This paper presents an algorithm to cancel the reflections 

that appear in the anechoic antenna measurement systems 

due to low frequency bands, AUT and probe supports... The 

algorithm is based on a modification of the ESPRIT [1-3] 

direction of arrival method and needs a very low number of 

frequencies to work – that is, a strict requirement in antenna measurement system. Actually, this algorithm will be applied to a planar near field scanner

Besada Sanmartin, Jose Luis

Burgos Martínez, Sara

Sierra Castañer, Manuel

Servicio de Coordinación de Bibliotecas de la Universidad Politécnica de Madrid

  
 
Cancellation of reflections in planar antenna 
measuring systems via ESPRIT algorithm 
Sara Burgos Martínez, M. Sierra Castañer, J.L. Besada Sanmartín 
Signals, Systems and Radio communications Department  
Polytechnic University of Madrid (UPM) 
sburgos@teleline.es, m.sierra.castaner@gr.ssr.upm.es, besada@gr.ssr.upm.es 
Abstract-  
This paper presents an algorithm to cancel the reflections 
that appear in the anechoic antenna measurement systems 
due to low frequency bands, AUT and probe supports… The 
algorithm is based on a modification of the ESPRIT [1-3] 
direction of arrival method and needs a very low number of 
frequencies to work – that is, a strict requirement in antenna 
measurement system. Actually, this algorithm will be applied 
to a planar near field scanner.  
INTRODUCTION 
 
One of the most important drawbacks of the antenna 
measuring systems in anechoics chambers is the difficulty to 
cancel all the reflections. When a high precision in 
measurements is required, the fact that certain reflection rays 
are involved may affect the radiation diagram and may cause 
errors over the specified limits.  
The reflection cancellation algorithms that exist are based 
on multifrequency measurements and they are generally 
impracticable, due to the time of measuring they need.   
There are some procedures based on FFT or Matrix Pencil 
Method to reduce the effect of reflections [4-7] but they need 
a very large number of measurements at different 
frequencies. 
In this paper, an algorithm that requires a reduced 
number of frequencies, of interference cancellations is 
explained. It’s based on modifications of Estimation of 
Signal Parameters Via Rotational Invariance Techniques 
(ESPRIT) and its application in planar antenna measuring 
systems.  
This presentation is organized as follows. In the next 
section, the planar measuring system of the ETSIT 
Polytechnic University of Madrid, where the measurements 
are to be fulfilled, is presented. The algorithm described to 
obtain the detected angles is elucidated in Section II. In 
section III, the signal reconstruction process is described.  
Then, in Section IV, the simulations and the results are 
presented. Finally, the conclusions obtained through the 
analysis of the results are discussed.   
I. PLANAR MEASURING SYSTEM OF THE ETSIT-
UPM 
The UPM has an antenna measurements laboratory with 
three anechoic chambers: one near field spherical system, one 
arc system and one big chamber (15.2 x 7.9 x 7.3 meters) 
shared by two systems: one compact range and one spherical, 
cylindrical and planar near field system.  
This last system occupies an area of 6 x 7.9 x 7.3 meters. 
The planar scanner has a useful surface of 4.75 x 4.5 meters, 
with errors in normal dimension lower than 240 νm (peak to 
peak) that allow a maximum frequency of 40 GHz. The 
system also has a linear slide (to place the AUT), a roll 
positioner (for polarization horn) and a roll over azimuth 
positioner (for the spherical and cylindrical system).  
This system is equipped with rotary joints, microwave 
cables and an antenna network analyzer to measure until 40 
GHz. The anechoic material allows the measurements from 
900 MHz, and the maximum diameter of the Antenna Under 
Test is 2.5 meters.  
Finally, the system is completed with a position controller 
and the required software to convert the acquired near field in 
far field values. Figure 1 shows a photograph of the planar 
scanner. 
 
 
Fig 1: Planar scanner at UPM. 
 
  
 
II. METHOD DESCRIPTION 
This technique is based on the implementation of the 
high-resolution direction-of-arrival (DOA) method, called 
ESPRIT. To simplify the detection algorithm, the number of 
signals has been set. To attain a higher precision of the 
detection angle, this technique has been repeated N times, 
where N represent the number of frequencies, which are 
randomly generated around the central frequency (f0). 
A.  SIGNAL GENERATION 
The objective of this algorithm is to determinate the 
direction-of-arrival (DOA) of “L” planar wave fronts, which 
have its focal point separated from a higher “h” from the 
receiver array.  
To allow this, first of all, the signal generation has to be 
completed. In order to describe mathematically the effect of 
the translation invariance of the array, it is useful to express 
the receiver array as being separated in two subarrays, 
identical in every aspect although physically distance from 
each other by a known displacement “d”. 
Namely, two subarrays must be considered, each one 
formed with one element less than the general array and 
separated by a quantity which coincides with the 
displacement between elements.  
 
Furthermore, each one of the wave fronts evaluated are 
assumed to be narrow-band sources, centred at same 
frequency evaluated (fi). As far as the arrival directions are 
concerned, they are going to be estimated in the ρ direction 
only, so as to simplify the problem. Besides, those wave 
fronts are supposed to come from a transmitter array, shaped 
by M elements. Accordingly, each signal arrives from M 
positions and strikes with a variable angle (φ) depending on 
the transmitter position. For that reason, the angle of 
incidence will have “L” components according to the number 
of wave fronts taken into account. 
In this paper, only two wave fronts have been studied. The 
first one corresponds to the direct ray and the second one is 
the one produced by the reflection. When the direct signal is 
considered, the angle “φ” depends only on the height of the 
focal point (h) and on the positions evaluated in transmission 
as well as in reception – with regard to a reference, which is 
the central element of the array. However, the angle “φ” 
analysed for the reflection requires additionally the distance 
existing between the reference and the position of the element 
that causes the reflection (D). 
Each one of the emitted signals is multiplied by the matrix 
“A” – steering matrix – for each element of the two 
subarrays. This matrix contains the information about the 
distance between the elements of the transmitter and the 
receiver measured, which depends on the height “h” and on 
the angle φ, as it is shown below:  
L,...,1p,
cos
hr
p
p >
κ
>                    (1) 
where: 
- L is the number of signals evaluated  
- φ = [φ1 , … , φL]. Note that φp is the direction-of-
arrival of the pth signal.   
  
 
For each of the signal contemplated, the steering matrices of 
each subarray formed by n elements are: 
÷ Analysing the first subarray: 
∴ ⊥ cf2k,r,,rr,e(t)A   n1irkjx ,i ¬θ¬>>> ¬¬ L               (2) 
÷ Taking into consideration the second subarray: 
∴ ⊥ cf2k,r,,rr,e(t)A 1n2jrkjy ,j ¬θ¬>>> ,¬¬ L             (3) 
Therefore, the steering matrix expresses the effect that the 
field experiences in the receiver array and can be written as 
follows:  
∴ ⊥yx A;AA>                                     (4) 
Besides, the signals required are supposed to be 
correlated. That is the reason why they are modelled as 
having a fixed level, which could be different for the direct 
and the reflected signal. This is not the case in this 
presentation, where the magnitude mentioned is assumed to 
be the same for both of them.  
To obtain the signals arriving in each of the “2n” elements 
of the receiver array, the steering matrix is multiplied by the 
signals coming from each of the “M” elements of the 
transmitter.  
And then, to get the total signal received, the “M” signals 
captured in each of the elements of the receiver array are 
added.  
As it is supposed to be a real system, additive noise is 
present in all the elements of the arrays. Thus, noise estimated 
is assumed to be a stationary zero-mean random process and 
is also included. 
Taking a vector notation for the outputs of the “M” 
elements of the transmitter array, and considering the 
Gaussian noise, the measurement model of the signal 
processing problem is given by: 
) ∗
∴ ⊥ ∴ ⊥L,,1p,n2,,1i
,(t)n)(f,A(t)S(t)x
M
1k
xpkki i
LL >>
,ρ¬> ∑
>
             (5) 
where the arrival directions are each of the θ directions.  
B.  ARRIVAL ANGLE DETECTING METHOD ESPRIT 
The ESPRIT method (Estimation of Signals Parameters 
Via Rotational Invariance Techniques) is based on the 
assumption that the noise employed is uncorrelated with the 
signals.  
Using the relation between induced subspaces by the two 
subarrays, which depends on the arrival angle, the DOA 
(direction-of-arrival) can be obtained. 
In other to calculate the arrival angle, the TLS (Total 
Least Squares) ESPRIT algorithm based on a covariance 
approach can be employed as it is summarised in the 
following steps: 
1. An estimation of the autocorrelation matrix from the 
measurements is found. For this reason, the 
autocorrelation is approximate using N samples of 
the signals as it is shown below:  
H
zz
^
X*X
N
1R ¬>                           (6) 
where N indicates the number of frequencies 
evaluated. 
  
 
2. A generalized eigendecomposition of the previous 
matrix is computed in its eigenvectors and 
eigenvalues. 
3. Then the number of sources is estimated. In this 
presentation, this integer has been fixed.  
4. The previous eigenvectors is decomposed into 
eigenvectors of the “x” subarray and of the “y” 
subarray. The first n components of each vector are 
considered to belong to the subarray “x” and the 
next “n” eigenvectors to the subarray “y”. The 
number of vectors of each subspace will be the 
quantity of signals considered in the step next.  
5. The eigendecomposition TLS (Total Least-Squares) 
is determined by using the following method:  
 
E-E
EE
EE
E
]E[E]E[EE
1
2212
2221
1211
yx
H
yx
.
¬>ζ






>
¬>
              (7)  
6. The eigenvalues of the matrix ζ  are calculated: 
γ 1…γL 
7. Finally, the arrival angles (DOA) are analyzed as 
follows:     
 






ξ¬
γ¬
>ρ
0
k
^
k d
argcsina              (8) 
III. SIGNAL RECONSTRUCTION 
Once the arrival angles have been obtained, the 
reconstruction process could begin. This procedure is 
repeated for each of the considered frequencies and can 
be described as follows: 
1. First of all, an estimation of the steering vector for the 
direct signal considering each element of the receiver 
array is achieved. It must be taken into account that, 
for the covered distance calculation, the position of 
the transmission array and the height between the 
transmitter and the receiver are employed.  
2. After that, an evaluation of the steering vector for the 
reflection is completed by obtaining each element of 
the receiver array. To enable this, the field studied is 
considered to be a far field, which depends of the 
arrival angle detected for the studied reflection (θrefl). 
In this case, the parameters used in the traversed 
interval are the position of the transmission array and 
the sinus of angle θrefl.  
3. Then, the steering matrix is defined by:  
∴ ⊥reflected,estmdirect,estmestm A,AA >            (9)  
4. The next phase involves solving the equation system 
used to reconstruct the signals (s(t) = [s1(t) , … , 
s2n(t)]). In this system formed by N equations – where 
N is the number of frequencies – the parameters 
involved are the estimated steering matrix (Aestm) and 
the total signals ( x(t) = [x1(t) , … , x2n(t)] ) stated in 
the relation (5). Note that those signals are 
independent from the frequency taken into account. 
5. To finish, the reconstructed signals are multiplied by 
the estimated steering matrix, and can be expressed 
as: 
    )t(s)0,f(A)t(xˆ iii ¬>ρ>              (10) 
In fact, the comparison between signals can not be 
fulfilled unless this calculation is achieved. Namely, 
it is necessary to multiply s(t) by Aestm in order to 
compare s(t) with the signals computed in the 
generation signal model, as described in the previous 
section. 
With those results, it is possible to reproduce the 
amplitude and phase of all the signals generated, that is to 
say:  
÷ the total signal – representing the sum of direct and 
reflected signals to which Gaussian noise is added, 
÷ the ideal signal – including only the noisy directed 
signal, 
÷ the reconstructed signal. 
That enables to compare all the signals and to calculate 
the medium quadratic error between them. 
IV. PERFORMED SIMULATIONS AND RESULTS 
In this section, simulation and results are presented to 
illustrate the performance of the designed algorithm.  
Many simulations have been performed, exploring 
different aspects by changing the parameters involved. In 
fact, in order to observe the evolution of the precision 
obtained, certain factors have been increased while setting 
the others. The analysed variables have been: the number of 
frequencies (N), the number of elements in the transition 
array (M) and in the receiver subarray (n), both separated 
half wavelength at central frequency.  
For each, the amplitude and phase diagrams have been 
presented. Besides, the detected arrival angles (Θd and Θrefl), 
the error created because of their estimation and the errors in 
the reconstruction and reflection process (Ereconstruct and 
Ereflection respectively) have also calculated. 
From all these studied scenarios, only two of the most 
relevant are exposed, which are: 
÷ Case 1: When M=3, n=14 and N increases. 
÷ Case 2: When N=3, n=14 and M increases. 
 
In those situations, the height between transmitter and 
receiver is set to one meter and the reflection element is 
supposed to be 2.85 meters from the reference. As the 
number of sources is assumed to be known in the 
implementation of ESPRIT, here it has been fixed to two. 
Furthermore, the group of frequencies randomly generated 
have been located around the central frequency f0=10 GHz. 
Finally, it must be taken into account that both signals – 
direct and reflected – have the same power (30 dB over the 
noise level).     
 
1. Case1: M=3, n=14 and N increases 
When M=3 and n=14, the next table shows the results 
achieved in these simulations: 
 
Parameter N = 3 N = 5 N = 8 N = 15 N = 35 
Θd (º) 0.0513 0.0903 0.0695 0.0773 -0.0438 
Θrefl (º) -78.0043 -79.9578   -81.5339 -79.6274 -80.5411
EΘd (º) 0.0513 0.0903 0.0695 0.0773 0.0438 
EΘrefl (º) 2.0451 0.0916 1.4846 0.4220 0.4917 
Ereconstruct 0.0176 0.0068 0.0010 7.7498e-4 5.386e-4
Ereflection 0.1007 0.1029 0.1007 0.1021 0.1010 
Table 1: Results increasing N, M=3, n=14 
  
 
 In particular, when N=15, the amplitude and the phase 
have the following diagrams: 
 
-0.15 -0.1 -0.05 0 0.05 0.1
31
32
33
34
35
36
37
38
amplitude, first frequency, L=2, ro=-1
receiver array positions (m)
20
lo
g1
(a
bs
(s
ig
na
ll)
) [
dB
]
total signal
ideal signal
reconstructed signal
 
Fig 2: Amplitude when M=3, n=14, N=15 
 
-0.15 -0.1 -0.05 0 0.05 0.1
-170
-160
-150
-140
-130
-120
-110
-100
-90
-80
-70
phase, first frequency, L=2, ro=-1
receiver array positions (m)
fa
se
(s
ig
na
l) 
[d
eg
re
es
]
total signal
ideal signal
reconstructed signal
 
Fig 3: Phase when M=3, n=14, N=15 
   
2. Case2: N=8, n=160 and M increases 
When N=8 and n=160, the next table illustrates the 
results reached in this case: 
 
Parameter M = 5 M = 13 M = 23 M = 43 M = 63 
Θd (º) 0.6101 0.3993 0.7503 0.3837 0.2508 
Θrefl (º) 88.2519 88.1127 88.4898 -88.1858 -89.2531
EΘd (º) 0.6101 0.3993 0.7503 0.3837 0.2508 
EΘrefl (º) 8.2026 8.0633 8.4404 8.1365 9.2037 
Ereconstruct 0.0260 0.0118 0.0094 0.0084 0.0080 
Ereflection 0.1806 0.0714 0.0430 0.0024 0.0054 
Table 2: Results increasing M, N=8, n=160 
 
Particularly, when N=23, the amplitude and the phase 
have the following diagrams: 
-1.5 -1 -0.5 0 0.5 1 1.5
-5
0
5
10
15
20
25
30
35
40
amplitude, first frequency, L=2, ro=-1
receiver array positions (m)
20
lo
g1
(a
bs
(s
ig
na
ll)
) [
dB
]
total signal
ideal signal
reconstructed signal
 
Fig 4: Amplitude when N=8, n=160, M=23 
These results indicate that the precision in the 
reconstruction algorithm increases as more frequencies are 
used – N rises. In fact, when 8 frequencies are employed, 
accurate results are achieved. Note also that the errors 
obtained in those signals (Ereconstruction) have been reduced 
quite a lot comparing then to those found for the total signals. 
Case 2 shows that reconstruction errors decrease as M 
rises, although the reconstruction is still very good for small 
dimensions of AUT.  However, for large antennas the error 
due to reflections is quite low. In this case, the algorithm 
cannot obtain better results.   
V. CONCLUSIONS 
This paper presents an algorithm to cancel the reflections 
in near field systems, using an estimation of the angles of 
arrival signals based upon ESPRIT method. The simulations 
show good estimations of the signals. However, this can be 
complemented by checking these results with antenna 
measurements and extending to a planar system, instead of 
using a linear system. 
REFERENCES 
[1] R. Roy and T. Kailath, “ESPRIT – Estimation of signal parameters via 
rotational invariance techniques”, IEEE Trans. Acoust., Speech, Signal 
Processing, Vol. 37, No. 7, pp. 984-995, July 1989. 
[2] M. Wax and T. Kailath, “Detection of Signals by Information 
Theoretic Criteria”, IEEE Trans. Acoust., Speech, Signal Processing, 
Vol. ASSP-33, No. 2, pp. 387-392, April 1985. 
[3] R. Roy, B. Ottersten, L. Swindlehurst, and T. Kailath, “Multiple 
invariance ESPRIT”, IEEE Trans. Acoust., Speech, Signal Processing, 
Vol. 40, No. 4, pp. 867-881, April 1992.  
[4] T. K. Sarkar and O. Pereira “Using the Matrix Pencil Method to 
Estimate the Parameters of a Sum of Complex Exponentials” IEEE, 
Antennas and Propagation Magazine, Vol. 37, No. 1, pp. 44-54, 
February 1995.  
[5] R. S. Adve, T. K. Sarkar, O. M. C. Pereira-Filho and S. M. Rao, 
“Extrapolation of Time-Domain Responses from Three-Dimensional 
Conducting Objects Utilizing the Matrix Pencil Method”, IEEE 
Transactions on Antennas and Propagation”, Vol. 45, No. 1, pp. 147-
156, January 1997  
[6] Y. Hua and T. K. Sarkar, “Generalized pencil-of-function method for 
extracting poles of an EM system from its transient”, IEEE 
Transactions on Antennas and Propagation”, Vol. 37, No. 2, pp. 229-
234, January 1989  
[7] S. Loredo Rodríguez, M. Rodríguez Pine, F. Las Heras Andrés, T. K. 
Sarkar, “Cancelación de ecos en cámaras de medida no anecoicas”, 
Simposio Nacional U.R.S.I, A Coruña, Septiembre 2003.  


Cancellation of reflections in planar antena measuring systems via esprit algorithm

This paper presents an algorithm to cancel the reflections that appear in the anechoic antenna measurement systems due to low frequency bands, AUT and probe supports... The algorithm is based on a modification of the ESPRIT [1-3] direction of arrival method and needs a very low number of frequencies to work – that is, a strict requirement in antenna measurement system. Actually, this algorithm will be applied to a planar near field scanner

Besada Sanmartín, José Luis

Archivo Digital UPM

http://oa.upm.es/44117/1/INVE_MEM_2004_238014.pdf

Cancellation of reflections in planar antena measuring systems via esprit algorithm

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