sensors Article
Multi-Objective Optimization of a Wireless Body Area Network for Varying Body Positions Łukasz Januszkiewicz 1, * , Paolo Di Barba 2 and Sławomir Hausman 1 1 2
*
Institute of Electronics, Lodz University of Technology, 90-924 Łód´z, Poland;
[email protected] Department of Electrical, Computer and Biomedical Engineering, University of Pavia, I-27100 Pavia, Italy;
[email protected] Correspondence:
[email protected]; Tel.: +48-691-565-277
Received: 26 August 2018; Accepted: 8 October 2018; Published: 11 October 2018
Abstract: The purpose of this research was to improve the performance of a wireless body area sensor network, operating on a person in the seated and standing positions. Optimization-focused on both the on-body transmission channel and off-body link performance. The system consists of three nodes. One node (on the user’s head) is fixed, while the positions of the other two (one on the user’s trunk and the other on one leg) with respect to the body (local coordinates) are design variables. The objective function used in the design process is characterized by two components: the first controls the wireless channel for on-body data transmission between the three sensor nodes, while the second controls the off-body transmission between the nodes and a remote transceiver. The optimal design procedure exploits a low-cost Estra, which is an evolutionary strategy optimization algorithm linked with Remcom XFdtd, a full-wave Finite-Difference Time-Domain (FDTD) electromagnetic field analysis package. The Pareto-like approach applied in this study searches for a non-dominated solution that gives the best compromise between on-body and off-body performance. Keywords: WBAN; wearable antenna; human body model; FDTD analysis; evolutionary optimization algorithms; computational electromagnetics
1. Introduction Wireless Body Area Networks (WBANs) are a lively field of research and development because they promise the long-awaited progress towards the widely-available monitoring of physiological parameters—vital signs—in healthcare, health and safety, military applications, and elsewhere [1]. This potential has been recognized by both research and engineering communities, resulting in efforts to standardize this class of wireless networks [2]. The standards establish a common framework for the development of WBAN applications, but many issues remain open for research and development, including the use of recognized optimization methods. Some research has been conducted into the improvement of WBANs, but mainly in the higher layers of the Open System Interconnection (OSI) model. For instance, in Reference [3] parameters such as payload length and the number of transmission retries were optimized and in Reference [4] the packet size was optimized. Research has also been conducted into the optimization of wearable antennas (e.g., Reference [5]). Nevertheless, one of the major and intrinsic difficulties with WBANs follows from the complex and unfavorable characteristics of the radio channel for both on-body and-off body links. There may be relatively high and variable path loss between some nodes, due in part to the presence of a human body: its posture and position relative to environmental elements. This problem is exacerbated during the outdoor operation of WBANs, when multipath propagation is weak and does not compensate for the high path loss of the direct node-to-node radio channel [6]. Much effort has been devoted to investigating path loss for various body positions, such as standing and sitting [7]. However, these have Sensors 2018, 18, 3406; doi:10.3390/s18103406
www.mdpi.com/journal/sensors
Sensors 2018, 18, 3406
2 of 16
focused on certain predefined and fixed postures. In this paper, we formulate and solve a somewhat different, multi-objective multi-parameter optimization problem, i.e., the automatic optimization of node position on the user’s body. Our objective is twofold: to reduce the on-body path losses between nodes and to improve the systemic off-body channel loss (considering the directivity of the wearable antenna system). The paper presents a different and more advanced approach in comparison to our previous work [8], in which we imposed a number of limiting design assumptions—for example, fixed positions for the head and arm nodes. The only degree of freedom was the placement of the chest node. The results were encouraging: a considerable decrease in the path loss between nodes using a single objective automated optimization procedure was achieved, based on evolutionary computing. The current paper has a more ambitious aim. Minimizing a multi-objective function, which simultaneously depends on a set of design variables, is a vitally important problem in many fields of engineering. It is part of many optimization routines which are used widely to search for possible improvements in already existing engineering designs, often developed by heuristic methods or inaccurate design formulas. This also refers to radio communication, where antenna design or wireless system performance can be improved—for instance, by reducing transmit power and battery energy consumption [9]. The design of electromagnetic devices and systems typically requires controlling several aspects of their performance, resulting in multiple design criteria that give rise to multi-objective design problems [10–16]. To cope with a vector of design criteria, a fully Pareto-like formulation or a preference-function approach can be used. In the former case, the set of best compromise solutions (also known as non-dominated solutions) has to be identified. In contrast, in the latter case, the single-objective algorithms can be exploited, especially those belonging to the evolutionary class, which have proven to be cost-effective and global-optimum oriented. In the research presented in this paper, we used a Pareto optimization algorithm. In the performance optimization loop for wireless body area networks (WBANs), we used a full-wave numerical electromagnetic code with a numerical model of the human body to calculate the objective function components, such as the path loss or the off-body radiation pattern. Standard body models are available in electromagnetic simulation programs, which are made for a human body in the standing (or lying) positions. It is possible to reposition these models into different poses with specialized programs (e.g., Remcom VariPose [17]), but because of the lack of a suitable programming interface, the software cannot be run automatically within an optimization loop. Our optimization procedure is currently adapted for two body postures: sitting and standing. For this purpose, two simplified models of a human body consisting of a set of cylinders are proposed. These were generated swiftly and automatically in Remcom XFdtd [18], which is a commercial package implementing full-wave Finite-Difference Time-Domain (FDTD) electromagnetic simulator, for each optimization step using the available scripting language. Our approach is flexible because it can be also used in the future for other body postures. The major goal of our current study was to develop a strategy for the automatic optimization of the location of WBAN nodes for varying body positions of the user. We used the Remcom XFdtd simulation program in this research, which utilizes the FDTD method, and the numerical human body model which we have elaborated. The model was verified by us experimentally [19]. We found that simulation results obtained for the 2.4 GHz ISM frequency band with the heterogenic NMR Hershey human body model in XFdtd are similar to the results of measurements obtained for a human subject and for the simplified 6-cylinder phantom. 2. Wireless Body Area Sensor Network The WBAN analyzed in this research, which we designed originally for monitoring the vital signs of firefighters, consists of miniature nodes which use transceivers operating in the 2.4 GHz ISM (Industrial, Scientific, and Medical) band. The studied network consists of three nodes which measure certain physiological parameters of the human body and transmit the data both to each other (on-body channels) and to a remote node located away from the body (off-body channel). In our computer
x Sensors 2018, 18, 3406
33 of of 16
other (on-body channels) and to a remote node located away from the body (off-body channel). In simulations, nodes use half-wave dipole antennas tuned to 2.4 GHz. dipoles with our computerallsimulations, all nodes use half-wave dipole antennas tunedWe to designed 2.4 GHz. We designed shortened geometry to match the antenna port impedance to 50 Ω, which resulted in a total length dipoles with shortened geometry to match the antenna port impedance to 50 Ω, which resulted in a of 54 length mm, a of conductor of diameter 1 mm, and point gap ofpoint 1 mm. One total 54 mm, adiameter conductor of a1 feeding mm, and a feeding gap of 1node mm.(connected One node to antenna 1; see Figure 1) contains a pulse-oximeter to measure blood oxidation and heart (connected to antenna 1; see Figure 1) contains a pulse-oximeter to measure blood oxidation rate. and The is attached toattached the ear-lobe and the node, to be located to theclose ear. Ittowas heartsensor rate. The sensor is to the ear-lobe andtherefore, the node,has therefore, has to close be located the assumed that this node has a fixed position on the left side of the head. Node 1 has a low-power ear. It was assumed that this node has a fixed position on the left side of the head. Node 1 has a transceiver and a miniature which enables dataenables transmission only to the two nodes low-power transceiver and abattery, miniature battery, which data transmission onlyother to the two located on the user’son trunk, constituting an on-body network. other nodes located the user’s trunk, constituting an on-body network.
Figure 1. The The wireless wireless body area sensor network on the simplified cylindrical human body model.
The trunk node, located on the user’s chest, measures measures the respiratory rate as well as the temperature and humidity of the firefighter’s clothes (antenna 2 in Figure 1). Another node performs the function of a pedometer and is placed on the user’s calf (antenna 3 in Figure 1). Both the trunk and leg nodes can receive data from the pulse-oximeter and and from from each each other other (on-body (on-body transmission). transmission). Nodes 2 and 3 are also capable of transmitting measurement data to the remote receiver (off-body transmission). Figure 2 presents the off-body transmission scenario. The received power in this link depends strongly on the wearable antenna gain, especially in an outdoor environment, in which the multipath effect is very small [6]. Due to the influence of the human body on the wearable wearable antenna radiation antenna gain can bebe very low. Depending on radiation pattern pattern for foraawide widerange rangeofofradiation radiationangles, angles,the the antenna gain can very low. Depending the position of the antenna on the human body, the antenna gain can be lower than − 10 dBi for a sector on the position of the antenna on the human body, the antenna gain can be lower than −10 dBi for a ◦ in the horizontal plane [20]. When the propagation path between the human body wider sector than wider100 than 100° in the horizontal plane [20]. When the propagation path between the human and remote receiver falls into low the of antenna radiation pattern, the power of the bodythe and the remote receiver fallsthe into thegain lowzone gainof zone the antenna radiation pattern, the power received signal can drop below the receiver’s sensitivity. of the received signal can drop below the receiver’s sensitivity. Figure 2 also presents the differences in the radiation patterns of the wearable wearable antennas. antennas. Antenna 2 is is located locatedon onthe theright rightarm armand and antenna is placed of calf. the calf. Incase, this antenna 3 is3 placed on on the the left left sideside of the In this case, the radiation of antenna 2 (with gain G ) presented in Figure 2a covers the right side of the the radiation of antenna 2 (with gain G2) presented in Figure 2a covers the right side of the body with 2 body withgain very on the leftthe side, while the radiation of antennain3Figure presented in Figure very low onlow the gain left side, while radiation of antenna 3 presented 2b (with gain G2b 3) (with gain to G3the ) is left directed to the leftnot side andthe does notside cover of the body is directed side and does cover right of the right body side completely. In thecompletely. proposed In the proposed system, both transceivers andsame 3 operate at the but same frequency, different time system, both transceivers 2 and 3 operate at2 the frequency, different timebut slots are utilized slots are utilizedthe formeasurement transmitting the data from the body to the receiver inThe the for transmitting datameasurement from the body to the remote receiver in remote the off-body link. off-body link. The remote receiver can select the stronger signal of the two that come from nodes remote receiver can select the stronger signal of the two that come from nodes 2 and 3, as presented 2 3, as 2c. presented in Figure 2c. transmission This two-antenna transmission improves the off-body inand Figure This two-antenna scenario improvesscenario the off-body communication communication performance because of the radiation pattern of one caninbebyfilled performance because the minima of the theminima radiation pattern of one antenna canantenna be filled the in by the radiation from the other antenna, depending on the positions of the antennas on the human radiation from the other antenna, depending on the positions of the antennas on the human body. In body. 2c, of thethe gain of the wearable of transceivers 2 and 3 operating different FigureIn 2c,Figure the gain wearable antennas antennas of transceivers 2 and 3 operating in differentintime slots time slots is G23 (φ) = sup(G (φ), G (φ)). The resultant gain G is equal to the greater of is defined asdefined G23(ϕ) =assup(G 2(ϕ), G3(ϕ)). The resultant gain G 23 is equal to the greater of the two, G 2the or 2 3 23 G3, over the angles in the horizontal plane, meaning that the receiver will always select the strongest available signal to detect. Therefore, it should be noted that G23 is not the sum of G2 and G3.
Sensors 2018, 18, 3406
4 of 16
two, G2 or G3 , over the angles in the horizontal plane, meaning that the receiver will always select the Sensors 2018,available 18, x 4 ofG16. strongest signal to detect. Therefore, it should be noted that G23 is not the sum of G2 and 3
Figure 2. The off-body communication scenario: (a) transmission for antenna 2 with gain G2 ; Figure 2. The off-body communication scenario: (a) transmission for antenna 2 with gain G2; (b) (b) transmission for antenna 3 with gain G3 ; (c) transmission for both antennas 2 and 3 with the transmission for antenna 3 with gain G3; (c) transmission for both antennas 2 and 3 with the resultant resultant gain G23 . It should be noted that in any given direction, G23 is not the arithmetic sum of G2 gain G23. It should be noted that in any given direction, G23 is not the arithmetic sum of G2 and G3 but and G3 but the greater of the two, because the two transceivers operate at the same frequency but in the greater of the two, because the two transceivers operate at the same frequency but in different different time slots. In that sense, this is not a two-element antenna array with the superposition of time slots. In that sense, this is not a two-element antenna array with the superposition of radiation radiation patterns but a switched pattern antenna. patterns but a switched pattern antenna.
This two-antenna switched-pattern approach presented also in [20], can give a better system This two-antenna approach presented in [20], acan givesplitter, a betterand system performance than a twoswitched-pattern antenna array operating with a single also transceiver, power two performance than a two antenna array operating with a single transceiver, a power splitter, and two waveguides. The wearable two-antenna array would suffer from a radiation pattern with deep interference waveguides. The wearable two-antenna array would suffer from a radiation pattern with deep minima which could cause a signal drop, particularly in outdoor environments [21]. The time-diversity in interference minima which could a signal drop, outdoor environments The off-body transmission from the twocause antennas located on particularly the opposite in sides of a body reduces the[21]. minima time-diversity in off-body transmission from the two antennas located on the opposite sides of a in the resultant horizontal pattern gain. Our solution can improve the link reliability in outdoor systems, body reduces the minima in the resultant horizontal pattern gain. Our solution can improve the link depending on the particular position of the antennas with respect to the body [20]. To obtain a stable and reliability in outdoor systems, depending on the particular position of the antennas respect reliable off-body link irrespective of the free movement of the user, the wearable antennaswith should haveto a the body [20]. To obtain a stable and reliable off-body link irrespective of the free movement of the quasi-omnidirectional pattern. In two-antenna systems, this can be achieved by the complementarity of user, the wearable should have a quasi-omnidirectional pattern. In two-antenna the radiation patternsantennas for antennas 2 and 3. Randomly selecting the locations of the antennas can systems, lead to a this can be achieved by the complementarity of the radiation patterns for antennas 2 and 3. ◦ poor off-body link, as may be observed in Figure 3, where for angles 210–315 , the gain of both antennas Randomly selecting the locations of the antennas can lead to a poor off-body link, as may be is below −20 dB. Because the antennas are close to the human body, which influences their radiation observed in Figure for angles 210–315°, the gain both antennasfor is applying below −20andB. Because properties, they have3,towhere be positioned appropriately. This wasofour motivation automated the antennas are close to the human body, which influences their radiation properties, they have to optimization procedure to the placement of the antennas. be positioned appropriately. This was our motivation for applying an automated optimization In the optimization process, the geometrical coordinates of nodes 2 and 3 on the trunk surface procedure to the placement of the antennas. are the design variables. They have an influence on both the path loss in the on-body link and the In the optimization process, the coordinates of nodes and 3 on on theopposite trunk surface radiation pattern in the off-body link. geometrical However, while the locations of the2 antennas sides are the design variables. They have an influence on both the path loss in the on-body and the of the body result in a desirable quasi-omnidirectional diversity pattern, at the same time, link the on-body radiation pattern in from the off-body link.attenuation, However, while the locations of the tissues. antennasThe ongoal opposite transmission suffers high signal introduced by the human was, sides of the body result in a desirable quasi-omnidirectional diversity pattern, at the same time, the therefore, to optimize the performance of the off-body link while maintaining good performance in the on-body transmission transmissionchannel. suffers from high signal attenuation, introduced by the human tissues. The on-body goal The was,on-body therefore, to optimize thenetwork performance of the off-body linkmatrix while parameters maintaining good performance of the was evaluated by scattering defined performance in the on-body transmission channel. for a 3-port network, where each port refers to an antenna port, as presented in Figure 4. The scattering The on-bodybyperformance matrix is defined Equation (1). of the network was evaluated by scattering matrix parameters defined for a 3-port network, where each port toA an = [S]·[ (1) [B] refers ] antenna port, as presented in Figure 4. The scattering matrix is defined by Equation (1). where: (1) [𝐵] = [𝑆] ∙ [𝐴] B: the vector of output signals S: the scattering matrix where: B: the vector of output signals S: the scattering matrix A: the vector of input signals. In the case of a network that consists of three antennas, the scattering matrix S is given by Equation (2).
Sensors 2018, 18, 3406
5 of 16
A: the vector of input signals.
Sensors 2018, 18, x 5 of 16 the18, case (2). SensorsIn 2018, x of a network that consists of three antennas, the scattering matrix S is given by Equation 5 of 16
a a SS SS S b1 b 11 12 S13 a 1 bb =SS SS SS ∙ a (2)(2) b2 b == S S21 S S22 S S23∙ a· a2 (2) a S S S b b3 b S S31 S S32 S S33 a a3 In the case of the network considered in this paper, the matrix is diagonally symmetrical. To In considered in in thisthis paper, the the matrix is diagonally symmetrical. Inthe thecase case ofthe thenetwork network considered paper, matrix isparameters diagonally symmetrical. characterize theof attenuation of the signal between the antennas, only three are needed.To In characterize the attenuation of the signal between the antennas, only three parameters are needed. In To characterize the attenuation of the the antennas, only three parameters are needed. , S , Sbetween are considered. what follows, only the parameters S signal considered. what follows, onlyonly the the parameters S S, S21 , S, S31 , Sare In what follows, parameters 23 are considered.
Figure 3. 3. The The radiation radiation patterns patterns of antennas in in the the off-body off-body link link obtained obtained for for their their initial initial positions positions Figure of antennas Figure 3.◦ The radiation patterns of antennas in the off-body link obtainedgain for value their initial positions ◦ 2 = 65°, z 2 = 0.32 m, ϕ 3 = 107°, z 3 = 0.21 m), normalized to the maximum equal to (ϕ (φ2 = 65 , z2 = 0.32 m, φ3 = 107 , z3 = 0.21 m), normalized to the maximum gain value equal to 6.5 6.5 dBi. dBi. 2 = 65°, z2 = 0.32 m, ϕ3 = 107°, z3 = 0.21 m), normalized to the maximum gain value equal to 6.5 dBi. (ϕ In this case, there is no significant improvement in the performance because the radiation patterns In this case, there is no significant improvement in the performance because the radiation patterns Instrongly this case, there is no significant improvement in the performance because the radiation patterns overlap. strongly overlap. strongly overlap.
Figure 4. The scattering parameters defined with reference to the on-body antenna signals. signals. Figure 4. The scattering parameters defined with reference to the on-body antenna signals.
3. Simplified Body Model for the Sitting Position 3. Simplified Body Model for the Sitting Position Various human body models and full-wave electromagnetic codes can be used to evaluate the Various human bodyand models and wireless full-wave electromagnetic codes can be used to of evaluate the performance of on-body off-body channels. Simplified cylindrical models the human performance of on-body and off-body wireless channels. Simplified cylindrical of of thethe human body are particularly useful for modeling different poses [22,23] because the models positions body body are particularly useful for modeling different poses [22,23] because the positions of the body parts can be easily modeled by translation and rotation of the cylinders. Cylindrical models are also parts can be when easily the modeled byposition translation and rotation the cylinders. Cylindrical areThis alsois convenient antenna is variable but itsofdistance to the body surfacemodels is fixed. convenient when the antenna position can is variable but its distance to the surface isinfixed. This is because the position of the antenna be controlled easily with twobody coordinates a cylindrical because the position of the antenna can be controlled easily with two coordinates in a cylindrical coordinate system. In the case of anthropomorphic models, where the body shape is complex coordinate system.maintaining In the case of anthropomorphic where body is complex (non-cylindrical), a fixed distance between models, the antenna andthe body (e.g.,shape the average across (non-cylindrical), maintaining a fixed distance between the antenna and body (e.g., the average across
Sensors 2018, 18, 3406
6 of 16
3. Simplified Body Model for the Sitting Position Various human body models and full-wave electromagnetic codes can be used to evaluate the performance of on-body and off-body wireless channels. Simplified cylindrical models of the human body are particularly useful for modeling different poses [22,23] because the positions of the body parts can be easily modeled by translation and rotation of the cylinders. Cylindrical models are also convenient when the antenna position is variable but its distance to the body surface is fixed. This is because the position of the antenna can be controlled easily with two coordinates in a cylindrical coordinate system. In the case of anthropomorphic models, where the body shape is complex Sensors 2018, 18, x 6 of 16 (non-cylindrical), maintaining a fixed distance between the antenna and body (e.g., the average across antenna surface, minimum, or another distance metric) is difficult. results of path the the antenna surface, the the minimum, or another distance metric) is difficult. TheThe results of path lossloss simulations on-body channel obtained simplified cylindrical model are satisfactorily simulations for for the the on-body channel obtained withwith the the simplified cylindrical model are satisfactorily similar to those obtained with a heterogeneous model geometry of the simplified model similar to those obtained with a heterogeneous model [23].[23]. TheThe geometry of the simplified model waswas adjusted to approximate shape the heterogeneousmodel, model,as asshown shownin in Figure Figure 5. adjusted to approximate thethe shape ofof the heterogeneous
(a)
(b)
Figure 5. The human body models: (a) simplified-cylindrical; (b) anthropomorphic (multitissue). Figure 5. The human body models: (a) simplified-cylindrical; (b) anthropomorphic (multitissue).
TheThe simplified modelmodel was verified with computer simulations carried outcarried using both simplified simplified was verified with computer simulations outthe using both the andsimplified the heterogeneous models. The heterogeneous model was modified in the Remcom VariPose [17] and the heterogeneous models. The heterogeneous model was modified in the Remcom program to obtain a sitting position. The results of measurements obtained for the cylindrical model VariPose [17] program to obtain a sitting position. The results of measurements obtained for the are cylindrical similar to those withtoathose human subject with [22,23]. Figuresubject 6 shows a comparison the a modelobtained are similar obtained a human [22,23]. Figure 6ofshows path loss between the chest antenna (G ) and the leg antenna (G ) computed using XFdtd with the 3 the leg antenna (G3) computed using comparison of the path loss between2the chest antenna (G2) and heterogeneous and the simplified model. maximum difference is around 3 dB. Figure 7 XFdtd with model the heterogeneous model and the The simplified model. The maximum difference is around shows a very good agreement between the on-chest antennathe (Gon-chest patterns 2 ) radiation 3 dB. Figure 7 shows a very good agreement between antenna (G2calculated ) radiationusing patterns the calculated two models. A significantly worse agreement (up to 12 dB difference) can be observed in Figure 8 be using the two models. A significantly worse agreement (up to 12 dB difference) can for observed the on-legin antenna Thison-leg discrepancy be This investigated in our future research since for the Figure gain. 8 for the antennawill gain. discrepancy will be investigated in our future purposes of the present study the approximation of the antenna directivity pattern is good enough research since for the purposes of the present study the approximation of the antenna directivity to test our optimization strategy. The simplified cylindrical model thereforecylindrical chosen formodel furtherwas pattern is good enough to test our optimization strategy. Thewas simplified optimization WBAN Its geometry canantenna be synthesized and integrated withcan the be therefore of chosen forantenna furtherplacement. optimization of WBAN placement. Its geometry antenna’s geometry within the XFdtd scripting language with very low computational effort in the synthesized and integrated with the antenna’s geometry within the XFdtd scripting language with optimization loop. The geometry the convenient of the antennas around the very low computational effort allows in the for optimization loop.movement The geometry allows for the convenient parts of the body in the cylindrical coordinate system of in thethe trunk or leg, maintaining a constant movement of the antennas around the parts of theaxis body cylindrical coordinate system axis of distance between the antennas and the body. the trunk or leg, maintaining a constant distance between the antennas and the body.
Sensors 2018, 18, x
7 of 16
Sensors 2018, 18, x
7 of 16
Sensors2018, 2018,18, 18, x Sensors 3406
77ofof1616
Figure 6. The system loss between the chest antenna (2) and leg antenna (3) (see Figure 4) obtained using the6.heterogeneous model and the model. Figure The system loss between thesimplified chest antenna (2) and leg antenna (3) (see Figure 4) obtained Figure between the chest antenna (2) Figure6. 6.The Thesystem systemloss lossmodel between antenna (2)and andleg legantenna antenna(3) (3)(see (seeFigure Figure4)4)obtained obtained using the heterogeneous andthe thechest simplified model. using the heterogeneous model and the simplified model. using the heterogeneous model and the simplified model.
Figure 7. The on-chest antenna (antenna 2) radiation pattern in the horizontal plane obtained using Figure 7.7.The antenna (antenna 2) radiation pattern in the horizontal plane obtained usingusing the the heterogeneous model and the simplified Figure Theon-chest on-chest antenna (antenna 2)model. radiation pattern in the horizontal plane obtained heterogeneous model and the simplified model. Figure 7. The on-chest antenna (antenna 2) radiation the heterogeneous model and the simplified model. pattern in the horizontal plane obtained using the heterogeneous model and the simplified model.
Figure 8. The on-leg inin thethe horizontal plane obtained using the Figure on-leg antenna antenna(antenna (antenna3)3)radiation radiationpattern pattern horizontal plane obtained using heterogeneous model and the simplified model. the heterogeneous model and the simplified model. pattern in the horizontal plane obtained using Figure 8. The on-leg antenna (antenna 3) radiation
Figure 8. The on-leg antenna (antenna 3) radiation the heterogeneous model and the simplified model. pattern in the horizontal plane obtained using the heterogeneous model and the simplified model.
Sensors 2018, 18, 3406
8 of 16
4. Optimization Problem 4.1. Formulation The problem with the optimal placement of wireless nodes can be posed as follows: given a sensor located at a fixed point on the head of a human body, find locations (g) for two other wireless sensors, which should be placed on the trunk or arms and on one leg for operation in the standing and sitting positions with twofold goals: minimize the on-body channel path loss represented by the objective function f1 (g) (3) and simultaneously maximize the off-body gain represented by the objective function f2 (g) (4), in the frequency band of 2.4 GHz. The following definitions will be used in the analysis: g ∈ f1 (m) and f2 ( x ) > f2 (m) (5)
Sensors 2018, 18, 3406
9 of 16
Sensors 18, x both objective functions with respect to m. The exploration capacity of the algorithm 9 of 16 i.e., if x 2018, improves is substantial: when Equation (3) is fulfilled, the search radius is increased, i.e., the region in which the in which offspring the subsequent offspring may in occur order to find an This even better subsequent may occur is broadened orderisto broadened find an evenin better improvement. feature improvement. This feature prevents trapped the trajectory from becoming in a local optimum, to sobe the prevents the trajectory from becoming in a local optimum, sotrapped the algorithm is considered algorithm is considered to becomputational global-optimum The computational cost is low global-optimum oriented. The costoriented. is low because in each iteration only two because solutionsin each iterationi.e., only solutions are necessary, i.e., thethe current—or parent—solutionoffspring m and the are necessary, the two current—or parent—solution m and relevant perturbation—or x. relevant perturbation—or offspring x. x) The selection operator (3) acts on (m, x) pair. The The selection operator (3) acts on the (m, pair. The convergence property of the the algorithm relies convergence property of deviation the algorithm on controlling standard which is on controlling the standard whichrelies is associated with eachthe variable: the deviation relevant Gaussian associated with each variable: the relevant Gaussian distributions tend to be deterministic as long as distributions tend to be deterministic as long as the current solution saturates the possible improvement solution saturates the possible improvement of the objective functions. ofthe thecurrent objective functions. The whole computational schemelinks linksthe theoptimization optimizationalgorithm algorithmwith withthe theFDTD FDTDanalysis analysisfor for The whole computational scheme objective function computation. relevant flowchart is shown in9.Figure 9. The optimization objective function computation. TheThe relevant flowchart is shown in Figure The optimization routines routines are implemented in Matlab while the S antenna parameters antenna in gain are implemented in Matlab while the evaluation of Sevaluation parametersof and gainand is performed theis performed in the Remcom XFdtd software ver. 7.6.0.2. Remcom XFdtd software ver. 7.6.0.2.
Figure 9. The flowchart of the computational scheme.
Starting from the initialFigure guess 9. solution, an optimization trajectory scheme. is originated, eventually leading The flowchart of the computational to the approximation of a non-dominated solution in the objective space. As a side product, the set of Starting the initial solution, ana optimization trajectory is originated, solution points from generated duringguess the search forms cloud, sampling the objective space. eventually leading to the approximation of a non-dominated solution in the objective space. which As a side product, In order to keep the computational cost moderate, the basic version of P-EStra, we used in the set of solution points generated during the search forms a cloud, sampling the objective space. this study, exploits the evolution of a single individual, i.e., one parent is used to create one offspring, toas keep cost moderate, the basic version of P-EStra,converges which we to used whichIn is order known the the (1 +computational 1) evolution strategy. As a consequence, the algorithm a in this study, exploits the evolution a single over individual, i.e., one parent used to create one single non-dominated solution g* whichofimproves the starting solution g0 is with respect to both offspring, which is known asf2the + 1) evolution strategy. a consequence, algorithm objective sub-functions f1 (g) and (g). (1 Even if the Pareto front is notAs explicitly computed,the it should be converges to a single non-dominated g* which the starting solution g0 with emphasized that the optimized solutionsolution g* belongs to theimproves subset of over the front dominating the initial respect gto both sub-functions f1(g) andstochastic f2(g). Even if the of Pareto front is not explicitly solution theobjective other hand, however, due to the behavior the algorithm, the location 0 . On computed, it should be emphasized that the optimized solution g* belongs to the subset of of the optimized solution g* along the relevant Pareto front is out of control. Our choicethe of front the thestrategy initial solution 0. On the the high othercomputational hand, however, due stochasticofbehavior of the (1dominating + 1) evolution followsgfrom cost of to thethe evaluation the objective algorithm, the location optimized solution g* along thefull-wave relevant FDTD Pareto simulations. front is out ofUsing control. sub-functions f1 (g) and f2of (g)the which involves time-consuming a Our choice of the with (1 +two 1) evolution strategy follows from the cost of the computer equipped NVIDIA TESLA C2075 accelerator cardhigh withcomputational two multicore Graphical evaluation of the sub-functions 1(g) and f2(g) which involves Processor Units (448objective CUDA cores each), the ftime necessary to calculate the time-consuming objective functionfull-wave values FDTD simulations. Using a computer equipped with two NVIDIA TESLA C2075 accelerator card was in the range of 25 minutes in each iteration. with two multicore Graphical Processor Units (448 CUDA cores each), the time necessary to calculate the objective function values was in the range of 25 minutes in each iteration.
Sensors 2018, 18, 3406 Sensors 2018, 18, x
10 of 16 10 of 16
5. Simulation Simulation and and Optimization Optimization Results Results 5. The results results presented a three-antenna system as The presented and and discussed discussedin inthis thissection sectionwere wereobtained obtainedfor for a three-antenna system described in Reference [20]. To make the results of our investigation more general, a very simple as described in Reference [20]. To make the results of our investigation more general, a very simple antenna was was modeled modeled in in this this study study with with the the radiation radiation pattern pattern independent independent of of rotation rotation around around the the antenna z-axis. The antennas are dipoles placed in a vertical position matched to operate at 2.45 GHz. The z-axis. The antennas are dipoles placed in a vertical position matched to operate at 2.45 GHz. The initial initial placement of the antennas was defined by the positions of the on pockets on the firefighter’s placement of the antennas was defined by the positions of the pockets the firefighter’s uniform, uniform, which were originally considered for the wireless sensors. The coordinates of the second which were originally considered for the wireless sensors. The coordinates of the second antenna antenna were ϕ 2 = 1.4 rad and z2 = 1.03 m. The coordinates of the third antenna were ϕ3 = −2 rad and were φ2 = 1.4 rad and z2 = 1.03 m. The coordinates of the third antenna were φ3 = −2 rad and 10 10 shows the the history of the process in theinobjective function space. zz33 == 0.23 0.23m. m.Figure Figure shows history of optimization the optimization process the objective function The initial values for the objective function components were S start = −105.8, Gstart = 0.034, where Sstart = space. The initial values for the objective function components were Sstart = −105.8, Gstart = 0.034, inf[S31,SS21,S23= ], inf[S Gstart = ,S G1+2 before optimization. The final values were Sstop = −89.8, Gstop = 0.27, where where start 31 21 ,S23 ], Gstart = G1+2 before optimization. The final values were Sstop = −89.8, Sstop == 0.27, S21, and = G1+2 after optimization. Both components were significantly increased G whereGSstop stop stop = S21 , and Gstop = G1+2 after optimization. Both components were significantly (improved). This solution achieved in 55 iterations which lasted approximately 24 h, most increased (improved). Thiswas solution was achieved in 55 iterations which lasted approximately 24 of h, which was taken up by the time-consuming computation of the objective function components G most of which was taken up by the time-consuming computation of the objective function components and S. S. Figures standing and and sitting sitting G and Figures1111and and1212present presentthe theinitial initialpositions positionsof of the the antennas antennas for for the the standing positions, respectively. These positions resulted in the scattering matrix values (as a function of positions, respectively. These positions resulted in the scattering matrix values (as a function of frequency) shown the radiation patterns in frequency) shown in in Figure Figure 13 13 (for (forthe thestanding standingand andsitting sittingpositions) positions)and and the radiation patterns Figure 14 (for the standing and sitting positions). The final coordinates of the antennas were ϕ 2 = 2.26 in Figure 14 (for the standing and sitting positions). The final coordinates of the antennas were rad,= z2.26 2 = 0.94 m, ϕ3 = −0.94 rad, and z3 = 0.28 m, respectively, as shown in Figures 15 and 16. The final φ rad, z2 = 0.94 m, φ3 = −0.94 rad, and z3 = 0.28 m, respectively, as shown in Figures 15 2 positions resulted in the scattering values (asmatrix a function of frequency) shown in Figure shown 17 (for and 16. The final positions resulted matrix in the scattering values (as a function of frequency) the standing and sitting positions) and the radiation patterns in Figure 18 (for the standing in Figure 17 (for the standing and sitting positions) and the radiation patterns in Figure 18 (for and the sitting positions). standing and sitting positions).
Figure 10. The history of the optimization process in in the the objective objective function function space. space.
Sensors 2018, 18, x
11 of 16
Sensors 2018, 18, x
11 of 16
Sensors 2018, 18, 3406 Sensors 2018, 18, x
11 of 16 11 of 16
Figure 11. The initial placement of antennas on the standing model. Figure 11. The initial placement of antennas on the standing model. Figure 11. The initial placement of antennas on the standing model. Figure 11. The initial placement of antennas on the standing model.
Figure 12. The initial placement of the antennas on the sitting model. Figure 12. 12. The The initial initial placement placement of of the the antennas antennas on Figure on the the sitting sitting model. model.
Figure 12. The initial placement of the antennas on the sitting model.
Standing
Sitting
Standing
Figure13. 13.The Theinitial initialS Sparameters. parameters. Figure
Sitting
Standing
Figure 13. The initial S parameters.
Sitting
Figure 13. The initial S parameters.
Sensors 2018, 18, x
12 of 16
Sensors 2018, x Sensors 2018, 18, 18, 3406 Sensors 2018, 18, x
1212 of of 16 16 12 of 16
Gmax = 3.7 dBi Gmax = 3.8 dBi Standing Sitting Gmax = 3.7 dBi Gmax = 3.8 dBi Gmax = 3.7 dBi Gmax = 3.8 dBi Figure 14. The initial radiation patterns. Standing Sitting Standing Sitting Figure 14. The initial radiation patterns. Figure14. 14.The Theinitial initialradiation radiationpatterns. patterns. Figure
Figure 15. The final placement of the antennas on the standing model. Figure 15.15. The final placement of the antennas onon thethe standing model. Figure The final placement of the antennas standing model. Figure 15. The final placement of the antennas on the standing model.
Figure 16. 16. The The final final placement placement of of the the antennas antennas on on the Figure the sitting sitting model. model.
Figure 16. The final placement of the antennas on the sitting model. Figure 16. The final placement of the antennas on the sitting model.
Sensors 2018, 18, x Sensors 2018, 18,18, 3406 Sensors 2018, x
13 of 16 13 13ofof1616
Standing Standing
Sitting Sitting
Figure 17. The S parameters for the final solution. Figure17. 17.The TheS Sparameters parametersfor forthe thefinal finalsolution. solution. Figure
Gmax = 4.5 dBi Gmax = 4.5 dBi Standing Standing
Gmax = 4.6 dBi Gmax = 4.6 dBi Sitting Sitting
Figure18. 18.The Theradiation radiationpatterns patternsfor forthe thefinal finalsolution. solution. Figure Figure 18. The radiation patterns for the final solution.
An additional additional run run of of our our multi-objective multi-objective optimization optimizationprocess processwas was performed performedfrom from aa different different An starting point. This time initial placement ofantennas the antennas was intentionally configured An additional run of the our multi-objective process was performed from a different starting point. This time the initial placement of optimization the was intentionally configured in such in a such a way thatThis should in relatively lowofpath-loss in the on-body communication scenario. starting point. time the initial placement the antennas was intentionally configured in such a way that should result in result relatively low path-loss in the on-body communication scenario. Antennas 2should and 3 were located relatively close to each on theside same of the (on body (on the front). way 3that result in relatively low path-loss in the communication scenario. Antennas 2Antennas and were located relatively close to each other, onother, theon-body same of side the body the front). The The aim3was tolocated check whether algorithm could improve theGGside component without significantly 2 and were relatively close to each other, on thethe same of the body (on the front). The aim was to check whether ourour algorithm could improve component without significantly deteriorating the component. The initialcoordinates coordinates the antennas were =rad, 0 rad, = 1.06 m, aim was to the check whether our algorithm could improve the G component 21.06 deteriorating SScomponent. The initial ofof the antennas were ϕ2φ=2 0without z2 =zsignificantly m, ϕ 3 φ = 0 rad, and z = 0.18 m while the initial values of the objective components were S = − 94.2, initial coordinates of the antennas werewere ϕ2 =S0start rad, z2 = 1.06 m,=ϕ3 start 3 S component. = 03deteriorating rad, and z3 =the 0.18 m while the The initial values of the objective components = −94.2, Gstart G=start = 0.00035, where inf[S ,S G1+2 before optimization. final values 0 rad, and z3S=start 0.18 mSwhile initial ofstart the=objective components were SThe start =were −94.2, Gstart start 31 21values 0.00035, where = inf[S 31,S= 21the ,S 23], G,S start = 23 G],1+2Gbefore optimization. The final values Sstop == were S = − 93.58, G = 0.337, where S = inf[S ,S ,S ], G = G The final coordinates 0.00035, where S start = inf[S 31 ,S 21 ,S 23 ], G start = G 1+2 before optimization. The final values were S stop stop Sstart = inf[S31,S21,S23 start start 21 23 1+2. were ϕ2 = 1.97 rad, z2 = −93.58, stop Gstop = 0.337, where ], start = G31 1+2. The final coordinates φ =G31.97 z2where = 0.92 φ=3 inf[S =m.−Once 1.53 z3==Gcomponents 0.23 m. final Once again, bothwere components −93.58, stop = rad, 0.337, start 31,S21rad ,S 23],and Gstart 1+2. The coordinates ϕ2 increase = 1.97 were rad, =were 0.92 m2 ϕ = −1.53 rad and z3S=m 0.23 again, both were improved. The in z2 improved. increase in the component was substantial. This optimization loop = 0.92 m ϕ3The = −1.53 radparticularly and z3 =G 0.23 m. Once again, both components Theand increase the G component was substantial. Thisparticularly optimization loop were lastedimproved. 54 iterations 24 h.in lasted 54 iterations and 24 h. The history of the process is presented in Figure 19, along with the thehistory G component was particularly substantial. optimization lasted 54 iterationssolution and 24 h. The of the process is presented in FigureThis 19, along with theloop cloud of intermediate cloud ofItintermediate solution It can be observed that even with significantly starting The history of the process is points. presented insignificantly Figure 19, along withstarting the cloud of intermediate solution points. can be observed that even with different points, thedifferent final solutions points, the final solutions from our two optimization runs are similar with respect to the objective points. It can be observed that even with significantly different starting points, the final solutions from our two optimization runs are similar with respect to the objective function values. function values. from our two optimization runs are similar with respect to the objective function values.
14 of 16 14 of 16
G component
Sensors 2018, 18, 3406 Sensors 2018, 18, x
nd case) in the objective function space. Figure 19. 19. The history of the optimization process (2nd Figure case) in the objective function space.
After optimization, optimization, the the value value of of gain gain G G1+2 forany anyazimuth azimuthand and any any of of the the two two body body postures postures 1+2for After (standing or sitting) takes on values that are always greater than around − 5 dB, which can be regarded (standing or sitting) takes on values that are always greater than around −5 dB, which can be as a satisfactory result, considering the radiation of the individual antennas (dipoles near regarded as a satisfactory result, considering thepatterns radiation patterns of the individual antennas the human body). This should enable the implementation of off-body communication. The worst (dipoles near the human body). This should enable the implementation of off-body communication. valueworst we obtained for obtained on-body communication path loss was 93 dB. loss Assuming a hypothetical IEEE The value we for on-body communication path was 93 dB. Assuming a 802.15.6 transceiver with a −transceiver 98 dBm sensitivity for existing ZigBee transceivers operating in hypothetical IEEE 802.15.6 with a(typical −98 dBm sensitivity (typical for existing ZigBee the 2.4 GHz band, for instance, Texas Instruments andTexas a maximum transmission power transceivers operating in the 2.4 GHz band, forCC2520) instance, Instruments CC2520) and of a 0 dBm (5 dBm for CC2520), the link budget is positive, albeit with a low margin of 5 dB. Given these maximum transmission power of 0 dBm (5 dBm for CC2520), the link budget is positive, albeit with we conclude thatGiven our methodology for we the conclude WBAN physical layer optimizationfor is successful. aresults, low margin of 5 dB. these results, that our methodology the WBAN
physical layer optimization is successful. 6. Conclusions and Future Work 6. Conclusions 6.1. Conclusions and Future Work In this paper, we have presented and discussed a methodology for optimizing a three-node 6.1. Conclusions WBAN design (node placement) with both on-body and off-body communication. Under this frame, In this paper, we lays havethe presented and for discussed a methodology forfinding optimizing a three-node the proposed approach groundwork a more general method for the optimal design WBAN design (node placement) with both on-body and off-body communication. Under this frame, of any WBAN configuration. The systematic exploitation of Pareto-like optimality is made possible by the proposed computing approach lays thewith groundwork a moreelectromagnetic general method for finding the optimal evolutionary linked the FDTD for full-wave simulation of antenna and design of any WBAN configuration. The systematic exploitation of Pareto-like optimality made radio channel performance. This computational method facilitates the search for innovativeisdesigns possible byisevolutionary computing linked with i.e., the FDTD full-wave electromagnetic of because it able to identify non-trivial solutions, solutions improving the prototypesimulation performance antenna and radio channel performance. This computational method facilitates the search for with respect to all design criteria, which is difficult using the traditional trial-and-error approach. innovative because it is able to non-trivial solutions, i.e., solutions to improving Specifically,designs in the research reported in identify this paper, we exploited our methodology improve the the prototype performance with respect to all design criteria, which is difficult using the traditional operation of a WBAN on a human body in both sitting and standing positions by searching for the trial-and-error approach. Specifically, in the research reported in this paper, we exploited our methodology to improve the operation of a WBAN on a human body in both sitting and standing
Sensors 2018, 18, 3406
15 of 16
best configuration of the nodes. Because we evaluate two objective criteria (multi) for two (many) body positions, the method can be qualified as many-multi-optimization. Our numerical experiments revealed significant improvements with respect to both design criteria, i.e., on-body and the off-body channel performance. 6.2. Future Work The assessment of our methodology presented in this paper is based on a small number of WBAN nodes (i.e., 3), with no need for routing. Nonetheless, our many-multi-optimization engine could be applied to a case with more nodes, further body positions, and additional design criteria. In future work, we, therefore, plan to apply our methodology in a more complex case with a number of nodes, involving multi-hop topologies and routing algorithms. In particular, we will consider energy efficiency, which is an area of great research interest, as one of the improvement criteria. However, whereas most of the many studies in the literature concentrate on the routing algorithms themselves, we will attempt to formulate and solve the node placement optimization problem using one of the existing efficient routing algorithms. Increasing the number of nodes will require greater computational effort since a larger number of scattering matrix elements sij will need to be evaluated. The routing simulation will be performed for the placement of each candidate node during the optimization process. A further focus of our future investigations will be the optimization of wireless networks operating in the ISM 5.8 GHz band as well as in the 3.6 GHz band allocated for the 5G (Fifth Generation) of wireless communication systems. For this purpose, we will analyze the performance of the network with different wearable antennas instead of simple dipoles. Author Contributions: Conceptualization: Ł.J.; Methodology: Ł.J.; P.D.B., S.H.; Software: P.D.B., Ł.J., S.H.; Formal Analysis: Ł.J.; Investigation: Ł.J.; Writing-Original Draft Preparation: Ł.J., P.D.B.; Writing-Review & Editing: S.H.; Visualization: Ł.J. Funding: This research received no external funding. Conflicts of Interest: The authors declare no conflict of interest.
References 1. 2. 3.
4.
5.
6. 7.
8. 9.
Ghamari, M.; Janko, B.; Sherratt, R.S.; Harwin, W.; Piechocki, R.; Soltanpur, C. A Survey on Wireless Body Area Networks for eHealthcare Systems in Residential Environments. Sensors 2016, 16, 831. [CrossRef] [PubMed] IEEE. IEEE Standard for Local and Metropolitan Area Networks—Part 15.6: Body Area Networks; IEEE: New York, NY, USA, 2012. Su, X.; Li, C.; Song, Y.; Yuan, X. WBAN on hardware: Implementation and optimization based on IEEE 802.15.6. In Proceedings of the International Conference on Computer, Information and Telecommunication Systems (CITS), Dalian, China, 21–23 July 2017; pp. 147–151. Promwongsa, N.; Sanguankotchakorn, T. Packet size optimization for energy-efficient 2-hop in multipath fading for WBAN. In Proceedings of the 22nd Asia-Pacific Conference on Communications (APCC), Yogyakarta, Indonesia, 25–27 August 2016; pp. 445–450. Sánchez-Montero, R.; Camacho-Gómez, C.; López-Espí, P.-L.; Salcedo-Sanz, S. Optimal Design of a Planar Textile Antenna for Industrial Scientific Medical (ISM) 2.4 GHz Wireless Body Area Networks (WBAN) with the CRO-SL Algorithm. Sensors 2018, 18, 1982. [CrossRef] [PubMed] Hausman, S.; Januszkiewicz, Ł. Impact of Indoor Environment on Path Loss in Body Area Networks. Sensors 2014, 14, 19551–19560. [CrossRef] [PubMed] Ambroziak, S.J.; Correia, L.M.; Katulski, R.J.; Mackowiak, M.; Oliveira, C.; Sadowski, J.; Turbic, K. An Off-Body Channel Model for Body Area Networks in Indoor Environments. IEEE Trans. Antennas Propag. 2016, 64, 4022–4035. [CrossRef] Januszkiewicz, Ł.; Di Barba, P.; Hausman, S. Field-Based Optimal Placement of Antennas for Body-Worn Wireless Sensors. Sensors 2016, 16, 713. [CrossRef] [PubMed] Zhang, Y.; Zhang, B.; Zhang, S. A Lifetime Maximization Relay Selection Scheme in Wireless Body Area Networks. Sensors 2017, 17, 1267. [CrossRef] [PubMed]
Sensors 2018, 18, 3406
10. 11. 12. 13. 14.
15. 16. 17. 18. 19. 20. 21.
22.
23. 24.
16 of 16
Di Barba, P.; Wiak, S.; Savini, A. Minimizing design criterion and sensitivity: Cost-effective evolutionary approach with application in mechatronics. Int. J. Appl. Electromagn. Mech. 2014, 46, 335–340. Di Barba, P. Multiobjective Shape Design in Electricity and Magnetism; Springer: Amsterdam, The Netherlands, 2010. Di Barba, P.; Mognaschi, M.E.; Palka, R.; Savini, A. Optimization of the MIT Field Exciter by a Multiobjective Design. IEEE Trans. Magn. 2009, 45, 1530–1533. [CrossRef] Di Barba, P.; Mognaschi, M.E.; Lowther, D.A.; Sykulski, J.K. A benchmark TEAM problem for multi-objective Pareto optimization of electromagnetic devices. IEEE Trans. Magn. 2018, 54. [CrossRef] Di Barba, P.; Dolezel, I.; Karban, P.; Kus, P.; Mach, F.; Mognaschi, M.E.; Savini, A. Multiphysics field analysis and multiobjective design optimization: A benchmark problem. Inverse Probl. Sci. Eng. 2014, 22, 1214–1225. [CrossRef] Di Barba, P.; Mognaschi, M.E.; Savini, A.; Wiak, S. Island biogeography as a paradigm for MEMS optimal design. Int. J. Appl. Electromagn. Mech. 2016, 51, S97–S105. [CrossRef] Bayraktar, Z.; Komurcu, M.; Bossard, J.A.; Werner, D.H. The Wind Driven Optimization Technique and its Application in Electromagnetics. IEEE Trans. Antennas Propag. 2013, 61, 2745–2757. [CrossRef] VariPose, A Voxel-Based Human Body Repositioning Tool, version 1.3, User’s Manual; Remcom, Inc.: State College, PA, USA, 2011. XFDTD 7.3 Reference Manual; Remcom Inc.: State College, PA, USA, 2012. Januszkiewicz, Ł.; Hausman, S. Simplified human phantoms for narrowband and ultra-wideband body area network modelling. COMPEL Int. J. Comput. Math. Electr. Electron. Eng. 2015, 34, 439–447. [CrossRef] Januszkiewicz, Ł.; Di Barba, P.; Hausman, S. Optimization of wireless body area network performance with simplified electromagnetic model of the body. Int. J. Appl. Electromagn. Mech. 2018, 57, 143–154. [CrossRef] Januszkiewicz, Ł. The analysis of textile antenna array radiation pattern. In Proceedings of the International Conference on Microwaves, Radar and Wireless Communications, Vilnius, Lithuania, 14–16 June 2010; Volume 18, pp. 1–4. Januszkiewicz, Ł. Simplified human body models for interference analysis in the cognitive radio for medical body area networks. In Proceedings of the 8th International Symposium on Medical Information and Communication Technology, Firenze, Italy, 2–4 April 2014; pp. 1–5. Januszkiewicz, Ł. Uproszczony model ciała człowieka do analizy systemów bezprzewodowych działajacych ˛ ˙ osób w róznych ˙ w poblizu pozycjach. Przeglad ˛ Elektrotechniczny 2015, 1, 156–158. (In Polish) [CrossRef] Di Barba, P. A fast evolutionary method for identifying non-inferior solutions in multicriteria shape optimisation of a shielded reactor. Int. J. Comput. Math. Electr. Electron. Eng. 2001, 20, 762–776. [CrossRef] © 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
