Sequential sensing scheme for cognitive radio
A method and system for determining whether a given electromagnetic frequency is in use. An incoming signal is sampled and a test statistic is calculated based on the magnitude of the received samples and a predetermined constant. A determination is then made regarding whether the frequency is in use, based on whether the test statistic has exceeded a threshold.
1. A method for determining whether a given electromagnetic frequency is in use, comprising the steps of:
applying a transformation to an amplitude of received samples;
adjusting the transformed samples by a constant based on a minimum detection signal-to-noise ratio;
combining the adjusted samples to produce a test statistic;
using a processor to make a determination regarding whether the frequency is in use based on whether the test statistic has exceeded or has fallen below a threshold; and
if a number of received samples reaches a maximum number of samples, making a determination regarding whether the frequency is in used based on whether the test statistic is above or below a final threshold.
2. The method of claim 1 , wherein said step of adjusting comprises subtracting the constant from each transformed sample.
3. The method of claim 2 , wherein the test statistic is
Λ
N
=
∑
i
=
1
N
(
r
i
2
-
Δ
)
,
where N is the number of received samples, r i is the i th received sample, and Δ is the constant.
4. The method of claim 1 , wherein said step of applying comprises squaring the amplitude of the samples.
5. The method of claim 1 , wherein the constant satisfies σ w 2 <Δ<σ w 2 (1+SNR m ), where σ w 2 is the noise variance and SNR m is the minimum acceptable signal-to-noise ratio according to error probability specifications.
6. The method of claim 1 , further comprising the step of adjusting thresholds to meet design specifications.
7. The method of claim 6 , further comprising the steps of calculating false alarm and misdetection probabilities to determine whether a particular set of thresholds meets design specifications.
8. The method of claim 7 , wherein the false alarm probability is calculated as
P
FA
,
M
=
∑
N
=
1
M
P
H
0
(
E
N
)
,
where M is a maximum number of samples and P H 0 (E N ) is the probability of the event E N under the null hypothesis H 0 .
9. The method of claim 7 , wherein the misdetection probability is calculated recursively.
10. A system for determining whether a given electromagnetic frequency is in use, comprising:
a transformation module configured to transform an amplitude of received samples;
an adjustment module configured to adjust the transformed samples by a constant based on a minimum detection signal-to-noise ratio and to combine the adjusted samples to produce a test statistic; and
a test module configured to use make a determination using a processor as to whether the frequency is in use based on whether the test statistic has exceeded or has fallen below a threshold and, if a number of received samples reaches a maximum number of samples, to make a determination regarding whether the frequency is in used based on whether the test statistic is above or below a final threshold.
11. The system of claim 10 , wherein the adjustment module includes a subtracter configured to subtract the constant from each squared sample.
12. The system of claim 11 , wherein the test statistic is
Λ
N
=
∑
i
=
1
N
(
r
i
2
-
Δ
)
,
where N is the number of received samples, r i is the i th received sample, and Δ is the constant.
13. The system of claim 10 , wherein the constant satisfies σ w 2 <Δ<σ w 2 (1+SNR m ), where σ w 2 is the noise variance and SNR m is the minimum acceptable signal-to-noise ratio according to error probability specifications.
14. The system of claim 10 , further comprising a threshold adjustment module configured to set thresholds to meet design specifications.
15. The system of claim 14 , wherein the threshold adjustment module is configured to calculate false alarm and misdetection probabilities to determine whether a particular set of thresholds meets design specifications.
16. The system of claim 15 , wherein the false alarm probability is calculated as
P
FA
,
M
=
∑
N
=
1
M
P
H
0
(
E
N
)
,
where M is a maximum number of samples and P H 0 (E N ) is the probability of the event E N under the null hypothesis H 0 .
17. The method of claim 15 , wherein the misdetection probability is calculated recursively.
18. A computer readable medium storing a computer readable program, wherein the computer readable program when executed on a computer causes the computer to:
calculate a test statistic based on the magnitude of a set of received samples adjusted by a constant;
make a determination regarding whether a frequency is in use based on whether the test statistic has exceeded or has fallen below a threshold; and
if a number of received samples reaches a maximum number of samples, make a determination regarding whether the frequency is in used based on whether the test statistic is above or below a final threshold.