Aerospace and Electronic Systems Magazine May 2018 - 26

Real-Time Adaptive Spectrum Sensing
Then, the optimal solution for the threshold λe* is defined as such,
for which both the Pmd and Pfa are within their predefined limits.


λe* = 1 +



1
−
Mγ

2
+
Mπ

2
M

1
 +
π



2M

γ − 1  σ w2 .
π


(17)



−1

−1

ESTIMATION OF THE STATES OF THE PRIMARY USER

Finally, the threshold λ is determined as below:
*
*
λe* ,

if λ *f ≤ λmd
and λe* ∈ λ *f , λmd

*
*
*
λ f or λmd , whichever is closer to λe ,
λ=
*
*

if λ *f ≤ λmd
and λe* ∈/ λ *f , λmd



*
*
>
no
solution,
if
λ
λ
f
md


EFFICIENCY-ACCURACY TRADE-OFF
The purpose of this analysis is to find the optimal balance between
the accuracy of the sensing process (associated with the sensing
time ts) and the efficiency (time) of the transmission period of the
SU so that a better opportunity to utilize the spectrum is achieved.
In order to do this, based on [22], [23], [24] we can form a closedform expression for the spectrum opportunity which includes the
sensing efficiency ξ (18), the likelihood ϕ that the channel occupancy is determined correctly, and the probability mass function
ψ of the discrete states (idle/active or ON/OFF) of the PU. The
sensing efficiency is defined as the fraction of the frame which is
used for the transmission time of the SU

ξ ( ts ) =

where μON and μOFF are the means of TON and TOFF, respectively.
We find the optimum value of ts by maximizing the function
within a specific interval. This interval is defined by the shortest
and longest periods, which ts can last within one frame.

T − ts
.
T

(18)

As discussed earlier, for each configuration of PU parameters
−1
−1
(Pr(ON) and Pr(OFF), μON
and μOFF
), there is only one optimal
value of the sensing time. Therefore, there is no need for the computationally intensive process of finding it, to be performed at each
spectrum sensing iteration. That is why we first estimate the parameters of the PU and then find the trade-off. This way we can set
it as a constant for a specific PU configuration. If we define three
types of PU transmission patterns-where Pr(ON) >> Pr(OFF),
Pr(ON) ≈ Pr(OFF), Pr(ON) << Pr(OFF), we can obtain one optimal ts for each of them. The SU can choose one of the three options
based on a simplistic estimation method. In this implementation,
we record every decision of the detector and at every 10th frame,
 ( ON ) and Pr
 ( OFF ) are estimated accordingly as given below:
Pr
 ( ON ) = Number of decisions for H1
Pr
10
Pr ( OFF ) = Number of decisions for H 0 .
10

(21)

This way, the receiver makes the decision on the PU's states
and consequently, takes the most probable value of the three, for ts.
The sensing time then remains constant for the rest of the next 10
frames, until the next estimation is performed.

Thus, the trade-off expression for the spectrum opportunity η
is formulated in [25] as

ALGORITHM DESCRIPTION AND EXPERIMENTAL SETUP

η ( ts ) = ξ ( ts )φ ( Pd , Pfa )ψ

ALGORITHM

(

)

T − ts
Pr ( OFF ) 1 − Pfa + Pr ( ON )(1 − Pd ) ψ .
=
T

(

)

(19)

In order to find the PDF of the alternating states of the PU,
we consider that they form a renewal process [22], [25], [42]. The
random variables TON, TOFF, and TRP describe the variations of the
"ON" state, the "OFF" state, and the renewal process the elements
of which are the sums of the respectable states, Ti RP = Ti ON + Ti OFF ,
i = 1, 2, 3, ..., n. The probabilities that the PU is active/idle are
Pr(ON) and Pr(OFF), correspondingly.
For the sake of space, the detailed definitions of the renewal
process and the specific derivation of the trade-off expressions are
not presented here but they can be found in [25]. The efficiencyaccuracy expression is thus formulated

η ( ts ) =

T − ts
T


 T − ts
c exp  −

 μON


 T − ts
 − exp  −

 μOFF


 
 

( Pr (OFF ) (1 − P ) + Pr (ON )(1 − P )) ,
fa

c=

( μOFF μON )

d

3

2
2
μOFF
− μON

MEASUREMENT TESTBED AND SOFTWARE

.

(20)
26

The logic, which drives the cyclostationary sensing process is
shown in Figure 1. After the measurement is performed, the algorithm calculates the variance of the signal power from the gathered
samples and the decision threshold. Then, the CAF is calculated,
the decision for the spectrum occupancy is made and if the spectrum is occupied, the algorithm will pause and wait until the end
of the frame. In the alternative case, the same action will be taken
because no actual transmission capabilities are implemented in the
receiver (such are not necessary because only the local spectrum
sensing scenario is studied in this article). The difference is, however, that in this case, the period of the interruption will be saved,
as a transmission period of the SU, together with the rest of the
parameters. Finally, the estimation of the channel attenuation is
done, followed by the calculation of the probability of detection.
The algorithm of the energy detector spectrum sensing program
follows the same pattern but goes through the specific steps of the
method, as described in the previous section.

The experiment was performed with the USRP hardware platform
and the GNU Radio software, which gives the opportunity for intu-

IEEE A&E SYSTEMS MAGAZINE

MAY - JUNE 2018



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