International Core Journal of Engineering 2020-26 | Page 163
the detection probability P d in (8) as following:
P d
P d CED
B 3
B
1 P 2 P
CED
d
§ © B 1 P
u 1 P d CED ¨
CED
f
CED
f
B 4
B
B 3
B 3 2 P
P d CED
·
¹
P d CED ¸
B
B
P
CED
f
CED
f
P d CED
algorithm uses two additional input logic operations ("AND"
and "OR") and takes up 4 memory locations to hold the
previous q i values. We can note that the complexity of 5IED
is slightly higher than that of 3EED. In this case, 5IED
requires a complement of 4 comparisons, and it only requires
an extra two memories locations and two comparisons of
memory compared to 3EED.
P d CED u (10)
4
1 P d CED § ¨ © B 1 P f CED B B 4 P d CED B B 3 · ¸ ¹ P f CED P d CED .
B
However, the 5IED introduces an additional delay of up to
three slots compared with energy detection, which is its only
disadvantage. Despite these complexity differences, with the
improvement of chip performance, the speed of data
processing becomes faster and faster in practical systems.
Therefore, it can be considered that the time spent in the
sensing process is the time spent in data sampling.
The P d from (10) 5IED depends only on B, and P f from (7)
depends on B and T. For T B o f (PU not sent), this is the
best condition for CR, we can rewrite P f in (7) to (11).
P f 5, IED
T B of
3 P f CED P f CED P d CED
2
P
CED 2
d
CED
f
P
2
P
CED 2
f
CED
d
P
TABLE I. C OMPUTATIONAL C OMPLEXITY A NALYSIS
(11)
.
Alg.
CED
3EED
5IED
5AND
5OR
Ideally, it is not hard to find that 5IED P f depends only on
CED P f DŽ Therefore, the exact expression for determining the
threshold of O is simple, taking the ideal value as the target
P f .
5 IED
f
P
1 3 2 P f 5 IED
2
.
º
·
¸ N 2 » V w 2 .
»
¸
¹
¼
AND
0
0
0
4
0
OR
0
0
0
0
4
1
3
5
1
1
M.
0
2
4
4
4
D.
1
2
4
1
1
In this section, we provide some simulations to evaluate the
performance of the method. We choose BPSK signal as s(n)
here, and our proposed algorithm is also applicable to any other
modulated signal. All of the results we provided are averaged
over 10 5 Monte Carlo realizations, where (T.) and (S.) represent
theory and simulation respectively. In all of the following
results, we evaluated P d in terms of analysis and simulation,
and the time record length is N=1000 samples.
(12)
CED
ª
§ 1 3 2 P 5 IED
f
« 1 Q 1 ¨
«
¨
2
©
¬
+
N-1
N-1
N-1
N-1
N-1
IV. A LGORITHM S IMULATION AND R ESULTS A NALYSIS
The well-known expression of the P f [15], the threshold
of O can be obtained from (12) as following:
O
×
N
N
N
N
N
A. Simulation Result Analysis
The influence of noise uncertainty is very important for
signal detection methods. The uncertainty of noise distribution
can be summarized as interval V 2 [(1 U ) V 2 , UV 2 ] where V 2
is the nominal noise power and U is the parameter to quantify
the uncertainty.
In Fig. 2, P f =0.01 and noise uncertainty is U = 0.09dB.
Obviously, noise uncertainty will lead to a serious increase in
P f , and noise uncertainty also has a serious impact on P d . When
P d decreases, the effect will be more obvious. This is mainly
because we use background noise in the experiment without
noise uncertainty. Therefore, when considering noise
uncertainty, the threshold is not accurate enough, which leads
to a serious increase in P f . We noted that without noise
uncertainty ( U = 0dB). The simulation results (diamond line)
match well with the theoretical results (black solid lines), thus
validating the correctness of the mathematical analysis and
assumptions in the preceding part 4.1. It is obvious from Fig. 2
that the new 5IED method is superior to the classic energy
detection method in the case of low SNR. Simulation results
show that the proposed method works well even at low SNR.
(13)
For N is the time record length (the number of signal
samples). It is worth noting that through our defined 5IED
algorithm for PU activities with B/T duty cycle, by (12) we
know that the value of O does not depend on the parameters
of the activity model (i.e. B and T ). As a result, with almost
"idle" systems, 5IED will be independent of PU activity.
B. Algorithm Complexity
We compared the complexity of the 5IED algorithm
considered by estimating the number of basic mathematical
and logical operations required in Table 1. Such as multipliers
(×), adders (+), and comparators ( ). In addition, an
evaluation was made to save the value of q i (noted as ’M.’)
and delay (sensed slot number, marked ‘D.’) required memory
location. For all algorithms, The N is from a record length of
sensing slot time. Compared with CED, all algorithms have
increased complexity. For example, 3EED needs to compare 2
more times and consume 2 memory locations to save the
previous E i value. And the 5IED needs to be compared 4 more
times, occupying 4 memory locations to hold the E i values,
and introducing an additional delay of up to 3 slots. For 5IED,
it calculate the complexity of the worst-case scenario when all
five decisions are required. Finally, each cooperative CED
In the wireless communication channel, since the signal is
multipath-propagated and the field strength at the receiving
point comes from different propagating paths, the delay time of
each path is different, and the superposition of component
waves in each direction generates standing wave field strength,
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