Efficient channel search with energy detection

1. A method for cognitive radio channel searching, the method comprising:

determining an energy detection threshold and a number of samples that will find a free channel in a minimum searching time, based on a number of channels K and a channel occupancy probability π 0 , constrained by a target acceptable misdetection probability and a target acceptable false alarm probability; and

searching the K channels with a signaling device using the determined energy detection threshold and the determined number of samples to find a free channel,

wherein determining comprises determining the number of samples based on the target misdetection α t probability and the target false alarm probability β t , and

wherein determining a number of samples includes solving for a minimum number of samples needed to achieve the target acceptable misdetection and false alarm probabilities t e min ;

t e min =┌(ξ −2 [Q −1 (α t )− Q −1 (1−β t )√{square root over (2ξ+1)}] 2 )┘

where ┌•┘ denotes the smallest integer not less than x, Q(•) is the complementary cumulative distribution function of the standard normal random variable, ξ is the signal-to-noise ratio, and α t and β t are the target acceptable false alarm and misdetection probabilities respectively.

2. The method of claim 1 , wherein searching the K channels comprises sampling a channel a determined number of times and calculating a test statistic based on the samples for the channel.

3. The method of claim 2 , wherein searching the K channels further comprises comparing the test statistic to the determined threshold to determine whether the channel is free.

4. The method of claim 2 , wherein the test statistic Λ N (k) is

Λ

N

(

k

)

=

∑

n

=

1

N

⁢



y

n

(

k

)



2

,

where k is an index designating the channel currently under search, N is the maximum number of samples, and y n (k) is the n th sample on channel k.

5. A cognitive radio device, comprising:

a search parameter determination module configured to determine an energy detection threshold and a number of samples that will find a free channel in a minimum searching time, based on a number of channels K and a channel occupancy probability π 0 , constrained by a target acceptable misdetection probability and a target acceptable false alarm probability; and

a search module configured to search the K channels with a signaling device using the determined energy detection threshold and the determined number of samples to find a free channel,

wherein the search parameter determination module is configured to determine the number of samples based on the misdetection probability and the false alarm probability, and

wherein the search parameter determination module is configured to determine a number of samples needed to achieve the target acceptable misdetection and false alarm probabilities t e min :

t e min =┌(ξ −2 [Q −1 (α t )− Q −1 (1−β t )√{square root over (2ξ+1)}] 2 )┘

where ┌•┘ denotes the smallest integer not less than x, Q(•) is the complementary cumulative distribution function of the standard normal random variable, ξ is the signal-to-noise ratio, and α t and β t are the target acceptable false alarm and misdetection probabilities respectively.

6. The cognitive radio device of claim 5 , wherein the search modules is configured to sample a channel a determined number of times and calculating a test statistic based on the samples for the channel.

7. The cognitive radio device of claim 6 , wherein the search modules is configured to compare the test statistic to the determined threshold to determine whether the channel is free.

8. The cognitive radio device of claim 6 , wherein the test statistic Λ N (k) is

Λ

N

(

k

)

=

∑

n

=

1

N

⁢



y

n

(

k

)



2

,

where k is an index designating the channel currently under search, N is the maximum number of samples, and y n (k) is the n th sample on channel k.