Robust noise power estimation

1. A method for estimating noise in a channel impulse response measurement, the method comprising:

calculating a first average energy, the first average energy being an average energy of a sequence of time-domain samples of the channel impulse response measurement;

setting a detection threshold;

identifying a first subset of the sequence of time-domain samples, each element of the first subset of the sequence of time-domain samples having an energy less than the detection threshold; and

calculating a second average energy, the second average energy being an average energy of the first subset of the sequence of time-domain samples.

2. The method of claim 1 , wherein the setting of the detection threshold comprises:

selecting the detection threshold to correspond, based on the first average energy, to a target false alarm probability, the target false alarm probability being less than 10%; or

selecting the detection threshold to correspond, based on the first average energy, to a target estimation bias, the target estimation bias being less than 10% of the first average energy.

3. The method of claim 1 , wherein:

the calculating of the first average energy comprises calculating a total energy of the sequence of time-domain samples; and

the calculating of the second average energy comprises:

setting an intermediate energy value equal to the total energy of the sequence of time-domain samples;

setting an intermediate sample count equal to a size of the sequence of time-domain samples;

for each sample, of the sequence of time-domain samples, that is not an element of the first subset:

subtracting, from the intermediate energy value, an energy of the sample, and

subtracting one from the intermediate sample count; and

setting the second average energy equal to:

a final value of the intermediate energy value,

divided by

a final value of the intermediate sample count.

4. The method of claim 1 , wherein the calculating of the second average energy comprises:

setting an intermediate energy value equal to zero;

setting an intermediate sample count equal to zero;

for each sample, of the sequence of time-domain samples, that is not an element of the first subset:

adding, to the intermediate energy value, an energy of the sample, and

adding one to the intermediate sample count; and

setting the second average energy equal to a numerator divided by a denominator, wherein:

the numerator equals a difference of:

the first average energy, and

a quotient of:

a final value of the intermediate energy value, and

a size of the sequence of time-domain samples; and

the denominator equals a difference of:

1, and

a quotient of:

a final value of the intermediate sample count, and

the size of the sequence of time-domain samples.

5. The method of claim 1 , further comprising calculating an inverse fast Fourier transform of a frequency domain channel response to form the channel impulse response measurement.

6. The method of claim 5 , wherein the sequence of time-domain samples of the channel impulse response measurement is a plurality of consecutive samples of the inverse fast Fourier transform.

7. The method of claim 6 , wherein a first-in-order sample of the sequence of time-domain samples is an nth element of the inverse fast Fourier transform, n being within 20% of one half of a size of the inverse fast Fourier transform.

8. The method of claim 7 , wherein a last-in-order sample of the sequence of time-domain samples is an mth element of the inverse fast Fourier transform, m being within 20% of nine-tenths of the size of the inverse fast Fourier transform.

9. A system for estimating noise, the system comprising:

a receiver, and

a processing circuit,

the processing circuit being configured to:

calculate a channel impulse response measurement;

calculate a first average energy, the first average energy being an average energy of a sequence of time-domain samples of the channel impulse response measurement;

set a detection threshold;

identify a first subset of the sequence of time-domain samples, each element of the first subset of the sequence of time-domain samples having an energy less than the detection threshold; and

calculate a second average energy, the second average energy being an average energy of the first subset of the sequence of time-domain samples.

10. The system of claim 9 , wherein the setting of the detection threshold comprises:

selecting the detection threshold to correspond, based on the first average energy, to a target false alarm probability, the target false alarm probability being less than 10%; or

selecting the detection threshold to correspond, based on the first average energy, to a target estimation bias, the target estimation bias being less than 10% of the first average energy.

11. The system of claim 10 , wherein the setting of the detection threshold comprises selecting the detection threshold to correspond, based on the first average energy, to a target false alarm probability, the target false alarm probability being less than 10%.

12. The system of claim 10 , wherein the setting of the detection threshold comprises selecting the detection threshold to correspond, based on the first average energy, to a target estimation bias, the target estimation bias being less than 10% of the first average energy.

13. The system of claim 9 , wherein:

the calculating of the first average energy comprises calculating a total energy of the sequence of time-domain samples; and

the calculating of the second average energy comprises:

setting an intermediate energy value equal to the total energy of the sequence of time-domain samples;

setting an intermediate sample count equal to a size of the sequence of time-domain samples;

for each sample, of the sequence of time-domain samples, that is not an element of the first subset:

subtracting, from the intermediate energy value, an energy of the sample, and

subtracting one from the intermediate sample count; and

setting the second average energy equal to:

a final value of the intermediate energy value,

divided by

a final value of the intermediate sample count.

14. The system of claim 9 , wherein the calculating of the second average energy comprises:

setting an intermediate energy value equal to zero;

setting an intermediate sample count equal to zero;

for each sample, of the sequence of time-domain samples, that is not an element of the first subset:

adding, to the intermediate energy value, an energy of the sample, and

adding one to the intermediate sample count; and

setting the second average energy equal to a numerator divided by a denominator, wherein:

the numerator equals a difference of:

the first average energy, and

a quotient of:

a final value of the intermediate energy value, and

a size of the sequence of time-domain samples; and

the denominator equals a difference of:

1, and

a quotient of:

a final value of the intermediate sample count, and

the size of the sequence of time-domain samples.

15. The system of claim 9 , wherein the calculating of the channel impulse response measurement comprises calculating an inverse fast Fourier transform of a frequency domain channel response.

16. The system of claim 15 , wherein the sequence of time-domain samples of the channel impulse response measurement is a plurality of consecutive samples of the inverse fast Fourier transform.

17. The system of claim 16 , wherein a first-in-order sample of the sequence of time-domain samples is an nth element of the inverse fast Fourier transform, n being within 20% of one half of a size of the inverse fast Fourier transform.

18. The system of claim 17 , wherein a last-in-order sample of the sequence of time-domain samples is an mth element of the inverse fast Fourier transform, m being within 20% of nine-tenths of the size of the inverse fast Fourier transform.

19. A system for estimating noise, the system comprising:

a receiver, and

means for processing,

the means for processing being configured to:

calculate a channel impulse response measurement;

calculate a first average energy, the first average energy being an average energy of a sequence of time-domain samples of the channel impulse response measurement;

set a detection threshold;

identify a first subset of the sequence of time-domain samples, each element of the first subset of the sequence of time-domain samples having an energy less than the detection threshold; and

calculate a second average energy, the second average energy being an average energy of the first subset of the sequence of time-domain samples.

20. The system of claim 19 , wherein the setting of the detection threshold comprises:

selecting the detection threshold to correspond, based on the first average energy, to a target false alarm probability, the target false alarm probability being less than 10%; or

selecting the detection threshold to correspond, based on the first average energy, to a target estimation bias, the target estimation bias being less than 10% of the first average energy.