American Journal of Biomedical Engineering
p-ISSN: 2163-1050 e-ISSN: 2163-1077
2016; 6(4): 95-114
doi:10.5923/j.ajbe.20160604.01

Mark E. Vickberg, Robert A. Sainati, Barry K. Gilbert
Special Purpose Processor Development Group, Department of Physiology and Biomedical Engineering, Mayo Clinic, Rochester, MN, USA
Correspondence to: Barry K. Gilbert, Special Purpose Processor Development Group, Department of Physiology and Biomedical Engineering, Mayo Clinic, Rochester, MN, USA.
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Copyright © 2016 Scientific & Academic Publishing. All Rights Reserved.
This work is licensed under the Creative Commons Attribution International License (CC BY). 
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This paper describes the technical tradeoffs that should be considered for the design of an on-body wireless link for physiological monitoring in an indoor environment. The desire to minimize the physical size of the on-body device, typically driven by comfort and aesthetic considerations, affects antenna performance to varying degrees, depending on the selected operating frequency of the wireless communications link. In addition, the complex indoor propagation environment also exerts a significant influence on communications system performance. An analytical analysis and simulation results exploring these topics are presented, followed by a design example and measurement results of an on-body device and gateway performance in a typical home environment.
Keywords: Body-worn unit, On-Body antenna, Indoor propagation, Biomedical electronics
Cite this paper: Mark E. Vickberg, Robert A. Sainati, Barry K. Gilbert, Design Considerations for Indoor Wireless Transmission between a Body-Worn Physiological Monitoring Device and a Gateway in a Home Environment, American Journal of Biomedical Engineering, Vol. 6 No. 4, 2016, pp. 95-114. doi: 10.5923/j.ajbe.20160604.01.
![]()  | Figure 1. Complete Radio Frequency Link from Patient at Home with Body Worn Health Monitoring Device to Monitoring Station Located in Medical Center with Three Long-Haul Link Options | 
. Antenna efficiency is defined as the ratio of the power radiated by the antenna to the total power input to the antenna, and can be expressed as the ratio of the antenna radiation resistance (Rr) to the total antenna resistance (Ra) where Ra includes the radiation resistance and ohmic (conductor) losses. The radiation resistance for an electrically short dipole can be expressed as [3]:
, Ω; where Δz is the dipole length, and λ is the free space wavelength.And the ohmic resistance ROhmic, for a circular cross section of wire with radius a and surface resistance RS is found by [3]:
, Ω; where RS is the surface resistance, a is the radius, µ is the permeability, and σ is the conductivity of the wire, and ω is the radian frequency.Combining these expressions gives the short dipole antenna efficiency as:
Figure 2 illustrates the resulting efficiency for an antenna made from copper, whose conductivity is σ = 5.7 X 107 (S/m), limited to a maximum length of 1.5”, and conductor radius of 0.007”. Clearly, the antenna efficiency at the lower end of the frequency range under consideration is quite poor, which in addition to constraining the communications range between the on-body device and the gateway, as well as degrading battery life, also results in a poor quality factor (Q) for the antenna. Note however that the lower Q may be advantageous since it may reduce the antennas sensitivity to impedance variations from interactions with the local environment (i.e. coupling to the body).![]()  | Figure 2. Antenna Efficiency for Copper Wire Short Dipole 1.5" (38 mm) Long and with 0.007” (0.2 mm) Radius | 
The estimated Q and usable bandwidth (bandwidth here is estimated as 1/Q) for an electrically small dipole operating in free space, using the dimensions from the efficiency example given above, is shown in Figure 3.![]()  | Figure 3. Short Dipole Antenna Q and Bandwidth for Copper Wire Antenna 1.5” (38 mm) Long and 0.007” radius | 
where the real part of γ, α, is the attenuation constant and β is the phase constant. The attenuation constant represents the losses and is given by [4]:
Where (μ) is the magnetic permeability, (ε) is the electric permittivity, and (σ) is the conductivity of the dielectric material.The magnitude of the electromagnetic wave that passes through the body may be determined from the number of skin depths 
 that the body represents for a given frequency, where:
Note that by definition, 
 is the depth at which the magnitude of the electric field is diminished by a factor of 1/e, resulting in a reduction of the original signal strength to approximately 37% of its original value. A plot of 
 over the frequency range of interest is shown in Figure 4, in which the average dielectric constant of the body is taken as that of water, which is approximately equal to 80, and an averaged conductivity of approximately 1 S/m, are assumed.![]()  | Figure 4. Skin Depth for a Dielectric Material Approximating a Torso with a Relative Dielectric Constant of 80 and a Conductivity of σ = 1 | 
![]()  | Figure 5. Vertical Dipole near a Perfectly Conducting Cylinder | 
where 
, Jn is the Bessel function of the first kind, and Hn is the Hankel function of the second kind.Using this expression, we calculated the radiation patterns over a frequency range from 300 MHz to 2.4 GHz, with a = 0.25 m (9.8”), and b = 0.2525 m (10”), where b is measured from the central axis of the cylinder, which places the antenna approximately 0.2” (5 mm) from the cylinder surface. The resulting radiation patterns are plotted in Figure 6. From the figure, the phi = 0 degree point represents radiation from the front of the body (assuming that the on-body device is located on the front of the torso) and the ± 180 ° values represent the radiation from the back. Note the pattern falloff to the sides and around the back, which increases as a function of frequency. Over the frequency range modeled, at 90 degrees from boresight, the pattern level falloff increases by 5.8 dB from the lowest to the highest frequency and at 180 degrees the falloff increases by 30 dB over the frequency range. Based on this analysis, the lowest possible frequency would be the best option if no other considerations are taken into account. Although not shown, a similar analysis of a horizontally oriented antenna yields a similar result. ![]()  | Figure 6. Radiation Pattern versus Frequency from a Vertical Dipole near a Perfectly Conducting Cylinder; (a = 0.25m, b = 0.2525m, θ = 90º) | 
![]()  | Figure 8. Simulated Directivity for 38 mm Diameter Vertically Polarized, Copper Dipole Antenna Placed at Various Distances from the Human Body | 
![]()  | Figure 9. Comparison of Simulated Front to Back Ratio for Vertically Polarized 1.5” (38 mm) Copper Dipole Antenna Placed at Various Distances in Front of the Human Body | 
![]()  | Figure 10. Comparison of Simulated Impedance Values for Vertically Polarized 1.5” (38 mm) Copper Dipole Antenna Placed at Various Distances in Front of the Human Body | 
where 
 is the power received, 
 is the power transmitted, 
 is the transmit antenna gain, 
 is the receive antenna gain, and λ is the free space wavelength. The variable dn represents the separation d between transmit and receive antennas, with the path loss exponent n [8] set equal to 2 for free space. Note that n for indoor propagation has been found to cover a range of values of approximately 1.8 to 4.8 [8], [10], [11] for various building types and constructions. Finally, L is the sum of the losses due to a variety of sources such as multipath and attenuation, as well as non-propagation dependent system losses. Note from the above that gain is more appropriate for system analysis than directivity, and is defined as the ratio of the radiation intensity to the power accepted by the antenna, and can be expressed as the antenna radiation efficiency times the directivity [9]. Setting the antenna gain to 1, which is a reasonable approximation given that an omnidirectional radiation pattern is desired, causes the antenna gain terms to drop out of the received power calculation. Rearranging the remaining terms, limiting loss components to only spreading of the electromagnetic wave and interactions in the propagating environment, the path loss (PL) can be expressed as:
Taking an average value of 3.3 for n, the path loss expected for three frequencies over distances of a typical residential house are plotted in Figure 11. Note that between the frequency extremes evaluated (300 MHz to 2450 MHz) there is a nearly constant 18 dB difference in path loss for the separation distances between the on-body device and gateway, as shown in the figure. In this case the lower frequency bound of 300 MHz was chosen simply to illustrate the trend as the frequency is lowered. Further, between the two common ISM bands, 915 MHz and 2450 MHz, there is also a very significant difference of approximately 10 dB in path loss.![]()  | Figure 11. Indoor Path Loss (propagation loss exponent = 3.3) | 
For a BER of 10-6,  SNRmin  falls in the range of 10.5 dB to 15 dB for the simple digital modulation techniques, such as frequency shift keying, that would likely be used for biomedical applications [1].
where B is the receiver bandwidth in Hz, which is related to the data rate requirements; F is the receiver noise factor, defined as the receiver input signal to noise ratio divided by the receiver output signal to noise ratio; k is Boltzmann’s constant; T is the system temperature in degrees Kelvin; and Lmax is the MAPL.Based on published specifications for commercial radio frequency integrated circuits (RFIC) considered for this analysis, and accounting for components and printed circuit board traces between the antenna connection and the input to the RFIC, we estimated the total receiver noise to be 15 dB, which is equal to a noise factor F of 31.6. Assuming omnidirectional coverage, values Gt and Gr are set to 1 for unity gain. To maximize battery time, Pt is set to the low power mode “maximum”, which is limited to -1.25 dBm based on FCC Part 15 rules. The bandwidth is set to 20 kHz based on several factors: 1) three axes of acceleration data, combined with; 2) non-diagnostic ECG; 3) an overhead component for data packetization; and 4) a compensation term for receiver pass band edge roll off [1]. Using these values, the maximum path loss is found to be 
.From Saunders and Aragón-Zavala [12], the COST 231 propagation model is modified to include the effects of attenuation through walls, floors, and shadowing:
where LT is the total loss, 
  represents the path loss determined above, 
  is the loss for wall type i, 
 is the number of walls of type i, 
  is the loss per floor, nf  is the number of floors in the path, and b is an empirically derived factor which accounts for the observed nonlinear function of the number of floors [13].Simplifying the previous equation for a single level house (including a basement) and combining with the indoor path loss model gives:
Using wall loss and floor attenuation values from Saunders and Aragón-Zavala [12] and Dobkin [14], the total path loss for the two ISM band cases for which attenuation values were available, were calculated and are presented in Figure 12. From the figure, the total path loss for the single-floor three-wall 915 MHz case is within 2 dB of the no-wall and no-floor case at 2450 MHz. ![]()  | Figure 12. Total Path Loss Including Wall and Floor Attenuation Examples | 
Expressing Q(t) as a probability of coverage is given as:
where 
, assuming LT < Lmax, σL is the standard deviation of the random part of the path loss,  Lmax - LT is the fade margin for the system, and all values on the right hand side of this expression are expressed in dB. Taking the location variable σL as 8 dB, based on estimates by Saunders and Zavala [12], and using the LT value calculated above for the worst case scenario, which included three walls and one floor, the final coverage probability is shown below in Figure 13. Note from the figure that distances plotted represent those that might be encountered in a house of typical size, and for these distances there is a significant difference in expected coverage for the two ISM band frequencies evaluated.![]()  | Figure 13. Probability of Coverage for Low Power Short-Haul Wireless Link Operating Mode in an Indoor Environment Including Losses from 3 Walls and 1 Floor | 
![]()  | Figure 14. Meander Line Antennas Printed on 6 mil Thick Printed Circuit Board Dielectric Material with 5, 10, 15, and 20 mil Wide Meander Traces and 11 to 33 Meanders | 
![]()  | Figure 15. Measured Meandered Monopole Antenna Return Loss | 
![]()  | Figure 16. Meandered Monopole Antenna Test in Anechoic Chamber with Plastic Pail Containing Phantom Material | 
![]()  | Figure 17. Comparison of Radiated Signals versus Angle for Meandered Monopole Antenna in Free Space and Against Plastic Pail Containing Phantom Material | 
![]()  | Figure 18. Front and Rear Views of Final Form Factor Combined Short-Haul and Platform Electronics | 
![]()  | Figure 19. Coverage Test Results using Short-Haul Circuit and Home Gateway |