Method and system for mitigating Fourier transform side lobes
View Patent ↗The present invention is directed to implementing theoretical foundations of frequency domain methods aiming to locally decrease the impact of aggregate side lobes of a few discrete frequency tones, in the vicinity of other “victim” frequencies. The family of frequency methods referred to makes use of one or more “canceller tones.” The “canceller tones” loads are optimized to minimize the aggregate power in the neighborhood of the victim frequencies. An exemplary method for decreasing an impact of aggregate side lobes of one or more discrete frequency tones in the vicinity of one or more victim tones comprises the steps of calculating an aggregate power of one or more side lobes of one or more disturber tones within a victim bandwidth; determining at least one optimal load to minimize the aggregate power wherein the at least one optimal load comprises a linear combination of the one or more disturber tones; and applying the at least one optimal load to one or more canceller tones for minimizing the impact of the one or more side lobes of the one or more disturber tones.
1. A method for decreasing an impact of aggregate side lobes of one or more discrete frequency tones in the vicinity of one or more victim tones, the method comprising the steps of:
calculating an aggregate power of one or more side lobes of one or more disturber tones within a victim bandwidth;
determining at least one optimal load to minimize the aggregate power wherein the at least one optimal load comprises a linear combination of the one or more disturber tones; and
applying the at least one optimal load to one or more canceller tones for minimizing the impact of the one or more side lobes of the one or more disturber tones.
2. The method of claim 1 , further comprising the steps of:
calculating a minimum aggregate power of the aggregate power; and
calculating a cancellation gain based on the minimum aggregate power.
3. The method of claim 1 wherein the canceller tones are identified from the disturber tones.
4. The method of claim 1 , where the aggregate power is based on an autocorrelation matrix of a vector at a scale of the victim bandwidth.
5. The method of claim 1 , wherein the aggregate power is represented as:
P
(
α
k
J
)
=
^
∫
F
1
F
2
❘
x
k
1
k
°
Q
(
f
)
❘
2
ⅆ
f
where F 1 and F 2 represent the victim bandwidth, x(f) represents a continuous Fourier Transform and k 1 , k Q represent Q disturber tones.
6. The method of claim 1 , wherein the at least one optimal load is represented as:
α
k
J
0
=
C
k
J
a
where C k J represents a linear operator, a represents a dimensional vector, and K J represents a vector of canceller tone indices.
7. The method of claim 6 , wherein the linear operator C k J is represented as:
C k J =−R k J ,k J −1 R k J ,
where R represents an autocorrelation matrix and k j represents the vector of canceller tone indices.
8. The method of claim 1 , wherein the at least one optimal load comprises a linear operator C K J based on a full rank approximation.
9. The method of claim 1 , wherein the step of determining the at least one optimal load further comprises the step of:
determining a sampling resolution in a frequency domain.
10. The method of claim 9 , wherein the sampling resolution is less than a DMT frequency spacing.
11. The method of claim 9 , wherein the step of determining the at least one optimal load further comprises a full rank approximation using the sampling resolution.
12. A system for decreasing an impact of aggregate side lobes of oneor more discrete frequency tones in the vicinity of one or more victim tones, the systemcomprising:
an aggregate power module for calculating an aggregate power of one or moreside lobes of one or more disturber tones within a victim bandwidth; and
an optimal load module for determining a least one optimal load to minimize theaggregate power wherein the at least one optimal load comprises a linear combination of the one or more disturber tones and applying the at least one optimal load to one or more canceller tones for minimizing the impact of the one or more side lobes of the oneor more disturber tones.
13. The system of claim 12 , further comprising:
a cancellation gain module for calculating a minimum aggregate power of the aggregate power and calculating a cancellation gain based on the minimum aggregate power.
14. The system of claim 12 , wherein the canceller tones are identified from the disturber tones.
15. The system of claim 12 , where the aggregate power is based on an autocorrelation matrix of a vector at a scale of the victim bandwidth.
16. The system of claim 12 , wherein the aggregate power is represented as:
P
(
α
k
J
)
=
^
∫
F
1
F
2
❘
x
k
1
k
°
Q
(
f
)
❘
2
ⅆ
f
where F 1 and F 2 represent the victim bandwidth, x(f) represents a continuous Fourier Transform and k 1 , k Q represent Q disturber tones.
17. The system of claim 12 , wherein the at least one optimal load is represented as:
α k 0 J =C k J a
where C k J represents a linear operator, a represents a dimensional vector, and k J represents a vector of canceller tone indices.
18. The system of claim 17 , wherein the linear operator C K J is represented as:
C KJ =−R kJ,kJ −1 R kJ ,
where R represents an autocorrelation matrix and k J represents the vector of canceller tone indices.
19. The system of claim 12 , wherein the at least one optimal load comprises a linear operator C K J based on a full rank approximation.
20. The system of claim 12 , further comprising: a sampling module for determining a sampling resolution in a frequency domain.
21. The system of claim 20 , wherein the sampling resolution is less than a DMT frequency spacing.
22. The system of claim 20 , further comprising:
a full rank module for calculating a full rank approximation using the sampling resolution.
23. At least one processor readable medium for storing a computer program of instructions configured to be readable by at least one processor for instructing the at least one processor to execute a process for performing the method as recited in claim 1 .
24. A system for decreasing an impact of aggregate side lobes of one or more discrete frequency tones in the vicinity of one or more victim tones, the system comprising:
calculating means for calculating an aggregate power of one or more side lobes of one or more disturber tones within a victim bandwidth;
determining means for determining at least one optimal load to minimize the aggregate power wherein the at least one optimal load comprises a linear combination of the one or more disturber tones; and
applying means for applying the at least one optimal load to one or more canceller tones for minimizing the impact of the one or more side lobes of the one or more disturber tones.