Efficient channel search with sequential probability ratio testing
View Patent ↗Methods and systems for cognitive radio channel searching are shown that include determining an upper threshold and a lower threshold that will find a free channel in a minimum average searching time based on a channel occupancy probability π0 and the number of channels K, constrained by a target acceptable misdetection probability and a target acceptable false alarm probability. The K channels are searched with a signaling device using the determined upper threshold and lower threshold to find a free channel.
1. A method for cognitive radio channel searching, the method comprising:
determining an upper threshold and a lower threshold that will find a free channel in a minimum average searching time based on a channel occupancy probability π 0 and a number of channels K, 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 upper threshold and lower threshold to find a free channel,
wherein determining comprises calculating an expected false alarm probability α and misdetection probability β based on the channel occupancy probability π 0 and the number of channels K, and
wherein the lower threshold a is calculated as
a
s
=
log
β
1
-
α
or the upper threshold b is calculated as
b
s
=
log
1
-
β
α
.
2. The method of claim 1 , wherein determining comprises minimizing an average searching time according to the expected false alarm probability α and an expected misdetection probability β.
3. The method of claim 2 , wherein said minimizing accounts for a switching delay that arises from switching between channels.
4. The method of claim 2 , wherein said minimizing includes:
min
α
,
β
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α
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π
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)
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to
:
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K
being less than or equal to the target acceptable false alarm probability,
β
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being less than or equal to the target acceptable misdetection probability, α+β<1, α>0, and β>0, where δ is a constant switching delay.
5. The method of claim 1 , wherein searching the K channels comprises collecting samples from each channel k and calculating a log-likelihood ratio (LLR) for the samples for each channel k.
6. The method of claim 5 , wherein searching the K channels further comprises comparing the LLR for each channel k to the determined upper and lower threshold to determine whether the channel is free or occupied.
7. The method of claim 5 , wherein the LLR Λ N (k) for a channel k is
Λ
N
=
∑
n
=
1
N
log
p
1
(
y
n
)
p
0
(
y
n
)
,
where N is the maximum number of samples, y n (k) is the n th sample on channel k, and p 0 (x) and p 1 (x) are probability density functions for a channel being free and occupied, respectively.
8. A method for cognitive radio channel searching, the method comprising:
determining an upper threshold and a lower threshold that will find a free channel in a minimum average searching time based on a channel occupancy probability π 0 and a number of channels K, constrained by a target acceptable misdetection probability and a target acceptable false alarm probability, comprising:
minimizing an average searching time according to an expected false alarm probability α and an expected misdetection probability β; and
searching the K channels with a signaling device, wherein searching includes:
sampling a channel;
calculating a log-likelihood ratio (LLR) for the samples for each channel k; and
comparing the LLR to the upper and lower thresholds to determine whether the channel is free or busy,
wherein determining comprises calculating an expected false alarm probability α and misdetection probability β based on the channel occupancy probability π 0 and the number of channels K, and
wherein the lower threshold a is calculated as
a
s
=
log
β
1
-
α
or the upper threshold b is calculated as
b
s
=
log
1
-
β
α
.
9. A cognitive radio device comprising:
a search parameter determination module configured to determine an upper threshold and a lower threshold that will find a free channel in a minimum average searching time based on a channel occupancy probability π 0 and a number of channels K, 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 upper threshold and lower threshold to find a free channel,
wherein the search parameter determination module is configured to calculate an expected false alarm probability α and misdetection probability β based on the channel occupancy probability π 0 and the number of channels K, and
wherein the search parameter determination module is configured to calculate the lower threshold a as
a
s
=
log
β
1
-
α
or the search parameter determination module is configured to calculate the upper threshold b as
b
s
=
log
1
-
β
α
.
10. The cognitive radio device of claim 9 , wherein the search parameter determination module is configured to minimize an average searching time according to an expected false alarm probability α and an expected misdetection probability β.
11. The cognitive radio device of claim 10 , wherein the search parameter determination module is configured to minimize the average search time by
min
α
,
β
E
(
T
)
=
1
-
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α
+
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-
1
)
π
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0
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1
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1
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)
μ
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]
log
1
-
β
a
+
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)
-
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subject
to
:
[
απ
0
+
(
1
-
β
)
(
1
-
π
0
)
]
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-
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(
1
-
β
)
(
1
-
π
0
)
]
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1
-
(
1
-
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0
)
K
being less than or equal to the target acceptable false alarm probability,
β
(
1
-
π
0
)
1
-
(
(
α
+
β
-
1
)
π
0
+
(
1
-
β
)
)
K
β
-
(
α
+
β
-
1
)
π
0
being less than or equal to the target acceptable misdetection probability, α+β<1, α>0, and β>0, where δ is a constant switching delay.
12. The cognitive radio device of claim 9 , wherein the search module is configured to collect samples from each channel k and to calculate a log-likelihood ratio (LLR) for the samples for each channel k.
13. The cognitive radio device of claim 12 , wherein the search module is configured to compare the LLR for each channel k to the determined upper and lower threshold to determine whether the channel is free or occupied.
14. The cognitive radio device of claim 12 , wherein the LLR Λ N (k) for a channel k is
Λ
N
=
∑
n
=
1
N
log
p
1
(
y
n
)
p
0
(
y
n
)
,
where N is the maximum number of samples, y n (k) is the n th sample on channel k, and nd p 0 (x) and p 1 (x) are probability density functions for a channel being free and occupied, respectively.