Dr. Bassim S. Mohammed                                        Al-Khwarizmi Engineering Journal, 4, 2, (2008) 51-58


 

1 

 

 

      

Al-Khwarizmi 

Engineering   

Journal 

Al-Khwarizmi Engineering Journal, Vol. 10, No. 1, P.P.83- 91 (2014) 

 

 

The Mutual Interaction effects between Array Antenna Parameters 

and Receiving Signals Bandwidth 
  

Bassim S. Mohammed*                    Emad S. Ahmed** 

Shahad D. Sateaa*** 
*,**,*** Department of  Electrical Engineering / University of technology 

*Email: Bassim_sayed@yahoo.com 

**Email: dr_emad_sa@uotechnology.edu.iq 

***Email: shahad4comm@yahoo.com 

   
(Received 5 September 2013; accepted 31 March 2014) 

 

 

Abstract 
  
 The presence of a single complex adaptive weight in each element channel of an adaptive array antenna is sufficient 

for processing of narrowband signals. The ability of an adaptive array antenna to null interference deteriorates rapidly as 

the interference bandwidth increases. The performance of narrowband adaptive array antenna with LMCV Beamforming 

algorithm is examined. The interaction effects between received signal angle of arrival and array parameters like the 

interelement spacing and the number of array element and the received signal bandwidth were studied. The output Signal 

to Interference plus Noise Ratio (SINR) and Interference to Noise Ratio (INR) are used as performance parameters for 

evaluation of these effects. It is found that the amount of degradation in the output SINR is increased significantly with 

the increase of array interelement spacing, number of array elements and when the angle of arrival of received signals are 

closet to end fire. 

  

Keywords:  Array parameters, recived signal bandwidth, narrowband adaptive array antenna. 

  

1. Introduction 
 
 Adaptive array antennas are playing an 

important role in many applications such as radar 

and communication system. Adaptive processor 

can perform filtering in both space and frequency 

domain. By adjusting the amplitude and phase of 

the wavefront in each sensor, it is possible to 

electronically steer the main beam towards the 

look direction (desired signal), while suppressing 

any undesired signal [1- 3]. 

The function of any adaptive array is to 

minimize the received power from one or more 

interference sources. The ability of the adaptive 

array antenna system to perform this function 

depends on many factors, some of which include 

the number of adaptive array elements, antenna 

aperture size, nulling bandwidth, number of 

interference sources, strength of signals, and 

spatial distribution of these sources [4]. 

In general, adaptive antenna array system is 

composed from M-element and adaptive processor 

as shown in Fig (1). Each sensor is followed by 

complex weight. This weight is calculated 

according to applied algorithm. The received 

signal vector X is multiplied by weight vector W 

and then summed to perform the output y(t). 

Adaptive processor subdivided into two ports, the 

signal processing and adaptive algorithm [5, 6]. 

The processer hold the information of received 

signal and processed them according to the 

operating algorithm to produce the optimum 

weights which optimize the performance of the 

adaptive system. Array antenna field pattern 

depends on the phase delay between array 

elements due to interelement spacing calculating 

on the operating frequency   , so the wide 

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Bassim S. Mohammed                      Al-Khwarizmi Engineering Journal, Vol. 10, No. 1, P.P. 83- 91 (2014) 
 

 

84 
 

bandwidth signals will cause a sever distortion on the final field pattern due to the phase.  

The amount of degradation in the adaptive 

array performance due to signal bandwidth does 

not generate a high attention from researchers, in 

this paper we will try to investigate interaction 

effects between array parameters and receiving 

signal bandwidth. In Section II, we formulate the 

equations needed to calculate the received signal 

covariance matrix for an array with M elements. In 

Section III, the LCMV beamformer is briefly 

reviewed to calculated output SINR and INR. 

Section IV, contains our simulations and results 

cases. Finally, Section V contains conclusions

.  

 
  

Fig. 1. M-elements adaptive array system. 

 
 

2. Mathematical Formulation 
 

M-isotropic linear array antenna elements are 

considered to be uniformly distributed with inter 

element spacing (d) at the carrier frequency   . 
The received signal by j

th
 element can be written 

as  

                                            … (1) 

Equation (1) in a vector form is          

                                          … (2) 

where                       are vectors 
      of dimension for desired, interference and 
thermal noise, respectively. 

If the desired signal is incident from angle 

    , then the desired signal vector  is  

                                            … (3) 

where m=1, 2, …, M and    is desired signal 
spatial propagation delay between element 

                                                      … (4) 

If the interference signal is incident from angle 

    , then the interference signal vector  is  

                                               … (5) 

where    is the interference signal spatial 
propagation delay between element 

                                                       … (6) 

The thermal noise voltage of the j
th
 array 

element is a random signal with zero mean and    
variance. The thermal noise components of 

channels are considered to be statistically 

independent. 

The output signal of array can be written as 

        
 
                                             … (7) 

In vector form Eq. (7) is   

                                                 … (8) 

where the weight vector (W) and the received 

signal vector (X) are vectors       dimension 
and given by 

                                                  … (9) 



Bassim S. Mohammed                      Al-Khwarizmi Engineering Journal, Vol. 10, No. 1, P.P. 83- 91 (2014) 
 

 

85 
 

                                                   … (10) 

The covariance matrix of a received signal 

vector is defined as  

                              … (11) 

where “E” is the expected value of random 

variable 

Since X (t) is a deterministic signal it has zero 

mean and it is considered as a stationary process, 

these assumptions leads to 

                                     … (12) 

where     is       autocorrelation matrix 
of received signals vector X(t). 

The arriving signal has a flat power spectral 

density with           amplitude over a 
bandwidth    centered at frequency    as shown 
in Fig(2), then the Fourier inverse of this signal is 

[7] 

        
                                         … (13) 

For single array element the auto correlation 

function is 

            
 

 
                                     …(14) 

where   is signal relative bandwidth  

                                                         … (15) 

 

 
  

Fig. 2. The power spectral density of received signal. 

 

  

The autocorrelation matrix     of all received 

signal is Hermitian (i.e.        
   ) expressed 

as 

                                             … (16) 

where                  are desired, interference 
and thermal noise        autocorrelation 
matrix respectively.  

The correlation matrix     of desired signal is 

                                         … (17) 

where m=n=1, 2, …, M and             are 
the matrix inverse of covariance matrix    . 

Substituting Eq.(14) into Eq. (17) gives 

                 
  
 

            
           

                                                                                …(18) 

where    is the power of desired signal and 
             is the desired signal relative 
bandwidth. 

                  
  

 
          

                                                                      …(19) 

where    is interelement phase shift due to desired 
signal 

                                            … (20) 

The correlation matrix     of interference signal is 
found to be 

                                             … (21) 

Substituting Eq.(14) into Eq. (21) gives 

         

        
  

 
             

            …(22) 

where    is the power of interference signal and 
             is the interference signal relative 
bandwidth. 

                  
  
 

         

                                                                 …(23) 

where     is interelement phase shift due to 
interference signal 

 

                                               … (24) 

The correlation matrix     of noise components 
are independent and equal to 

 

     
                                                      … (25) 

 

where    is the variance of thermal noise 
components. 

 

 

 

 

 



Bassim S. Mohammed                      Al-Khwarizmi Engineering Journal, Vol. 10, No. 1, P.P. 83- 91 (2014) 
 

 

86 
 

3. LCMV Beamforming 
    

The basic idea behind the Linearly Constrained 

Minimum Variance (LCMV) beamforming is to 

constrain the response of the beamformer, so 

signals from the direction of interest are passed 

with specified gain and phase. The weights are 

chosen to minimize output variance or power 

subject to the response constraint. This has the 

effect of preserving the desired signal while 

minimizing contributions to the output due to 

interfering signals and noise arriving from 

directions other than the direction of interest [8, 9]. 
 

     
           Subject to    

        …(26) 

where     is the autocorrelation matrix (   ), 
C is a        constraint matrix for look 
direction (desired direction). 

          
  

 
             

             

                                                                               … (27) 

The optimum steady state weight vector 

[        can be accomplished by method of 

Lagrange multipliers 

       
        

    
  

                       … (28) 

With the optimum weight vector given in Eq. 

(28), the output powers due to desired, 

interference and noise are given by 

               
      

 
             … (29) 

              
      

 
                 … (30) 

              
      

 
              … (31) 

 

Then the output SINR is given by 

        
     

           
                              …(32) 

and the output INR is given by 

       
     

     
                                                …(33) 

 

 

4. Simulation and Results 
 

The simulation cases programes are written by 

MATLAB 8.2 and the following assumptions are 

considered  

 Isotropic linear array antenn uniformaly 
distribution. 

 Desired signal input power is 0dB and 
interference input power is 20dB. 

 Interference sourece angle of arrival is from 

endfire (     ). 

 

CASE 1 

 

Ten isotripoic array elements with 0.5       
        inter element spacing is considered. A 
desired signal angles of arrival are assumed to be 

from (              ). 

Fig (3) shows that the output SINR is degraded 

with the increase of interference bandwidth for all 

desired signal angles of arrival.The degradation is 

increased when the desired signal angle of arrival 

moves towards end fire (decreased), this is due to 

the increase in element phase delay (     
         ) and this in turn leads to an increase in 
the interference relative bandwidth as given in 

Eq.(23). Fig. (4) shows that the output INR is 

increased when the interference bandwidth is 

increased which means more interference power 

will appear at the output of the system due to 

limation of narrowband array processor.  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 



Bassim S. Mohammed                      Al-Khwarizmi Engineering Journal, Vol. 10, No. 1, P.P. 83- 91 (2014) 
 

 

87 
 

 
 

Fig. 3. Output SINR plot versus interference relative bandwidth for different desired signals angle of arrival. 

 

 

 
 

Fig. 4. Output INR plot versus interference relative bandwidth for different desired signals angle of arrival. 

 

 

CASE 2 

 

Ten isotripoic array elements with desired 

signal angle of arrival from     and for different 
interelment spacings (d= 0.25, 0.5, 0.75   ). 

Fig. (5) shows that the output SINR is 

degraded when the interference bandwidth is 

increase for all inter element spacing (d= 0.25, 0.5 

and 0.75   ). The increase in the interelement 

spacing from 0.25   to 0.75   cause an increase 
in the effect of interference relative bandwidth as 

given in Eq.(23), so it causes a more degradation 

in the outpt SINR. Fig. (6) shows that the output 

INR is increased with the increase in the 

interferences bandwidth and interelment spacing 

this is due to the increase in the effect of 

interference bandwidth effect on a narrowband 

processor. 

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
1

2

3

4

5

6

7

8

9

10

Interference Relative Bandwidth

S
IN

R
 (

d
B

)

 

 

Desired angle of arrival =80°

Desired angle of arrival =60°

Desired angle of arrival =40°

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

Interference Relative Bandwidth

IN
R

 (
d

B
)

 

 

Desired angle of arrival =80°

Desired angle of arrival =60°

Desired angle of arrival =40°



Bassim S. Mohammed                      Al-Khwarizmi Engineering Journal, Vol. 10, No. 1, P.P. 83- 91 (2014) 
 

 

88 
 

 
 

Fig. 5. SINR plot versus interference relative bandwidth for different interelements spacing 
 

 
 

Fig.  6.  INR plot versus interference relative bandwidth for different interelements spacing 

 

 

CASE 3 

 

Two array sets with nine and four elements 

with 0.5   inter element spacing are considered. A 
desired signal angle of arrival is from     with 
relative bandwidth between 0 to 0.5. 

Fig. (7) shows that the system exhibit more 

degradation in the output SINR when the number 

of array antenna is increased from 4 to 9 (i.e. when 

the array system has wide operatere). This is due 

to the increase in the effect of interference 

bandwidth with the increase of array aperture 

(Array aperture = number of element   
interelement spacing) according to Eq. (23). It can 

be also shown that  when interference relative 

bandwidth is (0.3), the amount of drop in the 

output SINR is (3.504dB) for four elements and 

(3.608) for nine elements. 

Figure (8) shows the same reasons mentioned 

above that the output INR is higher for the case of 

nine element due to increase in the array aperture.  

 

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
1

2

3

4

5

6

7

8

9

10

Interference Relative Bandwidth

S
IN

R
 (

d
B

)

 

 

d= 0.25 lamda

d= 0.5 lamda

d= 0.75 lamda

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

Interference Relative Bandwidth

IN
R

 (
dB

)

 

 

d= 0.25 lamda

d= 0.5 lamda

d= 0.75 lamda



Bassim S. Mohammed                      Al-Khwarizmi Engineering Journal, Vol. 10, No. 1, P.P. 83- 91 (2014) 
 

 

89 
 

 
 

 Fig. 7. SINR plot versus interference relative bandwidth for different number of antennas. 

 

 

 
 

Fig. 8. INR plot versus interference relative bandwidth for different number of antennas. 

 

 

5. Conclusion 
  

It is found from the presented result in this paper 

there is a significant mutual effect between array 

parameters and receiving signal bandwidth. Theses 

mutual effects can be defend as follows  

Generally the performance of adaptive array 

system with narrowband processor is degraded 

with the increase of received signal bandwidth. 

The degree of degradation is depending on the 

array parameters as well as on the value of 

received signal bandwidth. The increase in the 

number of array element causes an increase in the 

array aperture which makes the array antenna 

sensitive to the bandwidth of received signal, wide 

aperture cause  more degradation in the output 

SINR. The received signal angle of arrival plays a 

role on the amount of bandwidth performance that 

the narrowband signal can be peer. It is found that 

the received signal is at the broadside angle the 

system is more sensitive for the received signal 

band width. The increase in the interelement 

spacing cause an in increase in the aperture of 

antenna which makes the effects of the received 

signal bandwidth more significant. 

 

 

6. References 
 

[1] Nordin Bin Ramli, “Study on Subband 

Adaptive Array for Space-Time Codes in 

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
1

2

3

4

5

6

7

8

9

10

 

 

X: 0.3

Y: 3.608

Interference Relative Bandwidth

SI
N

R
 (d

B
)

X: 0.3

Y: 3.504

M=9

M=4

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

 

 

X: 0.3

Y: -3.352

Interference Relative Bandwidth

IN
R

 (
dB

)

X: 0.3

Y: -2.95

M=9

M=4



Bassim S. Mohammed                      Al-Khwarizmi Engineering Journal, Vol. 10, No. 1, P.P. 83- 91 (2014) 
 

 

90 
 

Wideband Channel”, Ph. D Thesis, University of Electro-Communications, March, 2008. 

[2] B. Widrow, P. E. Mantey, L. J. Gri_Ths, and 

B. B. Goode, “Adaptive Antenna Systems”, 

Proceeding of the IEEE, Vol. 55, No. 12, pp. 

2143-2159, December, 1967. 

[3] N. Kikuma, Adaptive Antenna Technology (in 

Japanese), Ohmsha, Ltd., Oct. 2003. 

[4] Alan J. Fenn, “Adaptive Antennas and Phased 

Arrays for Radar and Communications”, 

Massachusetts Institute of Technology, 

Lincoln Laboratory, 2008. 

[5] Robert A. Monzingo, Randy L. Haupt and 

Thomas W. Miller, “Introduction to Adaptive 

Arrays”, 2
nd

 Edition, SciTech Publishing, 

2011. 

[6] Singh H. and Jha R. M., “Trends in Adaptive 

Array Processing”, International Journal of 

Antennas and Propagation, Vol. 1, 2012. 

[7] R. T. Compton, Jr., “The Bandwidth 

Performance of a Two-Element Adaptive 

Array with Tapped Delay-Line Processing”, 

Transactions on Antennas  and Propagation 

IEEE, Vol. 36, No. 1, pp. 5-14, January, 1988.  

[8] V. K. Madisetti, “The Digital Signal 

Processing Handbook”, 2
nd

 Edition, 1999. 

[9] D. H. Johnson and D. E. Dudgeon, Array 

Signal Processing: Concepts and Techniques, 

Signal Processing Series. Prentice Hall, 

Englewood Cliffs, NJ,1993. 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 



 (2014) 83- 91، صفحة 1، العدد10دمجلة الخوارزمي الهندسية المجل                                                            باسم سعيد محمد                     
 

 

91 
 

 

 

 

واستقبال إشارات النطاق الترددي معامالت مصفوفة الهوائياتآثار التفاعل المتبادل بين   
 

 **عماد شهاب احمد                        *          باسم سعيد محمد

 ***شهد ضاري ساطع                                                     
 الجامعة التكنولوجية/  قسم الهندسة الكهربائية  ***،**،*

Bassim_sayed@yahoo.com :البريد االكتروني*   

dr_emad_sa@uotechnology.edu.iq :البريد االكتروني**  

shahad4comm@yahoo.com : البريد االكتروني ***  

 

  
 

 الخالصة

 
أن قابلية  .ةالضيق ذات الحزمة الترددية شاراتاإل لمعالجة تكفي فقط تكيفيةمالمصفوفة العنصر من عناصرفي كل مصفوفة توازن معقدة واحدة  وجودان  

تم (. (LMCVمع خوارزمية  للحزمة الضيقة المتكيفةالهوائيات مصفوفة تم فحص اداء  .النظام لتخميد التداخل ستسوء بزيادة الحزمة الترددية لمصدر التداخل

 و (SINR) معامالت قياس الجودةتم استخدام  .اصرمعامالت مصفوفة الهوائيات وتأثيرات عرض الحزم لإلشارات المستلمةات المتباينة بين عنتأثيرالدراسة 

(INR) لقد توصل البحث الى أن مقدار التدهور في . في تقيم هذه التاثيرات على عمل المنظومة(SINR) بصورة ملحوظة بزيادة عدد الهوائيات زداد ي

 .end fireوالمساحة الفاصلة بين الهوائيات وكذلك عندما تكون زاوية الوصل لإلشارة المستلمة قريبة من 

 

 
 

mailto:Bassim_sayed@yahoo.com
mailto:dr_emad_sa@uotechnology.edu.iq
mailto:shahad4comm@yahoo.com