GENERATION OF CONSTANT ENVELOPE OR NEARLY-CONSTANT ENVELOPE SIGNALS SATISFYING A GIVEN FOURIER TRANSFORM MAGNITUDE

• US 20100106442A1
• Filed: 10/28/2008
• Published: 04/29/2010
• Est. Priority Date: 10/28/2008
• Status: Active Grant

• Current Assignee: C & P Technologies Inc.
• Original Assignee: C & P Technologies Inc.
• Inventors: LI, KE YONG, PILLAI, UNNIKRISHNA SREEDHARAN
• Granted Patent: US 8,050,880 B2
• Time in Patent Office: Days
• US Class Current: 702/77
• CPC Class Codes: G01S 7/35 Details of non-pulse systems
• CPC Class Codes: G06F 7/544 for evaluating functions by calculation G06F7/4824 takes precedence

Abstract

One or more embodiments of the present invention relates to an iterative method for generating an almost-constant, nearly constant, or substantially-constant envelope time signal with prescribed Fourier transform magnitude in the frequency domain, and a constant envelope time signal whose Fourier transform magnitude closely matches the prescribed Fourier transform magnitude in the frequency domain. Different starting points for the iterative algorithm give rise to different solutions and their accuracy can be adjusted using a monotonic error criterion presented here.

Claims

1. A method comprising

receiving an input signal during an initialization step, wherein a first modified time signal equals the input signal during the initialization step;

receiving a given Fourier transform magnitude function;

repeating the following steps for one or more iterations starting with a first iteration;

at the start of each iteration, computing a computed Fourier transform function of the first modified time signal, wherein for each iteration, each computed Fourier transform function is comprised of a computed Fourier transform magnitude function and a computed phase function in the frequency domain;

replacing the computed Fourier transform magnitude function for this iteration with the given Fourier transform magnitude function to form a modified Fourier transform function for this iteration comprised of the given Fourier transform magnitude function and the computed phase function for this iteration;

performing an inverse Fourier transform on the modified Fourier transform function for this iteration to obtain a second modified time signal in the time domain, wherein the second modified time signal for this iteration has a magnitude and phase function in the time domain;

if the difference between the first modified time signal for this iteration and the second modified time signal for this iteration is less than an error threshold, transmitting the second modified time signal as an output from a transmitter and stopping the iterations;

replacing the magnitude of the second modified time signal with a constant to form a revised first modified time signal for this iteration;

if the difference between the revised first modified time signal and the second modified time signal is less than the error threshold, transmitting the first modified time signal out from a transmitter, and stopping the iterations; and

if the difference between the revised first modified signal and the second modified time signal is not less than the error threshold starting a next iteration, wherein the first modified time signal for the next iteration is equal to the revised first modified time signal of this iteration.

2. The method of claim 1 wherein

the constant is selected so that the energy of the revised first modified time signal is the same as the energy of the second modified time signal.

3. The method of claim 1 wherein

the given Fourier transform magnitude function is flat over a range of frequencies.

4. The method of claim 1 wherein

the given Fourier transform magnitude function has a notch over a frequency band.

5. The method of claim 1 wherein

the difference between the first modified time signal and the second modified time signal relates to the difference between the computed Fourier transform magnitude function of the first modified time signal and the given Fourier transform magnitude function of the second modified time signal;

and

the difference between the first revised modified time signal and the second modified signal relates to the difference between the constant amplitude function of the first revised modified time signal, and the computed amplitude function of the second modified time signal.

8. The method of claim 1 wherein

the revised first modified time signal for this iteration, which is denominated as a k-th iteration, is given by f_k+1 defined as follows:

f_k+1P_AP_Mf_k=P_Ag_k,

where

g_k=P_Mf_k;

wherein f_k represents the first modified time signal for this iteration, which is denominated as the k-th iteration;

wherein the revised first modified time signal for this iteration, which is f_k+1, and the first modified time signal for this iteration, which is f_k, both have a constant envelope property;

wherein g_k represents the second modified time signal for this iteration and g_k has substantially constant envelope output;

wherein P_M is a Fourier transform magnitude substitution operator and is defined through the relation

9. The method of claim 8 wherein

the first modified time signal, which is f_k, at the time when the iterations are terminated possesses an exact constant envelope property and the Fourier transform magnitude function of the first modified time signal, at the time when the iterations are terminated substantially matches the given Fourier transform magnitude function M(ω

).

10. The method of claim 8 wherein

the second modified time signal, which is g_k, at the time when the iterations are terminated possesses a substantially constant envelope property and the Fourier transform magnitude function of the second modified time signal by design procedure matches the given Fourier transform magnitude function M(ω

) exactly.

11. The method of claim 1 wherein

when the iterations are terminated, the first modified time signal or the second modified time signal is transmitted out as part of a radar transmit waveform.

12. The method of claim 1 wherein

when the iterations are terminated, the first modified time signal or the second modified time signal is transmitted out as part of a communication transmission scheme.

6. A method comprising

receiving a given Fourier transform magnitude function at a data input device;

using a computer processor to determine a substantially constant envelope signal having a Fourier transform magnitude function which matches the given Fourier transform magnitude function; and

transmitting the substantially constant envelope signal out from a transmitter.

7. A method comprising

receiving a given Fourier transform magnitude function at a data input device;

using a computer processor to determine a constant envelope signal having a Fourier transform magnitude function that substantially matches the given Fourier transform magnitude function; and

transmitting the constant envelope signal out from a transmitter.

13. An apparatus comprising

a data input device configured to received an input signal during an initialization step, wherein a first modified time signal equals the input signal during the initialization step, the data input device also configured to receive a given Fourier transform magnitude function;

a transmitter;

a computer processor programmed to execute and repeat the following steps for one or more iterations starting with a first iteration;

at the start of each iteration, computing a computed Fourier transform function of the first modified time signal, wherein for each iteration, each computed Fourier transform function is comprised of a computed Fourier transform magnitude function and a computed phase function in the frequency domain;

replacing the computed Fourier transform magnitude function for this iteration with the given Fourier transform magnitude function to form a modified Fourier transform function for this iteration comprised of the given Fourier transform magnitude function and the computed phase function for this iteration;

performing an inverse Fourier transform on the modified Fourier transform function for this iteration to obtain a second modified time signal in the time domain, wherein the second modified time signal for this iteration has a magnitude and phase function in the time domain;

if the difference between the first modified time signal for this iteration and the second modified time signal for this iteration is less than an error threshold, transmitting the second modified time signal as an output from the transmitter and stopping the iterations;

replacing the magnitude of the second modified time signal with a constant to form a revised first modified time signal for this iteration;

if the difference between the revised first modified time signal and the second modified time signal is less than the error threshold, transmitting the first modified time signal out from the transmitter, and stopping the iterations; and

if the difference between the revised first modified signal and the second modified time signal is not less than the error threshold starting a next iteration, wherein the first modified time signal for the next iteration is equal to the revised first modified time signal of this iteration.

14. The apparatus of claim 13 wherein

the computer processor is programmed to select the constant so that the energy of the revised first modified time signal is the same as the energy of the second modified time signal.

15. The apparatus of claim 13 wherein

the given Fourier transform magnitude function is flat over a range of frequencies.

16. The apparatus of claim 13 wherein

the given Fourier transform magnitude function has a notch over a frequency band.

17. The apparatus of claim 13 wherein

the difference between the first modified time signal and the second modified time signal relates to the difference between the computed Fourier transform magnitude function of the first modified time signal and the given Fourier transform magnitude function of the second modified time signal;

and

the difference between the first revised modified time signal and the second modified signal relates to the difference between the constant amplitude function of the first revised modified time signal, and the computed amplitude function of the second modified time signal.

20. The apparatus of claim 13 wherein

the revised first modified time signal for this iteration, which is denominated as a k-th iteration, is given by f_k+1 defined as follows:

f_k+1=P_AP_Mf_k=P_Ag_k,

where

g_k=P_Mf_k;

wherein f_k represents the first modified time signal for this iteration, which is denominated as the k-th iteration;

wherein the revised first modified time signal for this iteration, which is f_k+1, and the first modified time signal for this iteration, which is f_k, both have a constant envelope property;

wherein g_k represents the second modified time signal for this iteration and g_k has substantially constant envelope output;

wherein P_M is a Fourier transform magnitude substitution operator and is defined through the relation

21. The apparatus of claim 20 wherein

the first modified time signal, which is f_k, at the time when the iterations are terminated possesses an exact constant envelope property and the Fourier transform magnitude function of the first modified time signal, at the time when the iterations are terminated substantially matches the given Fourier transform magnitude function M(ω

).

22. The apparatus of claim 20 wherein

the second modified time signal, which is g_k, at the time when the iterations are terminated possesses a substantially constant envelope property and the Fourier transform magnitude function of the second modified time signal at the time when the iterations are terminated matches the given Fourier transform magnitude function M(ω

) exactly.

23. The apparatus of claim 13 wherein

when the iterations are terminated, the computer processor causes the first modified time signal or the second modified time signal to be transmitted out from the transmitter as part of a radar transmit waveform.

24. The apparatus of claim 13 wherein

when the iterations are terminated, the computer processor causes the first modified time signal or the second modified time signal is transmitted out from the transmitter as part of a communication transmission scheme.

18. An apparatus comprising

a data input device configured to receive to receive a given Fourier transform magnitude function;

a transmitter;

a computer processor programmed to determine a substantially constant envelope signal having a Fourier transform magnitude function which matches the given Fourier transform magnitude function; and

wherein the computer processor is programmed to cause the substantially constant envelope signal to be transmitted out from the transmitter.

19. The apparatus of claim 18 wherein

a computer processor programmed to determine a constant envelope signal having a Fourier transform magnitude function which substantially matches the given Fourier transform magnitude function;

and

wherein the computer processor is programmed to cause the constant envelope signal to be transmitted out from the transmitter.