A Mode Based Model for Radio Wave Propagation in Storm Drain Pipes

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1 PIERS ONLINE, VOL. 4, NO. 6, A Mode Based Model for Radio Wave Propagation in Storm Drain Pipes Ivan Howitt, Safeer Khan, and Jumanah Khan Department of Electrical and Computer Engineering The University of North Carolina at Charlotte, Charlotte, NC 83, USA Abstract In this paper, we analyze the behavior of Storm Drain Pipes (SDPs) as multimode leaky waveguides for radio wave transmissions between.4.5 GHz within the Industrial, Scientific and Medical (ISM) band. The previous research on analyzing RF propagation inside underground structures focused on auto, railroad, subway, mine and sewer tunnels of diameters greater than 1.05 m. Our research provides a novel contribution by characterizing RF propagation inside narrow SDPs of diameter as low as 0.30 m. Understanding the behavior of SDPs as communication channels is not only important for designing portable military communication equipment, but also for other civil applications. We study the modal content of propagating waves and derive a mode based model (MBM) for predicting the received power. Empirical data gathered at selected sites in Charlotte, North Carolina is used to validate the MBM. Based on analysis of nonlinear curve fitting through the measured data, close agreement is found between the predicted and measured power. We also highlight the requirement of further work to improve the fitting of measured data with the predicted results. 1. INTRODUCTION In this paper, we present an analytical model for characterizing RF propagation in SDPs. The model provides an estimate of the received power at some distance d from the source and also provides an estimate for the contribution of propagating modes to the received power. Historically, research and experimentation into RF propagation through underground structures has examined ultra high frequency (UHF) propagation through coal mines for addressing communication needs of the coal mining industry [1]. Demands of mobile communications expanded research into RF propagation in railroad, auto and subway tunnels []. Holloway, et al. in [3] have numerically evaluated the frequency dependence of attenuation for various modes in underground, lossy wireless communication channels such as mines, tunnels, boreholes and shafts. This area was further investigated by Dudley [4]. He studied models for propagation in circular tunnels using excitation from a circular magnetic or circular current loop. In [5], he proposed a parsimonious model for field intensity in a tunnel as a function of axial distance. Multimode waveguide behavior of heating, ventilation and air conditioning (HVAC) ducts is proposed for high data rate wireless networks [6] and provided insight into developing the model presented in this paper. To date there is limited research into propagation issues associated with networked pipes such as storm drain pipes (SDPs). The closest parallel to such work is testing done for inspecting, repairing and cleaning of water reclamation tunnels [7]. Also, in 006, Kjeldsen, et al. conducted experiments on RF propagation through concrete tunnels at Military Operations and Urban Terrain (MOUT) facility at Camp Lejuene, NC []. Their aim was to conduct path loss measurements in order to gain better comprehension of critical propagation factors for designing an effective communication system for military operations in subterranean cavities. Our work focuses on understanding RF propagation inside concrete SDPs of diameters 1.37 m, 1.06 m, 0.76 m, 0.61 m, 0.46 m and 0.30 m. The aim is to formulate a reliable propagation model that can be used to predict received power at distance d from the source. We, therefore, propose a mode based model (MBM) for radio wave propagation inside SDPs and carry out experimental measurements at selected locations in Charlotte, North Carolina. We use the results from the measurement campaign to validate the MBM.. PROPOSED MODEL For RF propagation through lossy circular waveguides, the electromagnetic modes generated at the transmitter have varying levels of contribution to the transmitted signal [3]. Evanescent or

2 PIERS ONLINE, VOL. 4, NO. 6, stationary modes have exponential attenuation and suffer a rapid decay whereas propagating modes are the main source of power transfer from transmitter to the receiver. It is, therefore, of interest to understand properties of propagating modes. For modal analysis of electromagnetic wave propagation in circular waveguides, propagation constant, γ, is complex given by α + jβ, where α represents modal attenuation constant and β is phase constant for a particular mode. Phase constant is defined in [8] as β n = πf c 1 ( ) fc (1) f where f c is cut-off frequency for mode n. For cylindrical waveguides, the modal cut-off frequency is f c = cg () πa where c is velocity of light, a is the waveguide radius and g = p nm is the mth zero of the Bessel function J n (x) for Transverse Magnetic (TM) modes, and g = p nm is the mth zero of the Bessel function derivative J n(x) for Transverse Electric (TE) modes. The attenuation coefficient α n is dependent upon the cut-off frequency for a particular mode. The attenuation coefficient is given by BR s α n = ( ) (3) η 0 a 1 fc f where B = 1 for TM Modes and B = (f c /f) + (n /(p nm n )) for TE Modes; η 0 is the intrinsic impedance of free space and is equal to 10π when the medium inside the waveguide is air; R s is the real part of the intrinsic impedance of the waveguide walls given by R s = µ 0 πf/σ, where µ 0 is the permeability of air, i.e., 4π 10 7 H/m, and σ is the conductivity. The RF propagation model for HVAC proposed in [6] defines the total received power at distance d from the source, P R (d), as the sum of powers excited in propagating modes, i.e., P R (d) = N p n e αnd (4) n=1 where p n represents the power excited by the transmitting antenna in mode n. The value of p n is dependent upon the current distribution inside the source antenna and the impedance of the antenna. The model in (4) is based on modeling RF propagation through a galvanized steel duct and therefore assumes a lossless waveguide. The concrete SDPs can be modeled based on a lossy waveguide model, similar to circular underground concrete tunnels [5]. Therefore, the form of the SDP model is the same as (4) where the received RF signal power in the SDP is based on the summation of powers contained in each mode. The power contained in the nth mode is where the voltage amplitude A n can be expressed as P n = 1 A n (5) A n = A CLn e αnd (6) where α n is expressed in Nepers/m (Np/m) and A CLn is the coupling factor. Combining (5) and (6), the MBM can be expressed as P R (d) = N P n = 1 n=1 N A CL n e αnd (7) where P R (d) is in Watts. To analyze the MBM, the modal cutoff frequencies and the attenuation coefficients are computed using () and (3). Values are provided in Table 1 based on a.5 GHz operating frequency and for n=1

3 PIERS ONLINE, VOL. 4, NO. 6, various SDPs diameters. In evaluating these values the following constants were used: concrete permeability 4π 10 7 H/m; concrete conductivity, σ, 0.06 S/m; and the dielectric constant, κ, 4.5 [9]. In the next section a 1.07 m diameter SDP is chosen to illustrate the utility of the MBM. From Table 1, 196 modes are excited in the 1.07 m diameter SDP and in Table the modal attenuation constants for the ten lowest attenuation constants are provided in rank order from lowest to highest. Table 1: Modal analysis of SDPs as a function of pipe diameter. Number of modes Diameter Lowest cut-off Minimum Attenuation TE+TM modes (m) frequency (MHz) (TE 01 ) (db/m) at f=.5 GHz Table : Modal attenuation constants for 1.07 m diameter SDP at.5 GHz. Mode Attenuation Cut-off Constant (db/m) Frequency (GHz) TE TE TE TE TE TE TE TE TE TE EMPIRICAL MEASUREMENTS AND MODEL VALIDATION For the empirical measurements, an Agilent CSA Spectrum Analyzer N1996A-506 was used to measure the received power and an Agilent E448C analog signal generator was used as the signal source. Two GigaAnt dipole antennas with a nominal gain of dbi were used. The equipment set up used in the measurement campaign is illustrated in Figure 1. A CW signal at 0 dbm was generated between.4.5 GHz at 10 MHz steps. Coaxial cables were used to connect antennas to the transmitter and receiver. At each measurement location the received power was recorded at the eleven points over the frequency range and the mean and standard deviations were evaluated based on the eleven measurements. The measured data for the 1.07 m SDP is given in Table 3. To evaluate the MBM based on (7), the coupling loss parameter A CL n was estimated for all modes to be evaluated in the sum. This provides the mechanism by which we can gain insight into the possible modes present in the received power solution. By

PIERS ONLINE, VOL. 4, NO. 6, 008 638 Figure 1: Equipment setup.

the empirical data provides this insight.

procedure: (1) Modal cutoff frequencies and attenuation coefficients were computed as given in

(3) The parameters A CLn were estimated based on best fit coefficients for the MBM to minimize the

The values for P R (d) were estimated based on (7) using the coefficients obtained for A CLn.

The mean errors between the estimated and measured values are given in Table 4.

Table 3: Measured received power data for 1.07 m diameter SDP.

14 33.77 3.5 17.6 41.86.8 0.4 47.13 4.40 8.48 40.4 1.

4 PIERS ONLINE, VOL. 4, NO. 6, Figure 1: Equipment setup. varying the number of modes used in evaluating (7) and accessing the quality of the curve fit to the empirical data provides this insight. To achieve this, we employed a nonlinear least square curve fitting algorithm using the following procedure: (1) Modal cutoff frequencies and attenuation coefficients were computed as given in Table. () Analysis was based on 1,, 3, 5 and 7 modes with the lowest attenuations. (3) The parameters A CLn were estimated based on best fit coefficients for the MBM to minimize the error between the measured and the MBM model. The values for P R (d) were estimated based on (7) using the coefficients obtained for A CLn. The measured and estimated values of the received powers are plotted in Figure. The mean errors between the estimated and measured values are given in Table 4. From Figure we can observe the impact of varying the number of modes in evaluating P R (d). Table 3: Measured received power data for 1.07 m diameter SDP. Distance (m) Mean Power (dbm) Standard. Deviation (db) Table 4: Estimated power and mean error in evaluating the MBM received power. Estimated Powers Modes (dbm) Distance (m) Mean Error (db) 1 Mode Modes Modes Modes Modes

5 PIERS ONLINE, VOL. 4, NO. 6, If only mode 1 is considered, then the estimated power does not fit the measured received power and the error is relatively large. Note mode 1 is the dominant mode due to its lowest attenuation constant of 0.33 db/m. In contrast, when, 3, 5 and 7 modes are considered, the estimated power plot fits well to the measured power plot. Received Power(dBm) Measured Power -40 Mode =1 Modes= -45 Modes=3 Modes=5 Modes= Distance in meters Figure : Measured and estimated received power for 1.07 m diameter SDP for 1,, 3, 5 and 7 modes. Power(dBm) A CL1 A CL Distance in meters A CL3 Combined Estimated Power Measured Power Figure 3: Contribution of modal coefficients in total received power using 3 modes. To further elaborate this aspect, we have analyzed the individual contribution of each coefficient to the received power considering the 3 mode case. In Figure 3, individual graphs are provided indicating the contribution from each mode based on its estimated coupling loss coefficient. From the graphs, it is clear that A CL contributes very little to the overall received power. Nearly equal contribution comes from A CL 1 and A CL 3. The contribution from these two coefficients results in the overall estimated power. The above discussion indicates that the received power at distance d from the source can be specified by evaluating and combining the powers contained in individual modes. By evaluating the individual contributions of each mode, insight can be gained on the relative strength of the modes likely to contribute to the received power within the SDP. 4. CONCLUSION In this paper, we have proposed a mode based model to evaluate received power at distance d within the SDP. We undertook a measurement campaign to validate the MBM with empirical data. Our results indicate that evaluation of received power as sum of power contributions from propagating modes provides a good estimate of the actual measured power. The fitting of estimated data with the measured results can be further improved if the accuracy of measurements and size of the observations are increased. Also precise measurement of electrical conductivity values for SDP material can enable accurate evaluation of modal attenuation that can further improve the received power estimate. Within these limitations, we have found that the proposed model is a good approximation for estimating the received power at a particular distance in the SDP and provides insight into the modal content of the propagating signal. REFERENCES 1. Emslie, A., R. Lagace, and P. Strong, Theory of the propagation of UHF radio waves in coal mine tunnels, IEEE Trans. Antennas and Propag., Vol. 3, No., 19 05, March Kjeldsen, E. and M. Hopkins, An experimental look at RF propagation in narrow tunnels, Proc. IEEE Military Communications Conf. (MILCOM06), Washington D.C., October 3 5, Holloway, C. L., D. A. Hill, R. A. Dalke, and G. A. Hufford, Radio wave propagation characteristics in lossy circular waveguides such as tunnels, mine shafts, and boreholes, IEEE Trans. Antennas Propag., Vol. 48, No. 9, , September Dudley, D. G., Wireless propagation in circular tunnels, IEEE Trans. Antennas Propag., Vol. 53, No. 1, , January Dudley, D. G. and H. Y. Pao, Wireless propagation in circular tunnels, IEEE Trans. Antennas Propag., Vol. 53, No. 8, , August 005.

6 PIERS ONLINE, VOL. 4, NO. 6, Nikitin, P., D. D. Stancil, O. K. Tonguz, A. Cepni, A. Xhafa, and D. Brodtkorb, Propagation model for the HVAC duct as a communication channel, IEEE Trans. Antennas Propag., Vol. 51, , May DeHaan, J. and M. Jacobs, Tunnel communication test results, Project Notes , Hydroelectric Research and Technical Services Group, Bureau of Reclamation, U.S. Department of Interior, September Collin, R. E., Field Theory of Guided Wave, IEEE Press, New York, Ghuniem, A. M., Modes of electromagnetic wave propagation in circular concrete tunnels, Journal of Electromagnetic Waves and Applications, Vol. 19, No. 1, , 005.

A MODE BASED APPROACH FOR CHARACTERIZING RF PROPAGATION IN CONDUITS

Progress In Electromagnetics Research B, Vol. 20, 49 64, 2010 A MODE BASED APPROACH FOR CHARACTERIZING RF PROPAGATION IN CONDUITS I. L. Howitt and M. S. Khan Department of Electrical and Computer Engineering