Efficient cross-correlation with adaptive polar quantization
A system and method for signal cross-correlation using adaptive polar quantization and polar multiplication is disclosed. The method includes receiving a first and second complex signal. The method includes computing a first quantized phase and a first quantized magnitude based on a first adaptive polar quantization of a sample of the first complex signal and computing a second quantized phase and a second quantized magnitude based on a second adaptive polar quantization of a sample of the second complex signal. The method includes computing a polar multiplication based on the first quantized phase, the first quantized magnitude, the second quantized phase, and the second quantized magnitude to generate a rotated quantized phase and a multiplied quantized magnitude; converting to component real and imaginary parts; and computing a sum using complex addition.
1. A method for signal cross-correlation comprising:
1a) receiving a first complex signal and a second complex signal;
1b) computing a first quantized phase and a first quantized magnitude based on a first adaptive polar quantization of a sample of the first complex signal;
1c) computing a second quantized phase and a second quantized magnitude based on a second adaptive polar quantization of a sample of the second complex signal;
2) Computing a polar multiplication based on the first quantized phase, the first quantized magnitude, the second quantized phase, and the second quantized magnitude to generate a rotated quantized phase and a multiplied quantized magnitude;
3) Converting the rotated quantized phase and the multiplied quantized magnitude to component real and imaginary parts; and
4) Computing a sum of the component real and imaginary parts of the multiplied quantized magnitude and the rotated quantized phase via complex addition.
2. The method of claim 1 further comprising storing at least one of the first quantized magnitude and the first quantized phase in a first delay line; and storing at least one of the second quantized magnitude and the second quantized phase in a second delay line.
3. The method of claim 1 further comprising comparing the sum to a threshold.
4. The method of claim 1 , wherein the computing the first quantized phase and the first quantized magnitude based on the first adaptive polar quantization of the sample of the first complex signal comprises:
receiving the first complex signal characterized by a first real portion and a first imaginary portion;
computing a first vector magnitude of the sample of the first complex signal;
computing a first quantization threshold value from at least one first weighted sample of the first complex signal;
comparing the first vector magnitude of the sample to the first quantization threshold value;
associating the first quantized magnitude with the sample according to a comparison between the first vector magnitude of the sample and the first quantization threshold value; and
associating the first quantized phase with the sample of the first complex signal.
5. The method of claim 1 , wherein the computing the second quantized phase and the second quantized magnitude based on the second adaptive polar quantization of the sample of the second complex signal comprises:
receiving the second complex signal characterized by a second real portion and a second imaginary portion;
computing a second vector magnitude of the sample of the second complex signal;
computing a second quantization threshold value from at least one second weighted sample of the second complex signal;
comparing the second vector magnitude of the sample to the second quantization threshold value;
associating the second quantized magnitude with the sample according to a comparison between the second vector magnitude of the sample and the second quantization threshold value; and
associating the second quantized phase with the sample of the second complex signal.
6. The method of claim 1 , wherein the first adaptive polar quantization and the second adaptive polar quantization are configured to be executed via one or more adaptive polar quantization modules.
7. The method of claim 1 , wherein the computing of the polar multiplication is configured to be executed via a polar multiplication module.
8. The method of claim 1 , wherein the converting of the rotated quantized phase and the multiplied quantized magnitude to the component real and imaginary parts is configured to be executed via a polar-to-rectangular conversion module.
9. The method of claim 1 , wherein the computing of the sum of the component real and imaginary parts of the multiplied quantized magnitude and the rotated quantized phase via the complex addition is configured to be executed via a complex addition module.
10. The method of claim 1 further comprising storing the first quantized phase and the first quantized magnitude in a first delay line and storing the second quantized phase and the second quantized magnitude in a second delay line.
11. A system for signal cross-correlation comprising:
a controller configured to execute steps of a process based on instructions stored in memory, the steps comprising:
receiving a first complex signal and a second complex signal;
computing a first quantized phase and a first quantized magnitude based on a first adaptive polar quantization of a sample of the first complex signal;
computing a second quantized phase and a second quantized magnitude based on a second adaptive polar quantization of a sample of the second complex signal;
computing a polar multiplication based on the first quantized phase, the first quantized magnitude, the second quantized phase, and the second quantized magnitude to generate a rotated quantized phase and a multiplied quantized magnitude;
converting the rotated quantized phase and the multiplied quantized magnitude to component real and imaginary parts; and
computing a sum of the component real and imaginary parts of the multiplied quantized magnitude and the rotated quantized phase via complex addition.
12. The system of claim 11 , the steps further comprising storing at least one of the first quantized magnitude and the first quantized phase in a first delay line; and storing at least one of the second quantized magnitude and the second quantized phase in a second delay line.
13. The system of claim 11 , the steps further comprising comparing the sum to a threshold.
14. The system of claim 11 , wherein the computing the first quantized phase and the first quantized magnitude based on the first adaptive polar quantization of the sample of the first complex signal comprises:
receiving the first complex signal characterized by a first real portion and a first imaginary portion;
computing a first vector magnitude of the sample of the first complex signal;
computing a first quantization threshold value from at least one first weighted sample of the first complex signal;
comparing the first vector magnitude of the sample to the first quantization threshold value;
associating the first quantized magnitude with the sample according to a comparison between the first vector magnitude of the sample and the first quantization threshold value; and
associating the first quantized phase with the sample of the first complex signal.
15. The system of claim 11 , wherein the computing the second quantized phase and the second quantized magnitude based on the second adaptive polar quantization of the sample of the second complex signal comprises:
receiving the second complex signal characterized by a second real portion and a second imaginary portion;
computing a second vector magnitude of the sample of the second complex signal;
computing a second quantization threshold value from at least one second weighted sample of the second complex signal;
comparing the second vector magnitude of the sample to the second quantization threshold value;
associating the second quantized magnitude with the sample according to a comparison between the second vector magnitude of the sample and the second quantization threshold value; and
associating the second quantized phase with the sample of the second complex signal.
16. The system of claim 11 , wherein the first adaptive polar quantization and the second adaptive polar quantization are configured to be executed via one or more adaptive polar quantization modules of the system.
17. The system of claim 11 , wherein the computing of the polar multiplication is configured to be executed via a polar multiplication module of the system.
18. The system of claim 11 , wherein the converting of the rotated quantized phase and the multiplied quantized magnitude to the component real and imaginary parts is configured to be executed via a polar-to-rectangular conversion module of the system.
19. The system of claim 11 , wherein the computing of the sum of the component real and imaginary parts of the multiplied quantized magnitude and the rotated quantized phase via complex addition is configured to be executed via a complex addition module of the system.
20. The system of claim 11 , the steps further comprising storing the first quantized phase and the first quantized magnitude in a first delay line and storing the second quantized phase and the second quantized magnitude in a second delay line.