Spectrum sensing using energy measurement in wireless telemetry networks using logarithmic adaptive learning


ACTA IMEKO 
ISSN: 2221-870X 
March 2022, Volume 11, Number 1, 1 - 7 

 

ACTA IMEKO | www.imeko.org March 2022 | Volume 11 | Number 1 | 1 

Spectrum sensing using energy measurement in wireless 
telemetry networks using logarithmic adaptive learning 

Nagesh Mantravadi1, Md Zia Ur Rahman1, Sala Surekha1, Navarun Gupta2 

1 Department of Electronics and Communication Engineering, Koneru Lakshmaiah Education Foundation, K L University, Vaddeswaram,  
  Guntur, Andhra Pradesh, 522502, India  
2 Department of Electrical Engineering, University of Bridgeport, Bridgeport, CT 06604, USA 

 

 

Section: RESEARCH PAPER  

Keywords: Adaptive algorithm; cognitive radio; energy measurement; noise uncertainty; threshold point 

Citation: Nagesh Mantravadi, Md Zia Ur Rahman, Sala Surekha, Navarun Gupta, Spectrum sensing using energy measurement in wireless telemetry networks 
using logarithmic adaptive learning, Acta IMEKO, vol. 11, no. 1, article 34, March 2022, identifier: IMEKO-ACTA-11 (2022)-01-34 

Section Editor: Md Zia Ur Rahman, Koneru Lakshmaiah Education Foundation, Guntur, India 

Received December 28, 2021; In final form February 18, 2022; Published March 2022 

Copyright: This is an open-access article distributed under the terms of the Creative Commons Attribution 3.0 License, which permits unrestricted use, 
distribution, and reproduction in any medium, provided the original author and source are credited. 

Corresponding author: Sala Surekha, e-mail: surekhasala@gmail.com  

 

1. INTRODUCTION 

Radio frequencies are limited natural resources they are 
controlled by government authorities, in a particular band the 
primary users can exclusively use licensed spectrum even the 
secondary users are unoccupied as these unlicensed users are 
avoided for use. Due to the enormous growth in wireless 
communication applications the usage of radio frequencies is 
increasing rapidly. To overcome this spectrum utilization issues, 
cognitive radio systems are emerged with new technology [1]-[3] 
in wireless communications. Enormous efforts are used for 
enhancing the usage of efficiency of cognitive radio systems, 
there is huge change in the usage of frequencies, time and space 
domain and then secondary users are allowed without creating 
any interference to the primary users. To overcome these 
interferences [4], [5] in wireless communications and for 
increasing spectrum utilization IEEE 802.22 wireless frequency 

band can be used. With the help of these frequency bands, the 
data will be transmitted without causing interference in health 
care monitoring wireless application by using ZigBee, Wi-Fi, ad 
hoc networks with operating frequency less than 3 MHz. 
Orthogonal frequency division multiplexing (OFDM) is the 
eminent method used in wireless communication systems. 
Channel estimation issues raised in OFDM based cognitive radio 
system are discussed in [6]-[8], this is because of mean square 
error (MSE) of channel estimations. The unknown noise 
components effecting the spectrum sensing also studied. 
Performance evaluation of channel estimation techniques for 
imperfect channels is analysed for correlated channels of 
cognitive radio system, then mutual information is considered at 
the input and output to provide better communication sensing 
and channel uncertainty. The receiver's minimal mean square 
error is then computed to obtain the fading coefficients of the 
fading channel, as well as the anticipated attainable rate for 
Gaussian signalling and linear modulation schemes, assuming 

ABSTRACT 

To identify primary user signals in cognitive radios spectrum sensing method is used. Due to statistical variances in received signal, noise 
is present in primary user signals, this noise powers are varied due to random nature of noise signals and leads to noise uncertainty 
problem in the performance of energy detection. The task of energy measurement and further detecting the unused frequency 
spectrum is a key task in cognitive radio applications. For avoiding these problems, least logarithmic absolute difference (LLAD) 
algorithm is proposed in which noise powers are adjusted at sensing point of licensed users. With help of proposed method, estimated 
noise signals are eliminated. Sign regressor version of LLAD algorithm is considered due to it reduces computational complexity and 
convergence rate is improved. Further probability of detection (Pod), probability of false alarm (Pofa) is estimated to know threshold 
value. From results, it is clear that good performance in terms of Pofa versus Pod in range of low signal to noise ratio in multiple nodes. 
Therefore, the proposed energy measurement-based spectrum sensing method is useful in remote health care monitoring, medical 
telemetry applications by sharing the un-used spectrum.  

mailto:surekhasala@gmail.com


 

ACTA IMEKO | www.imeko.org March 2022 | Volume 11 | Number 1 | 2 

interference and channel estimation errors occur at primary 
users [9], [10]. Spectrum sensing is used to avoid difficulties with 
spectrum underutilization and interference. The most 
commonly used detection techniques are wavelet detection, 
cyclostationary detection, energy detection, and covariance 
detection. The first three techniques require prior information 
of the principal user signal, frequency components, interference, 
and noise variance, but the fourth approach requires no prior 
data and is hence the most often used spectrum sensing method. 
In addition, for energy sensing, circuit implementation and 
computing complexity are minimal. Spectrum sensing [11]-[17] 
performance is assessed in terms of false alarm and detection 
probabilities; it assumes that the primary user is idle or active 
during the spectrum sensing period, and then spectrum holes are 
detected in the spectrum frequency range based on this. There 
is a compromise between probability detection and false alarm, 
however by utilizing these factors, we can see if there was any 
interference among the primary and secondary users. In [18] 
Sensing trade-off in cognitive radios is studied when numerous 
primary users arrive randomly. The trade-off is also caused by 
the performance of cognitive radio spectrum utilization and 
spectrum sensing, which is based mostly on primary user 
activity. A numerical technique was used to investigate this 
trade-off utilizing cooperative spectrum sensing. The spectrum 
potential for successful communication between a transmitter 
and receiver of cognitive networks is being investigated. Also 
studied about when secondary user sensing time increases, false 
alarm probability reduced, it means there is high chances to 
secondary users are having to access idle channel, but less chance 
to transmit because of transmission time is limited. Main 
objective is efficiently use spectrum utilization with optimum 
sensing for improving spectrum opportunities of cognitive radio 
networks. Practically cognitive radios are having channel sensing 
errors because of miss detection and false alarms these problems 
will affect channel estimation [19] design also quality channel 
estimation error problems, receiver operating characteristics are 
also analysed for these parameters. Further cooperative 
cognitive radio is considered for analysis of fading scenarios 
occurred with improved energy detection method. For this 
Nakagami multipath fading is considered with power 2 based 
energy detection spectrum sensing [20], [21], then performance 
is improved in cognitive radio networks in terms of detection 
probability parameters and their operating curves also analysed. 
In spectrum sensing, there after spectrum allocation one of the 
promising methods is energy detection. In this work a new 
energy measurement methodology is proposed based on least 
logarithmic absolute difference algorithm. This methodology of 
energy detection and measurement is a key task in measurement 
technology as well as in cognitive radio-based communication 
systems. To overcome noise uncertainty problems double 
threshold-based spectrum sensing is studied for improving 

energy detection. This cognitive radio concept is widely used in 
health care applications, but interferences occurred due to 
wireless devices will affect the performance. To avoid these 
interferences occurred with health care, novel cognitive radio 
method is used by proposing modified normalized least mean 
square algorithm (MNLMS) for hospital environment 
applications so that errors/interferences occurred with medical 
devices are removed and their performance is evaluated using 
MATLAB simulations.  

2. SYSTEM MODEL 

Spectrum sensing is mostly used method for detecting 
spectrum holes of cognitive radio network. By using this method, 
we can decide primary user is absent or present. Energy detection 
block diagram is shown in Figure 1. By using hypothesis testing, 
detection problem is considered as 

𝑇0: 𝑧(𝑡) = 𝑤(𝑡) 

𝑇1: 𝑧(𝑡) = 𝑤(𝑡) + 𝑠(𝑡) , 
(1) 

where 𝑧(𝑡) is received sample signal, 𝑤(𝑡) is noise effect of 
transmitted signal, 𝑠(𝑡) is primary transmitted signal with 𝑡 =
1, … , 𝑇 length carried for identifying spectrum. 

Energy detection method [22] is considered for detecting 
spectrum holes, energy level is measured, then estimated noise 
variance by placing detection threshold value. Then secondary 
user decides statistics of energy detection as 

𝐷 = ∑[𝑧(𝑡)]2
𝑇

𝑡=1

 . (2) 

Decision static have central chi square distribution with T 
degrees of freedom when primary user signal is absent. It is 
having non central chi square distribution decision statistics 
when primary user is present. Central limit theorem with 
Gaussian approximation is used if detection samples are greater 
than 250, then mean and variance of decision static of primary 
user signal given as 

𝐷 ~ 𝑇(𝑇𝜎𝑤𝑡
2 , 2𝑇𝜎𝑤𝑡

4 ) for H1 

𝐷 ~ 𝑇(𝑇((𝜎𝑠𝑡
2 + 𝜎𝑤𝑡

2 , 2𝑇((𝜎𝑠𝑡+
2 𝜎𝑤𝑡

2 )2) for H0 . 
(3) 

In testing 𝑇0 and 𝑇1, false alarm and misdetection errors are 
occurred due to false identification of 𝑇0 and 𝑇1 . Energy detector 
performance is measured with probability of these two errors. 
Probability false alarm occurred due to showing of wrong 
spectrum band occupancy, probability of miss detection is due 
to it shows as primary user absence, but actually it is present, it is 
also called as probability detection. 

Probability false alarm, probability detection evaluated as 

 

Figure 1. Energy detector block diagram.  



 

ACTA IMEKO | www.imeko.org March 2022 | Volume 11 | Number 1 | 3 

𝑃ofa = 𝑄 (
𝛿𝑑 − 𝑇𝜎𝑤𝑡

2

√2 𝑇 𝜎𝑤𝑡
4

) (4) 

𝑃od = 𝑄 (
𝛿𝑑 − 𝑇(𝜎𝑠𝑡

2 + 𝜎𝑤𝑡
2 )

√2 𝑇(𝜎𝑠𝑡+
2 𝜎𝑤𝑡

2 )2
) , (5) 

where 𝛿𝑑  = 𝜎𝑤𝑡
2 (𝑄−1(𝑃ofa)√2𝑇 + 𝑇) is the threshold. 

2.1. Least Logarithmic Absolute Difference Algorithm 

Least logarithmic absolute difference (LLAD) technique 
elegantly and gradually adapts conventional cost function 
depends on amount of error in its implementation. 

In impulse-free noise environments, LMS and LLAD 
algorithm exhibits likely convergence behaviour, while LLAD 
algorithm is robust against impulsive interference and exceeds 
sign algorithm [23], [24]. Flowchart for LLAD algorithm is as 
shown in Figure 2. 

Mathematical Modeling 

𝑇 is filter length, 𝜇 is step size parameter is considered. 
Let the tap input be x(𝑛) and filter length 𝑇 is moderate to 

large, w(0) = 0 is considered as initial condition, x(𝑛) is 𝑇 -by-
1 tap input vector to filter 𝑛2 at time 𝑛 as  

[x(𝑛), x(𝑛 − 1), … , x(𝑛 − 𝑇 + 1)]T (6) 

w(𝑛) is tap weight vector, d(𝑛) is desired response at time 𝑛, 
ωo is an unknown vector, (. )

T is the transpose of (. ). 

To be computed:  

w(𝑛 + 1) is to be computed tap-weight vector at time 𝑛 + 1. 

Computation 

An unknown vector ωo is represented with linear model as 

d(𝑛) = ωo
T x(𝑛) + n𝑡  (7) 

The instantaneous estimate of gradient vector J is written as:  

∇’J(n) = − 2 x(𝑛) d∗(𝑛) + 2 d(𝑛) xT(𝑛) w(𝑛) (8) 

where x(𝑛) is the input tap vector, w(𝑛) is tap weight vector. 
w(𝑛) is random vector depends on x(𝑛) with its taps stored in 
a row vector given by 

[𝑤(𝑛), w(𝑛 − 1), … , w(𝑛 − 𝑇 + 1)]T (9) 

Output of the filter  

y(𝑛) = [w0(𝑛) x(𝑛) + ⋯ + w𝐿−1(𝑛) x(𝑛 − 𝑀 + 1)] 

= wT(𝑛) x(𝑛). 
(10) 

Expression for estimation error is given by  

e(𝑛) = d(𝑛) −  wT(𝑛) x(𝑛). (11) 

where the term wT(𝑛) x(𝑛) is inner product of w(𝑛) and x(𝑛). 
The normalized error cost function introduced using 

logarithmic function is given by  

 

Figure 2. Spectrum sensing using LLAD.  



 

ACTA IMEKO | www.imeko.org March 2022 | Volume 11 | Number 1 | 4 

J(e(𝑛)) = F(e(𝑛)) −
1

𝛼
 ln (1 + 𝛼 F(e(𝑛))) (12) 

Based on steepest descent method, general weight update 
recursion is given by 

w(𝑛 + 1) = w(𝑛) − 𝜇 ∇J(𝑛) (13) 

New recursive relation for ∇J(𝑛) is written as 

∇J(𝑛) = 𝐸{∇|e(𝑛)|2} = 𝐸{e(𝑛)∇e∗(𝑛)} 

∇e∗(𝑛) = −x∗(𝑛) 
(14) 

Thus, resultant expression for gradient vector is given by 

∇J(𝑛) = −𝐸{e(𝑛) x∗(𝑛)} (15) 

Also, first gradient of the relation in is given by Δw. F(e(𝑛)) 
The signum representation is given below:  

sign{x(𝑛)} = {

1: x(𝑛) > 0

0: x(𝑛) = 0

−1: x(𝑛) < 0

} (16) 

Step size boundary for convergence of mean square for LMS 
algorithm is given by 

0 < 𝜇 <
2

x𝑇 (𝑛) x(𝑛)
 (17) 

By substituting estimate of ∇’J(𝑛) in steepest descent 
algorithm, new recursive relation for updating tap weight vector 
is 

w(𝑛 + 1) = w(n) + 𝜇 x(𝑛)[d∗(𝑛) − xT(𝑛) ∙ w(𝑛)]. (18) 

To provide robustness against impulsive interferences, a cost 
function is introduced with normalized error by use of 
logarithmic function stated as  

𝐹(e(𝑛)) = 𝐸 [(e(𝑛))
2

] = 𝐸[|e(𝑛)|] . (19) 

Thus, the stochastic gradient update is given by  

w(𝑛 + 1)

= w(𝑛) + 𝜇 ∙ x(𝑛)
∂f(e(𝑛))

∂e(𝑛)
[

𝛼 f(e(𝑛))

1 + 𝛼 f(e(𝑛))
] , 

(20) 

where 𝛼 > 0 is a design parameter also F(e(𝑛)) as the 

conservative cost function for error signal e(𝑛). 

For |𝛼 F(e(𝑛))| ≤ 1, applying MacLaurin series using 
natural algorithm, equation (19) gives 

J(e(n)) = F(e(𝑛)) −
1

𝛼
(𝛼 F(e(𝑛)) − 𝛼 2 F2(e(𝑛))). (21) 

For low values of F(e(𝑛)), it is an infinite combination for 
conventional cost functions. For smaller values of error, cost 

function J(e(𝑛)) resemble F(e(𝑛)) for instance as 

F(e(𝑛)) −
1

𝛼
ln (1 + 𝛼 𝐹(𝑒(𝑛)))  →  F(e(𝑛)) (22) 

Thus general update expression of stochastic gradient is stated 
as  

w(𝑛 + 1)

= w(𝑛) + 𝜇 ∙ x(𝑛) ∙
∂f(e(𝑛))

∂e(𝑛)
[

𝛼 f(e(𝑛))

1 + 𝛼 f(e(𝑛))
] 

(23) 

Norm is power of least probable error ais at convex cost 
function, signed algorithm delivers slow rate of convergence. 

For F(e(𝑛)) = E[|e(𝑛)|] in (23), then resultant expression is 

w(𝑛 + 1)
= w(𝑛)

+ 𝜇 x(𝑛) sign(e(𝑛)) [
𝛼 (|e(n)|)

1 + 𝛼 (|e(n)|)
] . 

(24) 

Then the weight update relation of the LLAD algorithm 
becomes 

w(𝑛 + 1) = w(𝑛) + 𝜇 [
𝛼 x(𝑛) e(𝑛))

1 + 𝛼 (|e(𝑛)|)
] (25) 

To reduce computational difficulty of LMS, signed variants 
are preferable. Sign regressor version offers low computational 
complexity with a smaller number of multiplications among all 
signed variants. Here, sign regressor LLAD (SRLLAD) 
algorithm by applying sign function on each element. Is remains 
obtained as recursion of LMS for altering input tap vector. 

2.2. Sign based Least Logarithmic Absolute Difference (LLAD) 
algorithms 

LLAD algorithm is generalized version of higher order 
adaptive filter. Combination of LLAD in (25) with three types of 
sign variants results in SRLLAD, SLLAD and SSLLAD 
algorithms respectively. Hence weight update relations of signed 
LLAD based variants are given as follows. 

w(𝑛 + 1)
= w(𝑛)

+ 𝜇 sign{x(𝑛)} sign {e(𝑛) [
𝛼 (|e(𝑛)|)

1 + 𝛼 (|e(𝑛)|)
]} 

(26) 

w(𝑛 + 1)
= w(𝑛)

+ 𝜇 x(𝑛) sign {e(𝑛)  [
𝛼 (|e(𝑛)|)

1 + 𝛼 (|e(𝑛)|)
]} 

(27) 

w(𝑛 + 1)
= w(𝑛)

+ 𝜇 sign{x(𝑛)} sign {e(𝑛)  [
𝛼 (|e(𝑛)|)

1 + 𝛼 (|e(𝑛)|)
]}. 

(28) 

3. RESULTS AND DISCUSSION 

The proposed LLAD algorithm method for spectrum sensing 
is used to assess performance. The spectrum sensing of the 
transmitter of primary user and receiver of secondary user is 
evaluated. Spectrum sensing simulations are run for 5000 
samples, T is filter length it is chosen as 10 and distinct signals 
are acquired for each noise sample to process. For improved 
results, a received signal attenuation factor was introduced, and 
then the performance of energy detection was evaluated under 
various SNR situations. Because of the noise levels in the sensing 
spectrum, the main goal of developing an adaptive filter is based 
on spectrum sensing approach. Due to incorrect detection of test 



 

ACTA IMEKO | www.imeko.org March 2022 | Volume 11 | Number 1 | 5 

data, this spectrum sensing may result in probability detection 
and missed detection probability mistakes. Due to incorrect 
detection of test data, this spectrum sensing may result in 
probability detection and missed detection probability errors. 
The proposed technique adjusts the threshold value for each 
sensing event and then adjusts the noise power accordingly. 
When the size of the receiving antenna, the averaging of eigen 
values rises, resulting in a reduction in estimate error. The 
performance of noise power estimation is measured in terms of 
mean square error (MSE). When the antenna size and quantity 
of samples are increased, the steady state error reduces. The 
sensitivity of adaptive filter-based energy detection is measured 
in terms of probability detection, which is a function of SNR and 
a constant false alarm probability. The proposed LLAD 
algorithm performs better when probability detection is used. 
Noise uncertainty is not a problem for this proposed strategy. 
This detecting capability successfully identifies spectrum gaps, 
allowing for prevented spectrum reuse opportunities. To 
accomplish probability detection (Pod) and false alarm probability 
(Pofa) concurrently, SNR values are considered as minimal and 
number of samples, noise uncertainty relationship is adopted. To 
obtain greater probability detection without an adaptive method 
for spectrum sensing, noise uncertainty increases for minimal 
SNR levels. Even though there is no influence on how many 
received signal samples are examined for sensing spectrum, some 
restrictions on SNR for performance of probability detection 
beyond these limit false alarm values are sacrificed for values 
bigger than zero of noise uncertainty factor. For noise certainty 
levels greater than zero for every increasing SNR value, a larger 
number of samples are required for improved detection 
probability. It is obvious that raising SNR values improves 
detection sensitivity for noise circumstances in the proposed 
technique. Theoretical values for probability detection of 
different SNR levels for the basic energy detection technique and 
suggested energy detection using LLAD are determined using (4) 
and (5). Computational complexity of various LMS based 
adaptive algorithms shown in Table 1. With the suggested 
strategy, probability detection produces superior results, as 
shown in Table 2. Simulation curves for Pofa versus Pod for 
various SNR values are provided in Figure 3. For low SNR levels, 
detection probability performance is better, as shown in Table 2 
and Figure 3. Signal correlations create propagation fading in 
wireless communications, and their influence on the receiving 

antenna generates correlation losses in the received signal. The 
performance of the energy detector is initially unaffected by 
signal correlations, and noise power is evaluated using eigen 
values. The antenna correlation effect is avoided while 
calculating noise power estimate by using one primary user signal 
when calculating eigen values of antenna correlation effect on 
bigger eigen values compared to small eigen values. 

 The main goal of the proposed LLAD is to improve energy 
detection accuracy when used in low SNR and noise-uncertainty 
situations. The detection probability is then improved with 
constant false alarm probability and low SNR values. Threshold 
values are evaluated for energy detectors to perceive changes in 
noise power in order to minimize difficulties with noise 
uncertainties, therefore threshold values are adapted to compute 

Table 1. Computational Complexities of various sign LMS based adaptive. 

S.NO Algorithm Multiplications Additions Divisions 

1 LMS T+1 T+1 NIL 

2 LLAD T+4 T+2 1 

3 SRLLAD 4 T+2 1 

4 SLLAD T+3 T+2 1 

5 SSLAD T+2 T+2 1 

 

Figure 3. Pofa versus Pod for different SNR values.  

 

Figure 4. Convergence Curves for sign based LLAD adaptive algorithms.  

Table 2. Performance comparison of eigen value based spectrum sensing, proposed LLAD and its sign variants. 

SNR (dB) 0 -5 -10 -15 -20 

 Pfa Pd Pfa Pd Pfa Pd Pfa Pd Pfa Pd 

Eigen value-based 
spectrum sensing 

0.4 0.6789 0.3 0.6989 0.3 0.7125 0.3 0.7859 0.3 0.8752 

LLAD 0.2520 0.7824 0.3 0.8997 0.3 0.9581 0.3 0.9785 0.3 0.9969 

SR-LLAD 0.26 0.6241 0.2 0.6805 0.2 0.7825 0.2 0.8628 0.2 0.8853 

S-LLAD 0.3821 0.5645 0.4 0.7192 0.4 0.7403 0.4 0.7893 0.4 0.7990 

SS-LLAD 0.42 0.4561 0.5 0.4985 0.5 0.5782 0.5 0.5981 0.5 0.6782 



 

ACTA IMEKO | www.imeko.org March 2022 | Volume 11 | Number 1 | 6 

noise power estimation. When compared to spectrum sensing 
only by using energy detection, it provides improved results for 
the LLAD energy detection. The proposed approach for energy 
detection overcomes noise uncertainty difficulties, but it is also 
necessary to assess the signal correlation because it is based on 
noise power estimations with eigen values. If signal correlation 
occurs, the performances of energy detection and noise power 
estimates have an impact on spectrum sensing.  

Convergence becomes delayed by applying signum function. 
According to the illustrations, SRA variant is just lower than its 
non-signed variant. Figure 4 shows LLAD algorithm and its sign 
variants have a higher convergence rate than LMS. Hence 
SRLLAD algorithm is preferred when compared to LLAD and 
LMS algorithms. When the proposed LLAD algorithm exceeds 
the lower bound stability constraint [25], the normalized mean 
square deviation noise variance diverges. As a result of this 
equation Normalized mean square deviation provides higher 
stability for the proposed strategy. Normalized mean square 
deviation analysis yields higher convergence for modified 
normalized median LMS than NLMS and LMS for small step 
size noisy inputs. Because of instabilities, the standard modified 
normalized LMS method diverged at large step size values. 

In health care monitoring applications for remote patients, 
spectrum sensing with the proposed LLAD algorithm is utilized 
to reduce noisy inputs and interferences caused by wireless 
networks. The information of the patients is transmitted to 
doctors through cognitive systems by arranging wearable devices 
to patient body. The information is transmitted and received 
concurrently from both channels. In this case primary user of 
cognitive system takes higher priority over the secondary user. 
The data is accessible to secondary users, but not to primary 
users. This proposed LLAD Algorithm eliminates interference 
and disturbances that arise in this situation. Medical equipment’s 
are more sensitive than normal electric devices in health care 
accept. In these primary users are telemetry applications and 
secondary users are hospital information applications. By 
predicting spectrum holes the cognitive radio controller 
optimizes the performance of the system, cognitive radio 
controller regulates channel access, and probabilities are 
determined. For many data channels the loss and delay 
probabilities of cognitive radio system are enhanced. 

4. CONCLUSIONS 

The main objective of this paper is to reduce noise 
uncertainties during spectrum sensing using the proposed LLAD 
algorithm. Probability detection and false alarm probability are 
errors that arise as a result of spectrum sensing at the receiver, 
and their expressions are derived. After that, the impact of noise 
uncertainty on threshold parameter selection is investigated. The 
mean and mean square deviation analysis ensures stability for 
noisy primary user inputs. We considered Variable step size for 
improving the stability of the proposed spectrum sensing 
technique. The LLAD algorithm's performance is enhanced by a 
lower steady-state error rate and better convergence. In medical 
telemetry, this cognitive radio idea is utilized to minimize echo 
cancellations and signal correlations with noisy inputs at the 
primary user. As a consequence, we achieve improved outcomes 
in terms of noise uncertainty stability, convergence rate, and 
steady state error rate. The estimation of a false alert and the 
probability of detection were both computed as estimation 
parameters. 

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