An adaptive learning algorithm for spectrum sensing based on direction of arrival estimation in cognitive radio systems


ACTA IMEKO 
ISSN: 2221-870X 
December 2021, Volume 10, Number 4, 67 - 72 

 

ACTA IMEKO | www.imeko.org December 2021 | Volume 10 | Number 4 | 67 

An adaptive learning algorithm for spectrum sensing based 
on direction of arrival estimation in cognitive radio systems 

Sala Surekha1, Md. Zia Ur Rahman1, Aimé Lay-Ekuakille2 

1 Department of Electronics and Communication Engineering, K L University, Koneru Lakshmaiah Education Foundation,  
  Green Fields, Vaddeswaram, Guntur-522502, A.P., India 
2 Department of Innovation Engineering, University of Salento, Lecce, Italy 

 

 

Section: RESEARCH PAPER  

Keywords: Adaptive learning; beam forming; cognitive radio; direction of arrival; spectrum sensing  

Citation: Sala Surekha, Md. Zia Ur Rahman, Aimé Lay-Ekuakille, An adaptive learning algorithm for spectrum sensing based on direction of arrival estimation 
in cognitive radio systems, Acta IMEKO, vol. 10, no. 4, article 13, December 2021, identifier: IMEKO-ACTA-10 (2021)-04-13 

Section Editor: Francesco Lamonaca, University of Calabria, Italy 

Received May 28, 2021; In final form December 1, 2021; Published December 2021 

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: Md. Zia Ur Rahman, e-mail: mdzr55@gmail.com  

 

1. INTRODUCTION 

Telecommunication systems are rapidly using from past few 
decades it leads to increase in frequency spectrum usage. Due to 
lack of frequency spectrum, there is low utilization of licensed 
and unlicensed bands. To avoid interferences, secondary users 
always must be aware of primary user is absent or present in a 
particular frequency band. Further considered secondary user 
direction of arrival (DOA), it contains multiple input single 
output (MISO) and one receiving antenna for primary user and 
feedback based adaptive frequency algorithm. Non orthogonal 
multiple access [1] based cognitive radio network is used for 
secure beamforming to avoid interference in multiple input 
multiple output networks. In array sensors, estimation of number 
of channels is a problem and it is solved by considering direction 
of arrival in spectrum sensing method. Wideband spectrum 
sensing channel [2] is divided into two sub channels; each sub 
channel is connected with sensor for processing and then 
estimation of DOA is done. For multi band signals, two 

spectrum scenarios are considered from sub-Nyquist samples: in 
first scenario, spectrum sensing method is examined then DOA 
is considered as recovery for frequency spectrum problems by 
proposing uniform linear array (ULA) [3] with sensor at receiver 
then it is connected to equivalent circuit of analog front-end 
channel of modulated wideband converter (MWC). In second 
case, generalized likelihood ratio antenna beamforming [4] used 
for efficient and low complexity spectrum sensing. Localization 
technique is investigated in [5] depending on direction of arrival 
measurements for estimating primary users in cognitive radio 
networks. In [6], [7] new spectrum sensing techniques based on 
beamforming are proposed. Null steering and joint beam-based 
resource allocation [8] used in femtocell networks in spectrum 
sensing. Performance of transmitter localization done using 
sector power measurements for every senso then derived Cramer 
Rao Bound (CRB) [9],[10] for sector power estimation using 
DOA and mean square error is derived for analytical expression. 
Main objective of this paper, estimating DOA of various sensors 
for sensing [11], [12] the vacant spectrum and thereby facilitate 
channel allocation to secondary user. Here, we make use of an 

ABSTRACT 
In cognitive radio systems, estimating primary user direction of arrival (DOA) measurement is one of the key issues. In order to increase 
the probability detection multiple sensor antennas are used and they are analysed by using subspace-based technique. In this work, we 
considered wideband spectrum with sub channels and here each sub channel facilitated with a sensor for the estimation of DOA. In 
practical spectrum sensing process interference component also encounters in the sensing process. To avoid this interference level at 
output of receiver, we used an adaptive learning algorithm known as Normalised Least Absolute Mean Deviation (NLAMD) algorithm. 
Further to achieve better performance a bias compensator function is applied in weight coefficient updating process. Using this hybrid 
realization, the vacant spectrum can be sensed based on DOA estimation and number of vacant locations in each channel can be 
identified using maximum likelihood approach. In order to test at the diversified conditions different threshold parameters 0.1, 0.5, 1 
are analysed. 

mailto:mdzr55@gmail.com


 

ACTA IMEKO | www.imeko.org December 2021 | Volume 10 | Number 4 | 68 

adaptive learning algorithm based on normalized least absolute 
mean deviation (NLAMD) strategy. In section 2, the DOA 
estimation with an adaptive leaning algorithm is discussed, in 
section 3 simulation results are discussed. The proposed 
realizations are suitable for the development of medical telemetry 
networks as well in the development of smart cities, smart 
hospitals.  

2. DOA ESTIMATION BASED SPECTRUM SENSING 

In cognitive radios, spectrum sensing is mostly used method 
because it overcomes the low spectrum utilization problems of 
primary users. There are various spectrum sensing algorithms 
they are based on narrowband methods used to solve binary 
hypothesis. This binary hypothesis test is used for every sub 
channel. For assessing the primary user’s existence, sub channel 
assessed in spectrum sensing algorithm. In each sub channel 
received signal is expressed [13]as 

𝑦𝑘 = {
𝑤𝑘, ℎ0

𝑎𝑟𝑘 + 𝑤𝑘, ℎ1
 , (1) 

where 𝑎𝑟𝑘 is primary user received signal, 𝑤𝑘 is additive white 
Gaussian noise, ℎ0 and ℎ1 are hypothesis test used for primary 
user existence in every sub channel. Multiple hypothesis tests are 
employed for spectrum sensing algorithm, then by taking into 
consideration of all sub channels primary user signal is detected. 
By analysing all sub channel received signals, observed that noise 
is present in output signal. To discriminate this noise from 
primary user signals, DOA is estimated. By assuming received 
signal at sensor nodes in array processing, it looks like cognitive 
radio subchannel, to avoid these problems DOA estimation is 
considered in spectrum sensing and its block diagram is shown 
in Figure 1. DOA estimation is considered to get exact 
information of antenna and also to avoid interferences between 
primary and secondary users, further an adaptive learning 
process called normalised least absolute mean deviation 
(NLAMD) algorithm is considered for spectrum to reduce noise 
levels at output. By using adaptive filter, desired response of 
input signal is calculated as 

𝑑𝑘 = 𝑠𝑘
T𝑢0 + 𝑜𝑘 , (2) 

where 𝑠𝑘
  is input signal, u0 is unknown weight vector with ‘t’ taps 

and 𝑜𝑘 is output noise at time index ‘k’. Error output of desired 
signal is represented as 

𝑒𝑘 = 𝑑𝑘 − 𝑠𝑘
T𝑢𝑘 . (3) 

Here, 𝑢𝑘 = [𝑢𝑘1,𝑢𝑘2 ….. ,𝑢𝑘𝑇]
T is weight vector of adaptive 

filter. 
For above equation identification problem of adaptive system 

is solved by p-norm cost function minimization 

𝐽(𝑒𝑘) =
1

𝑝
E[|𝑒𝑘|

𝑝] =
1

𝑝
E[|𝑒𝑘 = 𝑑𝑘 − 𝑠𝑘

T𝑢𝑘|
𝑝] (4) 

where E[.] is the operator of statistical expectation for p>0. 

E[|𝑒𝑘|
𝑝] is replaced with |𝑒𝑘|

𝑝, then after calculation we get 
gradient of uk for p-norm error evaluated as 

𝜕𝐽(𝑒𝑘)

𝜕(𝑢𝑘)
= −|𝑒𝑘|

𝑝−1 sign[𝑒𝑘𝑠𝑘] . (5) 

By using gradient descent algorithm weight equation is 
updated as 

𝑢𝑘+1 = 𝑢𝑘 + 𝜔|𝑒𝑘|
𝑝−1sign[𝑒𝑘𝑠𝑘], (6) 

where ‘𝜔’ is step size selected appropriately used for balancing 
convergence rate and mean square error, ‘sign’ used for denoting 
sign function. For improving steady state rate and convergence 
rate above equation is updated with normalised least mean p-
power algorithm as 

𝑢𝑘+1 = 𝑢𝑘 + 𝜔
|𝑒𝑘|

𝑝−1sign[𝑒𝑘𝑠𝑘] 

||𝑠𝑘||𝑝
𝑃 + 𝜗

 . (7) 

Here ||.||p used for p-norm operation, small positive value 

𝜗 is also considered for avoiding denominator from zero. By 
selecting p-norm values as 1, then we obtain the NLAMD 
algorithm equation as 

𝑢𝑘+1 = 𝑢𝑘 + 𝜔
sign[𝑒𝑘𝑠𝑘] 

||𝑠𝑘||1
1 + 𝜗

 . (8) 

In sparse models, L1 norm is used for relaxation in least 
absolute shrinkages and operator selector algorithms, and it is 
employed in various adaptive filter algorithms. By using L1 norm, 
weight equation of NLAMD algorithm is updated to minimise 
cost functions and it is given as 

𝐽𝑑(𝑒𝑘) =
𝑑𝑘 − 𝑠𝑘

T𝑢𝑘

||𝑠𝑘||1
1 + 𝜗

+ ||𝑢𝑘||1 , (9) 

where  is adopted parameter to know the difference between 
estimation error and sparsity. Then we get the updated equation 
for NLAMD sparse algorithm using gradient descent method 
using cost function equation (9) as 

𝑢𝑘+1 = 𝑢𝑘 + 𝜔
sign(𝑒𝑘𝑠𝑘)

||𝑠𝑘||1
1 + 𝜗

− 𝜎 sign(𝑢𝑘) . (10) 

Here, 𝜎 = 𝜔  is a regularised parameter. NLAMD algorithm 
with sparse system and L1 norm is denoted as ZA NLAMD 
algorithm. 

In bias compensated systems [14], considered a noisy input 
system for NLAMD algorithm. Input noise vector of a system is 
defined as 

�̅�𝑘 = 𝑠𝑘 + 𝑜𝑖𝑛𝑘 , (11) 

where 𝑜𝑖𝑛𝑘 noisy input vector it is represented as 𝑜𝑖𝑛𝑘 =

[𝑜𝑖𝑛1𝑘,𝑜𝑖𝑛2𝑘,……,𝑜𝑖𝑛𝑀𝑘]
T
, and its limit is 𝑜𝑖𝑛,𝑡𝑘(𝑙 ∈ [1,𝑀] ), 

their input variance is represented as 𝜎𝑖𝑛
2  and is estimated by 

using some unknown info. To recover the biased estimation 
problems for NLAMD algorithm of equation (10), an unbiased 

estimation vector 𝑏𝑘 is taken into consideration as 

𝑢𝑘+1 = 𝑢𝑘 + 𝜔
sign(�̂�𝑘�̂�𝑘)

||�̂�𝑘||1
1 + 𝜗

− 𝜎 sign(𝑢𝑘)+ 𝑏𝑘 . (12) 

By using above equation, we get bias compensated vector as 
below [15]  

𝑏𝑘 = 𝜔𝜎�̂�|�̂�
2

𝑘√
2
(π𝜎�̂�|�̂�

2

𝑘
)

⁄ (
𝑢𝑘

||�̂�𝑘||1
1 + 𝜗

) . (13) 

Noisy input parameter variances 𝜎𝑜𝑖𝑛 
2

𝑘
, 𝜎�̂�|�̂�

2

𝑘
 and 𝜎𝑢𝑘

2  are 

estimated accurately by computing these variance parameters as 



 

ACTA IMEKO | www.imeko.org December 2021 | Volume 10 | Number 4 | 69 

𝜎𝑜𝑖𝑛𝑘
2 =

𝜎�̂�|�̂�
2

𝑘

𝑀𝜎𝑢𝑘
2 +𝑖 +

𝜎�̂�|�̂�
2

𝑘
(𝑀)

�̂�𝑘
T�̂�𝑘

 . (14) 

𝜎�̂�|�̂�
2

𝑘
= ℵ𝜎�̂�|�̂�

2

𝑘−1
+(1 −ℵ)�̂�𝑘

2 (15) 

𝜎𝑢𝑘
2 = ℵ𝜎𝑢𝑘−1

2 + (1 − ℵ)
1

𝑀
𝑢𝑘
T𝑢𝑘 . (16) 

Equation (13) is substituted into (12), we get final bias 
compensated NLAMD (BC-NLAMD) adaptative learning 
process updated as  

𝑢𝑘+1 =

(

 
 
 

1 +

𝜔
√
2
(π𝜎�̂�|�̂�

2

𝑘
)

⁄ 𝜎𝑜𝑖𝑛
2

 

||�̂�𝑘||1
1 + 𝜗

)

 
 
 

𝑢𝑘

+ 𝜔
sign(�̂�𝑘�̂�𝑘)

||�̂�𝑘||1
1 + 𝜗

−𝜎 sign(𝑢𝑘) . 

(17) 

Using this weight recursion, the noise in the received signal is 
minimised and accurate direction of arrival is estimated. The BC-
NLAMD algorithm accurately estimates the DOA and helps in 

finding the vacant spectrum and the flowchart of the proposed 
adaptive learning algorithm is shown in Figure 2.  

3. RESULTS AND DISCUSSION 

This section demonstrates the experimental results for 
evaluating the performance of proposed bias compensated 
adaptive learning algorithm and is compared with absolute mean 
deviation (AMD) and normalised absolute mean deviation 
(NAMD) methods with output Gaussian noise. Input and output 
noises generated using zero white mean Gaussian noise and β 
stable distribution respectively for better performance of 
proposed algorithm and its characteristic function is expressed 
as, 

𝑓𝑡 = e
𝑗𝛿𝑡− |𝑘|

𝛽[1+𝑗𝜏 sign(𝑡)𝑄𝑡,𝛽 , (18) 

where 

𝑄𝑡,𝛽 = 𝑓(𝑥) = {
tan

𝛽 π

2
, 𝛽 ≠ 1

2

π
log𝑡, 𝛽 = 1

 (19) 

with characteristic exponent 0 < 𝛽 ≤ 2, skewness −1 ≤ 𝜏 ≤
1 , scale parameter range 0 < < ∞ and location parameter 
−∞ < 𝛿 < ∞. 

 

Figure 1. DOA estimation Block diagram for spectrum sensing.  

 

Figure 2. Flow chart of spectrum sensing DOA estimation using BC-NLAMD algorithm.  



 

ACTA IMEKO | www.imeko.org December 2021 | Volume 10 | Number 4 | 70 

Occupied subchannel locations are estimated using spectrum 
sensing method with choosing of Q subchannels. In cognitive 
radio applications, using spectrum sensing correlation between 
channels are identified. In our framework for identifying 
spectrum location direction of arrival is taken into consideration. 
By using DOA, we can identify spectrum location using the 
proposed BC-NLAMD adaptive learning process. Output signal 
with various combinations is considered as one white signal with 
one DOA, one white signal with 3 DOA, two white signals with 
one DOA and three DOA. Performance of adaptive algorithm 
is studied in terms of convergence rate, beam pattern and 
number of active taps. In mobile environments, more than one 
multipath is considered, in those each multipath have different 
gains and it has amplitude and phase components. 

Case 1: One white signal with one DOA 

In this type, one signal with one path is considered it arrives 
at base station with 60 degrees angle and amplitude 0.5, it is 
propagated at different threshold values 0.1, 0.5 and 1. For 
different threshold control values, delay and steady state error are 
calculated as discussed in second section. For threshold value of 
0.1, it improves convergence rate for proposed BC NLAMD 
algorithm when compared to LMS [16] algorithm. For threshold 
values of 0.5 and 1 steady state is converged faster than basic 
LMS algorithm. Improvement in convergence rate is identified 
by using taps in adaptive filter algorithm. For narrow band 
theoretical values, threshold value need only one tap but however 
it has delay cost and convergence rate problems. Hence, we 
considered beam pattern with NLAMD algorithm using 
MATLAB in DOA estimation, it steers main beam with 60 
degrees direction with beam strength of two, it is due to power 
signal reduced by factor 0.5. For every simulation, convergence 
rates are given in terms of number of samples, it is required for 
steady state and it is shown in Table 1. 

Case 2: One white signal with 3 DOAs 

These simulations are studied for effects of multipath smart 
antenna systems. Multipath antennas with three different 
direction of arrivals -20, 30 and 60 degrees are considered for 
base station. At antenna system each multipath have a difference 
of one sampling period of 1/fc and their corresponding gains also 
introduced with amplitudes as shown in Figure 3. For proposed 
method, three different weight vectors for each multipath are 
used for spectrum sensing. Convergence rate for white signal 
with three DOAs gives better convergence rate for proposed bias 
compensated NLAMD algorithm when compared to AMD 
algorithm as shown in Figure 4. By proposed algorithm, antenna 
systems show similar beam pattern compared to basic AMD 
algorithm and it has ability to steer beams in multiple directions 
with zero interference directions for each beam, gain is inversely 
proportional to corresponding multipath of antenna. 

Case 3: Two white signals with one DOA 

Two different signals are transmitted with one DOA each and 
its effect is same as sending two multipaths for one signal 
separated by one sample period at least, it is due to two signals 
are uncorrelated for each other with amplitude of 0.5 and 1 at 
threshold values of 0.1, 0.5 and 1. It gives good convergence rate 
for second signal when compared to first signal. For smaller 
amplitude it gives longer response to adapt taps and then signal 
is estimated. Narrow threshold gives an ability to adapt smaller 
number of taps for better performance of proposed NLAMD 
algorithm and their beam patterns for corresponding DOA are 
shown in Figure 5 and Figure 6 respectively. 

Case 4: Two white signals with three DOAs 

In this case, two input sequences are considered each 
sequence with three multipath components is simulated. At the 
base station, multipath signals of second and third are used 
behind first multipath signals from various directions. For each 
signal, only two sets of multipath are considered. At base station, 
second and third multipath have the same weight vector. 
Compared the convergence rate with basic LAD algorithm. Four 
beam patterns are considered from Shannon theory, 3rd 
multipath pattern with two main lobes in direction of second and 
third multipaths, they are shown in Figure 7 and Figure 8 
respectively. Convergence rates for first signal, second signal in 
case of DOA 3 is shown in Table 2 and Table 3 respectively in 
terms of number of samples considered to reach steady state. 
From the tables, it is clear that for DOA3 of proposed algorithm 
converged faster for second signal when compared to first signal. 
In Figure 7, only two multipath signals are visible because 2nd and 
3rd signals have same weight vectors. 

Main aim of proposed BC-NLAMD algorithm is for detecting 
frequency spectrums in cognitive radio antenna systems. 
NLAMD algorithm is used for low computational complexity, 

 

Figure 3. BCNLAMD Beam pattern for one white signal with DOAs.  

 
Figure 4. Error for received signal using BCNLAMD algorithm with threshold 
value of 0.1. 

Table 1. BCNLAMD Beam pattern for one white signal with DOAs.  

Algorithm Steady state Delay 

LAMD [17] 65 0 

BBNLMS [18] 50 0 

FFA [19] 35 0 

PID [20] 25 8 

ENLMS [21] 15 12 

BCNLAMD for 0.1 40 0 

BCNLAMD for 0.5 45 7 

BCNLAMD for 1.0 55 14 



 

ACTA IMEKO | www.imeko.org December 2021 | Volume 10 | Number 4 | 71 

better stability and good robustness to avoid implementation 
errors. However, NLAMD algorithm is poor convergence and it 
is increased by using bias compensated NLAMD algorithm and 
it requires system with sparse channels. In wireless channel, 
spatial properties are exploited with detection guide systems. 
Beam patterns are analysed and they are compared with Shannon 
theorem. Proposed results are compared with threshold point of 
spectrum sensing algorithm for BC-NLMAD algorithm. Then it 
gives better results for BC-NLMAD in terms of faster 
convergence, low computational complexity and particularly 
narrow band threshold gives better performance of antennas. It 
is due to delay period presence, on that time system waits for set 
of samples those are undetermined before actually converging 
for desired signal. However, system performance is improved at 

a cost of increased computational complexity that will need 
increased number of taps adaptation for narrow threshold point 
in proposed algorithm and it reduces error at output signals. 
Beam patterns are obtained with according to expectations of 
Shannon theorem, and further proposed algorithm with active 
taps steers beams in desired signal direction. Spatial filtering is 
particularly used in wireless communication systems. Hence by 
proposed algorithm performance of system is increased with 
active taps weights in updated equation so that improves 
frequency utilization for cognitive radio systems. 

4. CONCLUSION 

In this paper, the vacant spectrum is sensed by using DOA 
measurement in wireless communication systems. Interferences 
occurred with cognitive radio systems are avoided by considering 
DOA estimation for spectrum sensing. In wireless 
communications, antenna system are new developing 
technologies with new adaptive beam forming algorithms, it will 
provide high frequency spectrum then it improves quality of 
service of cognitive radio systems. Further to reduce noise signals 
from received signal proposed a bias compensated NLAMD 
algorithm. Using this adaptive learning algorithm, performance 
of cognitive radio-based antenna beam streams and convergence 
rate is improved. By using sign regressor function in weight 
update equation of proposed algorithm computational 
complexity is reduced. Performance of BCNLAMD algorithm in 
presence of multipath users and multipath effects are analysed 
using MATLAB simulations and hence convergence rate is 
improved due to active taps used in adaptive learning algorithm 
leads to better spectrum efficiency in cognitive radios.  

 
Figure 5. Error signal for BCNLAMD algorithm for 0.1 value.  

 
Figure 6. BCNLAMD Beam pattern for two white signals with one DOA. 

Table 2. Convergence rate of first signal, DOA3.  

Algorithm Steady state Delay 

LAMD [17] 55 0 

BBNLMS [18] 60 20 

FFA [19] 70 45 

PID [20] 80 65 

ENLMS [21] 90 70 

BCNLAMD for 0.1 35 60 

BCNLAMD for 0.5 55 40 

BCNLAMD for 1.0 125 95 

Table 3. Convergence rate of second signal and DOA3 

Algorithm Steady state Delay 

LAMD [17] 45 0 

BBNLMS [18] 55 0 

FFA [19] 62 20 

PID [20] 70 40 

ENLMS [21] 85 55 

BCNLAMD for 0.1 25 35 

BCNLAMD for 0.5 45 25 

BCNLAMD for 1.0 95 65 

 

Figure 7. Received error signal for BCNLAMD algorithm.  

 
Figure 8. BCNLAMD beam pattern for two white signals with 3 DOAs. 



 

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