Frame and carrier synchronization for unbursted packetized transmissions using constant-amplitude continuous-phase frequency-modulation

1. A method for performing carrier phase and frequency offset correction on samples x 1 (n) of a received signal, wherein n is a time index, wherein the received signal includes a series of frames, wherein each frame includes a preamble and payload data, wherein the preamble of each frame includes multiple repetitions of a base pattern, wherein the multiple repetitions of the base pattern conform to a first constant-amplitude continuous-phase frequency modulation scheme, the method comprising:

a computer system applying a first frequency correction to the samples x 1 (n) based on a coarse estimate for a carrier frequency offset in order to determine samples x 2 (n);

the computer system computing values θ(p) of a function θ for a number of values of positive integer index p, said number of values being greater than one, wherein θ(p) is a phase difference between a first subsequence of the samples x 2 (n) and a second subsequence of the samples x 2 (n), wherein the first and second subsequences reside within a first of the preambles, wherein the first and second subsequences are separated by a sample distance equal to p repetitions of the base pattern;

the computer system computing a fine estimate for residual carrier frequency offset by estimating a linear slope of the function θ relative to the positive integer index p;

the computer system applying a second frequency correction to the samples x 2 (n) based on the fine estimate for the residual carrier frequency offset in order to determine samples x 3 (n);

the computer system computing a complex inner product between a model sequence g(n) and a subsequence of the samples x 3 (n), wherein the subsequence of the samples x 3 (n) resides within the first preamble, wherein the model sequence g(n) corresponds to a subsequence of a known model of the multiple repetitions of the base pattern;

the computer system applying a phase correction to the samples x 3 (n) based on an angle of the inner product in order to obtain samples x 4 (n).

2. The method of claim 1 , further comprising:

the computer system computing a discrete Fourier transform R(k) of a subsequence of the samples x 1 (n), wherein the subsequence of the samples x 1 (n) corresponds to the multiple repetitions of the base pattern within the first preamble; and

the computer system computing the coarse estimate for the carrier frequency offset by maximizing a cyclic cross-correlation between a magnitude of R(k) and a magnitude of spectrum P(k), wherein P(k) is a discrete Fourier transform of the known model of the multiple repetitions of the base pattern.

3. The method of claim 1 , further comprising:

demodulating a payload portion of the samples x 4 (n) to obtain information bits;

and driving an output device with an output signal derived from the information bits.

4. The method of claim 3 , wherein said demodulating the payload portion of the samples x 4 (n) comprises performing maximum likelihood sequence estimation on the payload portion of the samples x 4 (n).

5. The method of claim 1 , wherein said computing the fine estimate for the residual carrier frequency offset includes performing a least squares linear fit on data including a set of pairs {(p,θ(p))} to obtain the linear slope of the function θ relative to positive integer index p.

6. The method of claim 1 , wherein the samples x 1 (n) of the received signal are obtained at a rate that is an integer multiple of a symbol rate.

7. The method of claim 1 , wherein the payload data conforms to a second constant-amplitude continuous-phase frequency modulation scheme different from the first constant-amplitude continuous-phase frequency modulation scheme.

8. A non-transitory computer-readable memory medium storing program instructions, wherein the program instructions, when executed by a computer system, cause the computer system to:

receive samples x 1 (n) of a received signal, wherein n is a time index, wherein the received signal includes a series of frames, wherein each frame includes a preamble and payload data, wherein the preamble of each frame includes multiple repetitions of a base pattern, wherein the multiple repetitions of the base pattern conform to a first constant-amplitude continuous-phase frequency modulation scheme;

apply a first frequency correction to the samples x 1 (n) based on a coarse estimate for a carrier frequency offset in order to determine samples x 2 (n);

compute values θ(p) of a function θ for a number of values of positive integer index p, said number of values being greater than one, wherein θ(p) is a phase difference between a first subsequence of the samples x 2 (n) and a second subsequence of the samples x 2 (n), wherein the first and second subsequences reside within a first of the preambles, wherein the first and second subsequences are separated by a sample distance equal to p repetitions of the base pattern;

compute a fine estimate for residual carrier frequency offset by estimating a linear slope of the function θ relative to the positive integer index p;

apply a second frequency correction to the samples x 2 (n) based on the fine estimate for the residual carrier frequency offset in order to determine samples x 3 (n);

compute a complex inner product between a model sequence g(n) and a subsequence of the samples x 3 (n), wherein the subsequence of the samples x 3 (n) resides within the first preamble, wherein the model sequence g(n) corresponds to a subsequence of a known model of the multiple repetitions of the base pattern;

apply a phase correction to the samples x 3 (n) based on an angle of the inner product in order to obtain samples x 4 (n).

9. The non-transitory computer-readable memory medium of claim 8 , wherein the program instructions, when executed by the computer system, further cause the computer system to:

compute a discrete Fourier transform R(k) of a subsequence of the samples x 1 (n), wherein the subsequence corresponds to the multiple repetitions of the base pattern within the first preamble; and

compute the coarse estimate for the carrier frequency offset by maximizing a cyclic cross-correlation between a magnitude of R(k) and a magnitude of spectrum P(k), wherein P(k) is a discrete Fourier transform of the known model of the multiple repetitions of the base pattern.

10. The non-transitory computer-readable memory medium of claim 8 , wherein the program instructions, when executed by the computer system, further cause the computer system to:

demodulate a payload portion of the samples x 4 (n) to obtain information bits; and

drive an output device with an output signal derived from the information bits.

11. The non-transitory computer-readable memory medium of claim 10 , wherein said demodulating the payload portion of the samples x 4 (n) comprises performing maximum likelihood sequence estimation on the payload portion of the samples x 4 (n).

12. The non-transitory computer-readable memory medium of claim 8 , wherein said computing the fine estimate for the residual carrier frequency offset includes performing a least squares linear fit on data including a set of pairs {(p,θ(p))} to obtain the linear slope of the function θ relative to positive integer index p.

13. The non-transitory computer-readable memory medium of claim 8 , wherein the samples x 1 (n) of the received signal are obtained at a rate that is an integer multiple of a symbol rate.

14. The non-transitory computer-readable memory medium of claim 8 , wherein the payload data conforms to a second constant-amplitude continuous-phase frequency modulation scheme different from the first constant-amplitude continuous-phase frequency modulation scheme.

15. A computer system comprising:

a processor; and

memory storing program instructions, wherein the program instructions, when executed by the processor, cause the processor to:

receive samples x 1 (n) of a received signal, wherein n is a time index, wherein the received signal includes a series of frames, wherein each frame includes a preamble and payload data, wherein the preamble of each frame includes multiple repetitions of a base pattern, wherein the multiple repetitions of the base pattern conform to a first constant-amplitude continuous-phase frequency modulation scheme;

apply a first frequency correction to the samples x 1 (n) based on a coarse estimate for a carrier frequency offset in order to determine samples x 2 (n);

compute values θ(p) of a function θ for a number of values of positive integer index p, said number of values being greater than one, wherein θ(p) is a phase difference between a first subsequence of the samples x 2 (n) and a second subsequence of the samples x 2 (n), wherein the first and second subsequences reside within a first of the preambles, wherein the first and second subsequences are separated by a sample distance equal to p repetitions of the base pattern;

compute a fine estimate for residual carrier frequency offset by estimating a linear slope of the function θ relative to the positive integer index p;

apply a second frequency correction to the samples x 2 (n) based on the fine estimate for the residual carrier frequency offset in order to determine samples x 3 (n);

compute a complex inner product between a model sequence g(n) and a subsequence of the samples x 3 (n), wherein the subsequence of the samples x 3 (n) resides within the first preamble, wherein the model sequence g(n) corresponds to a subsequence of a known model of the multiple repetitions of the base pattern; and

apply a phase correction to the samples x 3 (n) based on an angle of the inner product in order to obtain samples x 4 (n).

16. The computer system of claim 15 , wherein the program instructions, when executed by the processor, further cause the processor to:

compute a discrete Fourier transform R(k) of a subsequence of the samples x 1 (n), wherein the subsequence corresponds to the multiple repetitions of the base pattern within the first preamble; and

compute the coarse estimate for the carrier frequency offset by maximizing a cyclic cross-correlation between a magnitude of R(k) and a magnitude of spectrum P(k), wherein P(k) is a discrete Fourier transform of the known model of the multiple repetitions of the base pattern.

17. The computer system of claim 15 , wherein the program instructions, when executed by the processor, further cause the processor to:

demodulate a payload portion of the samples x 4 (n) to obtain information bits; and

drive an output device with an output signal derived from the information bits.

18. The computer system of claim 15 , wherein said computing the fine estimate for the residual carrier frequency offset includes performing a least squares linear fit on data including a set of pairs {(p,θ(p))} to obtain the linear slope of the function θ relative to positive integer index p.

19. The computer system of claim 15 , wherein the samples x 1 (n) of the received signal are obtained at a rate that is an integer multiple of a symbol rate.

20. The computer system of claim 15 , wherein the payload data conforms to a second constant-amplitude continuous-phase frequency modulation scheme different from the first constant-amplitude continuous-phase frequency modulation scheme.