Integrated circuit implementation of methods and apparatuses for monitoring occupancy of wideband GHz spectrum, and sensing respective frequency components of time-varying signals using sub-nyquist criterion signal sampling

1. An integrated circuit apparatus to determine an N-point Fast Fourier Transform (FFT) of a time-varying signal so as to sense one or more frequency components of the time-varying signal, the apparatus comprising:

an input/output interface to receive a first sub-sampled set of samples of the time-varying signal sampled at a first sampling rate below a Nyquist rate of the time-varying signal and a second sub-sampled set of samples of the time-varying signal sampled at a second sampling rate below the Nyquist rate of the time-varying signal, wherein the second sampling rate is different from the first sampling rate; and

at least one processor communicatively coupled to the input/output interface to:

A) compute a first Fast Fourier Transform (FFT) for the first sub-sampled set of samples of the time-varying signal; and

B) compute a second FFT for the second sub-sampled set of samples of the time-varying signal,

wherein:

each of the first FFT and the second FFT is a low-radix FFT;

the time-varying signal has a frequency bandwidth of interest BW and a Nyquist sampling criteria of N samples in a sampling time T, wherein N=T×BW;

the first sampling rate is BW/p 1 samples/second, wherein p 1 is less than N;

the second sampling rate is BW/p 2 samples/second, wherein p 2 is less than N; and

p 2 and p 1 are co-prime numbers.

2. The apparatus of claim 1 , wherein the apparatus is implemented as an Application Specific Integrated Circuit (ASIC).

3. The apparatus of claim 1 , wherein the at least one processor computes the N-point FFT of the time-varying signal based at least in part on A) and B), and wherein the input/output interface is configured to output a digital representation of the N-point FFT so as to provide an indication of the one or more frequency components of the sampled time-varying signal.

4. The apparatus of claim 1 , wherein:

at least one of the first and second FFTs is a radix-2 FFT; and

another of the first and second FFTs is a radix-3 FFT.

5. An integrated circuit apparatus to determine an N-point Fast Fourier Transform (FFT) of a time-varying signal so as to sense one or more frequency components of the time-varying signal, the apparatus comprising:

an input/output interface to receive a first sub-sampled set of samples of the time-varying signal sampled at a first sampling rate below a Nyquist rate of the time-varying signal and a second sub-sampled set of samples of the time-varying signal sampled at a second sampling rate below the Nyquist rate of the time-varying signal, wherein the second sampling rate is different from the first sampling rate; and

at least one processor communicatively coupled to the input/output interface to:

A) compute a first Fast Fourier Transform (FFT) for the first sub-sampled set of samples of the time-varying signal; and

B) compute a second FFT for the second sub-sampled set of samples of the time-varying signal,

wherein:

each of the first FFT and the second FFT is a low-radix FFT;

the input/output interface is configured to provide to the at least one processor:

the first sub-sampled set of samples at the first sampling rate;

the second sub-sampled set of samples at the second sampling rate;

a third sub-sampled set of samples at the first sampling rate and time-shifted from the first sub-sampled set by a first number of samples; and

a fourth sub-sampled set of samples at the second sampling rate and time-shifted from the second sub-sampled set by a second number of samples; and

the at least one processor further is configured to compute:

C) a third FFT for the third sub-sampled set of samples of the time-varying signal; and

D) a fourth FFT for the fourth sub-sampled set of samples of the time-varying signal, wherein the N-point FFT of the time-varying signal is based at least in part on A), B), C) and D).

6. The apparatus of claim 5 , wherein:

the first number of samples is one sample; and

the second number of samples is one sample.

7. The apparatus of claim 5 , wherein:

the input/output interface is configured to further provide to the at least one processor:

a fifth sub-sampled set of samples at the first sampling rate and time-shifted from the first sub-sampled set by a third number of samples; and

a sixth sub-sampled set of samples at the second sampling rate and time-shifted from the second sub-sampled set by the third number of samples; and

the at least one processor further is configured to compute:

E) a fifth FFT for the fifth sub-sampled set of samples of the time-varying signal; and

F) a sixth FFT for the sixth sub-sampled set of samples of the time-varying signal, wherein the N-point FFT of the time-varying signal is based at least in part on A), B), C), D), E) and F).

8. The apparatus of claim 7 , wherein:

the first number of samples is one sample;

the second number of samples is one sample; and

the third number of samples is 32 samples.

9. A system, comprising:

the integrated circuit apparatus of claim 1 ; and

an analog-to-digital converter (ADC) apparatus, communicatively coupled to the input/output interface of the integrated circuit apparatus, to provide the first sub-sampled set of samples at the first sampling rate and the second sub-sampled set of samples at the second sampling rate.

10. The system of claim 9 , wherein:

the input/output interface is configured to provide to the at least one processor:

the first sub-sampled set of samples at the first sampling rate;

the second sub-sampled set of samples at the second sampling rate;

a third sub-sampled set of samples at the first sampling rate and time-shifted from the first sub-sampled set by a first number of samples; and

a fourth sub-sampled set of samples at the second sampling rate time-shifted from the second sub-sampled set by a second number of samples; and

the at least one processor of the integrated circuit apparatus further computes:

C) a third FFT for the third sub-sampled set of samples of the time-varying signal; and

D) a fourth FFT for the fourth sub-sampled set of samples of the time-varying signal, wherein the N-point FFT of the time-varying signal is based at least in part on A), B), C) and D).

11. The system of claim 10 , wherein:

the first number of samples is one sample; and

the second number of samples is one sample.

12. The system of claim 11 , wherein:

the at least one input/output interface is configured to further provide to the at least one processor:

a fifth sub-sampled set of samples at the first sampling rate and time-shifted from the first sub-sampled set by a third number of samples; and

a sixth sub-sampled set of samples at the second sampling rate and time-shifted from the second sub-sampled set by the third number of samples; and

the at least one processor of the integrated circuit apparatus further computes:

E) a fifth FFT for the fifth sub-sampled set of samples of the time-varying signal; and

F) a sixth FFT for the sixth sub-sampled set of samples of the time-varying signal,

wherein the N-point FFT of the time-varying signal is based at least in part on A), B), C), D), E) and F).

13. The system of claim 12 , wherein:

the first number of samples is one sample;

the second number of samples is one sample; and

the third number of samples is 32 samples.

14. The apparatus of claim 1 , wherein Nis greater than 700,000.

15. The apparatus of claim 14 , wherein N=746,496.

16. The apparatus of claim 1 , wherein:

the first FFT is a B 1 -point FFT, wherein R 1 =N/p 1 ; and

the second FFT is a B 2 -point FFT, wherein R 2 =N/p 2 .

17. The apparatus of claim 1 , wherein the frequency bandwidth of interest BW is at least approximately 1 GHz.

18. The apparatus of claim 1 , wherein the one or more frequency components of the time-varying signal occupy less than or equal to approximately 5% of the frequency bandwidth of interest BW.

19. The apparatus of claim 18 , wherein the one or more frequency components of the time-varying signal occupy less than or equal to approximately 2% of the frequency bandwidth of interest BW.

20. The apparatus of claim 19 , wherein the one or more frequency components of the time-varying signal occupy less than or equal to approximately 0.1% of the frequency bandwidth of interest BW.

21. The apparatus of claim 1 , wherein the one or more frequency components of the time-varying signal respectively represent at least one of:

a Bluetooth signal;

a GSM signal;

a CDMA signal;

a Wi-Fi signal; and

a WiMax signal.

22. An Application Specific Integrated Circuit (ASIC) apparatus to determine an N-point Fast Fourier Transform (FFT) of a sampled time-varying signal so as to sense one or more frequency components of the sampled time-varying signal, the time-varying signal having a frequency bandwidth of interest BW and a Nyquist sampling criteria of N samples in a sampling time T, wherein N=T×BW, the sampled time-varying signal including a first sub-sampled set of B 1 samples of the time-varying signal and a second sub-sampled set of B 2 samples of the time-varying signal, the apparatus comprising:

an input/output interface to receive the first sub-sampled set of B 1 samples and the second sub-sampled set of B 2 samples, wherein B 1 =N/p 1 , B 2 =N/p 2 , and wherein p 2 and p i are co-prime numbers and both less than N; and

at least one processor communicatively coupled to the input/output interface to:

A) compute a first B 1 -point Fast Fourier Transform (FFT) for the first set of B 1 samples of the time-varying signal;

B) compute a second B 2 -point FFT for the second set of B 2 samples of the time-varying signal; and

C) compute the N-point FFT of the sampled time-varying signal based at least in part on A) and B),

wherein:

each of the first B 1 -point FFT and the second B 1 -point FFT is a low-radix FFT; and

the input/output interface is configured to output the N-point FFT from C) so as to provide an indication of the one or more frequency components of the sampled time-varying signal.

23. A system, comprising:

the ASIC apparatus of claim 22 ; and

an analog-to-digital converter (ADC) apparatus, communicatively coupled to the input/output interface of the ASIC apparatus, to provide the first sub-sampled set of samples at the first sampling rate and the second sub-sampled set of samples at the second sampling rate.

24. The ASIC apparatus of claim 22 , wherein p 1 is based on a first radix and p 2 is based on a second radix.

25. The ASIC apparatus of claim 24 , wherein the first radix and the second radix are small integers.

26. The ASIC apparatus of claim 25 , wherein the first radix is 2 or 4 and the second radix is 3.

27. The ASIC apparatus of claim 22 , wherein the sampled time-varying signal is a sparse wideband signal.

28. The ASIC apparatus of claim 27 , wherein the bandwidth of interest for the sampled time-varying signal is approximately 1 GHz.

29. The ASIC apparatus of claim 28 , wherein one or more frequency components of the sampled time-varying signal occupy less than or equal to approximately 0.1% of the bandwidth of interest for the sampled time-varying signal.

30. An application specific integrated circuit (ASIC) apparatus for calculating a Fast Fourier Transform (FFT) of a signal, the ASIC apparatus comprising:

an input/output interface adapted to receive a discrete z-point signal, z being a product of at least two numbers;

one or more first x n -word memory blocks configured to store x n signal points sub-sampled by z/x n from the z-point signal;

one or more second y m -word memory blocks configured to store y m signal points sub-sampled by z/y m from the z-point signal, wherein x and y are co-prime numbers and n and m are natural numbers, and

a microprocessor for calculating the FFT of the signal, the microprocessor comprising:

a bucketization microarchitecture to sub-sample the received signal and alias signal points to buckets whose number is less or equal to z, and

a reconstruction microarchitecture designed to estimate a magnitude value and a frequency index of one or more frequency components of the z-point signal.