# Tanawut Tantisopharak

Akkarat Boonpoonga

Monai Krairiksh

Phaophak Sirisuk

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Combination between CMA and On-Off 
Algorithms for Adaptive Array Antenna  
 
#Tanawut Tantisopharak1, Akkarat Boonpoonga2, Phaophak Sirisuk2 and Monai Krairiksh1 
1 Faculty of Engineering, King Monkut’s Institute of Technology Ladkrabang 
Bangkok 10520, Thailand, s8060960@kmitl.ac.th, kkmonai@kmitl.ac.th 
2 Department of Computer Engineering, Mahanakorn University of Technology 
Nongchok, Bangkok 10530, Thailand, akkarat@mut.ac.th, phaophak@mut.ac.th 
 
 
 
1. Introduction 
 
 During the last decade, an adaptive antenna has considerable received the interest for 
mobile communication systems. This is because it can increase the system capacity by reducing 
interference. To achieve the interference reduction, an adaptive algorithm is necessary.   There are a 
number of the adaptive algorithms proposed to improve the signal-to-interference plus noise ratio 
(SINR) in such the systems i.e. [1]. Recently, an adaptive on-off algorithm was introduced to 
achieve a high SINR [2]-[3]. This approach maximizes the array output power. The SINR 
improvement using the algorithm depends on the strength of received signals. Namely, the 
algorithm work well if the power of the desired signal is sufficiently stronger than that of 
interference. It is know that generally an adaptive antenna using on-off algorithm adjusts its main 
beam to the desired signal.  Nevertheless, its nullity does not appear at the interference direction.  
 Another popular adaptive algorithm recently proposed in [4] is a constant modulus 
algorithm (CMA) which is a blind algorithm. The algorithm does not need a training sequence for 
adaptation. It can eliminate interference with the condition that the transmitted signal has a constant 
envelope, for example, a frequency- or phase-modulated signal. This is because the interference 
signal involves the amplitude fluctuation on the received signal. The main drawback of applying the 
CMA to the adaptive antenna system is its slow convergence property. It was reported that the 
convergence behavior of CMA heavily depends on its initial condition [5]. Recently, the problem of 
CMA convergence property was resolved by using the concept of the digital beam-switching 
initialization for CMA [6]. However, it is still sensitive to convergence because there are only 
sixteen initial beams used for adaptation of CMA. Moreover, an adaptive antenna using CMA has a 
nullity at the interference signal but it does not guarantee whether its main beam directs to the 
desired signal. 
  In this paper, we propose a combination between CMA and on-off algorithms. The on-off 
algorithm is utilized to generate an initial beam for CMA. Then, CMA is used for adaptation to 
eliminate interference. After introduction, a combination between CMA and on-off algorithms is 
presented via its derivation in Section 2. Simulation results are shown to validate the performance 
of the proposed technique in Section 3.  Finally, the conclusions are drawn in Section 4. 
 
2. On-off and CMA Adaptive Array Antenna 
 
The 2009 International Symposium on Antennas and Propagation (ISAP 2009)
October 20-23, 2009, Bangkok, THAILAND
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0w
2w
1Nw −
1w
0w
2w
1Nw −
1w
0x
2x
1Nx −
1x
0x
2x
1Nx −
1x
 
 
Figure 1: Architecture of the proposed technique 
 
 Fig.1 depicts the architecture of the proposed adaptive array antenna using a combination 
between on-off and CMA algorithms. The four-element linear array antenna with element spacing d 
of 0.25λ is used. The complex signals received by nth antenna element and then down converted are 
digitized by analog-to-digital converters (ADCs). The received signals can be defined as 
 ( ) ( ) ( )k k k= +x As η  (1) 
where ( )ks  and ( )kη are the transmitted signal and additive noise vectors, respectively. The matrix 
A=[1 e-jkdcosϕ … e-j(n-1)kdcosϕ]T denotes an array response and the received signal vector is defined in [6] 
 The adaptive on-off algorithm is used for yielding the maximum array output power. The 
adaptive weight is updated by 
 w(i) = ejα(i). (2) 
Here, α is a progressive phase between each element, which can be obtained from 
 0coskdα φ= −  (3) 
where ϕ0 are the main beam directions in azimuthal plane and can be adjusted by using the iterative 
algorithm as given by 
 ϕ0(i+1) = ϕ0(i) + ψ(i)  (4) 
where ψ(i) is the on-off variable which is chosen for the weight drives the output power to its 
maximum using the rule that [2] 
 
      ( )dP t
dt
  > 0      D = 1 
                     < 0      D = -1 (5) 
 1) if D = 1, then ψ(i+1) = ψ(i) and this means that if the output power P(t) increases, then 
the direction of the next iteration is in the same direction as the previous one. 
 2) if D = -1, then ψ(i+1) = -ψ(i), and this means that P(t) is decreasing. Therefore the 
direction of the next iteration must be changed. 
 Hence, D = 1 is maintained as long as power increases. 
 The output from on-off algorithm has been used as the effective input of the CMA antenna 
system ( )x k  which can be expressed as 
 x̃i(k) = wixi(k).  (6) 
Collecting the effective input x̃i(k), we may write      
 x̃(k) = [x ̃0(k) x̃1(k) … x̃N-1(k)]T. (7) 
The complex effective input signal xĩ(k) is then multiplied by an adjustable complex weight w̃i(k).  
Therefore, using matrix-vector notation the adaptive array output is written as 
 y(k) = w̃(k)Hx̃(k) (8) 
where 
 w̃(k) = [w̃0(k) w̃1(k) … w̃N-1(k)]T (9) 
The 2009 International Symposium on Antennas and Propagation (ISAP 2009)
October 20-23, 2009, Bangkok, THAILAND
- 126 -
where H is the vector conjugate transpose. The CMA adjusts the weight vector w̃(k) in a way that 
the cost function is minimized based on the stochastic gradient steepest descent method. The weight 
updated equation is defined as [4] 
 w̃(k+1) = w̃(k) - 4µx̃(k)y*(k)(|y(k)|2 - σ2). (10) 
 
3. Simulation Results 
 
 The simulations were conducted to evaluate the performance of the proposed system. The 
desired and interference signals were π/4-QPSK-modulated and propagated through an additive 
white Gaussian noise (AWGN) channel. In practical wireless environments, the desired signal 
power is normally larger than that of the co-channel interference. Here, the power of the desired 
signal was set to be 3 dB stronger than that of interference. The signal-to-noise ratio (SNR) was set 
to be 30 dB.  In our simulations, the incident angle of desired (ϕD) and interference (ϕI) signals were 
30° and 150°, respectively. Fig.2 illustrates the radiation pattern of the antenna after adjusting the 
main beam direction to the desired signal direction by using an on-off algorithm. With the on-off 
algorithm, the main beam of the antenna directs to 30° (desired signal direction) as seen in the 
figure. However, the nullity does not appear at the interference direction (150°). The resulting SINR 
is not enough. Therefore, the SINR should be further increased by using CMA in order to increase 
SINR. 
 
 
 
Figure 2: Radiation pattern obtained from only on-off algorithm. 
 
 
                
                   
Figure 3: Radiation patterns obtained from a combination of CMA and on-off algorithm. 
 
 The antenna pattern obtained from the on-off algorithm is used as an initial beam for CMA. 
Fig.3 shows the radiation pattern after respectively performing on-off and CMA algorithms. The 
main beam of the antenna obtained from on-off and CMA algorithms direct to 27° close to the 
desired signal direction (30°) as seen in the figure in which the nullity appear at 150°. By using a 
combination between CMA and on-off algorithm, it is clear that the main beam and nullity of the 
final antenna pattern are in the direction of the desired signal and interference, respectively.  
 
The 2009 International Symposium on Antennas and Propagation (ISAP 2009)
October 20-23, 2009, Bangkok, THAILAND
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Table 1: SINR obtained from the adaptive array antenna 
Incident Angle SINR (dB) On-off Algorithm Proposed System 
ϕD=30, ϕI=150 14.4 50.2 
ϕD=60, ϕI=150 11.7 50.2 
ϕD=90, ϕI=150 15.8 50.0 
ϕD=30, ϕI=100 27.4 50.2 
ϕD=60, ϕI=100 7.5 49.9 
 
 Besides only a simulation case seen above, Table 1 shows the SINR improvement with five 
different cases of the incident angles of the received signals. As seen in the table, all SINRs 
obtained from the conventional on-off algorithm are relatively small, which depend on the antenna 
pattern. The SINRs obtained from a combination of CMA and on-off algorithms are approximately 
50 dB higher than that from only on-off algorithm. The on-off algorithm adjusts only the antenna 
main beam to the desired signal while does not guarantee whether the nullity of the antenna appears 
at the interference direction. On the other hand, the antenna pattern obtained from performing only a 
CMA has the nullity at the interference direction but its main beam does not direct to the desired 
signal direction.  According to Fig. 3 and table 1, it reveals that the proposed system operates very 
well by reducing the interference and maximizing the array output power. 
 
4. Conclusions 
 
 In this paper, a combination of CMA and on-off algorithms has been proposed. In the 
proposed technique, an on-off algorithm is utilized to maximize the array output power. The beam 
whose main beam almost direct to the desired signal is employed as an initial beam for CMA. With 
the initial beam, CMA is used to adjust the nullity of the antenna to the interference signal. The 
simulation results show that the nullity obtained from the proposed antenna appears at the 
interference direction while the main beam directs to the desired signal. 
 
Acknowledgments 
 
 This work was supported by the Senior Research Scholar Program (Grant No. RTA 
5180002). 
 
References 
 
[1] T. Sukhonthaphong, P. Ngamjanyaporn, C. Phongcharoenpanich and M. Krairiksh, “Covariance 
Matrix Adjustment for Interference Cancellation Improvement in Adaptive Beamforming,” 
ECTI Trans. Electric. Eng., Electron., and Commun., Vol. 1, no. 1, pp. 27-37, Aug. 2003. 
[2] T.A. Denidni and G.Y. Delisle, “A Nonlinear Algorithm for Output Power Maximization of an 
Indoor Adaptive Phased Array,” IEEE Trans. Electromagn. Compat., Vol. 37, no. 2, pp. 201-
209, May 1995. 
[3] T.A. Denidni, D. McNeil and G.Y. Delisle, “Experimental investigations of a new adaptive 
dual-antenna array for handset applications,” IEEE Trans. Veh. Technol., Vol. 52, no. 6, pp. 
1417-1423, Nov. 2003. 
[4] J.R. Treichler and B.G. Agee, “A New Approach to Multipath Correction of Constant Modulus 
Signals,” IEEE Trans. Acoust. Speech Signal Process., ASSP-31, no. 2, pp. 459-472, Apr. 1983. 
[5] K. Takao and H. Matsuda, “The Choice of Initial Condition of CMA Adaptive Arrays,” IEICE 
Trans. Commun., Vol. E78-B, no. 11, pp. 1474-1478, Nov. 1995. 
[6] T. Tantisopharak, A. Boonpoonga, P. Sirisuk and M. Krairiksh, “Simple Initialization Scheme 
for CMA Adaptive Antenna by Using Digital Beam Synthesis,” Proc. 5th Int. Conf. Electrical 
Engineering/Electronics, Computer, Telecommunications and Information Technology (ECTI-
CON 2008), Vol. 1, pp. I-289-I-292, May 2008. 
 
The 2009 International Symposium on Antennas and Propagation (ISAP 2009)
October 20-23, 2009, Bangkok, THAILAND
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Combination between CMA and On-Off Algorithms for Adaptive Array Antenna

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Combination between CMA and On-Off Algorithms for Adaptive Array Antenna

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