Neural Blind Separation for Electromagnetic Source Localization and Assessment

Transcription

1 Neural Blind Separation for Electromagnetic Source Localization and Assessment L. Albini, P. Burrascano, E. Cardelli, A. Faba, S. Fiori Department of Industrial Engineering, University of Perugia Via G. Duranti 1/A-4, Perugia 614, Italy Abstract - In this paper we present a possible approach to electromagnetic source localization using a hybrid blind separation minimum search inversion algorithm. The total electrical field versus time emitted by the working antennas, located at different and unknown geographical positions, is used to reconstruct each separate contribute via a suitable neural network technique. When the emitted electric field and the related base frequencies have been separated for each emitting antenna, the unknown location of each emitter, is determined with a minimum-search numerical technique. The theory here presented has been applied with success to a practical problem dealing with amplitude-modulated radio-transmissions. I. INTRODUCTION Recently many countries of the world, in consequence of the growth of telecommunication systems and of the related exposure of humans to electromagnetic fields, have promoted and approved central or local government laws, or adopted national or international standards, as regulation for the control and the limitation of the electromagnetic fields generated by radio-telecommunication stations [1] [] [3] [4] [5]. These regulations usually include the control of the generated electromagnetic field levels in two different steps: 1) Authorization To have the authorization for building-up a new radio-telecommunication station, or for the substantial modification of an existing one, the electromagnetic field produced in the environment must be predicted in the station design; moreover the electromagnetic field in the environment must be measured when the station has been realized; ) Environmental control The electromagnetic fields are periodically measured, in order to control if the limits are exceeded. In this case, according to the different regulations and procedures, all the interested emitting stations, and their exact locations, must be determined. In addition, the fraction of the electromagnetic field produced for each emitting station (i.e. for each transmission frequency) must be evaluated, in order to compute the power reduction factor to be applied to each transmitting station, or to apply other equivalent methods of reduction to conformity. A problem similar to the one evidenced in point two can be found in case of interferences between two or more transmitting station or channels. In this case, the individuation of the interfering antennas and/or transmitting station is often a difficult task especially when the interferences are created by a small local emitter. The size of the antennas, in fact, could be small and their location could be difficult to recognize by aerial view or by other similar searching methods. In this paper we present a possible approach aimed to solve this kind of problem. The behavior of the electric field versus time, measured quasi-simultaneously in different locations, is used, via a suitable neural network technique, to reconstruct each separate contribute. When the emitted electric field, and the related base frequencies, or channels, have been separated for each emitter, the unknown locations of each antenna, or emitting systems, are determined with a minimum-search numerical technique. The theory here presented has been applied with success to a practical problem dealing with amplitude-modulated radio-transmissions. II. ELECTROMAGNETIC SOURCE SEPARATION In this paragraph the technique used for the electromagnetic source separation is described. In order to perform electromagnetic source localization and assessment, some measurements of the electrical field strength versus time are taken in different locations. The different electrical fields emitted by the antennas cannot be measured directly, because electrical fields interact additively and only their superposition can be measured. It is therefore necessary to separate out the contribution of each antenna from the cumulative time-recordings. This fundamental dataprocessing operation should be performed in the lack of information about the waveforms emitted by the antennas, about the source position and nominal power, and should therefore rely on a blind signal processing technique known as Independent Component Analysis (ICA) [6]. The aim of ICA technique is to recover a number of statistically independent signals from their unknown linear mixtures, under simple consistency conditions [7] [8] [9]. Namely, a mixture of statistically independent source signals is supposed to be observed:

2 u(t) = M s(t) (1) where M is an unknown constant real-valued full-rank m n mixing matrix and s(t) is the vector-stream containing the n source signals to be separated. The only hypotheses made on the unknown sources are: 1) each s i (t) is an Independent Identically Distributed (IID) stationary random process; ) the s i (t) s are statistically independent at any time; 3) at most one among the source signals may have Gaussian distribution. 4) the number m of observations exceeds the number n of sources. For separating out the independent sources from their linear mixture, a neural network with m inputs and n outputs can be used; this network is described by the relationship: o(t) = W u(t) () where u(t) is the neural network input vector and W denotes the network connection-matrix. As the mixing model is linear, a linear separating structure is effective, and the network's output o(t) is taken as an estimate of the true source stream s(t). Under the above conditions, the sources may be recovered up to arbitrary scaling and permutation [4]. As a by-product, an estimate of the mixing matrix M can be obtained, which describes the physics of wavepropagation in the source localization and assessment problem. In fact, under the cylindrical wave propagation hypothesis, it can be readily seen that the entries M rc have the structure: M rc = f(d rc )exp(jγd rc ) (3) where the function f(.) describes the emitted energy loss and the phasor accounts for the emitted field phase rotation, due to wave propagation, and d rc denotes the distance between the r-th emitter and the c-th receiver. Consequently, each row of the estimated mixing matrix, normalized to e.g. its first entry, equals the electrical field ratio between the field emitted by an antenna, as received by a sensor, and the field emitted by the same antenna as received by the first sensor. Triangularization then allows locating the sources. III. ELECTROMAGNETIC SOURCES LOCALIZATION The inversion problem deals with the identification of the electromagnetic sources positions starting from the separation results. The electric field value emitted by an electromagnetic source S in a point P i in the free space is a function of the distance between the source and the point, and it can be written in the following form: ( x, y, z, x, y z) Ei = h i i i, (4) where E i is the electric field value in the point P i, x i, y i and z i are the Cartesian coordinates of the point P i, and x, y and z are the Cartesian coordinates of the source position. In our problem we have a set of electric field ratio for a specific source carried out from the separation algorithm described in the previous paragraph. In order to identify the antenna position we can define the following functions from (4): ( x, y, z, x, y, z) h( x, y, z, x, y z) Ei gij = h j j j i i i, (5) E j m G i = g ij j= 1 where m is again the number of the points considered, E i /E j is the electric field strength ratio for two generic points P i and P j and h is the function of the electric field amplitude versus antenna coordinates for the typical radio-transmission antenna considered. This formulation gives estimation results that prove invariant to arbitrary scaling factors. The relationship between the energy-loss function f(.) and the antenna characteristic function (4) is: f d = h x, y, z, x, y, z (7) ( ) ( ) rc r r r When several electromagnetic field sources are present in the region of the space under attention, for each antenna it is possible to estimate its position by the relative set of electric field ratio provided by the separation algorithm, using the inverse procedure presented above. c IV. EXPERIMENTAL RESULTS In order to check the proposed electromagnetic source localization and evaluation technique, we present in this section some numerical results obtained under the following working-hypotheses: 1) The emitting stations perform radio-transmissions at frequencies in the range of frequencies dedicated to the Amplitude Modulation (A.M.) transmissions (5 khz - MHz) and with the typical emission power of these antennas (5- kw); ) The wave-propagation is cylindrical and the far-field power-loss model holds true, i.e. the function f(.) has the expression: c c (6) f(d) = k/d (8) where the constant k depends on the emitted power value; 3) The time-dynamics of the emitted signals follows the Amplitude-Modulation model, i.e. the source signals have the expression: s i (t) = (1+m a m i (t))cos(ω t+ϕ) (9) with m i (t) being the modulating signal, m a being the amplitude-modulation deepness, and ω and ϕ being the carrier frequency and phase, respectively; 4) The spatial area interested by electromagnetic monitoring is a square with a km side. With these working hypotheses, a set of three emitting stations has been randomly generated and simulated, and an environmental electromagnetic noise - perceived as a fourth

3 source - has been generated as well, with a signal-to-noise ratio (SNR) of about 1. About the measurement scheme, we supposed to collect samples from a number of time-measures taken over a regular grid of 4 4 points, uniformly-spaced in spatial area interested by electromagnetic monitoring. An exemplary schematic of the experimental set-up is shown in Figure 3, while a simulated recording of sixteen waveforms is shown in the Figure 1. The mixed waveforms are first fed to the separating neural network, which is able to recover the three original amplitude-modulation contributions, plus the environmental noise, up to component re-ordering and scaling. The separating network has been trained by the JADE algorithm [7]. An example of waveforms as recovered by the ICA neural network is reported in the Figure. Figure 3 shows instead the result of the source localization through triangularization by non-linear functional optimization, which seems indeed quite accurate and reliable. We have seen that regular measurement grids internal to the investigated region have better performances. Moreover, the more the antennas are located inside the grid, the more reliable and accurate is their localization. V. CONCLUSION AND FURTHER WORK In this paper we have proposed an hybrid technique that allows in a first step the separation of the electromagnetic signals in the time-domain, via a blind source separation neural algorithm, and in a second step the individuation of the positions of each antenna, via a minimum-search inversion algorithm. The theory described in the paper has been applied to a practical problem dealing with amplitude-modulated radiotransmissions, and the locations of the antennas have been individuated with very small errors. The preliminary results presented here seem to be promising, but further efforts must be done in order to approach the cases of antennas of different kinds, of different propagation conditions, determined in some cases by specific geographical and atmospheric conditions. References [1] ICNIRP: Guidelines for limiting exposure to timevarying electric, magnetic, and electromagnetic fields (Up to 3 GHz), Health Physics, Vol 74, No. 4, pp , Apr [] IEEE Std. C IEEE Standard for safety levels with respect to human exposure to radio-frequency electromagnetic fields, 3kHz 3 GHz, New York, 1999 [3] IEEE Std. C , IEEE Recommended practice for the measurements of potentially hazardous electromagnetic fields RF and microwave, New York 1991 [4] D. Slater, Near Field Antenna Measurements, Artech House, 1991 [5] ITU-R Rec.S.M.36-7, Determination and measurements of the power of amplitude-modulated radio transmitters, 1998 [6] P. Comon (1994). Independent Component Analysis, A new concept?, Signal Processing, Vol. 36, pp [7] J.-F. Cardoso (1999). High-order contrasts for independent component analysis, Neural Computation, Vol. 11, No. 1, pp [8] S. Fiori (). Blind Signal Processing by the Adaptive Activation Function Neurons, Neural Networks, Vol. 13, No. 6, pp [9] S. Fiori (). Blind Separation of Circularly Distributed Source Signals by the Neural Extended APEX Algorithm, Neurocomputing, Vol. 34, No. 1-4, pp. 39 5

4 u 1 1 x u u u 1-1 x u 3 u u 4 u x u 5 u u 6 u u 7 u 15 x x u 8 u Fig.1: Some temporal traces representing observable source signals at sensor locations.

5 o o o o Fig. : Amplitude modulation sensor signals as recovered by ICA neural network.

6 x 15 O = Antenna position, = Measurement point, + = Esteem antenna position y [m] x [m] x 1 5 Fig. 3: Schematic of the simulated measures and result of source localization by triangularization.