Method and apparatus for signal separation

1. A method of parameterizing an input signal having a plurality of mixed baseband signals, the method comprising the steps of:

applying a non-linear transform to an input signal, in order to eliminate carrier effects from the input signal and to produce a non-linearly transformed signal having distinct, recognizable features in a plane defined by phase modes and amplitude modes;

passing the non-linearly transformed signal through a low pass filter to produce a linear combination of data symbols and DC components;

determining the DC components, wherein the DC components have probability density functions with distinct amplitude and phase modes;

separating, using the probability density functions, a plurality of mixed baseband signals from the input signal to produce separated signals; and

coordinate transforming each of the separated signals from polar coordinates to Cartesian coordinates to produce coordinate transformed signals.

2. A method of parameterizing an input signal according to claim 1 , wherein said non-linearly transforming comprises:

passing an input signal through a conjugate delayed product multiplier having an iterative delay estimator; and

generating at least one of a complex output of the input signal and a real output of the input signal.

3. A method of parameterizing an input signal having a plurality of mixed baseband signals, the method comprising the steps of:

applying a non-linear transform to an input signal;

passing the input signal through a low pass filter to produce a linear combination of data symbols and DC components;

determining the DC components, wherein said DC component determining step is selected from performing a least squares operation, performing a null space projection, and performing a polynomial solution;

separating a plurality of mixed baseband signals from the input signal to produce separated signals; and

coordinate transforming each of the separated signals from polar coordinates to Cartesian coordinates to produce coordinate transformed signals.

4. A method of parameterizing according to claim 3 further comprising extracting features from the separated signals using cyclostationary feature extraction.

5. A method of parameterizing according to claim 4 , wherein said cyclostationary feature extraction is selected from performing a non-linear operation and performing a joint time-frequency autocorrelation.

6. A method of parameterizing an input signal having a plurality of mixed baseband signals, the method comprising the steps of:

applying a non-linear transform to an input signal;

passing the input signal through a low pass filter to produce a linear combination of data symbols and DC components;

determining the DC components;

separating a plurality of mixed baseband signals from the input signal to produce separated signals;

coordinate transforming each of the separated signals from polar coordinates to Cartesian coordinates to produce coordinate transformed signals; and

conducting cyclostationary feature detection on the coordinate transformed signals.

7. A method of recovering at least one baseband source signal from a plurality of mixed signals, the method comprising the steps of:

down-converting and digitizing a plurality of mixed signals in an RF bandwidth;

polyphase channelizing the digitized bandwidth;

re-assembling the channels into an original order of an original spectrum and polyphase reconstructing the original spectrum;

passing an input signal selected from the polyphase channelized signal and the polyphase reconstructed signal through a nonlinear transform and a low-pass filter to produce non-linear transformed signals, wherein the non-linear transform eliminates carrier effects from the input signal to produce a non-linearly transformed signal having distinct, recognizable features in a plane defined by phase modes and amplitude modes;

determining DC components of each of the non-linear transformed signals, wherein the DC components have probability density functions with distinct amplitude and phase modes;

separating, using the probability density functions, a plurality of mixed baseband signals to produce separated signals; and

coordinate transforming each of the separated signals from polar coordinates to Cartesian coordinates to produce coordinate transformed signals.

8. A method of recovering at least one baseband source signal from a plurality of mixed signals, the method comprising the steps of:

down-converting and digitizing a plurality of mixed signals in an RF bandwidth;

polyphase channelizing the digitized bandwidth;

re-assembling the channels into an original order of an original spectrum and polyphase reconstructing the original spectrum;

passing one of the polyphase channelized signal and the polyphase reconstructed signal through a non-linear transform and a low-pass filter;

determining DC components of each of the non-linear transformed signals;

separating a plurality of mixed baseband signals by performing:

x ( t )= As ( t )+ u ( t )

s ( t )=[ s 1 ( t ), s 2 ( t )] T

Q (ω)=∥ x ( t )− As ( t )∥ 2

s ′( t )=( A H A ) −1 A H x ( t )

Q (ω)=∥ x ( t )− A ( A H A ) −1 A H x ( t )∥ 2

where x(t) represents the output of the low pass filter in vector notation, u(t) represents the low pass version of noise related terms, Q(ω) represents the cost function of a least squares approach, and s′(t) minimizes Q(ω); and

coordinate transforming each of the separated signals from polar coordinates to Cartesian coordinates.

9. A method according to claim 7 , wherein said passing step comprises the steps of:

passing the input signal through a conjugate delayed product multiplier having an iterative delay estimator; and

generating at least one of a complex output of the input signal and a real output of the input signal;

wherein the input signal is selected from the polyphase channelized signal and the polyphase reconstructed signal.

10. A method of recovering at least one baseband source signal from a plurality of mixed signals, the method comprising the steps of:

down-converting and digitizing a plurality of mixed signals in an RF bandwidth;

polyphase channelizing the digitized bandwidth;

re-assembling the channels into an original order of an original spectrum and polyphase reconstructing the original spectrum;

passing one of the polyphase channelized signal and the polyphase reconstructed signal through a non-linear transform and a low-pass filter;

determining DC components of each of the non-linear transformed signals, wherein said DC component determining step is selected from performing a least squares operator, performing a null space projection, and performing a polynomial solution;

separating a plurality of mixed baseband signals to produce separated signals; and

coordinate transforming each of the separated signals from polar coordinates to Cartesian coordinates to produce coordinate transformed signals.

11. A method according to claim 6 further comprising extracting features from the separated signals using cyclostationary feature extraction.

12. A method according to claim 11 , wherein said cyclostationary feature extraction is selected from performing a non-linear transform operation and performing a joint time-frequency autocorrelation.

13. A method of recovering at least one baseband source signal from a plurality of mixed signals, the method comprising the steps of:

down-converting and digitizing a plurality of mixed signals in an RF bandwidth;

polyphase channelizing the digitized bandwidth;

re-assembling the channels into an original order of an original spectrum and polyphase reconstructing the original spectrum;

passing one of the polyphase channelized signal and the polyphase reconstructed signal through a non-linear transform and a low-pass filter;

determining DC components of each of the non-linear transformed signals;

separating a plurality of mixed baseband signals to produce separated signals; and

coordinate transforming each of the separated signals from polar coordinates to Cartesian coordinates to produce coordinate transformed signals; and

conducting cyclostationary feature detection on the coordinate transformed signals.

14. A digital radio receiver comprising:

a channel transformer adapted to polyphase channelize a communications signal, re-assemble the channels into contiguous channels, and polyphase reconstruct the original transmission spectrum;

a non-linear transform operator adapted to receive one of the polyphase channelized signal and the polyphase reconstructed signal from said channel transformer and adapted to produce a linear combination of data symbols, and DC components;

a low-pass filter connected to said non-linear transform operator for producing a linear combination of data symbols and DC components;

a first signal separator connected to said low-pass filter and adapted to separate a plurality of mixed baseband signals;

a coordinate transform operator connected to said first signal separator and adapted to transform the separated signals from polar coordinates to Cartesian coordinates to produce coordinate transformed signals; and

a second signal separator connected to said coordinate transform operator and adapted for signal separation of the coordinate transformed signals.

15. A spread spectrum receiver comprising:

a channel transformer adapted to polyphase channelize a communications signal, re-assemble the channels into contiguous channels, and polyphase reconstruct the original transmission spectrum;

a non-linear transform operator adapted to receive one of the polyphase channelized signal and the polyphase reconstructed signal from said channel transformer and adapted to produce a linear combination of data symbols, and DC components;

a low-pass filter connected to said non-linear transform operator for producing a linear combination of data symbols and DC components;

a first signal separator connected to said low-pass filter and adapted to separate a plurality of mixed baseband signals;

a coordinate transform operator connected to said first signal separator and adapted to transform the separated signals from polar coordinates to Cartesian coordinates; and

a second signal separator connected to said coordinate transform operator and adapted for signal separation of the separated signals from said coordinate transform operator.

16. A spread spectrum receiver according to claim 15 , wherein said second signal separator is adapted for cyclostationary feature detection selected from non-linear transform operation and joint time-frequency autocorrelation.

17. A spread spectrum receiver according to claim 15 further comprising a CDMA processor connected to said second signal separator for demodulating and decoding the separated signals.

18. A receiver according to claim 14 further comprising:

a down-converter connected to said channel transformer for digitizing and down-converting a full RF band.

19. A receiver according to claim 14 , wherein said non-linear transform operator comprises a conjugate delay product multiplier having an iterative delay estimator.

20. A receiver according to claim 14 , wherein said first signal processor is adapted to perform one of a least squares operation, a null space projection, and a polynomial solution.