Detection and estimation of narrowband interference by matrix multiplication

1. A method of processing a signal, the method comprising:

based on a frequency domain representation S[0]-S[M−1] of the signal, selecting a set identifying at least two tones namely a strongest tone and a tone adjacent thereto, the strongest tone being selected for being at a maximum value relative to background noise, across all M tones in the frequency domain representation;

based on the selected set, identifying from among M complex numbers S[0]-S[M−1] in the frequency domain representation, a corresponding set of complex numbers denoting a vector Z;

using at least one processing unit to multiply the vector Z with each of a plurality of columns of a predetermined matrix G;

based on the products resulting from the vector multiplication of Z and G, determining and storing in a computer-readable memory coupled to said at least one processing unit, at least one of: (A) a flag indicating presence or absence of a narrowband interference in said signal; and (B) an estimate of a frequency of said narrowband interference in said signal, and wherein:

S is a signal sample;

M is a selected integer value;

Z is a vector; and

G is a predetermined matrix.

2. The method of claim 1 wherein as per (B) said estimate is determined and stored in said computer-readable memory, the method further comprising:

choosing a product from among the M products, based on at least one predetermined criterion; and

using the chosen product to compute the estimate;

wherein the estimate is at a second resolution finer than a first resolution of M tones S[0]-S[M−1] in the frequency domain representation.

3. The method of claim 1 wherein said selecting of the set comprises:

identifying as said strongest tone, a frequency kmax at which T−1[k]*S[k] is maximized;

wherein T[k] is proportional to power spectrum of said background noise and S[k] is an element in S[0]-S[M−1] at frequency k, and wherein:

T is a vector; and

k is a position within a vector.

4. The method of claim 1 wherein said determining comprises:

computing an absolute value of each of the products; and

identifying a position m of a maximum among the absolute values resulting from said computing, wherein m is an integer value.

5. The method of claim 1 wherein said determining comprises:

computing a function A of each of the real component and imaginary component of the products; and

identifying a position m of a maximum among the values of function A resulting from said computing.

6. The method of claim 5 wherein:

said function A is an approximation of the absolute value of each of the products.

7. The method of claim 5 wherein:

said strongest tone is at a frequency kmax; and

said estimate is a function F of kmax, m and the number of products, wherein:

F is an estimate function;

k is an integer value; and

m is an integer value.

8. The method of claim 7 wherein:

said function F is kmax+½(−1+m/L), and wherein L is a selected integer value.

9. The method of claim 1 wherein:

said strongest tone is at a frequency kmax in the frequency domain representation of the signal, wherein k is an integer value;

said adjacent tone is kmax−1; and

the selected set includes each of kmax−1, kmax, and kmax+1.

10. The method of claim 9 wherein:

the selected set further includes at least one of kmax−2 and kmax+2.

11. The method of claim 1 wherein:

said adjacent tone is on a first side of said strongest tone in the frequency domain representation of the signal;

the selected set comprises another adjacent tone on a second side of the strongest tone;

the vector Z is a complex vector of size 1×n, wherein n is a selected integer value; and

the matrix G is of size n×2L; and wherein L is an integer.

12. The method of claim 1 further comprising, prior to selecting the selected set identifying at least the strongest tone and the adjacent tone:

applying a plurality of frequency-specific thresholds, to pick a group of candidate tones from among M tones in the frequency domain representation of the signal; and

applying a predetermined criterion on the group of candidate tones to identify said strongest tone.

13. A circuit for processing a signal, the circuit comprising at least a processor and a memory coupled to the processor, the circuit comprising:

means, based on a frequency domain representation S[0]-S[M−1] of the signal, for selecting a set identifying at least two tones namely a strongest tone and a tone adjacent thereto, the strongest tone being selected for being at a maximum value relative to background noise, across all M tones in the frequency domain representation;

means, based on the selected set, for identifying from among M complex numbers S[0]-S[M−1] in the frequency domain representation, a corresponding set of complex numbers denoting a vector Z;

means for multiplying the vector Z with each of M columns of a predetermined matrix G;

means, based on M products resulting from the vector multiplication of Z and G, for determining and storing in said memory, at least one of: (A) a flag indicating presence or absence of a narrowband interference in said signal; and (B) an estimate of a frequency of said narrowband interference in said signal, and wherein:

S is a signal sample;

M is a selected integer value;

Z is a vector; and

G is a predetermined matrix.

14. The circuit of claim 13 wherein as per (B) said estimate is determined and stored in said computer-readable memory, the circuit further comprising:

means for choosing a product from among the M products, based on at least one predetermined criterion; and

means for using the chosen product to compute the estimate;

wherein the estimate is at a second resolution finer than a first resolution of M tones in the frequency domain representation.

15. The circuit of claim 13 wherein said means for selecting the set comprises:

means for identifying as said strongest tone, a frequency kmax at which T−1[k]*S[k] is maximized;

wherein T[k] is proportional to power spectrum of said background noise and S[k] is an element at frequency k in S[0]-S[M−1], and wherein:

T is a vector; and

k is a position within a vector.

16. The circuit of claim 13 wherein said means for determining comprises:

means for computing an approximation of an absolute value of each of the M products; and

means for identifying a position m of a maximum among the absolute values resulting from said computing, wherein m is an integer value.

17. The circuit of claim 13 wherein:

said strongest tone is at a frequency kmax; and

said estimate is a function of kmax, m and M, wherein:

k is an integer value; and

m is an integer value.

18. The circuit of claim 13 wherein:

said strongest tone is at a frequency kmax in the frequency domain representation of the signal, wherein k is an integer value;

said adjacent tone is kmax−1; and

the selected set includes each of kmax−1, kmax, and kmax+1.

19. The circuit of claim 13 wherein:

said adjacent tone is on a first side of said strongest tone in the frequency domain representation of the signal;

the selected set comprises another adjacent tone on a second side of the strongest tone;

the vector Z is a complex vector of size 1×3; and

the matrix G is of size 3×; and wherein integer M is an even number.

20. The circuit of claim 13 further comprising:

means for applying a plurality of frequency-specific thresholds, to pick a group of candidate tones from among M tones in the frequency domain representation of the signal; and

means for applying a predetermined criterion on the group of candidate tones to identify said strongest tone.