# Neural Network Synthesis Beamforming Model For Adaptive Antenna Arrays

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2 The angular behavior of the far field E of a linear uniformly spaced array of 2N radiators can be written as E( ) j 2N I e n n1 jk xn sin( j ) (1) With I n the weighting coefficient, x n the position of the nth element. Desired pattern are usually complex, and optimal realisable pattern can only be defined with respect to some error criterion. We will consider the minmax norm, defined as to solve). The neural network training set was formed by some significant results obtained from the above method of synthesis. The main components of the neural beamformer include preprocessing, a neural network, and postprocessing, Fig. 1. Interfering signal Preprocessing Input (Desired signal) Err ) max E ( ) E ( ), j=1,,m (2) ( j c j d j j Where M is the number of the sampled angular direction, Ed is the required pattern field, and Ec is the calculated pattern field. With this norm we have equal relative error (equal decibel ripple) in the pattern region and equal side lobes in the side-lobe region. For the real field synthesis case, eqn. 1 is taken and the excitation distribution is symmetrical and conjugated with the array centre. The computed formulation is N ' Ec( j ) In cos( k xn sin( j )) (3) n1 With x n ', the relative position of the nth element with the array centre. In the case of power synthesis, the error to minimise is equal to the difference between the modulus of the computed function and the required one. Since the above method is not practical for real time implementation, an adaptive algorithm must be used to adapt the weights of the array in order to track the desired signal and to place nulls in the direction of the interfering signals. 3. NEURAL NETWORKS The choice of neural network architecture is crucial for developing a successful application. The neural feed-forward network with a backpropagation learning algorithm is able to solve nonlinear function models (complicated Postprocessing Output Neural Synthesized Excitations Fig. 1. A neural network Synthesis model Preprocessing and postprocessing configure the network interfaces to perform particular functions, which are in our case synthesis and steer signal. The neural network approximates the function, that we are modelling by adapting its internal structure to map the problem space. Pre-processing: Network pre-processing exploits antenna expertise to simplify and enhance neural network inputs. It removes redundant or irrelevant information, eliminates artificial discontinuities in the input function space, and reduces problem inputs to a small set of relevant information. In the pre-processing two steps should be done. The first step of preprocessing divides the space in 17 sectors, repeated every 1 in the interval from -85 degrees to +85 degrees inclusive. More accurate space division sectors can be reached by increasing the number of element arrays. The input vector to the entry of network is in the form of a 17 bit binary code (one bit for each sector); all of 8

3 the bits were set to zero except one (+1) or two (+1 and -1) A bin input of +1 indicates a source exactly on (main lobe) in the sector, the bin location of represents no source in the sector and the bin location of -1 indicates a null interfering in the sector. This step has the advantage to decrease considerably the number of unknown variables. Convergence may then be achieved more rapidly. The second step of pre-processing reduces the ponderation phase discontinuities between consecutive array elements. Discontinuities make it difficult for the network to learn the mapping from a small discrete set of training points. To eliminate this difficulty we use the sine and cosine of the phase ponderations as final processed inputs. We train the output nodes to emit values between -1 and +1, inclusive, which represent the cosine and sine of phase for each antenna element. Post-processing: For our simulation an eight elements array antenna is used. Each output vector contains eight values of amplitude, eight cosines and eight sinuses for the phase differences between antenna elements. This technique performs well for steering lobe with low side level and steering lobe with null interfering in any desired direction. 4. SIMULATION RESULTS FOR NEURAL NETWORK SYNTHESIS BEAMFORMING In adaptive antenna the flexibility of the array weighting, which should be adjusted to specify the array pattern, is an important property. This property may be exploited to steer the beam in all possible directions and to cancel interfering sources operating at the same frequency as that of the desired source, providing that the spatial separation is large enough Neural Network Synthesis Model For Steering Lobe With Low Side Lobe Level In this paragraph, we present (table 1) the neural synthesis simulation results (Fig. 2) for the steering lobe with a low side lobe level. Table 1: Excitations for different steering lobe with low side lobe level teta, deg. Fig. 2. Adapted pattern of eight elements linear array for desired lobe with low side lobe level at = -1 (sector 8), -33 (sector 6), -48 (sector 4) respectively 4.2. Neural Network Synthesis Model For Steering Lobe With Interference Nulling The interference is one of the most important considered problems, operation and maintenance of mobile communications systems. Undesired signals can be attenuated by appropriate phase and amplitude excitation.

4 Table 2 presents the results of neural synthesis simulation. These simulations have been done (Fig. 3, 4 and 5) to obtain the desired signal and to place nulls in the direction of the interfering signals teta, deg. Fig. 5. Interference nulling at -6 (sector 3) and steering lobe at -22 (sector 7). Table 2: Excitations for different steering lobes and interference nulling. -1 As the figures indicate, we can observe the performance of our network. The network has shown its ability to generate reasonable results in all checked cases. This algorithm holds not only for the examples presented above, but also appears to be general for all cases of synthesized desired characteristics of steered beams, an adaptive algorithm used to adapt the weights of the array in order to track the desired signal and to place nulls in the direction of the interfering signals Fig. 3. Interference nulling at (sector 9) and steering lobe at 28 (sector 12) teta, ged. Fig. 4. Interference nulling at (sector 5) and steering lobe at -8 (sector 8). 5. CONCLUSION The presented method is very practical for neural network implementation. The convergence and the generalization of the results are efficiently reached and the obtained not trained solutions are very accurate. The neural approach based on the (FF) Neural Network with BP shows good simulation results and allows a real time synthesis of desired steering beam with nulling interference directions 8. REFERENCES [1] L. C. Godara, Applications of Antennas Arrays to Mobile Communications, Part II: Beam- Forming and direction of Arrivals Considerations, Proc. of IEEE, Vol. 85, no. 8, pp , August 1997.

5 [2] Phased Array Antenna Handbook, Robert. J. Mailloux. Published by Artech House. [3] D. Cailleu, N. Haese, P.A. Rolland, "Microstrip adaptive array antenna, Electronics Letters, vol. 32, no. 14, 4th July, 1996, p [4] V.U. Reddy, A. Paulraj, and T. Kailath,"Performance analysis of the optimum beamformer in the presence of correlated sources and its behavior under spatial smoothing," IEEE trans. Acoust. Speech, Signal Processing, ASSP, pp , [5] T.O Donnel, J. Simmers, and D. Jacavanco, Neural Beamforming for Phased Array Antennas, in proceedings of the 1992 Antenna Applications Symposium, University of Illinois [6] H.L. Southall, J. A. Simmers and T.O Donnel, Direction Finding in Phased Arrays with a neural Beamformer, IEEE transactions on Antennas and propagation, AP-43, December 1995, pp [7] Rammal. M, Contribution to the study and the synthesis of networks of printed antennas, PHD thesis, Limoges University, Faculty of Sciences, Jan.1993.

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