Chirp receiver

1. A method of synchronising the frequency and timing of a receiver with a synchronisation chirp signal from a transmitter, comprising:

receiving the synchronisation chirp signal, the synchronisation chirp signal comprising a sequence of symbols, the sequence of symbols including at least a first symbol having a first gradient g 1 and a second symbol having a second gradient g 2 , wherein the magnitudes of the first gradient and the second gradient are both greater than one, and the magnitude of the first gradient is different to the magnitude of the second gradient;

correlating the sequence of received symbols with expected symbols to form a correlator output;

determining timing and frequency offsets between the transmitter and the receiver from the correlator output; and

adjusting the relative timing and frequency of the receiver and the synchronisation signal by the determined timing and frequency offsets.

2. A method according to claim 1 , wherein determining the timing and frequency offsets comprises determining fractional timing and frequency offsets between the transmitter and the receiver.

3. A method according to claim 2 , wherein each received symbol comprises one or more identical chirps, each chirp having N samples, and wherein the fractional timing offset is a function of the magnitude of the correlator output at the expected integer timing offset and a function of the magnitude of the correlator output at g samples from the expected integer timing offset.

4. A method according to claim 3 , wherein the fractional timing offset is a function of the magnitude of the correlator output at the expected integer timing offset and a function of the magnitude of the correlator output at g samples prior to the expected integer timing offset.

5. A method according to claim 3 , wherein the fractional timing offset is a function of the magnitude of the correlator output at the expected integer timing offset and a function of the magnitude of the correlator output at g samples after to the expected integer timing offset.

6. A method according to claim 2 , wherein each received symbol comprises one or more identical chirps, each chirp having N samples, and wherein the fractional frequency offset is a function of the magnitude of the correlator output at the expected integer timing offset and a function of the magnitude of the correlator output at one sample from the expected integer timing offset.

7. A method according to claim 6 , wherein the fractional frequency offset is a function of the magnitude of the correlator output at the expected integer timing offset and a function of the magnitude of the correlator output at one sample prior to the expected integer timing offset.

8. A method according to claim 6 , wherein the fractional frequency offset is a function of the magnitude of the correlator output at the expected integer timing offset and a function of the magnitude of the correlator output at one sample after to the expected integer timing offset.

9. A method according to claim 1 , wherein determining the timing and frequency offsets comprises determining integer timing and frequency offsets between the transmitter and the receiver.

10. A method according to claim 9 , comprising determining integer timing and frequency offsets from the correlator peak position of the first symbol and the correlator peak position of the second symbol.

11. A method according to claim 1 , further comprising:

buffering the received symbols;

after the step of adjusting the relative timing and frequency of the receiver and the synchronisation signal, extracting the buffered received symbols;

correlating the sequence of buffered received symbols with expected symbols to form a correlator output;

determining timing and frequency offsets between the transmitter and the receiver from the correlator output; and

adjusting the relative timing and frequency of the receiver and the synchronisation signal by the determined timing and frequency offsets.

12. A method according to claim 1 , further comprising:

buffering the received symbols;

after the step of adjusting relative timing and frequency of the receiver and the synchronisation signal, extracting the buffered received symbols;

applying fractional time offsets and fractional frequency offsets to the extracted buffered received symbols to form a set of offset received symbols;

correlating the sequence of offset received symbols with expected symbols to form a correlator output;

determining timing and frequency offsets between the transmitter and the receiver from the correlator output; and

adjusting the relative timing and frequency of the receiver and the synchronisation signal by the determined timing and frequency offsets.

13. A chirp receiver comprising:

a receiving unit configured to receive a synchronisation chirp signal, the synchronisation chirp signal comprising a sequence of symbols, the sequence of symbols including at least a first symbol having a first gradient g 1 and a second symbol having a second gradient g 2 , wherein the magnitudes of the first gradient and the second gradient are both greater than one, and the magnitude of the first gradient is different to the magnitude of the second gradient;

a correlator configured to correlate the sequence of received symbols with expected symbols to form a correlator output;

a determination unit configured to determine timing and frequency offsets between the transmitter and the receiver from the correlator output; and

an adjustment unit configured to adjust the relative timing and frequency of the receiver and the synchronisation signal by the determined timing and frequency offsets.

14. A chirp receiver according to claim 13 , wherein the determination unit is configured to determine fractional timing and frequency offsets between the transmitter and the receiver.

15. A chirp receiver according to claim 13 , wherein the determination unit is configured to determine the integer timing and frequency offsets between the transmitter and the receiver.

16. A chirp receiver according to claim 13 , wherein the correlator is configured to correlate each received symbol in the sequence of received symbols with an expected symbol having a gradient matching the gradient of the received symbol.

17. A chirp receiver according to claim 13 , wherein the correlator is configured to:

mix the first symbol with a generated symbol having a gradient 1−g 1 to form a first mixed symbol;

mix the second symbol with a generated symbol having a gradient 1−g 2 to form a second mixed symbol; and

correlate both the first mixed symbol and the second mixed symbol with a symbol having unity gradient.

18. A chirp receiver as claimed in claim 13 , further comprising a processor configured to negotiate the gradients of the symbols in the synchronisation chirp signal between the transmitter and the receiver.

19. A chirp receiver as claimed in claim 13 , further comprising a buffer configured to buffer the received symbols.

20. A chirp receiver as claimed in claim 13 , further comprising:

a buffer configured to buffer the received symbols;

a linear interpolator configured to apply fractional time offsets to the buffered received symbols; and

a mixer configured to apply a fractional frequency offset to the buffered received symbols.