36-44 Al-Khwarizmi Engineering Journal,Vol. 12, No. 1, P.P. Multi-Dimensional Angle of Arrival Estimation by Circular Phased Adaptive Department of (Received Abstract In this paper the use of a circular Constrained Minimum Variance Beam Arrival (AOA) estimation in 2-D as we 3-D estimation), rather than interference can compared with the modified Multiple Signal Classification ( system has exhibited astonishing results for equivalent to the MUSIC technique (for for sources which are under the estimation Finally, the proposed system needs le Eigen value decomposition techniques active detecting means such as radars. Keywords: Angle of Arrival Estimation, 1. Introduction Over the last decade, the AOA estimation or guesstimate the direction and location of the transmitting sources is the most desirable activities used in electronic ware-fare and security activities [1-4]. The AOA estimations of the received signals by anarray antennas has gained a great attention in the array signal processing subject such as radar and wireless communication system [5]. Most of new directions finding techniques such as Multiple Signal Classification (MUSIC), Estimation of Signal Parameter via Rotational Invariance (ESPRIT) and others [6] had studied in contexts of one dimensional 1 (azimuth angle) cases. These techniques are based on Eigen value decomposition of the covariance matrix to the sampled input ��� These techniques need intensive computa process so that they might not be suited for real Khwarizmi Engineering Journal,Vol. 12, No. 1, P.P. 36- 44 (2016) Dimensional Angle of Arrival Estimation by Circular Phased Adaptive Array Antennas Bassim Sayed Mohammed Department of Electrical Engineering /University of Technology Email:bassim_sayed@yahoo.com (Received 16 February 2015; accepted 12 November 2015) the use of a circular array antenna with adaptive system in conjunction with forming (LCMVB) algorithm is proposed to meet the requirement of Angle D as well as the Signal to Noise Ratio (SNR) of estimated sources (Three Dimensional rather than interference cancelation as it is used for. The proposed system was simulated, tested and Multiple Signal Classification (MUSIC) technique for 2-D estimation. The results system has exhibited astonishing results for simultaneously estimating 3-D parameters with accuracy equivalent to the MUSIC technique (for estimating elevation and azimuth angles), and it has privilege for sources which are under the estimation process. needs less computational time and hardware complexity when it is used by MUSIC technique. Also, it has cost effectiveness with respect to (3 , MUSIC, Adaptive Array Antenna System. Over the last decade, the AOA estimation or guesstimate the direction and location of the most desirable fare and security The AOA estimations of the received signals a great attention in ject such as radar tem [5]. Most of ing techniques such as Classification (MUSIC), via Rotational nce (ESPRIT) and others [6] had been contexts of one dimensional 1-D . These techniques are based Eigen value decomposition of the covariance of the array. These techniques need intensive computation not be suited for real time application (where the required be trucked on line). One dimension is suffic AOA for the land and sea transmit assuming that the elevation angle is very s For airborne transmitting estimation of these sources needs a two Dimensional (2-D) real time estimator (elevation θ and azimuth φ). Adaptive array antenna with fast algorithm and less compu offers an effective passive mean active means (like radars elevation and azimuth of the these transmitting sources. This use is very important in a real war environment because it is a passive and secured activity from the point of view of the electronic ware fare missions(reconnaissance activity). Unlike the active systems(radar detected and jammed by electronic Al-Khwarizmi Engineering Journal (2016) Dimensional Angle of Arrival Estimation by Circular Phased array antenna with adaptive system in conjunction with modified Linearly ) algorithm is proposed to meet the requirement of Angle of of estimated sources (Three Dimensional celation as it is used for. The proposed system was simulated, tested and D estimation. The results show the D parameters with accuracy approximately estimating elevation and azimuth angles), and it has privilege to estimate SNR computational time and hardware complexity when it is compared with has cost effectiveness with respect to (3-D) where the required signals are to One dimension is sufficient for estimating land and sea transmitting sources, elevation angle is very small. For airborne transmitting means, the AOA sources needs a two D) real time estimator (elevation Adaptive array antenna with fast convergence algorithm and less computational time process effective passive means tool rather than (like radars) to estimate the elevation and azimuth of the platform that carried these transmitting sources. This use is very important in a real war because it is a passive and secured of view of the electronic reconnaissance activity). Unlike the active systems(radars) which can be detected and jammed by electronic means or Bassim Sayed Mohammed destroyed by weapons. The adaptive array antenna is mainly used for suppressing the interference, multipath and jammer signals, while researches talks about the ability of using adaptive array antenna system as angle of arrival estimator [7]. Most of the previous researchers use of linear array antenna to estimate angles only. Simultaneous (2-D) estimation n to use a circular array antenna. Figure (1) shows a circular array antenna mounted on x parallel to the z-y plane with elevation angle θϵ[0,/2π] and azimuth angle covariance matrix Rxx of the received signals now carrying complete information elevation and azimuth angles as well as the levels of the received signals. We can information in conjunction with the adaptive processors and algorithms to simultaneously extract the (elevation θ, azimuth φ SNR). Fig. 1. Uniformly circular array 2. Two-Dimension Mathematical Formulation The Uniform Circular Array (UCA) geometry is shown in Figure (1), the antenna element assumed to be identical, omnidirectional, and uniformly distributed over a circumference of a circle of radius R in the x-y plane. A spherical coordination system is used to represent the angle of arrival of the incoming plane wave, the origin of the coordination system located at the array. Source elevation angles ���0, � up from y-axis toward the z-axis and the azimuth angles�� 0,2�� are measured from x the y-axis, the elements N of the array is displaced by an angle of [6] �� � � � ��� � � 1,2,…,�and the radius R will be R=N*d*λ/2π Al-Khwarizmi Engineering Journal, Vol. 12, No. 37 destroyed by weapons. The adaptive array antenna suppressing the interference, signals, while very few of using adaptive arrival estimator previous researchers discuss the use of linear array antenna to estimate azimuth estimation needs to use a circular array antenna. Figure (1) shows a circular array antenna mounted on x-y plane and y plane with elevation angle azimuth angle φϵ[0,2π]. A the received signals is w carrying complete information about the d azimuth angles as well as the input can explore this on with the adaptive s to simultaneously as well as the Uniformly circular array system. matical The Uniform Circular Array (UCA) geometry 1), the antenna elements directional, and uniformly distributed over a circumference of a y plane. A spherical tem is used to represent the angle of the incoming plane wave, the origin of the coordination system located at the center of � are measured axis and the azimuth are measured from x-axis toward axis, the elements N of the array is displaced and the radius … (1) Where d is the inter element spacing and wave length of the operating frequency. For k snapshot the received signal vector ���,�,�� � ∑ ������,� �!" Where ������,�,�� ,���� signal and the thermal noise vectors of a lengt (1×N) respectively. D is the numb signals under angle of arrival If the received signal is incident from elevation angle � and azimuth � vector is given by [8] #��,�,�� � $ %&�'°)*+,� Where A is signal amplitude, � is arbitrary carrier phase angle distributed [0 2�] and Uis the array vector corresponding to the incident angles of the received signals and defined by [8] - � �./��, ��0%& 12 3 ∗5∗678 Where ./��, �� is the element field patt T is denotes to the vector transpose. The thermal noise vol channels are assumed to be mutually uncorrelated random signals with zero mean and and it can be expressed as #���� � #"���,# ,… #� The adapted array output of Figure by multiplication of the received signals with the adapted weight vector [W]and it can be expressed as 9��� � ∑ :�����!" and in the vector form ;��� � <*# � #*< Where W and X vectors are given by < � :",: ,…. ,:��* # � �",� ,……,���* Signal and noise in the adaptive array antenna system may be described in the terms of statistics properties, so this make possible to evaluate the system by its statistical average where E[.] is the expected value of any random signal, the evaluation of st directly to interested quantities related to the second statistical moment such as covariance matrix, which is closely related to correlation matrix for stationary signals. , No. 1, P.P. 36- 44 (2016) Where d is the inter element spacing and λ is the wave length of the operating frequency. For k snapshot the received signal vector will be � �,�� >�������� … (2) �� are the ith received signal and the thermal noise vectors of a length D is the number of received signals under angle of arrival estimation process. If the received signal is incident from elevation �, then received signal �- … (3) Where A is signal amplitude, :° center frequency, is arbitrary carrier phase angle distributed [0, Uis the array vector corresponding to the incident angles of the received signals and defined 678�?�@A6�BC,D�E� * … (4) is the element field pattern and T is denotes to the vector transpose. The thermal noise voltages in the array channels are assumed to be mutually uncorrelated with zero mean and F variance be expressed as [7] �����* …(5) The adapted array output of Figure.2 is performed the received signals with the [W]and it can be expressed … (6) … (7) Where W and X vectors are given by … (8) … (9) Signal and noise in the adaptive array antenna system may be described in the terms of the statistics properties, so this make possible to evaluate the system by its statistical averageG ∙�, [.] is the expected value of any random ation of statistical average leads to interested quantities related to the second statistical moment such as covariance matrix, which is closely related to correlation matrix for stationary signals. Bassim Sayed Mohammed Fig. 2. Adaptive array antenna model The covariance correlation matrix of received signals vector is defined as [6] IJJ � G K∗K*� � K∗K*�LLLLLLLLL Where IJJ is � M � autocorrelation matrix of received signal and it is Hermitian (i.e. NOO∗ P ). 3. Two Dimensional (2D) MUSIC Estimator The MUSIC technique is a simple, popular, high resolution and efficient Eigen structure method for angle of arrival estimation. In order to estimate ��, �� by MUSIC, a circular array antenna system is used. The MUSIC spatial spectrumfor��, �� is given by [6] TU��,φ� � "WX�?,Y� ZDZD[W∗�?,B� Where W��,�� is a spatial vector given by W��,�� � �.\��,��%C&]∗ 12 3 ∗5∗^��?∗ ��� _ � 1,2… � and .]��,��is the z pattern. Z� is a noise subspace composed from (N-D) Eigen vector associated with the channel thermal noise components 4. Mathematical Model for Proposed Estimator A circular array antenna with radius R in the x y plane is used in conjunction with the Linearly Constrained Minimum Variance Beam forming (LCMVB) algorithm as a proposed system to estimate elevation angle ��� and azimuth ��� of received signals as well as signal to noise ratio (SNR) (i.e.3-D estimation). The adaptive array output of Figure expressed as[8]. Al-Khwarizmi Engineering Journal, Vol. 12, No. 38 Adaptive array antenna model. The covariance correlation matrix of received … (10) autocorrelation matrix of signal and it is Hermitian (i.e.NOO � (2D) MUSIC is a simple, popular, t Eigen structure estimation. In order to by MUSIC, a circular array antenna system is used. The MUSIC spatial … (11) is a spatial vector given by `a^�YC,b�� * … (12) is the zth element is a noise subspace set matrix D) Eigen vector associated components. Proposed 3-D A circular array antenna with radius R in the x- y plane is used in conjunction with the Linearly imum Variance Beam forming (LCMVB) algorithm as a proposed system to and azimuth angle as well as signal to noise ure. (2) can be G|9��,�,��| � G|d*K∗ � d*IJJ��,�,��d∗ It is required to minimized the array output power according to the following cost function given by ef�'d*IJJ��,�,φ�d∗ Subjected toW*d � Wgd Where (T)is the transpose notation, complex conjugateand dagger conjugate notation [*]T. Finding dahi��,�� to satisfy Eq. (14) and Eq. (15) can be accomplished by the method of Lagrange multipliers. Adjoining the constraint Eq. (15) to Eq. (14) performs the The minimization of this function is giving by ef�'∗j�d,d∗� � d*I > λ ld The gradient of Eq. (16) with respect to to mn∗j�d,d∗� � IJJ�o,� The minimum value of Eq. (17 IJJ��,�,��dahiX > W∗�� Therefore the optimal weight dahiP ��,�� � pIJJC"��,� So the Lagrange multipliers evaluated from the constraint given by Eq. (15 W*��,��dahi��,�� � 1 W*��,�� pIJJC"�o,�,��W It then follows that λ is given by λ�θ,φ� �– W*��,��IJJC"� Combining Eq. (19) and Eq. (21) then yields to the optimum constrained weight vector dahi��,�� � Isstu�o,?, Wv�?,B�Isstu� If dahi ��,��is substituted output of the array system optimum when the azimuth angle elevation angle ���of constrain coincide with the azimuth and elevation of any , No. 1, P.P. 36- 44 (2016) ∗��,�,��| … (13) It is required to minimized the array output power according to the following cost function … (14) d∗ � 1 … (15) is the transpose notation, (*) is a dagger ( † ) is a transpose to satisfy Eq. (14) and Eq. (15) can be accomplished by the method of Lagrange multipliers. Adjoining the constraint Eq. (15) to Eq. (14) performs the cost function. The minimization of this function is giving by IJJ��,�,��x∗ ldgW∗��,�� p 1y� … (16) ) with respect tod∗leads �,��dz > W∗��,��λ … (17) The minimum value of Eq. (17) is given by �,��λ � 0 … (18) Therefore the optimal weight vector is � ,��W∗��,��λ … (19) grange multipliers λ may now be om the constraint given by Eq. (15). �W∗�θ,φ�λ� � 1 … (20) λ is given by �o,�,��W∗��,���C" … (21) Combining Eq. (19) and Eq. (21) then yields to the optimum constrained weight vector � ,B�W∗�?,B� �o,?,B�W∗�?,B�� … (22) is substituted into Eq. (3), the output of the array system 9��,��will be when the azimuth angle ��� and constrain vector W��,�� is coincide with the azimuth and elevation of any Bassim Sayed Mohammed Al-Khwarizmi Engineering Journal, Vol. 12, No. 1, P.P. 36- 44 (2016) 39 0 10 20 30 40 50 60 70 80 90 0 5 10 15 20 25 30 35 Estimated Elevation-angle of arrival (Degree) O u tp u t S N R L e v e l X: 60 Y: 31.01 X: 45 Y: 30.99 theta =45. deg. SNR=14.91 dB theta =60. deg. SNR=14.92 received signals in the range of ���0, �, and�� 0,2��and it can be expressed as y��,�,�� = dahi* ��,��K��,�,�� … (23) It can be seen from Eq. (22) that for each received signals we have an optimum weight vector dahi ��,�� related to the incident angles of these signals. This weight vector is updated (i.e. changes its value) according to the received environments. 5. Signal to Noise Ratio SNR(|,}) Estimation Since we calculate the optimum weight vector dahi ��,�� according to Eq. (22), this weight vector maximized the output of the array in the direction of received signals according to the constraint condition Eq. (15). So the output voltage of the proposed array system due to ith received signal is 9���,�,�� and due to the nthchannel thermal noise voltage is 9���� and they can be expressed as 9���,�,�� = d*��,��K���,�,�� … (24) 9���� = d*��,��K���� … (25) Then the output powers for signals and noise can be written as G|9���,�,��| = |d*��,��K�∗��,�,��| = d*��,��I����,�,��d∗��,�� … (26) Where ~����,�,�� is a covariance matrix of ith received signal under angle of arrival estimation and it is equal to ~����,�,�� = K�∗���,�,�� ∗ K�*��,�,�� … (27) Similarly the out power due to thermal noise is G|9����| = |d*��,��K���,�,��| = d*��,��I��d∗��,�� … (28) I�� = �� �, where �� is the second moment of noise signals (noise power) and � is an identity matrix of dimensions (N×N). I��is diagonal matrix due to thermal noise voltages in the channels, they are uncorrelated signals (random signals). Now the output SNR��,��which can be estimated to each received signal to perform (3-D) estimation (i.e. elevation, azimuth and SNR estimation) is equal to ��~��,�� = /|����),?,B�| 1 /|�D�)�|1 = d �����?,B�I���),?,B�d����),?,B� d�����),?,B�IDDd����),?,B� …(29) 6. Simulation Results All simulation programs were written in MATLAB 7.10 and the following assumption are considered:- a) The number of array elements are taken to be ten (N=10), isotropic and circularly distributed on a circumference of circle in x-y plane. b) The radius of the circle (R) of ten elements array with inter-element displacement 0.5λ is equal to 0.8 λ according to Eq. (1). c) The received signals are considered to be statistically independent and uncorrelated. The proposed 3-D adaptive array antenna estimator in conjunction with (LCMVB) algorithm is tested, evaluated and compared with MUSIC DF technique according to the following scenarios. A- Senario1:- A two airborne transmitters are cosidered to be transmittedon a same frequency with equal output powers.The received signals are assumed to be arrived from different elevation and azimuth angles.θ1=45 o, φ1=150 o, θ2=60 o, and φ2=200 o .The input received powers areassumed to be equals and equal to 5dB. Figures(3,4,5)show the result of estimating elevation and azimuth angles in 2-D (θ �� φ versus SNR) and estimating in 3-D (θ ��� φversus SNR) of the two transmitters by the use of proposed adaptive system. It can be seen that the estimated angles in both planes are coincide with the true angles of arrival of received signals. Since the input received powers are assumed to be equales (5 dB), it can be seen that the proposed system gives equal output SNR (14.1 dB) for both received signals, which means that the proposed system cansimultaneously estimate(θ,φ and SNR) parameters for all received signals. Fig. 3. Elevation angle θ estimation by proposed model. Bassim Sayed Mohammed Al-Khwarizmi Engineering Journal, Vol. 12, No. 1, P.P. 36- 44 (2016) 40 Fig. 4. Azimuth angle φ estimation byproposed model. Fig. 5. Estimated θ and φ versus SNR by proposedmodel. While figures(6,7,8) for MUSIC technique show the estimation of � ��� � angles versus DF output level. It can be seen that the DFoutput level for the estimated signals are not related in any way to the received signals input powers, because the MUSIC DF output level which is given by Eq.(11) is related to the noise subspace Eigen vector set (Z�) and not to the input signals parameters.The accuracy of estimated angles are seemed to be identical for both cases. Fig. 6. Elevation angle θ estimation by MUSIC. Fig. 7. Azimuth angle φ estimation by MUSIC. Fig. 8. Estimated(θand φ)versus DF level by MUSIC. 0 50 100 150 200 250 300 350 0 5 10 15 20 25 30 35 X: 200 Y: 30.99 Estimated Azimuth-angle of arrival (Degree) O u tp u t S N R L e v e l X: 150 Y: 31.01 phi =200. deg. SNR=14.91 dB phi =150. deg. SNR=14.91 dB 0 10 20 30 40 50 60 70 80 90 0 20 40 60 80 100 120 140 160 X: 60 Y: 154.3 Estimated Elevation-angle of arrival (Degree) M U S IC ( D F ) p o w e r L e v e l (d B ) X: 45 Y: 158.4 theta =60. deg. theta =45. deg. 0 50 100 150 200 250 300 350 0 20 40 60 80 100 120 140 160 X: 200 Y: 154.3 Estimated Azimuth-angle of arrival (Degree) M U S IC ( D F ) p o w e r L e v e l (d B ) X: 150 Y: 158.4 phi=200 deg. phi=150 deg. Bassim Sayed Mohammed Al-Khwarizmi Engineering Journal, Vol. 12, No. 1, P.P. 36- 44 (2016) 41 B- cenario 2:- two cases are considered.First, the two transmitters are transmitting from the same azimuth angles and from different elevation angles θ1=30 o, φ1=150 o,θ2=60 o, and φ2=150 o.Second,twotransmitters are transmitting from eqaul elevation angles and from different azimuth angles θ1=50 o,φ1=100 o,θ2=50 o,and φ2=200 o. The two sources transmit on the same frequency with different transmitting powers. The input received powers from sources are considered to6dB and 9dB It can be seen from figures(9and10) that the proposed system estimate ( �,� and SNR) for the two transmitter in both cases with a high accuracy although the two transmitters transmit from the same azimuth or same elevation angles with different transmitting powers. It is also obvious that the output SNR's of received signals are directly related to the input received powers from sources. The (6 dB) input power gives (15.55 dB) output SNR while the (9 dB) input power gives (18.58) dB output SNR in both figures, which means that the proposed system are fulfill the designing requirments for estimating (3-D) parameters. Fig. 9. Estimated (| ��� }) versus SNR by proposed system for equal azimuth and different elevation angles . Fig. 10. Estimated (θ ��� }�versus SNR by proposed system for different azimuth and equal elevation angles. C- Scenario 3:- A three transmitters are transmitting on same frequency with different transmitting powers. The received signals are assumed to be from different elevation and azimuth anglesθ1=45 o, φ1=150 o, θ2=60 o,φ2=200 oand θ3=75 o, φ3=250 o.Theinput received powers from sources are cosidered to be 6, 9 and 12 dB. Figure (11) shows (3-D) plot for proposed system.The result shows that the angle of arrival estimation for the three transmitters are quite accurate and identical to the angles of arrival estimated by MUSIC techniquesee Figure (12). It can also be seen that the proposed system estimates the output SNR's for the received signals and shows different output SNR's levels,since the input powersof recived signals are assumed to be different while, a MUSIC technique hasn't this capability. Figure (12) shows that the DF level for the received signals which they have different input powers are equals this means that MUSIC technique can be considered a (2-D) estimator rather than (3-D) estimator as the case of proposed system. Bassim Sayed Mohammed Al-Khwarizmi Engineering Journal, Vol. 12, No. 1, P.P. 36- 44 (2016) 42 Fig. 11. Estimated �| ��� }� versus SNR by proposed model for three sources with different input levels. Fig. 12. Estimated (| ��� }� versus DF level by MUSIC for three sources with different input levels. 7. Conclusions A uniformly circular array antenna with a modified adaptive algorithm is proposed to be used as an angle of arrival estimator in two planes (θ and φ) and output SNR estimator (i.e.3-D estimator). The proposed (3-D) angle of arrival estimation results shows that the system is equivalent to the MUSIC technique from the point of angle of arrival estimation accuracy view and it has a privilege over MUSIC that it can estimate output SNR for the received signals under two planes angle of arrival estimation while MUSIC does not has this capability. The estimated output SNR can be used to estimate the distance to the transmitting sources, since the estimated SNR is directly related to the transmitted power and distance between transmitting source and estimator (receiving side). Comparing the proposed model with the well know MUSIC technique shows that the proposed model does not need any hard ware or software orthogonality which is used by MUSIC to calculate noise subspace eigenvectors Z�. The orthogonality techniques which are based on Singular Value Decomposition (SVD) technique or eigenvalue decomposition technique are computationally intensive and they need more RAM size and more time processso that they might not be suited for real time application where the received signals must be tracked in real time. The optimum adapted weight vector Woptm in the proposed system is directly calculated and used to estimate �,�and SNR with minimum computing steps. This means that the proposed system can be used in a real time to track the received signals. The proposed model also offers the capability to analyze and listen to the received signals(hearing and technical analyzing features ) while performing angle of arrival estimation which is an important tools for supporting Electronic war-fare Counter Measures(ECM) and Electronic war-fare Supporting measures (ESM)activities against these sources. 8. References [1] Bassim Sayed and Noori Hussain “An alternative approach for angle of arrival estimation”, 8th European conference on antenna and propagation (EUCAP, 2014), pp.2639-2643, 2014. [2] Bassim Sayed and Noori Hussain “Angle of arrival and signal to noise ratio estimation for broadband signals by phased adaptive array antennas”, 8th European conference on antenna and propagation (EUCAP, 2014), pp.311-315, 2014. [3] Bassim Sayed and Noori Hussain “Adaptive array antenna used for signal to noise ratio and angle of arrival estimation” 7th European conference on antenna and propagation (EUCAP, 2013), pp.2000-2004, 2013. [4] X. Liu and G. Liao, “Direction finding and mutual coupling estimation for bistatic MIMO radar,” signal processing, vol.92, no.2, pp.517-522, 2012. Bassim Sayed Mohammed Al-Khwarizmi Engineering Journal, Vol. 12, No. 1, P.P. 36- 44 (2016) 43 [5] S.Shirvain Moghaddam and F. Akbari, “Improving LMS/NLMS-based beam forming using Shirvain-Akbari array”, American Journal of Signal Processing, vol. 2, no. 4, pp. 70-75, 2012. [6] S. Shirvain Moghaddam and F. Akbari, “A novel ULA-based geometry for improving AOA estimation”, EURASIP journal on advances in signal processing, vol. 2011, no. 39, 2011. [7] S. Shirvain Moghaddam , F. Akbari and V. T. Vakili, “A novel array geometry to improve DOA estimation of narrowband sources at the angles close to end fire”, in proceeding of 19th Iranian conference on electrical engineering (ICEE2011), pp. 1- 6,Tehran,Iran,May 2011. [8] S. Kikuchi, H. Tsuji and A. Sano, "Pair- matching method for estimating 2-D angle of arrival with a cross-correlation matrix," IEEE Antennas Wireless Propag. 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