Implementation of a control system of intelligent antennas based on the Sequential Quadratic Programming (SQP) Algorithm N.Nemri1, A. Hammami1, R.Ghayoula(1,2), A.Gharsallah1, H. Trabelsi1 D. Grenier2, (1)

Unit of Research in High Frequency Electronic Circuits and Systems, Faculty of Mathematical, Physical and Natural Sciences of Tunis, Tunis El Manar University, Campus Universitaire Tunis - El Manar – 2092, Tunis, Tunisia (2)

Department of Electrical and Computer Engineering, Universite Laval, Que., G1K 7P4, Canada [email protected]

Abstract— This paper describes a global electromagnetic optimization technique using SQP’s method and apply it to guide the radiation pattern of linear antenna array in a certain direction, without any mechanical rotation or movement that is only by controlling the phase parameters of N equally spaced and symmetric elements. This paper investigates how the implementation on STM8 of the signal processing in hardware affects the performance of the adaptive array antenna. Index Terms — Linear Antenna Array, SQP, Beamforming, Implentation, Control system, STM8S-discovery.

I. INTRODUCTION Smart antennas are a new technology for wireless systems that use a fixed set of antenna elements in an array. The signals from these antenna elements are combined with a sophisticated signal processor to improve the performance of the system. However, most content of the smart antenna array processing are focused on the application of conventional narrowband and wideband systems [1]. These antennas are one of the promising technologies in wireless communications for systems to provide interference reduction and enhance user capacity. This is achieved by focusing the radiation only in the desired direction and adjusting itself to changing traffic conditions or signal environments. The signals from these elements are combined to form a switchable beam pattern that can be directed to the desired user [2]. The most important of all the benefits of a smart antenna is the ability to serve more users per base station thereby increasing revenues of network providers and also giving network subscribers less probability of blocked or dropped calls [3]. There are basically two types of smart antennas systems: fully adaptive and multiple fixed beams. Many studies have shown that fully adaptive smart antenna offer increased capacity and are less complex compared to the multiple switched fixed beams [4]. The aim of the multiple fixed-beam system is to increase the gain in the direction of the desired user and to reduce gain in the direction of other users (interferers). The multiple fixed- beam approach is simpler compared to the fully adaptive approach [3]. The horizontal

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beam shape produced by the antenna array is dependent upon the complex weights (magnitude and phase) applied to each array column. The complex weights are provided by the array feed network. The total feed network is realised by cascading a 4x4 Butler matrix beam forming network. However this type has disadvantages: • The beamwidth and the direction of pointing change with the frequency. • The interconnection between the RF component is quite complex for a large matrix. • The number of components is large when the number of elements of the network is high. Adaptive antennas are considered the most performing systems in the smart antennas. The adaptive antenna directs the radiation pattern in the direction or users directions and sends zeros in the directions of interference and noise signals to optimize communication. This system is able to adapt its surrounding electromagnetic in an automatic manner, contrary to the antennas switched fixed beams.

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Beamforming Unit 1

X1(t) Ȧ1

2

X2(t)

3

ADC

M

X3(t)

Ȧ3

Xn(t) ȦN

Antenna Array Adaptive Processor

Ȧ2

DOA Estimation

× × ×

+

Signals Received y(t)

×

Adaptive Algorithm

Fig. 1. Structure and principle of the adaptive system (in reception)

The 8th European Conference on Antennas and Propagation (EuCAP 2014)

Where ϕn ∈ [ϕ0 , ϕ1 ,...,ϕN −1 ] represents the phase excitation of

Beamforming Unit 1 Ȧ1

2 3

Ȧ2 DAC

Ȧ3

the nth element (the antenna in the beginning is taken as reference of phase: (ϕ0 = 0) , xn represents the position of the

× ×

nth elements, k = 2π

Signals Emitted

×

incidence of desired signal or interfering signal. This problem consists in determining the phase ϕ n

Divisor

( n = 1,2,..., n −1)

M Antenna Array

ȦN

×

which one must apply to the elements of the 2

network in order to maximize the function F (θ , ϕ ) in the direction θ0 and to minimize this same function in the directions θ i with ( i = 1, 2,..., I ) .

Adaptive Algorithm

The general multi-objective optimization problem is posed as follows: Minimize − fθi (ϕ )

Adaptive Processor

Subject to − fθi (ϕ ) ≤ δ j

Fig. 2. Structure and principle of the adaptive system (in emission)

The principle of operation is briefly as follows: • The intelligent BTS detects the position of the user and parasites through an algorithm to estimate the angle of arrival (DOA). • The system identifies the signals coming from the user, and interference to calculate the weights to form a beam that is oriented towards the user and sends zeros in the directions of parasites. The structure of an adaptive antenna based on the detection of the arrival directions of the sources is shown in Fig 1 and Fig 2. To obtain the optimal weights, various methods are possible; the choice of the algorithm that achieves the optimal solution is a crucial step because it depends on the speed of convergence and complexity of hardware integration. II. OPTIMIZATION OF LINEAR ARRAY WITH SEQUENTIAL QUADRATIC PROGRAMMING (SQP) ALGORITHM Optimization of linear array antenna is considered as a multi-objective problem. Many approaches have been developed to solve this problem. The sequential quadratic programming (SQP) algorithm are very well known and are considered one of the most powerful method for solving nonlinear constrained optimization problems [5,8]. In this paper, we use the SQP method to solve a multiobjective problem described by equation (1) in order to obtain phase excitations for the phased linear array antenna to achieve high directivity, narrow beamwidth, and low side lobes. In this work, all parameters are unchanging only phase excitations are optimized. To evaluate the effectiveness of this proposed method, we consider a linear array of N isotropic antenna elements placed along the x-axis. The array factor is described by the following formula:

F (θ ) = 1 +

λ is the wave number and θ is the angle of

n = N −1

¦e(

j kxn sin θ +ϕ n )

(1)

−2π ≤ ϕn ≤ 2π

j = me + 1,..., m

(2)

n=1,2,...,N-1

Where: fθ ( ϕ ) = 1 +

n = N −1

¦

j kx sin θ +ϕ n ) e( n

2

(3)

n=0

T

fθ1 = ª¬ fθ1 , fθ2 ,... fθme º¼ is the vector of objective functions, me is the numbers of the desired signal, θi , θ j and δ j are the i th th

directions of the desired signals, the j directions of interfering signals, and the levels in the regions of the suppressed sectors respectively, and m is the number of the sampled angular direction. In order to achieve this goal, we use the method of optimization Sequential Quadratic Programming (SQP) Algorithm [9-10] which is the most widely used algorithm for non-linearly constrained optimisation [10-11]. The principal idea of SQP is to transform nonlinear optimization problems including nonlinear equality and inequality constraints to a sequence of quadratic subproblems, based on a quadratic approximation of the Lagrangian function which is defined as: m

(

L (ϕ , λ ) = − fθ1 (ϕ ) + ¦ λi fθi (ϕ ) − δ i i =2

)

(4)

Where ϕ ∈ R N −1 , λ = ( λ ,..., λm ) ∈ R m is the vector of the Lagrange multiplier. The solution of the Quadratic Programming sub-problem based on a quadratic approximation of Lagrangian and the linearization of constraints: 1 T Minimize −∇fθi (ϕ k ) d + d T M k d 2 T Subject to ∇fθi (ϕ k ) d + fθi (ϕ k ) = δ i i = 2,..., me (5) T

∇fθi (ϕk ) d + fθ j (ϕk ) ≤ δ j T

n =1

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j = me + 1,..., m

The 8th European Conference on Antennas and Propagation (EuCAP 2014)

N −1 and M k is an approximation of the Hessian Where d ∈ R

of the Lagrange function ∇ϕ L (ϕk , λk ) . 2

The solution to the QP sub-problem produces a search direction vector dk , which is used to form a new iterate ϕk +1 .

ϕ k +1 = ϕk + α k d k

To verify the performance achievable using the proposed approach, numerical results are obtained for several arrays. An six linear patch array (band 2.45 GHz, substrate Plexiglas with 4 mm height), uniformly (l/2) spaced has been realised (Fig. 4). We used variable phase shifters to control the various values of phases.

(6)

Where αk ∈ ]0,1] is the step size in the search direction. III. SIMULATIONS AND RESULTS SQP's method will be used in the synthesis of linear antenna array in order to guide the radiation pattern of a smart antenna in a certain direction, without any mechanical rotation or movement that is only by controlling the phase parameters of 6 equally spaced elements ,which are spaced by a 1/2 wavelength. The excitations phase of the six elements will be chosen in the range of [ −π , π ] .

Fig. 4. Antenna array

For the 6 elements array (equi-amplitude), the array factor can be written as: 6

j kx sin θ +ϕn ) AF (θ ) = 1 + ¦ e ( n

(7)

n =1

Fig.5.a. Radiation pattern of 6 elements /2 spaced array optimized using [email protected] Deg

y

−3

−2

−1

1

2

Fig.5.b. Tomography of radiation pattern of 6 elements optimized using SQP [email protected] Deg

3 x

d Fig. 3. Geometry of 6 elements linear array

For simulating the SQP's algorithm, in a period lasting only 5 seconds , we use a personal computer with Intel® Core(TM) i5-2450 CPU @2.50GHz and 4 Go RAM under Windows 7. The results of the stimulation approach proposed earlier are presented in table 1. To make more clear the different possibilities given by the chosen method for purpose of showing the effectiveness of SQP's method, there are different results showed in figure (5, 6, 7, 8 and 9) of syntheses of linear antenna array at a wanted pattern.

Fig.6.a. Radiation pattern of 6 elements /2 spaced array optimized using [email protected] Deg.

Fig.6.b. Radiation pattern of 6 elements /2 spaced array optimized using [email protected] Deg.

TABLE I. PHASE WEIGHTS FOUNDED FOR DIFFERENT STEERING USING SQP ALGORITHM

Element

@ - 40°

@ -25°

Phases Values @ 15°

@ 45°

@ 70°

#1 #2 #3 #4 #5 #6

109.2549 -6.4472 -122.1489

10.1781 -65.8931

-116.4685 -69.8811

41.8019 -169.0812

-62.8616 106.2828

-141.9644 141.9644

-23.9237 23.9237

-63.6396 63.6396

-84.5725 84.5725

65.8931

69.8811

169.0812

-106.2828

-10.1781

116.4685

-41.8019

62.8616

122.1489 6.4472 -109.2549

Fig.7.a. Radiation pattern of 6 elements /2 spaced array optimized using [email protected] Deg.

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Fig.7.b. Tomography of radiation pattern of 6 elements optimized using SQP [email protected] Deg

The 8th European Conference on Antennas and Propagation (EuCAP 2014)

Fig.8.a. Radiation pattern of 6 elements /2 spaced array optimized using [email protected] Deg.

Fig.8.b. Tomography of radiation pattern of 6 elements optimized using SQP [email protected] Deg

Fig.9.a. Radiation pattern of 6 elements /2 spaced array optimized using [email protected] Deg.

Fig.9.b. Tomography of radiation pattern of 6 elements optimized using SQP [email protected] Deg

To demonstrate the performance of the method described in the previous section for steering beam in desired direction by controlling the phase excitation of each array element, several examples of uniform excited linear array with halfwavelength-spaced isotropic elements were performed. This algorithm does not only hold the examples presented above, but also appears to be general for all cases of synthesised desired characteristics of steered beams. IV. IMPLEMENTATION OF THE ANTENNA CONTROL PART After having finalized the model control antenna array, we proceed in what follows, implementation of phases synthesized by our SQP algorithm. A. Hardware Description In works about the development of digital implementation of algorithms optimizations, the execution of the synthesis procedure is done in real time, the drawback of this method lies in the calculation time which is quite important. In our case we offer a parallel process, by a microcontroller STM8SDiscovery, in this case the synthesized phases which exhibit electronic scanning of the whole useful zone [-70 °, 70 °][12], are stored in the EEPROM memory of the microcontroller which provides a brief calculation time compared to the implementation of the whole optimization algorithm on microcontrollers, or on development kits. The purpose here is to provide a software solution that allows to interface the control card based on the STM8S microcontroller at the block of digital phase shifters. Every phase shifter has the role of affecting a complex feed angle for each antenna network, so for an antenna array consisting of 6 sources we need six shifters.

The phase shifter is used to create a phase shift (delay) on an output signal from an input signal without affecting the signal. And to excite the antenna array by phase already synthesized, we used a digital phase shifter, DST-13-480/1S [13], operating at the frequency 2.45 GHz. Our solution is to create a database which will be implemented in the microcontroller's ROM. When the user selects the desired position (with the keyboard instaled in control board) for which he wishes to steer the radiation diagram of the antenna, a match with this database made in real time in order to find the values of the phases appropriate for each antenna element. In order to make reliable to the global functioning of our system, we offer a direct link between the phase shifters and the ports of the microcontroller. Each phase shifter is driven with digital control of 8 bits, in total we need 48 bits to satisfy the implementation of any application of excitation. The STM8S features 38 pins which form all ports (GPIOx) on which there are 26 configurable pins set in output mode. With this description we are able to excite 3 digital phase shifters with a single microcontroller using ports B, D, and a concatenation of the A and C ports with the configuration of their data registers in output mode (Output Data Register). Then we have to use three cards, two to control the phase shifters and the third to ensure the synchronization of the whole system as well as the acquisition of the angular position of the user. B. Software Description The first microcontroller loads by reading the return values of the algorithm of location of the target (sector_lobe) and generating synchronization signal which serves to adjust the time of updating the weightings between the two other microcontrollers. The second and the third STM8S are loaded by map the reading of the generated synchronization signal by the first card and to update excitations of the phase shifters. The program starts with the storage of weightings synthesized in the EEPROM of each microcontroller, then the scaling of all weightings with the addition of 2ʌ (360 °) for each negative phase, then the quantification and a rounding of obtained values before storing them again in the Flush memories of the matrices of microcontrollers in order to prepare them to excite the digital phase shifters. The updating of the outputs is done with a test on the input value (Sector_lobe) which will be injected into the port B (GPIOB) of the first microcontroller (STM_Master) using a keyboard of 16 keys. This interpretation is managed by an interruption of Timer 1. In this routine, the keyboard is read line by line, its status is coded on 16 bits in a variable which will be decoded and stowed in a buffer as a string. Then a test on the value of buffer causes the generation of a synchronization signal coded on 8 bits that will be transmitted via a UART connection (TX) (serial transmission) with other STM8S cards. For the other cards, the synchronization signal is detected by each UART_RX microcontroller (2 and 3), with the value of this signal we led to a selection of excitations to update the output according to suitable ports.

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The 8th European Conference on Antennas and Propagation (EuCAP 2014)

The global system incorporates 5 parts where we find a selection input (Sector_lobe) that sets forth the return of source localization algorithm (MUSIC, ESPRIT…), and points out the angular position of the user. The control means generates the outputs (synthesized phases) that are going to be the inputs for the digital phase shifters when the pointing angle is given. Then we find the step of modulator/ demodulator, which will be ensured by modulators AD8349 in the case of diffusion and AD8347 demodulator in the event of reception [14]. The following figure shows the general architecture of proposed control system with the addition of an LCD display which is used to show the different phases of progress of the program.

(a)

(b)

(c) Fig 10. Card Control

V. CONCLUSION In this article we have put in place the necessary elements for a telecommunications system using smart cards STM8SDiscovery. For the realization of this prototype, we have demonstrated the feasibility of a smart communication system. The architecture presented in this paper was performed using digital phase shifters controlled (Phase Shifters) demodulator AD8347, AD8349 modulator, linear antenna array, control board STM8S-Discovery that contain a C language description (generator phases synthesized). This study allowed the update of an intelligent telecommunications system, by

showing its performance with particular interest in the context of base station antennas for telecommunications networks terrestrial wireless. REFERENCES [1] N.V.Mani and Ranjan Bose, “Smart antenna design for beamforming of UWB signals in Gaussian noise,” 2008 International ITG Workshop on Smart Antennas (WSA 2008), pp 311-316. [2] W. L. Stutzman and G. A. Thiele (1981), “Antenna theory and design,” Jhon Wiley & Sons, New York [3] Freeborn Bobor-Oyibo, S. J. Foti, and David Smith, “A Multiple Switched Beam Smart Antenna with Beam Shaping for Dynamic Optimisation of Capacity & Coverage in Mobile Telecommunication Networks,” 978-1-4-4244-2193-0/08/$25.0 ©2008 IEEE, pp 356-95 [4] C A. Osserein et al., “Downlink capacity comparison between different smart antenna concepts in a mixed service WCDMA system,” in proc. IEEE Veh. Technol. Conf. Fall, Atlantic City NJ, 2001, Vol. 3, pp.1528-1532. [5] R. Wilson. “A Simplicial Algorithm for concave programming,” PhD Thesis, Harvard University, 1963. [6] M.J.D Powell, “A Fast Algorithm for nonlinearly constrained optimization calculation,” G.A. Waston (Ed.), Numerical Analysis, Dundee, Springer-Verlag, Berlin, 1977, pp. 144-157 [7] M.A Abramson and S.Korea, “Sequential quadratic programming and the ASTROS structural optimization system,” vol. 32, pp. 24-32 1998 [8] P. T. Boggs and J. W. Tolle, “Sequential quadratic programming for large-scale nonlinear optimization,” vol. 124, pp. 123-137, 2000. [9] M. Mouhamadou, P. Vaudon, “ComplexWeight Con- trol of Array Pattern Nulling,” International Journal of RF and Microwave Computer-Aided Engineering, pp. 304–310, 2007. [10] M. Mouhamadou, P. Vaudon, “Smart Antenna Array Patterns Synthesis: Null Steering and multi-user Bealforming by Phase control,” Progress In Electro- magnetics Research, Vol. 60, pp. 95–106, 2006. [11] A. Hammami, R. Ghayoula, and A. Gharsallah, “Planar array antenna pattern nulling based on sequential quadratic programming (SQP) algorithm,” in Eighth International MultiConference on Systems Signals Devices, 2011, pp. 1–7. [12] N.Fadlallah, M.Rammal, H.Rammal, P.Vaudon, R.Ghayoula and A.Gharsallah “General synthesis method for linear phased antenna array,” IET Microwaves, Antennas & Propagation 2008, Vol. 2, No. 4, pp. 338-342, [13] PULSAR MICROWAVE CORPORATION “Digital Phase Shifters Switched Bit Digital Controlled, 0.05-4.00 GHz,” [Online].http://www.pulsarmicrowave.com/products/phase_shift ers/digitalcontrolled.htm [14] N. Nemri, A. Smida, R. Ghayoula, H, Trabelsi, and A. Gharsallah “Phase-Only Array Beam Control using a Taguchi Optimisation Method,” Mediterranean Microwave Sympsium (MMS), pp 97-100, September 2011.

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