# Multiple Signal Direction of Arrival (DoA) Estimation for a Switched-Beam System Using Neural Networks

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2 PIERS ONLINE, VOL. 3, NO. 8, the contribution of each signal to the total measured power depends only on its angle of incidence. The input power coming from each beam is measured through an appropriate meter connected to the switching network. -1 Power (db) Angle (degrees) Figure 1: Radiation pattern of an eight patches SBS. Consider a random set of N signals arriving in a 12 sector from angles ϕ i, i = 1... N, 6 ϕ i 6. The angles compose a vector ϕ = (ϕ 1, ϕ 2,..., ϕ N ). If beam switching takes place, each one of the eight beams P j gives a total power P tj, j = , where: P t1 = P 1 (φ 1 ) + P 1 (φ 2 ) P 1 (φ N ) P t2 = P 2 (φ 1 ) + P 2 (φ 2 ) P 2 (φ N ) P t8 = P 8 (φ 1 ) + P 8 (φ 2 ) P 8 (φ N ) (1) Equation (1) gives a power vector P = (P t1, P t2,..., P t8 ), thus a mapping between P and the corresponding vector ϕ is established. Our aim is to utilize this mapping to accomplish DoA estimation, based on neuro-computational techniques. A set of M angle vectors ϕ m is created, each one composed by randomly selected N angles of arrival. The index m denotes the mth angle vector. The random angle values are equal to integer multiples of ϕ, within the prespecified angular range. The value of the step angle ϕ was defined equal to. degrees. A collection of randomly created pairs (ϕ m, P m ) is generated that is used as training set for the NNs. The number of pairs is M = 3 or M = 4. Considering the entire set of different possible vectors ϕ m, the training set volume is very small. This shows the effectiveness and the generalization capabilities of a properly trained NN. Multilayer Perceptron (MLP) NNs are used, [16], composed by: 1) an input layer of eight nodes which is fed by the vectors P m, 2) an output layer of N nodes that gives the corresponding vectors ϕ m, and 3) one or two hidden layers. The number of hidden layers and the number of each layer s nodes depends on the value of N. The criterion of their choice is the better NN training convergence and the results accuracy. The activation function of the hidden layers is the hyperbolic tangent function and the activation function of the output layer is linear. The NNs training has been performed to MATLAB using the learning algorithm Levenberg-Marquardt (LM) [17]. The LM algorithm provides a relatively fast numerical solution to the minimization of the performance function, which is the Mean Square Error (MSE) (i.e., the averaged squared error between the network outputs and the target outputs during the training). The training stops when the MSE minimization reaches a plateau. Since the training of the NNs is over, the DoA estimation procedure is summed up to the following four steps: a) Simultaneous arrival of N signals. b) Beam switching and measurement of the total power for each beam. c) Feeding of the trained NN with the measured power vector. d) NN calculation of the DoA estimation vector.

3 PIERS ONLINE, VOL. 3, NO. 8, DOA ESTIMATION SIMULATIONS In this section the results of simulated DoA estimation tests using the proposed NN-SBS method are presented. The simulation procedure has been performed to MATLAB, following the steps mentioned in the end of Section 3. Vectors ϕ m are randomly generated and from Equation (1) the vectors P m are calculated. These power vectors correspond to the power that would be measured in a real DoA estimation problem. The vectors P m are fed to the proper NN that instantly gives as output the DoA estimation vectors. The accuracy of the technique is tested by comparing the estimated DoA vector with the initial vector ϕ m, which is considered as the real DoA. In Figure 2, DoA estimation simulation diagrams are shown, for 1, 4, 8, and 1 incoming signals. The number of random arrivals tested for each case is 12, so as to obtain uniform angle of arrival distribution. Table 1: DoA estimation simulations results. Number of Signals Mean Value ϕ DoA Standard Deviation ϕ DoA ϕ DoA < (%) 1,13,7 1, 4 1,77 1,46 96,42 8 2,34 1,87 9,68 1 2,41 1,98 89,84 The absolute difference between real and estimated DoA, ϕ DoA, is statistically processed over the sample of 12 arrivals, and the results are shown in Table 1. The table gives the mean value and the standard deviation of ϕ DoA, and the percentage of ϕ DoA that is less than degrees. The simulations results and diagrams show a robust behavior of the NN and achievement of accurate 1 Signal 14 Distribution of Difference between Real and Estimated DoA ---1 Signal Signals Difference between Real and Distribution of Difference between Real and Estimated DoA Signals Difference between Real and

4 PIERS ONLINE, VOL. 3, NO. 8, Distribution of Difference between Real and Estimated DoA Signals 8 Signals Difference between Real and 6 Distribution of Difference between Real and Estimated DoA -- Signals 1 Signals Difference between Real and Figure 2: DoA estimation simulations diagrams. DoA estimation, even if the number of incoming signals is greater than the number of the antenna elements.. CONCLUSION A new DoA estimation method (NN-SBS) for a switched-beam system using neural networks was described. The synthesis, the requirements and the accuracy of the proposed method provide some interesting advantages. The most widespread super resolution algorithms (MUSIC, ESPRIT, Matrix Pencil etc.) need measurements at every antenna element and intensive signal processing in order to perform eigen-decomposition processes. Other NN based techniques require at least the calculation of the signal autocorrelation matrix. In the proposed method only power measurements at a single point of the system is needed, saving cost, complexity and time. Additionally, due to the simplicity of the technique and the speed of NNs, real time applications can be easily served into existing base stations. Finally, contrary to the majority of DoA estimation algorithms, accurate results are obtained even for a big set of incoming signals. ACKNOWLEDGMENT This work is implemented in the framework of Measure 8.3 through the O.P. Competitiveness 3rd Community Support Programme and is co-funded by: 7% of the Public Expenditure from the European Union European Social Fund, % of the Public Expenditure from the Hellenic State Ministry of Development General Secretariat for Research and Technology, and Private Sector (INTRACOM S.A.).

5 PIERS ONLINE, VOL. 3, NO. 8, REFERENCES 1. Liberti, J. C., Jr. and T. S. Rappaport, Smart Antennas for Wireless Communications: IS-9 and Third Generation CDMA Application, Prentice Hall PTR, New Jersey, Godara, L. C., Application of antenna arrays to mobile communications, part II: Beamforming and direction-of-arrival considerations, Proc. IEEE, Vol. 8, , August Chandran, S., Advances in Direction of Arrival Estimation, Artech House, Boston, London, Schmidt, R. O., Multiple emitter location and signal parameter estimation, IEEE Transactions on Antennas and Propagation, Vol. 34, No. 3, , March Ray, R. and T. Kailath, ESPRIT-estimation of signal parameters via rotational invariance techniques, IEEE Transactions on Acoustics, Speech, Signal Processing, Vol. ASSP-37, , Eric, M. and B. Igric, Practical implementation and performance estimation of MUSIC method implemented on signal processor TMS 32c3, Scientific-Technical Review, Vol. LIV, No. 1, Kim, J.-T., S.-H. Moon, D. S. Han, and M.-J. Cho, Fast DOA estimation algorithm using pseudocovariance matrix, IEEE Transactions on Antennas and Propagation, Vol. 3, No. 4, , April. 8. Koh, J. and T. K. Sarkar, High resolution DOA estimation using matrix pencil, Antennas and Propagation Society International Symposium, IEEE, Vol. 1, , June Yilmazer, N., J. Koh, and T. K. Sarkar, Utilization of a unitary transform for efficient computation in the matrix pencil method to find the direction of arrival, IEEE Transactions on Antennas and Propagation, Vol. 4, No. 1, , January Du, K.-L., A. K. Y. Lai, K. K. M. Cheng, and M. N. S. Swamy, Neural methods for antenna array signal processing: A review, Signal Processing, Vol. 82, 47 61, Zooghby, A. H., C. G. Christodoulou, and M. Georgiopoulos, A neural network-based smart antenna for multiple source tracking, IEEE Transactions on Antennas and Propagation, Vol. 48, No., , May Mochida, E. and Y. Iiguni, Adaptive DOA estimation using a radial basis function network, Electronics and Communications in Japan, Part 3, Vol. 88, No. 9, 11 2,. 13. Taillefer, E., A. Hirata, and T. Ohira, Direction-of-arrival estimation using radiation power pattern with an ESPAR antenna, IEEE Transactions on Antennas and Propagation, Vol. 3, No. 2, , February. 14. Varlamos, P. K. and C. N. Capsalis, Direction-of-arrival estimation (DoA) using switched parasitic planar arrays and the method of genetic algorithms, Wireless Personal Communications, Vol. 28, 9 7, Butler, J. and R. Lowe, Beam forming matrix simplifies design of electronically scanned antennas, Electronic Design, Apr Christodoulou, C. and M. Georgiopoulos, Applications of Neural Networks in Electromagnetics, Artech House, Boston, London, Demuth, H. and M. Beale, Neural Network Toolbox for Use With MATLAB, User s Guide (Fifth Edition), The Math Works, Inc., 1998.

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