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Design consideration of indoor wireless transmission between wearable physiological monitoring equipment and gateway in home environment

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  • Save American Journal of Biomedical Engineering 2016, 6(4): 95-114 DOI: 10.5923/j.ajbe.20160604.01 Design Considerations for Indoor Wireless Transmission between a Body-Worn Physiological Monitoring Device and a Gateway in a Home Environment 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 Abstract 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 1. Introduction Although physiological monitoring devices such as pulse oximeters and electrocardiogram (ECG) monitors have been in use to a large extent in the hospital environment, and to a much smaller degree in the private home or in assisted care facilities, such devices typically comprise sensors attached to the body, with the patient tethered by wires to the accompanying electronics, which in turn are mounted on a stand or placed on a table alongside the patient bedside. New devices that integrate on-body sensors and accompanying electronics into a small body-worn unit are currently in development, with first generation units now undergoing initial deployment. Combining the sensor functions and support electronics into a single unit removes the patient tether but still requires the device to be periodically returned to healthcare professionals for data offloading, or alternatively, requires patient interaction with the device for status checks and periodic data uploads. Next generation on-body devices may include a wireless link to a nearby gateway, which in turn may be connected through various means back to a medical monitoring center. One such example that was based on the analysis presented herein can be found in [1]. In addition to removing the burden from the patient to interact manually with the device * Corresponding author: (Barry K. Gilbert) Published online at Copyright © 2016 Scientific & Academic Publishing. All Rights Reserved for data uploads, the presence of the wireless link enables additional functionality to be realized. With the benefit of continuous wireless connectivity, real-time alerts and data snapshots may be automatically transmitted to the medical team for immediate analysis. Such a system is depicted in Figure 1. Note in the figure inset the indoor “short-haul” communications link between the body-worn device and the notional gateway. This paper will describe the indoor short-haul link. A discussion of the “long-haul” link, from the house to the monitoring medical center, is presented in [2]. Such a wireless communications link from an on-body biomedical device operating in an indoor environment requires consideration of several design elements. Technical requirements such as the optimum frequency at which to operate the link, the data rate needed to transmit physiological data within the required time frame, and maximum device run time between battery charging cycles, or battery replacements if primary (non-rechargeable) batteries are used, all need to be balanced against non-technical considerations. For example, regulatory requirements influence frequency and data rate options, whereas component availability and cost constraints often affect choices made that in turn directly constrain battery and run time options. Two key elements that have a strong influence on the performance of the short-haul wireless link are the on-body device antenna performance, and operational boundary conditions generated by the indoor propagation environment. Several design considerations will be examined in the 96 Mark E. Vickberg et al.: Design Considerations for Indoor Wireless Transmission between a Body-Worn Physiological Monitoring Device and a Gateway in a Home Environment sections that follow, with special emphasis on these critical items. 1.1. Aims Requirements for the addition of a wireless capability to an on-body medical device include minimizing the size increase over the basic (non-wireless) on-body device design, and maximizing the wireless coverage within the indoor environment. Additionally, the design needs to be conservatively planned to maximize the chances for a successful transmission by minimizing nulls in the on-body device’s antenna radiation pattern. Further, the design should support coverage within a typically sized private home and should be scalable to accommodate larger structures and multistory dwellings. An additional requirement for the proposed system includes support for three transmission modes that include: 1) a ping mode for system status and periodic functional verification of the wireless link; 2) an alert triggered by a physiological event; and 3) a snapshot of measured physiological data immediately preceding the alert event. The data snapshot in particular affects the data rate requirements, which in turn impact antenna performance. 1.2. Structure of the Paper In Section 2 we will first present the impact that the size of the on-body device has on the design of its antenna by exploring effects on antenna efficiency, quality factor, and usable bandwidth, followed by an analysis and simulation results of the human body’s interaction with the antenna. Section 3 will present the indoor propagation and coverage expectation for a private home environment that would typically be encountered by the wireless on-body biomedical monitoring device and gateway system. Finally, Section 4 will present a design example including test results of the on-body device and a corresponding gateway in a home environment. 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 American Journal of Biomedical Engineering 2016, 6(4): 95-114 97 2. On-Body Device Antenna Antenna options for on-body medical devices are very limited due to the desire to minimize device size and the need for an omnidirectional radiation pattern. A wide range of frequencies are used for on-body (or in-body) medical devices, including: the Medical Device Radiocommunications Service (MedRadio) from 401 MHz to 457 MHz; the Wireless Medical Telemetry Service (WMTS) in the 608 MHz to 614 MHz, 1395 MHz to 1400 MHz, and 1427 MHz to 1432 MHz frequency bands; the new Medical Body Area Networks (MBAN) frequencies at 2360 MHz to 2400 MHz; and the ubiquitous 900 MHz and 2.4 GHz Industrial, Scientific, and Industrial (ISM) bands. Given these frequency options, the wireless link between the on-body device and the gateway will most likely need to operate between 400 MHz and 2.4 GHz. With an on-body device maximum dimension of 1.5”, the resulting antenna electrical size will be between 0.05 λ and 0.30 λ, where λ is the free space wavelength for a given frequency. At the lower frequency range an antenna of this dimension is well within the < 0.1 λ size that is typically defined as “electrically small”. Such antennas are generally difficult to impedance match for all but a very narrow band of frequencies, and suffer from poor radiation efficiency. Although the higher frequency range should be less sensitive to these performance issues, the impact of the body on the radiation pattern increases with frequency. 2.1. Antenna Efficiency, Q, and Bandwidth We first examine the lower frequency range noted in the previous paragraph, which implies an electrically small antenna. One antenna performance parameter that is significantly affected by an electrically small antenna is the antenna efficiency (???????????????? ). 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]: ???????????????? = 20????????2 �???????????????????????? 2 � , 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]: ????????????????ℎ???????????????????????? = ???????????????? 2???????????????? ???????????????? = 3 ???????????????? 2???????????????? �????2???????????????????? 3 , Ω; where ???????????????? 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: ???????? = = = ???????????????? ???????????????? 20 ???????? 2 �???????????????????????? 2 � ???????? ???????????????? ???????????????? + ????????????????ℎ ???????????????????????? �20???????? 2 �???????????????????????? 2 � �+ �2???????????????????????????????? �????2???????????????????? 3 � 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). The antenna Q relates to its usable bandwidth, and is defined as the total energy stored by the antenna divided by the power dissipated per cycle. The energy stored by the antenna is represented by the reactive component (XA) of the antenna’s impedance, whereas the power dissipated is represented by the total antenna resistance Ra. For an electrically short dipole, XA is found using the expression below [3], and RA is found using the expression given above for efficiency. −120 ???????????????? ???????????????? = ???????????????????????? �???????????????? �2????????� − 1� , ???????? ???????? 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. To place the bandwidth results into perspective, if the wireless link between the on-body device and the gateway were to be operated at low power under FCC Part 15 rules, using for example one of the ISM band frequencies, the bandwidth requirement would be determined by the amount of data that needed to be transmitted and the duration during which the data transmission needed to occur. By FCC rules, this low power transmission scenario is limited to approximately 1 mW. Such power levels may be sufficient for situations in which the on-body device and gateway are located in close proximity, e.g., within the same room. When longer transmission distances are needed, or when there may be more signal loss due to building construction, obstructions, or nulls in the antenna radiation pattern, higher transmission power may be required. FCC Part 15 rules also allow for higher power operation but place additional requirements on the modulation type and spectral components of the transmitted signal. One such requirement for the higher power operation is that the signal occupies a minimum 500 kHz 6 dB bandwidth. From Figure 3, this bandwidth requirement establishes a lower limit to the carrier frequency to be between 500 MHz and 600 MHz. 98 Mark E. Vickberg et al.: Design Considerations for Indoor Wireless Transmission between a Body-Worn Physiological Monitoring Device and a Gateway in a Home Environment Figure 2. Antenna Efficiency for Copper Wire Short Dipole 1.5" (38 mm) Long and with 0.007” (0.2 mm) Radius Figure 3. Short Dipole Antenna Q and Bandwidth for Copper Wire Antenna 1.5” (38 mm) Long and 0.007” radius 2.2. Human Body Impact on Antenna Radiation Pattern Ideally, the antenna radiation pattern for the on-body device would radiate in an omnidirectional pattern so that the orientation of the wearer would not affect the ability to close the communications link between the on-body device and the gateway. For an antenna operating in free space, a vertically polarized dipole presents such a radiation field pattern. American Journal of Biomedical Engineering 2016, 6(4): 95-114 99 However, when such an antenna is placed in close proximity to the body, several interactions between the body and the antenna may occur, depending on the separation distance between the body and antenna, as well as on the operating frequency. Radiation fields from the antenna may pass through the body, reflect and diffract from the body, or travel along the body surface. To quantify the electromagnetic energy that may pass through the body, we first consider the attenuation that the body presents at a given frequency. For a general dielectric material, the propagation constant (γ) of a plane wave is given as: ???????? = ???????? + ???????????????? where the real part of γ, ????????, is the attenuation constant and ???????? is the phase constant. The attenuation constant represents the losses and is given by [4]: ???????? = ???????? �????2???????????? ��1 + ???????? 2 �????????????????� − 1� 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: 1 1 ???????????????? = ???????? = ???????? �????2???????????? ��1 + �????????????????????????�2 − 1� 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. From Figure 4, the skin depth over the frequency range of interest is nearly constant at approximately 2 inches, giving 4.75 skin depths for an average torso dimension of 9.5 inches from front to back, which is equivalent to 41 dB of loss. Given the estimated loss through the body over the frequency range it is very unlikely that the primary communications path will be through the body. To evaluate the non-transmission effects of the body on the antenna radiation pattern we first adopt an analytical approach in which the torso is represented by a perfectly conducting cylinder. As shown in Figure 5, the model includes a vertically polarized dipole aligned to the cylinder axis and placed in close proximity to the cylinder. To approximate the radiation pattern produced by this configuration, Jordan and Balmain [5] provided a closed-form solution to this problem, as given below. ????????(????????, ∅) ∞ = sin(????????) � ???????????????? (????????)???????? �???????????????? (???????????????? ????????????????????????(????????) ???????? =0 − ???????????????? (????????a sin(θ)) ????????????(????2)(???????????????? sin(????????)) ????????????(????2)(???????????????? sin(????????))� cos(????????∅) where ???????????????? = �12 ???????? = 0 ???????? ≠ 0 , ???????????????????????????????? ???????????????????????????????????????????????? ???????? = 2???????? , ???????? 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. 2.3. Simulations The analysis described in the previous section was based on a simplified model of the human torso, which was represented as a perfectly conducting cylinder with dimensions approximating those of a typical adult. A full analytical analysis based on a more realistic model is not practical using a similar approach; however, current 3D electromagnetic simulation tools, in particular CST Microwave Studio, includes a numerical model of a complete human which includes electrical properties of the various tissue types for a variety of frequencies. Figure 7 shows the antenna location, “Hugo” body model, coordinate system, and far field antenna radiation pattern for the simulations that follow. Note from the figure, the “front” facing direction for Hugo is aligned along the y axis and is located at 270 degrees for the 2D plots. Using the Hugo model with the antenna orientation given above, and a 1.5” (38 mm) copper wire dipole antenna representing the maximum-case dimension for the body worn unit, several simulations were completed in which the antenna-to-body distance was varied for three frequencies. From these simulations, the effects on the radiation pattern and antenna impedance were evaluated. Figure 8 shows the radiation pattern for four distances, 2.5 mm, 20 mm, 40 mm, and 50 mm. For each of these positions the radiation patterns 100 Mark E. Vickberg et al.: Design Considerations for Indoor Wireless Transmission between a Body-Worn Physiological Monitoring Device and a Gateway in a Home Environment at 450 MHz, 900 MHz, and 2450 MHz were simulated, where the frequencies selected were based on the frequencies available from the Hugo body model. Note from the figure that all radiation patterns are shown in comparison to the same dipole antenna radiating in free space. The Hugo model was removed from the simulation for the free space dipole reference. All radiation patterns are plotted in terms of directivity, which is defined as the ratio of the radiation intensity in a given direction from the antenna to the radiation intensity averaged over all directions [6], for the given antenna, frequency, and location. Realized gain, through impedance matching, is more appropriate for system analysis and will be considered in the impedance results section that follows. Note that for panel ‘A’ the 450 MHz and 900 MHz patterns are very similar, with 10 to 18 dB less falloff in directivity, as compared to the 2450 MHz case, at the 90 degree back side of Hugo (recall that 270 degrees faces forward). At the other end of the separation range examined, i.e., 50 mm, panel ‘D’ shows the 900 MHz and 2450 MHz cases with very similar performance, whereas the 450 MHz case still shows 5 dB less falloff than the 2450 MHz case. In the middle range, 20 mm, panel ‘B’ shows that the 900 MHz case falls between the 450 MHz and 2450 MHz examples. Overall the trend observed from the analytical analysis from the previous section holds; that is, as the frequency is reduced, the impact on the antenna radiation pattern, as it pertains to omnidirectionality, by the body is also reduced. In addition to the variation in the falloff in the directivity towards the back of the radiation patterns with increasing frequency, the forward directivity also varies across the range of frequencies and distances studied. One figure of merit that may be used that includes both of these radiation pattern “features” is the front to back ratio. To simplify the comparison, the directivities at 270 degrees and 90 degrees were recorded, with the difference plotted below in Figure 9. Note once again that the frequency dependent effects on the radiation pattern (for the given fixed length antenna) are well illustrated; i.e., as the operating frequency is increased, the potential to have dropouts in coverage when the transmission path is behind the body is greatly increased due to the effect on the antenna radiation pattern. Note from the figure, at 30 mm separation distance between the “on-body” device and the body there is over 25 dB of difference in directed power from the lowest frequency studied (450 MHz) to the highest frequency (2450 MHz). Recall that front to back ratio is used here only to illustrate the differences in the radiation patterns. If the edge of coverage is determined by the radiation pattern peak, then directions in which the pattern is reduced (pattern nulls), which are not necessarily limited to the back of the pattern, that were used to calculate the front to back ratio, would fail to close the link. Good engineering practice would normally account for this reduction by adding design margin. However, in general, as the variations between the pattern peaks and minimums increases, i.e. increased front to back ratio, additional margin is needed to compensate for the difference and the total effective coverage area for a given frequency is reduced. Figure 4. Skin Depth for a Dielectric Material Approximating a Torso with a Relative Dielectric Constant of 80 and a Conductivity of σ = 1 American Journal of Biomedical Engineering 2016, 6(4): 95-114 101 Figure 5. Vertical Dipole near a Perfectly Conducting Cylinder Figure 6. Radiation Pattern versus Frequency from a Vertical Dipole near a Perfectly Conducting Cylinder; (a = 0.25m, b = 0.2525m, θ = 90º) Figure 7. CST Simulation of a Vertically Polarized Dipole Antenna Placed Directly in Front of the CST Hugo Human Body Model. A) 3D Far Field Antenna Radiation Pattern and Coordinate System, B) 2D Far Field Antenna Radiation Pattern 102 Mark E. Vickberg et al.: Design Considerations for Indoor Wireless Transmission between a Body-Worn Physiological Monitoring Device and a Gateway in a Home Environment 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 American Journal of Biomedical Engineering 2016, 6(4): 95-114 103 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 In addition to the radiation patterns presented above, the antenna impedance was also simulated for all of the cases presented; Figure 10 shows the simulation results. As depicted in panel ‘A’ of the figure, the real part of the impedance appears to be well behaved over the frequency range and the antenna to body separation distances simulated. At 1.5” (38 mm) antenna length, the 2450 MHz case represents a wavelength of 31% λ and the simulated impedance is close to the expected value for a dipole antenna approximately one quarter wavelength long. Similarly, the 900 MHz and 2450 MHz cases are electrically short and as expected have a real part of the impedance value that is relatively low. This low impedance, along with the increasing imaginary part shown in panel ‘B’, sets a lower bound on the usable bandwidth of the short dipole due to impedance matching limitations. Note that the antenna patterns shown above can be interpreted as gain plots only if impedance matching is applied. Impedance matching is also necessary to limit loss of signal between transmitter/receiver circuits and the antenna. Without such matching, transmit power would be reduced. Compensating for such loss by increasing transmit power will consume more battery power, and receive sensitivity will be reduced. 3. Considerations for Indoor Propagation In addition to the impact that the body has on the short-haul link performance, the indoor environment that the link is operated within also plays a significant role in the performance and coverage of a given on-body device and gateway design. For brevity, we focus on the far field propagation for the indoor wireless link analysis. Any interactions between the antenna and nearby structures, such as furniture, walls, the floor, etc., that the on-body device may be in close proximity to, are not considered in this analysis. As an electromagnetic wave moves through space it interacts with objects in the environment by reflecting, scattering, or passing through (transmission) the materials encountered. Analysis of the complex interference environment that results from these interactions is nontrivial for all but the simplest cases and is variable as persons and objects are moved within the volume analyzed. To model such an environment the path loss exponent from Friis formula, given below [7], for free space propagation is modified to account for the increased losses found in the typical indoor propagation environment: ???????????????? (????????) = ???????????????? ???????????????? ???????????????? ????????2 (4????????)2???????????????? ???????? 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: ????????????????(????????????????) = 20???????????????????????? 4???????? � ???????? � + 10????????????????????????????????(????????) 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 104 Mark E. Vickberg et al.: Design Considerations for Indoor Wireless Transmission between a Body-Worn Physiological Monitoring Device and a Gateway in a Home Environment 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. 3.1. Indoor Coverage Estimates The maximum distance for a successful wireless link between a given gateway and the on-body device is designated as the gateway’s coverage area and is based on numerous transmitter, receiver, and propagation environment parameters. Some parameters, such as allowable transmit power and antenna gains, are limited by FCC rules, whereas the propagation environment is largely affected by building construction materials, objects in rooms, humans, etc., which in turn impact attenuation, reflections, scattering, etc. and the resulting multipath environment. On the receiver side, the minimum signal to noise ratio sets the limit for the receive power required to recover the transmitted message successfully. For digital modulation, which would be the likely choice due to the data transmission needs of body-worn physiological monitoring devices, and to leverage existing wireless protocols and component availability, the acceptable bit error rate (BER) is used to set the limit for a successful transmission. Although consumer electronics applications accept BER as “low” as 10-3 (1 error for every 1000 bits transmitted) for Bluetooth, or 10-5 for WiFi, we chose a more conservative BER of 10-6 to increase system robustness for medical alerts. Translation from BER to equivalent SNR is dependent on the modulation technique and is related to the ratio of the amount of energy-per-bit (Eb) to the noise (N0), normalized to a one Hertz bandwidth, and the ratio of the bit rate (R) and bandwidth (B) of the transmitted signal. ???????????????????????????????????????????????? = ???????????????? ????????0 ???????? ???????? For a BER of 10-6, ???????????????????????????????????????????????? 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]. 3.2. Path Loss In addition to the frequency dependent indoor path loss considered above, maximum allowable path loss (MAPL) estimates the total loss that can be accepted while still maintaining ???????????????????????????????????????????????? . Substituting the receive power requirements as determined by SNRmin, and the receiver noise performance into Frii’s formula, and solving for the loss term, yields the expression for maximum loss given below: ???????????????????????????????? = ???????????????? ???????????????? ???????????????? ????????(????????????????????????)(???????????????????????????????????????????????? ) 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 ???????????????????????????????? (????????????????) = 102.7 ????????????????. From Saunders and Aragón-Zavala [12], the COST 231 propagation model is modified to include the effects of attenuation through walls, floors, and shadowing: ???????????????? = ???????????????? + ???????? � ???????????????????????? ???????????????????????? + ???????????????? (???????? � ???????????????? ???????? +2) ��???????? ???????? +1�−???????? � ????????=1 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: 4???????? ????????????????(????????????????) = 20???????????????????????? � ???????? � + 10????????????????????????????????(????????) ???????? + � ???????????????????????? (????????????????)???????????????????????? + ???????????????? (????????????????) ????????=1 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. 3.3. Coverage Estimate Since most rooms include static objects such as furniture and other household items, as well as dynamic objects, such as the movement of people and pets, the real world presents a very complex and variable multipath environment. Such environments are subject to shadowing, which is the fading caused by changes in the scatterers for the different paths, depending upon the relative locations of the on-body unit

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