Index Terms - Attenuation Constant(α), MB-OFDM Signal, Propagation Constant( β), TWI.

Transcription

1 Through-The-Wall Propagation and Channel Modeling G. Nagaraja 1,G.Balaji 2 1 Research Scholar in Department of Electronics and Communications Engineering, Shri Venkateshwara University, Gajraula, Amorha, Uttarpradesh, India 2 Asst.professor, Sai Spurthi Institute of Technology, B.Gangaram, Sathupally, Telangana, India Abstract - This paper deals with handling through the wall propagation which is a competitive topic keeping in view the Wall complexity. Wall is composed of different compositions mainly because of the material used during construction. Effect of electromagnetic wave propagation as the wave passes through the wall & free space propagation are considered. Free space & through wall propagations are considered keeping in view the path of the wave through the wall followed by the free space. Index Terms - Attenuation Constant(α), MB-OFDM Signal, Propagation Constant( β), TWI. I. INTRODUCTION Channel modeling usually include the characterization of different channel parameters like path loss, shadowing, multipath delay spread, coherence bandwidth, multipath arrival times, average multipath intensity profile and received amplitude distribution of the multipath components. Through-the-wall propagation and channel modeling are inter-linked terms where the study and analysis of through wall propagation gives a complete support for channel modeling in TWRI. Different UWB channel models for indoor environment exist in literature. Since no researcher in the literature as given in [5] has attempted modeling of the nonhomogeneity of the wall structure which is of course the most prominent issue in TWI, the author of considers this as the main objective of this paper. In other words, the modeling [6] of the multi-layered wall for TWI which is a special case for non-homogeneous wall is considered here. II. PROPAGATION THROUGH MATERIALS Consider a transverse electromagnetic (TEM) plane wave propagating in the +Z direction. Its mathematical representation is given by Where ω=2πf is the angular frequency of the wave, f is frequency in hertz s. γ is the Propagation constant dependent on frequency and is given by [2] [1] (Henry/Metre) For most non-magnetic materials µ = µ r µ o = µ o (free space permeability) can be safely assumed. The dielectric polarization loss may be accounted for by a complex permittivity ε(ω)=ε (ω)- j ε (ω), where ε = ε r ε o is the real permittivity with ε r being the relative permittivity constant which is always greater than one. The imaginary part of the complex permittivity, ε represents the dielectric loss [5]. The dielectric loss is also represented by a parameter referred to as loss tangent. The expression for loss tangent is given by Materials will have some conductivity which causes the electric current to flow through it, in addition to the existing electric field. When current flows through a material some of the energy is converted into heat (there exists loss in energy from EM wave). This is called conductivity loss and its effect is modeled in the expression [3] 184

2 by adding one more term in the equation of complex permittivity and is given by = [4] Where σ is the conductivity of the material. The effective loss tangent is given by [5] The complex effective relative permittivity is given by [6] The complex propagation constant is α = 0, = [7] For a TEM plane wave propagating inside the material = [8] Where [9] = [10] It is clear from the above equations that the attenuation constant and phase constant are the functions of the material properties like the permittivity and the effective loss tangent (includes the conductivity loss). At high frequencies there will be the sudden change in the electric field and the dipoles in the materials try to reorient according to the applied field. In the process of doing that dipoles interact with each other and leads to violent collisions usually called dipole relaxation. Because of this dipole relaxation at very high frequencies in the range of gigahertz s there exist loss in the EM wave after propagating through the material. III. HOMOGENEOUS WALL The effect of wall is modeled by identifying the features of wall like the width and composition. One method of getting these is by deriving the wall transfer function. The calculation of transfer function differs from the conventional way where the ratio of output to the input signal is taken. Instead the received [8] signal is taken with and without wall and getting the ratio, usually called insertion transfer function. In other words it is the ratio of two radiation transfer functions of with and without the wall. While taking the received signal without wall it is assumed that the free space is of same width as that of the wall. = = [11] Where Therefore = C = 3, speed of light in free space. = = [12] 185

3 If ISSN: represents the transfer function when dielectric wall is present then = [13] Fig 1: Pictorial representation of transfer function measurement of homogeneous wall Therefore the overall transfer function H (jω) is given by = = = [14] Fig 2: Pictorial representation of multiple reflections inside the wall 186

4 IV. TWO-LAYER WALL WITH FREE SPACE IN BETWEEN As a first step in solving the non-homogeneous dielectric wall problem consider two-layer dielectric wall with free space in between as shown in Figure 3. Since it is cumbersome to solve the problem of getting insertion transfer function by following the same steps as done earlier in case of homogeneous wall, a move on calculating the electric & magnetic (E & H) fields at five different regions. The electric and magnetic fields in region-i can be written as Where, = = = ; = [ + ] [15] = [ - ] [16] = = 120 Free space wave impedance. V. TWO-LAYER WALL WITHOUT FREE SPACE IN BETWEEN The relation between incident and transmitted electric field (transmitted through two layers) can easily be found by following the sequence of steps as in section. Fig 3: Pictorial representation of two layer wall with free space in between. Fig 4: Pictorial representation of three layer wall without free Space in between 187

5 VI. THREE-LAYER WALL WITHOUT FREE SPACE IN BETWEEN Following the same steps as in section VI to obtain the relationship between the incident and transmitted fields is obtained. The electric and magnetic field expressions in region-i, region-ii & region-iii are same as that of Eq. 15 to Eq. 16 and Eq. 17 to Eq.18. The fields in region IV is given by = [ + ] [17] = [ - ] [18] Where = and = Fig 5: Pictorial representation of three layer wall without free space in between. In region-v Fig 6: Pictorial representation of N - layer wall 188

6 VII. GENERALIZATION FOR N LAYER WALL Now it is at the verge of generalizing the transfer function to N layered wall. Here the knowledge of section IV, V, VI and VII is used. Recalling the expression that relates the incident and transmitted fields in homogeneous, two-layered with and without free space and three layered walls. The expressions are rewritten here for simplicity of understanding. VIII. CONCLUSION In order to get the understanding on the effect of wall at different frequencies, the magnitude and phase spectrum is plotted. The material composition of the wall cannot be determined directly but can be [8] estimated based on the attenuation of the signal. The frequency response of the homogeneous wall with zero conductivity is shown in Figure 7. Before drawing some observations on the frequency response of homogeneous wall it is noteworthy to have a glance on good channel frequency response. For distortion less transmission the magnitude response should be constant and the phase should vary linearly with negative slope and pass through [7] the origin within the operating frequency range. Ideally it is not possible to achieve this but practically this can be satisfied approximately by permitting a certain amount of linear distortion. Amplitude and phase distortion are two different distortions that usually occur in the Channel. Sometimes the amplitude response is not constant inside the frequency band of interest, i.e. the frequency components of the input signal are transmitted with different amounts of attenuation. This effect is called [1] amplitude distortion. If each frequency component of input signal has different delays when it propagates through the channel the output signal has a different waveform compared to the input. This is called phase or delay distortion. Fig 7: Frequency response of homogeneous wall with epsr=4.44, sigma=0 and different widths. It can be intuitively noted from Figure7 that the magnitude response of the homogeneous wall reaches to -10 db at 1.84 GHz for d=0.125m. After that the fall off is an exponential decay. A-48.9 db magnitude is observed at 10 GHz which indicates that the signal is reduced by a factor of 105 with the same wall width. This high frequency reduction in magnitude is because of the interaction of dipoles with each other while it tries to orient according to the applied field. For different wall widths the magnitude and phase plots are compared with zero conductivity. As the width of the wall increases the magnitude plots also have major reduction because the wave has to travel more time in the wall. The phase plot is not up to the requirement. It has an exponential decay (for d=0.125m) till GHz (with small decay factor) and between 1.09 GHz and 3.23 GHz (with large decay factor). After this the phase varies linearly with negative slope (minimizes the phase distortion) at different band of frequencies. As the width of the wall increases [3] the repetitive nature of the phase spectrum occurs even earlier and starts at 0.54 GHz for d=0.25m. If it is assumed that the linearity of phase between certain frequencies (ex: GHz; d=0.125) Multi-band OFDM signals are suitable for the reduction of this phase distortion. By choosing proper orthogonal carrier frequency one can achieve this. The frequency spectrum for homogeneous wall with width d=0.125m and for different conductivities is shown in Figure

7 As the value of conductivity increases the flatness of the magnitude spectrum does not persist and the variation can be observed in the figure. This exists only up to certain frequencies and after that the curves almost merge together indicating the less effect at high frequencies. One can observe the diminution of magnitude spectrum with increase in conductivity. The phase [4] plot shifts to right and the unevenness increases as the conductivity increases, but still the repetitive nature of phase plot continues. Fig 8 : Frequency response of homogeneous wall with epsr = 4.44, d = 0.125m and different conductivities Following the insertion transfer function that is derived in sections3.4 and 3.5 for two-layered wall with and without free space in between, the frequency spectrum is plotted for different cases and is shown in Figure 9. The two layers of wall are made of brick with ε r =4.44 and thickness 0.125m. The free space in between the layers is of thickness 0.125m. By reducing the free space between the layers to zero it is considered as homogeneous wall with twice the width. The first two curves indicate the two layered wall with and without free space in between. Even though there is no much variation in the magnitude spectrum there exists a slight variation in phase plot indicating the possibility of phase distortion at lower frequencies. The repetitive nature of phase spectrum continues in either case at higher frequencies. As a third case [2] the second layer permittivity is doubled with no space in between the layers which intuitively shows the reduction in magnitude spectrum. This is very significant at high frequencies and is augmented by db at 10 GHz frequency. Fourth and fifth are similar to third case but the conductivity of the wall is varied. This obviously leads to the conductivity loss and the same is shown in figure. In addition the phase distortion also tries to dominate because of the irregular variation of the phase plot. Fig 9: Frequency response of two layered wall for different cases 190

8 Fig 10: Frequency response of a room with front and back wall A special case of Figure 9 is shown in Figure 10. With conductivity of 1 Siemens/m of two walls and separation of 5m between the walls (considering a room of 5m width) the spectrum is plotted. It is observed from the previous results and Figure 10 that the free space between the layers increases the delay distortion and has major effect on different frequencies. This can also be extended to multiple rooms case to analyze the effect at different frequencies. Fig.11: Frequency response for N=3, 4, 9 layered walls By increasing the number of layers to 3, 4 and 9 the magnitude and phase spectrum is shown in Figure11. For each case the width of the layer is fixed and is considered as 0.125m and the conductivity is also assumed to be zero. The relative permittivity for three-layered wall is(4, 8, 12), four-layered wall case (4, 8, 12, 16) and for nine-layered wall case the permittivity s are (2, 4, 6, 8, 10, 8, 6, 4, 2). It is apparent that the attenuation increases and the repetitive nature of phase spectrum occur earlier with increase in the number of layers. The attenuation at 10 GHz for 3, 4, and 9 layered walls are respectively given as db, -281 db and db respectively and the repetitive nature of phase plot starts at 0.23 GHz, GHz and GHz for 3, 4 and 9 layer walls respectively. This Paper addresses the mathematical model for the wall structure. Since wall is usually a non-homogeneous entity, a novel approach for calculating wall transfer function for multi-layered wall is proposed. Simulation results for multi-layered walls with various cases are analyzed. On the whole it is observed that as the width of the wall increases and if the number of [5] layers of the wall is more the magnitude spectrum sees rapid decay whereas some nonlinearity is observed in the phase spectrum. By increasing the free space between the layers of a wall the phase distortion predominates compared to the magnitude response. Multi-layered transfer function can be extended to any number of layers and has a very good usage in real-time application for selecting the proper band of frequencies for through-wall-imaging application. 191

9 REFERENCES [1] C. A. Balanis, Antenna Theory - Analysis & Design, U. S. A: John Wiley & Sons, Inc, [2] Alain. Gauge, Chrustophe, Jean-Marc. Ogier. Ondrej Sisma,"UWB Radar: Vision through a Wall," Telecommunication Systems, vol. 38, pp , [3] J. David. D. Ferris and N. C. Currie, "A Survey of Current Technologies for Through-the-wall Surveillance (TWS)," SPIE, vol. 3577, pp , [4] C.A.Balanis Advanced Engineering Electromagnetic, Canada: John Wiley & Sons, Inc, [5] Signal Processing Analysis of UWB Radar used in TWI. [6] Keith.G.Balmain, Edward C. Jordan, Electromagnetic Waves and Radiating Systems, New Delhi: Prentice Hall of India, [7] Oral. Buyukozturk. Dr and Hong. C. Rhim, "Radar Imaging of Concrete Specimens for Non-Destructive Testing," Construction and Building Materials, Elsevier, vol. 11, no. 3, pp , [8] F.Nekoogar, Ultra-Wideband Communications: Fundamentals and Applications, Prentice Hall, [9] A. Muqaibel and A. Safaai-Jazi, "Characterization of wall dispersive and attenuative effects on UWB radar signals," Journal of the Franklin Institute, Elsevier, vol. 345, pp , AUTHOR BIOGRAPHY Research Scholar in Department of Electronics and Communications Engineering, Shri Venkateshwara University, Gajraula, Amorha, Uttarpradesh, India. G.Balaji working as a Asst.prof in ECE department of Sai spurthi institute of technology.b.gangaram, sathupalli, khammam (dt), telangana..he has teaching experience of 8 years. He is one of the research members of R&D department and his research area is communications.he is one of the member of ISTE. 192