Systems and methods for communicating by modulating data on zeros
View Patent ↗Systems and methods for transmitting data using various Modulation on Zeros schemes are described. In many embodiments, a communication system is utilized that includes a transmitter having a modulator that modulates a plurality of information bits to encode the bits in the zeros of the z-transform of a discrete-time baseband signal. In addition, the communication system includes a receiver having a decoder configured to decode a plurality of bits of information from the samples of a received signal by: determining a plurality of zeros of a z-transform of a received discrete-time baseband signal based upon samples from a received continuous-time signal, identifying zeros that encode the plurality of information bits, and outputting a plurality of decoded information bits based upon the identified zeros.
1. A data transmission method, comprising:
receiving a continuous-time signal;
sampling the received continuous-time signal, using an analog-to-digital converter, to obtain a discrete-time baseband signal;
decoding a plurality of information bits from the discrete-time baseband signal by:
determining a plurality of zeros of a z-transform of the discrete-time baseband signal; and
identifying, from the plurality of zeros, zeros that encode the plurality of information bits, wherein the identified zeroes comprise at least one zero that has a radius that is not equal to one; and
outputting a plurality of decoded information bits based upon the identified zeros.
2. The data transmission method of claim 1 , wherein the plurality of zeros of the z-transform comprise:
the plurality of zeros that encode the plurality of information bits; and
at least one zero introduced by multipath propagation of a transmitted continuous-time signal.
3. The data transmission method of claim 1 , wherein the z-transform of the discrete-time baseband signal comprises a zero for each of a plurality of encoded bits.
4. The data transmission method of claim 3 , wherein each zero in the z-transform of the discrete-time baseband signal is limited to being one of a set of conjugate-reciprocal pairs of zeros.
5. The data transmission method of claim 4 , wherein:
each conjugate reciprocal pair of zeros in the set of conjugate-reciprocal pairs of zeros comprises:
an outer zero having a first radius that is greater than one; and
an inner zero having a radius that is the reciprocal of the first radius;
the inner and outer zero have phases that are the same phase;
the first radius of the outer zero in each pair of zeros in the set of conjugate-reciprocal pairs of zeros are the same; and
the phases of the outer zeros in each pair of zeros in the set of conjugate-reciprocal pairs of zeros are evenly spaced over one complete revolution.
6. The data transmission method of claim 4 , wherein the discrete-time baseband signal is a Huffman sequence.
7. The data transmission method of claim 1 , wherein at least one zero of the z-transform of the discrete-time baseband signal encodes at least two of the plurality of information bits.
8. The data transmission method of claim 7 , wherein the at least one zero of the z-transform of the discrete-time baseband signal that encodes the plurality of information bits is limited to being a zero from a set of more than two zeros.
9. The data transmission method of claim 7 , wherein the at least one zero of the z-transform of the discrete-time baseband signal that encodes the plurality of encoded bits is limited to being a zero from a set of multiple conjugate-reciprocal pairs of zeros.
10. The data transmission method of claim 9 , wherein each conjugate-reciprocal pair of zeros in the set of multiple conjugate-reciprocal pairs of zeros have unique phases.
11. The data transmission method of claim 9 , wherein each zero in the set of multiple conjugate-reciprocal pairs of zeros has the same phase.
12. The data transmission method of claim 11 , further comprising determining a most likely set of zeros for the z-transform of the discrete-time baseband signal used to generate a transmitted continuous-time signal using an autocorrelation codebook.
13. The data transmission method of claim 12 , further comprising performing a weighted comparison using an inverse discrete Fourier transform of delayed and weighted samples of the received continuous-time signal.
14. The data transmission method of claim 1 , wherein the plurality of decoded information bits are obtained by performing a weighted comparison of samples of the z-transform of the discrete-time baseband signal with each zero in a set of zeros.
15. The data transmission method of claim 14 , wherein each zero in the z-transform of the discrete-time baseband signal used to generate a transmitted continuous-time signal is limited to being one of a set of conjugate-reciprocal pairs of zeros.
16. The data transmission method of claim 15 , further comprising: separating zeros of the discrete-time baseband signal that encode information bits from zeros of the discrete-time baseband signal introduced by multipath propagation of the transmitted continuous-time signal by selecting a predetermined number of the zeros of the discrete-time baseband signal based upon the distance between each zero in the discrete-time baseband signal and a corresponding closest zero in the set of conjugate-reciprocal pairs of zeros.
17. The data transmission method of claim 1 , wherein the zeros that encode information bits are identified from the plurality of zeros, based on a set closest to the zeros of the discrete-time baseband signal determined based upon a given distance measure.
18. The data transmission method of claim 1 , further comprising estimating characteristics of a channel over which the received continuous-time signal was transmitted.
19. The data transmission method of claim 1 , wherein:
the continuous-time signal is received by a receiver comprising a plurality of receive antennas; and
the plurality of receive antennas determines the plurality of decoded information bits based upon a plurality of received continuous-time signals.
20. The data transmission method of claim 1 , wherein the plurality of information bits are encoded so that at least one pole is located at the origin of the z-transform.