Spectrum sleuth for identifying RF transmitter in an environment

1. A system for identifying radio frequency (RF) transmitters in an environment, the system comprising:

at least one RF listening station configured to receive RF signals and acquire measurements of their RF power as a function of reception time, t, and frequency f; and

a processing hub configured to identify RF transmitters operating in the environment by:

receiving the RF power measurements;

fitting to the RF power measurements a probability mixture model (PMM) that provides a probability density as a function of magnitude of the RF power measurements, the PMM comprising a plurality of probability density functions (PDFs), at least two of which PDFs are of a different type, the fitting comprising:

determining a set of defining parameters θ PMM for the PMM, the defining parameters comprising a number, “K”, for a number of the plurality of PDFs, and for each PDF, parameters defining the PDFs; and,

iteratively partitioning the RF power measurements into a plurality of sub-blocks of power measurements;

for each given sub-block in an i-th iteration fitting a sub-block PMM comprising a plurality of sub-block PDFs to the RF power measurements in the given sub-block independent of RF power measurements in other sub-blocks of the i-th iteration to determine a set of defining parameters for the sub-block PMM, the set of defining parameters for the sub-block PMM having a number for the plurality of PDFs in the sub-block PMM;

clustering sub-block PDFs from different sub-blocks to determine clusters of PDFs; and

determining K responsive to a number of clusters; and, identifying RF transmitters in the environment responsive to the PMM.

2. The system according to claim 1 wherein identifying RF transmitters comprises assuming that the number of RF transmitters in the environment is equal to K and associating each RF transmitter with a different one of the K PDFs.

3. The system according to claim 1 wherein the processing hub is configured to determine for each of a plurality of the RF power measurements an association probability for the RF power measurement and each of at least one of the identified K RF transmitters that provides a measure of the probability that an RF signal for which the RF power measurement was acquired was transmitted by the identified RF transmitter.

4. The system according to claim 3 wherein an association probability for the RF power measurement and a given identified RF transmitter of the K identified RF transmitters is a function of the PDF associated with the identified RF transmitter evaluated at a magnitude of the RF power measurement.

5. The system according to claim 3 wherein the processing hub is configured to use the association probabilities for a given RF transmitter of the K identified transmitters to determine an RF bandwidth of the identified given RF transmitter.

6. The system according to claim 5 wherein using the association probabilities to determine the RF bandwidth comprises integrating the association probabilities over time t for each of a plurality of frequencies f to determine a function of frequency for the given RF transmitter and using the function of frequency to determine a bandwidth of the given RF transmitter.

7. The system according to claim 6 wherein using the function of frequency to determine the bandwidth comprises identifying a range of frequencies for which the function of frequency f is substantially greater than zero, and determining the range of frequencies as a bandwidth of the given RF transmitter.

8. The system according to claim 6 wherein the processing hub is configured to use the function of frequency to classify the RF transmitter as to type of RF transmitter.

9. The system according to claim 8 wherein using the function of frequency to classify the RF transmitter comprises determining a standard deviation for the function of frequency and using the standard deviation to classify the identified RF transmitter.

10. The system according to claim 3 wherein the processing hub is configured to use the association probabilities for a given RF transmitter of the K identified transmitters to determine a use duty cycle for the identified RF transmitter that provides a percentage of time that the identified RF transmitter transmits.

11. The system according to claim 10 wherein using the association probabilities to determine the use duty cycle comprises integrating the association probabilities over frequency f to determine a function of time t for the given RF transmitter and using the function of time to determine a use duty cycle of the given RF transmitter.

12. The system according to claim 11 wherein determining the use duty cycle comprises using the function of time to determine a percentage of a time period for which the function of time is substantially greater than zero.

13. The system according to claim 11 wherein the processing hub is configured to use the function of time to classify the RF transmitter as to type of RF transmitter.

14. The system according to claim 13 wherein using the function of time to classify the RF transmitter comprises determining a standard deviation for the function of time and using the standard deviation to classify the identified RF transmitter.

15. The system according to claim 1 wherein the PMM comprises two different types of PDFs chosen from a group comprising: a Gaussian PDF, a Rayleigh PDF, and a Ricean PDF.

16. A method for monitoring radio frequency (RF) transmitters in an environment, the method comprising:

acquiring RF power measurements as a function of reception time, t, and frequency f for RF signals in an environment;

fitting to the RF power measurements a probability mixture model (PMM) that provides a probability density as a function of magnitude of the RF power measurements wherein the PMM comprises a plurality of probability density functions (PDFs), at least two of which PDFs have a different form;

identifying a number of RF transmitters operating in the environment responsive to the PMM:

determining association probabilities for the RF power measurements and the identified RF transmitters; and,

using the association probabilities to determine bandwidths for the identified RF transmitters; and use duty cycles for the identified RF transmitters.

17. A system for identifying radio frequency (RF) transmitters in an environment, the system comprising:

at least one RF listening station configured to receive RF signals and acquire measurements of their RF power as a function of reception time, t, and frequency f; and

a processing hub configured to identify RF transmitters operating in the environment by:

receiving the RF power measurements;

fitting to the RF power measurements a probability mixture model (PMM) comprising a plurality of probability density functions (PDFs) that provides a probability density as a function of magnitude of the RF power measurements, by iteratively partitioning the RF power measurements into a plurality of sub-blocks of power measurements; for each given sub-block in an i-th iteration fitting a sub-block PMM comprising a plurality of sub-block PDFs to the RF power measurements in the given sub-block independent of RF power measurements in other sub-blocks of the i-th iteration to determine a number for the plurality of sub-block PDFs in the sub-block PMM;

clustering sub-block PDFs from different sub-blocks to determine clusters of PDFs; and

determining a number, “K”, for a number of transmitters in the environment, responsive to a number of clusters.