Rf Propagation

RF Propagation in Short Range Sensor Communications Mark Dapper, Jeffrey S. Wells, Tony Schwallie, and Leak Huon L-3 Nova Engineering, Inc. 5 Circle Freeway Drive, Cincinnati, Ohio 45246 ABSTRACT Short-range RF propagation models with antenna elements placed at or near the earth’s surface often fail to accurately predict path loss. Adequate mathematical models can be developed and validated to ensure deployed communication systems maintain link closure. Specifically, Unattended Ground Sensor (UGS) systems are deployed to be physically undetected, that is, the units are frequently buried with the antenna extended above earth’s surface. This paper reviews the physical effects that determine propagation loss and synthesizes a mathematical model to predict this loss. These predictions are compared to real world propagation measurements in both open fields and in dense foliage for ranges up to 500m. Keywords: RF Propagation, Sensor Communications, VHF/UHF Communications, Antennas at Ground, UGS, Unattended Ground Sensor, AUMSS, PEWD, TRSS, REMBASS

1. INTRODUCTION The prediction of path loss is very important for specifying the performance and planning the deployment of communications devices. Even at close range, the path loss can be considerable as the waveform is absorbed in vegetation, trees, and other obstacles. Unattended Ground Sensor systems typically have their antenna element located at or near ground and are deployed over various terrains from smooth hills, plains, dense foliage, as well as a myriad of other physical attenuating factors along the RF propagation path. Some of these sensor systems include the U.S. Army’s REMBASS, U.S. Army’s AUMSS, U.S. Army’s PEWD, U.S. Air Force’s TASS, and the U.S. Marine Corp’s TRSS. All these systems are deployed in a similar manner; that is, they are either hand emplaced or air delivered and are utilized to detect and analyze enemy troop movement without risk to human life. Understanding the RF propagation characteristics associated with deploying these devices is key in establishing mission objectives and maintaining link closure.

Figure 1: Tactical Remote Sensor System (TRSS) Repeater/Relay

Several models exist by which to simulate the propagation, differing in their capability and range of application. This paper targets propagation modeling at ranges of less than 500 meters with antennas mounted on the ground where other

models, such as the Longley - Rice model fall short. (The Longley – Rice model is accurate at ranges 1km – 2000km and at antenna heights >0.5 meters). This paper provides a mathematical model of propagation over a plane reflecting surface and adds a mathematical model of foliage loss to obtain a predictable loss associated with the terrain of which the unit is fielded. This model is then compared to field test data to empirically validate the mathematical model. The paper will begin by establishing the reference and background information inclusive of free space path loss, propagation near the ground, terrain loss, and foliage loss. After completion of the simulated studies, the paper will discuss field test results.

2. FREE SPACE PATH LOSS We begin with the standard equation for propagation in free space2 . Although free space propagation is rarely encountered, it provides a basic insight into RF propagation and establishes the lower bound for path loss. Path loss is given by 2

⎤ ⎡ c Pr = G tx ∗ G rx ∗ ⎢ ⎥ . Pt ⎣ 4 ∗π ∗ f ∗ d ⎦

(1)

The free space path loss, Lf, can be expressed in decibels as L f = 10 log G tx + 10 log G rx − 20 log f − 20 log d + k ,

where

(2)

f = frequency (Hz) Gtx= transmitter antenna gain (linear) Grx= RX Antenna Gain (linear), d = distance (meters), and k = 147.6 = 20*log(c/4/Π)

-30 TX and RX Antenna Gains = 0dBi -40

-50

-60 450 MHz -70

-80

300 MHz 153 MHz 100 MHz

-90

-100

-110 1 10

10

2

10

3

Distance in Meters

Figure 2: Free Space Path Loss as a Function of Distance

10

4

Free space propagation follow an inverse square law with distance, that is, the received power is reduced by 6 dB when the range is doubled.

3. PROPAGATION OVER A REFLECTING SURFACE Figure 3 depicts a simple two ray model for propagation over a flat surface. The signal at the receiver is the vector sum of the direct and reflected rays. The amplitude and phase of the reflected waves propagating over ground varies with point of reflection, ground constants such as dielectric constant and conductivity, and polarization2 . To compute the effective transmission of the reflected wave we compute the complex reflection coefficient.

Figure 3: Propagation over Reflecting Surface

The reflection coefficient ρ can be calculated as a function of the angle of incidence ψ, as

ρ=

(ε r − jx )sinψ − (ε r − jx )cos2ψ (ε r − jx )sinψ + (ε r − jx )cos2ψ

(3)

where 18 ∗ 109 ∗ σ , f

(4)

ψ = tan −1 ( htx ) ,

(5)

x=

d tx

htx = height of transmitting antenna (meters) dtx = distance to the angle of incidence , and σ = Conductivity (Siemens).

The dielectric constants and conductivity vary with respect to the attributes of the earth. Typical values for each of these are shown in Table 1. Table 1. Dielectric constant and conductivity

Sea Water

σ (siemens)

εr

5

81 -2

Fresh Water

1 x 10

Good Ground (wet)

2 x 10-2

25-30

Average Ground

5 x 10-3

15

-3

4-7

Poor Ground (dry)

1 x 10

81

-0.94 Frequency 153 MHz epsilon r = dielectric constant -0.95

sigma = conductivity (siemens) epsilon = 27, sigma = .02, (good ground) r

-0.96 epsilon r = 15, sigma = .005, (average ground) -0.97

epsilon r = 5, sigma = .001, (poor ground)

-0.98

-0.99

-1 0.1

0.2

0.3

0.4 0.5 0.6 0.7 Antenna Height (meters)

0.8

0.9

1

Figure 4: Magnitude of the Reflection Coefficient for Smooth Earth

Figure 4 demonstrates that for scenarios of practical interest, the magnitude of the reflection coefficient is close to unity. Furthermore, the angle of the reflection coefficient for small grazing angles is close to 180 degrees. This results in nearcancellation of the direct and reflected rays and gives rise to the characteristic inverse R4 variation of path loss with distance for antennas close to ground. The total received field strength, E, associated with the radio waves propagating and reflecting on the earth’s surface is given by

2⎫ ⎧ ⎡ c ⎤ ⎪ ⎧ 2π ⎪ ⎫ E = ⎨G tx G rx ⎢ ⎬ • ⎨1 + ρ exp(1 − j ( ∆R )⎬ ⎥ λ ⎭ ⎣ 4πfd ⎦ ⎪⎭ ⎩ ⎪⎩ where

∆R =

2 ∗ ht '∗hr ' d

,

,

(6)‡

(7)

d = distance (meters), ht’= TX antenna height above the earth’s tangent plane through the point of reflection (m), hr’= RX antenna height above the earth’s tangent plane through the point of reflection (m), Grx= RX Antenna Gain (linear), Gtx= TX Antenna Gain (linear), ρ = Earth Reflection Coefficient (Vertical), λ = wavelength in meters. If we examine (6) we see that it consists of two terms that modify the natural inverse R2 characteristic. The first term represents the direct ray, and the second term, a complex exponential modified by the reflection coefficient.

‡

See Reference (2).

By converting [6] to logarithmic form we can calculate the propagation loss associated with transmitting along a reflecting surface such as those applications where antenna elements are very near ground as shown in Figure 5. As illustrated in Figure 5, the propagation loss follows an inverse fourth power law (12 dB for each distance doubled) with range rather than the inverse square low of free space. Propagation over Earth (Reflecting) -40 RX and TX Antenna height = 0.25 meters Dielectric Constant = 13 Conductivity = 0.012 siemens

-60

-80 100 MHz 153 MHz Total Path Loss (dB)

-100

300 MHz 450 MHz

-120

-140

-160

-180 1 10

2

3

10

4

10

10

Distance in Meters

Figure 5. Propagation Loss for Transmission Over a Reflecting Surface (earth)

Figure 6 demonstrates the variation of path loss with antenna height at 150 MHz. From [6] we see that increasing antenna height effectively applies a rotation of the reflected ray relative to the direct ray which reduces the magnitude of the cancellation of the direct and reflected rays. This effect can be quite dramatic, for example, as much as 12 dB at 150 MHz as the antennas are moved from ground level to an elevation of 0.7 meters. Propagation Over A Plane Reflecting Surface -20 RX and TX Antenna Heights are Equal -40 -60

ht=0.7 meters ht=0.5 meters

Total Path Loss (dB)

-80

ht=0.25 meters ht=0.1 meters

-100 -120

-140 -160

-180 1 10

10

2

10

3

Distance in meters

Figure 6. Propagation Near Ground as Antenna Height Varies

10

4

4. SHORT RANGE FOLIAGE LOSS Loss of the waveform via absorption by trees and vegetation can be substantial. This loss should be accounted for in deploying communications systems. The loss is mathematically added to the previously calculated losses (propagation over ground) to determine the overall expected path loss. It is common to call this additional loss the foliage factor.

Figure 7. Propagation in Foliage

As described in Weissberger3, the following equation may be applied when the propagation rays are blocked by dense and leafy trees. For ranges from 14 to 400 meters the foliage loss in decibels can be modeled as 0.284 )(d 0.588) , L f = 1.33( f f

(8)

and for ranges less than 14 meters 0.284 )(d f ) L f = 0.45( f

(9)

where df is the distance through the foliage (meters), and f is frequency in GHz. It should be noted that according to Weissberger3, the propagation loss between trees with leaves and trees without leaves (Summer/Winter) was 3 – 5 dB. A plot of propagation loss due to foliage is shown in Figure 8. 70

60

50 Foliage Loss (dB) 40 450 MHz 300 MHz 30 153 MHz 100 MHz 20

10

0 1 10

2

10 Distance in Meters

Figure 8. Loss Due to Foliage

10

3

The graph indicates that at a transmission frequency of 153 MHz an additional loss of approximately 22dB is predicted if the dense foliage exists at a depth of 300 meters. When the height of the canopy is less than the distance between transmitting and receiving antennas, propagation is dominated by diffraction over the top of the canopy. For this reason, excess foliage losses greater than 20 to 30 dB are not commonly found in practice.

5. PROPAGATION OVER TERRAIN OBSTACLES Terrain obstacles are responsible for additional path loss. When direct line-of-sight is obstructed, or nearly obstructed, propagation is largely influenced or dominated by the process know as diffraction. Diffraction results in an apparent lossy bending of the wave around an obstruction into a shadowed area. Again, it should be pointed out that the model being generated is for close range communications where transmitter and receiver pairs are relatively local to one another (i.e. < 1000 meters). The terrain model we use here is based on the “knife-edge” model in which any obstruction is replaced with an absorbing plane normal to the direct path between the transmitter and receiver. Further, we take the maximum height of the obstacle within the terrain area that blocks the propagation rays and models them as a single obstruction with a height of (h), and calculate a diffraction parameter know as the Fresnel-Kirchoff diffraction parameter [2] using the distances of the receiver (d1) and transmitter (d2) from the terrain obstruction. The concept is similar to the Bullington model in that the terrain is replaced by a single equivalent point of intersection from the transmit and receiver terminals. This geometry is depicted in the following figure:

Knif

e-Ed

iffr ac ge D

tion

h RX

TX

d1

d2

Figure 9: Diffraction model using ‘knife-edge’ approach

The Fresnel-Kirchoff diffraction parameter, ν, is calculated using the following equation† υ=h

2( d 1 + d 2 )

λ d1 d 2

(10)

where d1 and d2 are the distances from the obstacle to the transmitter and the receiver in meters, and h is the height of the obstacle in meters. A plot of the diffraction parameter vs. height of the terrain obstacle is shown in Figure 10. The graph is plotted for transmitter and receiver located 150 meters away from the obstacle (300 meters total propagation distance). For example, an obstacle in the propagation path of a 153 MHz ray at a height of 15 meters corresponds to a diffraction parameter of 1.8.

†

The Fresnel-Kirchoff Equation is derived in reference 2 (pages 37-39).

5 4.5 4 300 MHz 3.5 153 MHz 3

Diffraction Parameter

100 MHz 2.5 2 1.5 1 0.5 0

0

5

10 15 20 Terrain Height (meters)

25

30

Figure 10. Diffraction Parameter as a Function of Obstacle Height (d1 = d2 = 150 meters)

The path loss can now be computed as a function of the Fresnel diffraction parameter. The following equation, derived from reference 2 (page 42), expresses the path loss Ldiff as a function of the diffraction parameter ν.

[

(1+ j) 1 − j1 −(C (v )− jS (v ))] 2 2

Ldiff =20log10 2

(11)

5

0

-5 Excess Path Loss (dB) -10

-15

-20

-25 -3

-2

-1 0 1 Fresnel-Kirchoff Diffraction Parameter

2

Figure 11. Path Loss vs. Diffraction Parameter

3

The loss associated with a diffraction parameter of 1.8 (using the result from the previous example (153 MHz, 15 meters, TX and RX 150 meters)) yields and additional path loss of approximately 18 dB. If the diffraction parameter were 1.0 then the loss would be 13.5 dB.

6. PUTTING THE MODEL TOGETHER Thus far we have calculated the propagation loss associated with surface earth with reflecting waves (Lp), foliage loss (Lf), terrain using knife edge approach (Ldiff). Summing these losses together then represent the short range path loss with antenna near ground. Thus, (12)

Ltotal = Lp + Lf + Ldiff That is for a range greater than 14 meters, range > 14 meters, L total = {10 log G tx + 10 log G rx + 20 log h rx + 20 log h tx − 40 log d } 0.284 0.588 )( d f )} + {1.33( f 1 (1 + j) 1 [ − j − (C ( v ) − jS ( v ))]} + 20 log { 10 2 2 2

(13)

Given the following scenario, we can predict path loss as a function of antenna height for these various parameters: • Frequency of operation = 153 MHz • TX and RX distance = 100 - 700 meters • Foliage and Trees for a depth of 100 meters • Terrain Roughness or obstacle of 10 meters • RX and TX distance is symmetrical to obstacle • RX and TX antenna gain = -0 dBi The following graph utilizes [13] to plot path loss as a function of antenna height. RF Propagation Model for Short Range Sensor Comms -100

100 meters of dense foliage 153 MHz, Terrain Height Obstacle 10 meters -105 Dielectric Constant of Surface 15 (Average Soil) Conductivity .005 Siemens (Average Soil) -110 Antenna Gains 0 dBi (TX and RX) -115 100 meters Total Path Loss -120 (dB) -125 200 meters 300 meters -130 400 meters

-135

500 meters -140

600 meters 700 meters

-145 -150 -1 10

10 Antenna Height (meters)

Figure 12. Path Loss Prediction for Composite Model

0

It is important to understand the limitations of this additive model if one is to apply it successfully. For instance, if an obstruction large with respect to the distance between transmitter and receiver, propagation may be dominated by shadowing (diffraction) with free-space propagation to and from the diffraction object propagation. Fortunately, for many common situations the additive loss model produces reasonable path loss estimates.

7. FIELD TESTING – ACTUAL RESULTS To validate the analytical predictions, we have conducted a series of experiments with representative sensor data radios. One series of tests is summarized in figure 13. For these series of tests we measured the link margin for a 100 mW, 1200 bits/sec sensor radio link as a function of distance at 150 MHz. The antennas were quarter wave monopoles (approximately 0.5 meters) placed on the surface. For the purpose of this test we defined link margin as the amount of power required to close the link in excess of that required to maintain a BER of 10-4 . This corresponds to a receiver power level of approximately –110 dBm for the particularly equipment used in this test. We note substantial variability from location to location, as one might expect, although a general inverse R4 characteristic is apparent. The model developed previously predicts a loss of approximately 80 dB for the various configurations at a range of 100 meters. The data shows an actual path loss equal to +20 dBm (power output) – (-110 dBm, receiver sensitivity) – 55 dB (margin) = 75 dB, in close agreement with the prediction. 80.00 70.00 60.00

margin (dB)

flat grassy plain 50.00 flat plain with dry foliage 40.00

low intervening hill without foliage inverse R^4

30.00 20.00 10.00 0.00 0

200

400

600

800

range (meters)

Figure 13: Link Margin for a 100 mW data radio as a function of range

A second test has been conducted with dense semi-tropical foliage between a transmitter and receiver spaced by 300 meters, buried in the ground with quarter wave monopole antennas extended above ground (see Figure 14). This test was conducted at 9600 bits/sec with a 100 mW transmitter. Test results show that there is essentially no link margin at 300 meters, corresponding to a path loss of approximately 120 dB. This compares favorably to the path loss predicted in Figure 12.

Figure 14: Foliage Environment for Propagation Test

8. CONCLUSION This paper has developed a model for RF propagation with link ranges < 500 meters, VHF/UHF, and antenna elements that are placed near the ground. We have further shown that model predictions are in reasonable agreement with experimental results, for several scenarios. More data must be collected to fine tune this model and extend its application to higher frequencies and longer ranges.

9. REFERENCES [1] [2] [3] [4] [5]

Bertoni, Radio Propagation for Modern Wireless Systems, Prentice Hall, Upper Saddle Rive, New Jersey, 2000. Parsons, The Mobile Radio Propagation Channel, Halted Press – Wiley and Sons, New York, 1992 Weissberger, An Initial Critical Summary of Models for Predicting the Attenuation of Radio Waves by Trees, ESD-TR-81-101, EMC Analysis Center, Annapolis, MD, 1982 Boithias, Radiowave Propagation, McGraw-Hill, 1987 Vizmuller, RF Design Guide – Systems, Circuits, and Equations, Artech House, Norwood, MA, 1995

This material is in the public domain and may be reprinted without permission; citation of this source is appreciated. This white paper has been released into the public domain in accordance with International Traffic in Arms Regulations (ITAR) 22 CFR 120.11(a)(6). Copyright ©2007 L-3 Nova Engineering, Inc.

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