IN the RF (Radio Frequency)-challenged environments, Increasing the Capacity of Magnetic Induction Communications in RF-Challenged Environments

Transcription

1 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 6, NO. 9, SEPTEMBER Inreasing the Capaity of Magneti Indution Communiations in RF-Challenged Environments Zhi Sun, Member, IEEE, Ian F. Akyildiz, Fellow, IEEE, Steven Kisseleff, Student Member, IEEE, and Wolfgang Gerstaker, Senior Member, IEEE Abstrat Magneti Indution (MI) tehniques enable effiient wireless ommuniations in dense media with high material absorptions, suh as underground soil medium and oil reservoirs. A wide range of novel and important appliations in suh RF-hallenged environments an be realized based on the MI ommuniation mehanism. Despite the potential advantages, the major bottlenek of the MI ommuniation is the limited hannel apaity due to the low MI bandwidth. In this paper, the Spread Resonane (RS) strategy is developed for the MI ommuniation in RF-hallenged environments whih greatly inreases the MI hannel apaity. Speifially, instead of using the same resonant frequeny for all the MI oils, the spread resonane strategy alloates different resonant frequenies for different MI relay and transeiver oils. An optimization solution for the resonant frequeny alloation is formulated to maximize the MI hannel apaity whih aptures multiple unique MI effets, inluding the parasiti apaitor in eah MI oil, the Eddy urrents in various transmission media with limited ondutivities, and the random diretion of eah oil. Numerial evaluations are provided to validate the signifiant hannel apaity improvements by the proposed SR strategy for MI ommuniation systems. Index Terms Magneti indution ommuniations, hannel apaity, RF-hallenged environments. I. Introdution IN the RF (Radio Frequeny)-hallenged environments, inluding the underground soil medium, oil reservoirs, and mines and tunnels, it is extremely diffiult to establish reliable and effiient wireless ommuniation [], []. However, many novel and important appliations in those RF-hallenged environments are reently envisioned to enhane the seurity or the produtivity of our modern soiety, suh as underground oil gas extration, mine disaster prevention and resue, onealed border patrol and intruder detetion, intelligent agriulturing, underground pipeline tank monitoring, earthquake and landslide foreast, among others [], [], [3], [4]. All the above appliations require the realization of wireless ommuniation in the RF-hallenged environments, whih reate signifiant hallenges ompared to lassial eletromagneti (EM) waves Manusript reeived August 6, ; revised January 8 and April 7, 3. The editor oordinating the review of this paper and approving it for publiation was D. I. Kim. Z. Sun is with the Department of Eletrial Engineering, University at Buffalo, the State University of New York, Buffalo, NY 46, United States ( zhisun@buffalo.edu). I. F. Akyildiz is with the Shool of Eletrial and Computer Engineering, Georgia Institute of Tehnology, Atlanta, GA 333, United States ( ian@ee.gateh.edu). S. Kisseleff and W. Gerstaker are with the Institute for Mobile Communiations, University of Erlangen-Nurnberg, Erlangen, Germany ( kisseleff@lnt.de; gerstaker@nt.e-tehnik.uni-erlangen.de). Digital Objet Identifier.9/TCOMM /3$3. 3 IEEE []. Speifially, there are two major problems, namely, extremely short ommuniation ranges and highly unreliable hannel onditions [], [5], [6]. Reent developments of the magneti indution (MI) tehniques [7], [8], [9] have great potential to solve the above problems and enable effiient wireless ommuniation in RFhallenged environments. Instead of using propagation waves, the MI-based ommuniation utilizes the near field of a oil. As a result, the MI oils working at HF or lower frequeny bands an realize muh more reliable hannel in the dense medium suh as soil and oil. However, the MI-based ommuniation in their original form still suffer from the limited ommuniation range problem due to the high attenuation rate of the magneti field in the near region. To enlarge the ommuniation range of the original MI tehniques, the MI waveguide tehnique [], [], [], [3], [4], [5], [6] an be utilized. The MI waveguide onsists of multiple resonant relay oils that are deployed in between two nodes. The MI waveguide struture is first proposed in [], [], [], [6], where the relay oils are losely plaed so that strong oupling between adjaent oils is formed. In [5], [6], we employed the MI waveguide tehnique for wireless ommuniation where the relay oils are expeted to be plaed as sparsely as possible. In this ase, the oupling between adjaent relay oils is very weak. The wireless ommuniation between two transeivers is aomplished by the onseutive weak magneti indution between adjaent MI relay oils, as shown in Fig.. By this way, the ommuniation range is greatly enlarged ompared to the EM wave-based and the original MI tehniques. For example, in the soil medium, the range of the Mia sensor is less than 4 m []; with similar devie size and power, the original MI tehnique has a ommuniation range around m [5], while the MI waveguide an reah a range of more than m [5]. Moreover, the relay oils in the MI waveguide do not onsume extra energy sine the magneti indutions are passively relayed. Those low ost oils are easy to deploy and do not need ontinuous maintenane. In addition, the lifetime of the wireless system an be greatly prolonged sine the MI-based devies an be reharged wirelessly using the indutive harging tehnique [7], [4]. This property is favorable in RF-hallenged environments sine it is very diffiult to exhange devie batteries. Despite the above advantages, the original MI waveguidebased ommuniation tehnique has an inherent bottlenek, i.e., the limited hannel apaity. Typially, the relative oupling strength (ratio of the mutual indution to the self indu-

2 3944 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 6, NO. 9, SEPTEMBER 3 Fig.. TX Coil MI Coupling Magneti Field Relay Coil MI Coupling Relay Coil MI Coupling Relay Coil The MI ommuniation using a MI waveguide. MI Coupling tion) between adjaent oils in MI waveguide is in the order of 4 or even smaller. Aordingly, the hannel bandwidth of the MI waveguide is very limited [5]. If the transmission distane is inreased to a ertain threshold, the MI hannel bandwidth an be very low []. This limited bandwidth orresponds to the very low hannel apaity. Therefore, although the MI waveguide-based ommuniation an over a large range in the RF-hallenged environments, the ahievable data rate is not satisfatory. In many envisioned appliations, suh as the border patrol and the mine disaster resue, a signifiant volume of data needs to be timely transmitted on the MI hannels. Therefore, it is of a great importane to inrease the hannel apaity in urrent MI waveguidebased ommuniation systems. The strategy to inrease the bandwidth of the strongly oupled MI waveguide has been investigated in []. However, to date, the solution to inrease hannel apaity of the loosely oupled MI waveguide for wireless ommuniation is still not lear. In this paper, we propose the Spread Resonane (SR) strategy for the MI waveguide-based ommuniation system in RFhallenged environments, whih an dramatially inrease the hannel apaity of suh systems. In partiular, different from the existing MI waveguide where all MI oils use the same resonant frequeny, the spread resonane strategy alloates unique and optimal resonant frequenies for different MI relay and transeiver oils. The spread resonane frequenies an effetively enlarge the MI hannel bandwidth while the optimal entral operating frequeny minimizes the path loss. Therefore, the MI hannel apaity is greatly inreased by the SR strategy. We formulate and solve an optimization problem for the resonant frequeny alloation to maximize the MI hannel apaity, whih aptures multiple unique MI effets, inluding the parasiti apaitane in eah MI oil, the Eddy urrents in various transmission media with limited ondutivities, the bakground noise as well as the noise generated by the MI waveguide itself, and the random diretion of eah oil. Finally, omprehensive numerial evaluations are onduted to further validate the hannel apaity improvements by the proposed SR strategy for the MI ommuniation systems. The remainder of the paper is organized as follows. In Setion II, the related studies are introdued. In Setion III, the SR strategy is developed in detail and the optimal solution is formulated to alloate the resonant frequenies in the SR strategy. Then, in Setion IV, numerial studies are performed. Finally, the paper is onluded in Setion V. II. Related Work Due to the unique advantages of the MI tehniques in the RF-impenetrable media, the MI ommuniation systems have been developed in many different senarios. In [7], an MI RX Coil ommuniation system is developed for the naval mine warfare(miw) operations to provide a reliable wireless ommand, ontrol and navigation hannel. In [8], the MI ommuniation system is used as an alternative to the Bluetooth. The high path loss of MI is utilized to reate a personal ommuniation bubble area with minimum interferenes. In [9], the MI is used for underground soil medium where it is proven that the MI transmission is not affeted by soil properties and requires less power and lower operating frequenies than the EM waves. In [], the MI tehnique is implemented in an intra-body network, where the information is transmitted from and to some implanted miniature devies at multiple sites within the human body. In [3], the MI tehnique is developed to loate and trak the underground animals. Through a two-month field experiment, the MI loalization system is proven to suessfully trak wild European badgers within their burrows. In [7], [4], the MI tehnique is utilized to transfer wireless energy for a relatively long distane. Moreover, the effets of parasiti apaitane of the MI energy transfer system is disussed in [4]. The hannel apaity of the above MI ommuniation system that uses a single pair of oils has been investigated in [8], [9]. All the above MI systems use single pairs of MI oils that require either high transmission power or large oil size to reah reasonable transmission ranges. To enlarge the transmission range, the MI waveguide struture is utilized. The MI waveguide is first proposed in [] and intensively investigated in [], [], [3], [6]. The theoretial results are also validated by the field experiments in [4], [5]. In [5], the impat of the Johnson on the MI waveguide is investigated. In [6], a resonant transduer is developed to redue the refletion on the terminals of the strongly oupled MI waveguide. Similarly, in [], a thinfilm formed MI waveguide is developed to ahieve the low propagation loss and high bandwidth. All the above MI waveguide with strongly oupled relay oils is designed to realize artifiial delay filters, dieletri mirrors, distributed Bragg refletors, among others. However, the above MI waveguide investigations do not over the appliations of wireless ommuniations. In [6], [5], we introdue the loosely oupled MI waveguide struture in the field of wireless ommuniations, whih an greatly enlarge the ommuniation range in many RFhallenged environments without inreasing the MI oil size and transmission power. In [7], the hannel model of the MI waveguide ommuniation under pratial apaitane onstraints is derived. The noise models for the MI waveguide ommuniation system are investigated. Besides the pointto-point ommuniation, the MI hannel apaity is learly shown to be extremely low, espeially in the far region of the transmitter. Although the MI waveguide-based ommuniation system ahieves good transmission range in RF-hallenged environments, the above studies fous on minimizing the path loss, while the bandwidth and the hannel apaity are not onsidered at all. Hene, the hannel apaity of MI waveguide an be even smaller than that of the original MI system. In this paper, we propose the SR strategy to enlarge the bandwidth while keeping the path loss on an aeptable level. As a result, the MI hannel apaity signifiantly inreases.

3 SUN et al.: INCREASING THE CAPACITY OF MAGNETIC INDUCTION COMMUNICATIONS IN RF-CHALLENGED ENVIRONMENTS 3945 Fig.. Us Us Coil (TX) C R C L R L Z, M UM Z, Coil (Relay ) C L Z L R C R Coiln- (Relay n-) Cn- L UMn- L Zn-,n- Zn,n- R Mn Cn- R UMn Coiln (RX) The high frequeny MI waveguide model and the equivalent iruit. It should be noted that the methods of using multiple resonane frequenies an also be found in other MI systems. However, the objetive of the multiple resonane frequenies is different in this paper. For example, in [9], [3], two resonant frequenies are involved in a single MI transeiver: one is for the ommuniations while the other is for the energy transfer. In this paper, we assign spread resonant frequenies to different relay oils, whih aims to broaden the MI bandwidth. Moreover, the optimal position of eah spread resonant frequeny is theoretially determined in this paper. III. Spread Resonane Strategy In SR strategy, the resonant frequeny of eah MI oil is deviated from the original entral operating frequeny in a ontrolled manner. The gain of this method is that the MI hannel bandwidth an be signifiantly enlarged if the deviation is properly hosen. However, the drawbak of the spread resonant frequeny is that the path loss of the MI waveguide system may inrease as the resonant frequenies are spread. It is hallenging to jointly determine the optimal resonant frequeny deviation and the optimal entral operating frequeny: First, sine eah MI oil has a unique resonant frequeny, it beomes very ompliated to alulate the path loss and the bandwidth of the MI waveguide. Consequently, a ompliated and non-linear optimization problem is formulated and needs to be solved. Seond, sine the entral operating frequeny is expeted to be as high as possible to enhane the mutual indution, the impat of the parasiti apaitane [3], [33] of the MI oils annot be ignored any more. Third, similarly, due to the high entral operating frequeny, the skin depth effets in the transmission medium aused by the eddy urrents [35], [36] need to be modeled for the MI waveguide system, espeially in the medium with a not negligible ondutivity. In this setion, we first formulate the problems of the optimal resonant frequeny alloation and entral operating frequeny seletion in the SR strategy. Then, we speifially investigate the influene of the parasiti apaitane and skin depth, respetively. Later we develop the analytial solution of the optimization problem. A. Problem Formulation We onsider the wireless ommuniations between two transeivers in the RF-hallenged environments, espeially dense media suh as soil, rok, and rude oil. The MI waveguide system onsists of n + MI oils {Coil, Coil,...Coil n }, L Cn L Zn-,n R RL RL Cn R where Coil is the transmitter, Coil n is the reeiver, and the rest are rely oils, as shown in Fig.. The number of MI oils n is set to be an even number for simpliity. The entral operating frequeny is denoted as f. The permittivity and the ondutivity of the transmission medium are ɛ m and σ m, respetively. Aording to our previous analysis [5], if the transmission medium does not ontain magnetites, the permeability of the medium is the same as that of the air, whih is μ. It should be noted that in the transmission medium with magnetites, the permeability is higher and the MI performane an be enhaned. However, this situation is out of the sope of this paper sine most transmission media in the nature do not ontain magnetite material. Sine we only onsider the point-to-point ommuniation, there is no interferene from other pairs of transeivers. Then, we start from the lassi hannel apaity formula [3]: C = B log ( + P t L p ); () N where B is the hannel bandwidth; P t is the transmission power; L p is the path loss; and N = N ambient is the ambient noise power. The average ambient noise power is around -5 dbm, whih is measured in underground soil medium [34]. Aording to our analysis in [5], the path loss L p is a funtion of the signal frequeny f,i.e.l p ( f ). Then based on (), the hannel apaity of the MI waveguide an be alulated as f +B/ ( C MI = log + P ) t L p ( f ) d f ; () f B/ N ambient where the transmission power P t and the ambient noise level N ambient are onstants and are determined; while the hannel bandwidth B and the path loss L p ( f ) need to be designed to maximize the MI hannel apaity. Different from the traditional EM wave-based wireless hannel, the MI bandwidth B is not a onstant but vary as the onfigurations of the MI waveguide system hange. In addition, the MI waveguide path loss L p ( f ) is no longer a simple exponential funtion due to the onseutive magneti indution. Moreover, different from the existing analysis [5], [] on the MI waveguide ommuniation systems, the SR strategy assigns different resonant frequenies to different MI oils and needs to onsider the influene of the parasiti apaitane and the skin depth, whih reate even more hallenges in alulating L p ( f ), B, andc MI. Without loss of generality, we denote the resonant frequenies for MI oil {Coil, Coil,...Coil n } as f n Δ f, f ( n )Δ f,..., f,..., f + n Δ f,whereδf is the frequeny interval between two adjaent oils. Δ f defines the intensity of how widely the resonant frequeny is spread. Then the optimal resonant frequeny alloation and entral operating frequeny seletion in SR strategy an be formulated as Given : Transmission distane d, Medium permitivity ɛ, Medium ondutivity σ, Number of MI oils, Coil parameters; Find : Central operating frequeny f, Intensity of resonant frequeny spread Δ f ; s.t. : MI hannel apaity C MI ( f ) is maximized. (3)

4 3946 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 6, NO. 9, SEPTEMBER 3 To solve above optimization problem, the MI hannel apaity C MI ( f ) needs to be analytially expressed first. In the following part of this setion, we first alulate bandwidth and path loss of the MI waveguide under the SR strategy, where the effets of parasiti apaitane, spread resonant frequenies, and skin depth are aurately modeled. Then, the analytial solution of the optimization problem given in (3) is developed. B. Modeling the Influene of Parasiti Capaitanes and the Spread Resonant Frequenies In high frequeny iruits, the parasiti apaitanes are formed due to the distributed eletrial oupling between any two onduting objets of the iruit [3]. In MI-waveguides, the MI oils are made of wire loops without the magneti ore and the outer shell. Hene, the oupling between the ore and the shell an be ignored. In addition, eah MI oil has only one layer of winding. Hene, the layer-to-layer apaitane between two neighboring layers does not exist. Moreover, sine the different oils are far enough from eah other, the oupling between different oils an be ignored. Therefore, the parasiti apaitanes in MI waveguides are formed only due to the oupling between two turns in the winding. In transformer design, the overall effet of parasiti apaitanes an be modeled as a lumped apaitor. Sine the MI waveguide an be modeled as a multi-stage transformer, the lumped apaitor model is also appliable. Hene, we provide a high frequeny transformer model for the MI waveguide system under the SR strategy in the first row in Fig.. In the model, C p is the lumped apaitor model of the parasiti apaitane in the MI waveguide; M i (i =,..., n) is the mutual indution between the i th oil and the (i ) th oil; U s is the voltage of the transmitters battery; L is the oil self indution; R is the wire resistanes of the oil; {C i, i =,,..., n} are the apaitors loaded in the i th oil; R L is the mathed load of the reeiver that maximizes the reeived power at the entral operating frequeny f. It should be noted that with the signal frequeny deviation from the entral frequeny, there will be refleted power from the MI reeiver that auses additional path loss. All MI oils have the same onfigurations expet the loaded apaitor {C i, i =,,...,n}, whih is used to ahieve the resonant status on the resonant frequeny. Sine different oils are alloated different resonant frequenies in SR strategy, the loaded apaitanes C i are also different. Other than the loaded apaitanes, all the oils have the same parameters, inluding the wire resistane R,oil radius a, and number of turns N t. The equivalent iruits of the high frequeny multi-stage transformer is shown in the seond row in Fig., where U Mi U Mi = jωm i Z i,i + jωl + U M = jωm U s jωc + R + ω Mi Z i,i = jωl + Z i+,i + jω ( jω ( jωc +R ) i jω + jω jωl jω + jωl jωc +R ) i jω + jωc +R i jωc i +R, (i =, 3,...,n); jωc p ; jωc p + jωl, (i =,,...n ); ω Mn Z n,n = jωl + ; jω ( jωcn +R +Z L ) jω + jωcn +R +Z L ω Mi Z i,i = jωl + Z i,i + Z, = jωl + ω M jω ( jω ( jωc +R ) jω +Z (i+)i+ jωc +R ) jω + jωc +R, (i =, 3,...n); jωc +R. (4) In (4), f is the signal frequeny and ω = π f is the orresponding angle frequeny; the oil self indution L = μπn t a; the oil wire resistanes R = N t πa R where R is the unit length resistane of the wire determined by the material and thikness; Z i(i ) is the influene of the i th oil on the (i ) th oil and vie versa; U Mi is the indued RMS (root mean square) voltage on the i th oil; U s is the RMS voltage of the signal at the transmitter oil. The mutual indutions M i is substantially influened by the skin depth effet, whih will be disussed in the next subsetion. We utilize a method proposed in [33] to determine the lumped apaitor model C p for the parasiti apaitane in the MI waveguide system. We assume that the oating material of the wire on the oil has a relative permittivity ɛ ; the diameter of the bare wire is D b ; and the diameter of the oated wire is D. Then, the value of the parasiti apaitane C p an be alulated by the following formula: C p = [ ɛ N t ɛ aros( πa ln D + ot.5 aros( ln D D b ɛ D ln D b ɛ ) (5) D b ) ot( π ]; ) where ɛ is the permittivity of the vauum permittivity; and ɛ = ɛ ɛ is the relative permittivity of the wire oating material. Aording to (5), we an ontrol the parasiti apaitane at an aeptable value by: ) inreasing the number of turns of the oil; ) using thiker wire oating; and 3) using oating material with lower permittivity. By utilizing the multi-stage high frequeny transformer model and it s equivalent iruit, the path loss and the bandwidth of the MI waveguide ommuniation system an be alulated. Before alulating the MI hannel apaity, we need to solve the remaining question, i.e. modeling the skin depth effets on the mutual indution M i. C. Modeling the Influene of Skin Depth The skin depth desribes how the time-varying EM field is distributed within a ondutive material, i.e. how deep the EM field an exist beneath the surfae of the ondutor. In RFhallenged enviornments, although the transmission medium generally onsists of non-ondutive materials, it an have a ertain level of ondutivity under ertain irumstanes, suh as in wet soil, oil reservoirs, and opper mines. If the operating frequeny is low, the skin depth is very large and the EM field an be onsidered to exist anywhere in the medium. Hene, the skin depth an be ignored. However, in SR strategy, the operating frequeny is supposed to be as high as possible.

5 SUN et al.: INCREASING THE CAPACITY OF MAGNETIC INDUCTION COMMUNICATIONS IN RF-CHALLENGED ENVIRONMENTS 3947 Then, the skin depth beome muh smaller. Consequently, the EM field has enough strength only within a shorter range around the MI oil. Beyond this range, the EM field may beome extremely weak. The small skin depth an signifiantly weaken the mutual indution between adjaent MI oils in a MI waveguide ommuniation system, whih indues the additional loss of the magneti field. Aording to [5], the MI oil is modeled as a magneti dipole sine the intervals between adjaent oils are muh larger than the oil size. Hene, the mutual indution an be dedued by the magneti potential A of the magneti dipole. The expression of A in non-ondutive medium is provided in [5]. However, in SR strategy, A will have an additional attenuation fator G due to the skin depth effet. The additional attenuation fator G is a funtion of the distane between the two MI oils r and the skin depth δ in the medium. G(r,δ) an be alulated aording to the model provided in [35], where x 3 r G(r,δ)= x + [x + j( r δ ) ] exp [ x j( δ )] dx. The skin depth δ is a funtion of the operating frequeny, the medium permeability μ, the medium permitivity ɛ, andthe medium ondutivity σ, whih an be alulated by [36]: δ = ω μɛ ( + σ ω ɛ (6) ). (7) The skin depth effet an be aurately haraterized by the additional attenuation fator G(r,δ) in (6). However, (6) ontains integral omputations that is not favorable in most optimization problems. Hene, we approximate (6) by a simpler funtion of the ratio of oil interval r andskindepthδ. By analyzing the numerial results of (6), we an approximately math G(r,δ) as an exponential funtion of r δ as follows: ( G(r,δ).4 exp.883 ( r ).67 ). (8) δ where the data fitting is onduted under the ondition that the relative skin depth r δ is in the range from to. It should be noted that G(r,δ)isalmostwhen r δ =. Sine G(r,δ)is monotonially dereasing and non-negative, the approximation done in (8) is appliable for all values of r δ from to infinity. Then, the mutual indution of the i th oil and the (i ) th oil an be alulated by: M i μπnt a 4 4r G(r i,δ) ( sin θ i 3 t sin θr i + os θt i os θr), i (9) where r i is the distane between the i th oil and the (i ) th oil; θt i and θi r are the angles between the oil radial diretions and the line onneting the two oils. D. Optimization Solution By substituting (5) and (9) into (4), the equivalent iruit model of the MI waveguide system under the SR strategy is ompleted. Given the iruit parameters, the reeived power P r at the reeiver oil an be alulated. By investigating the P r as funtions of the transmission distane and the operating frequeny, the path loss and the bandwidth of the MI waveguide ommuniation system an be derived. To obtain the lowest path loss, the loaded apaitor should be as small as possible to ahieve high operating frequeny. However, aording to the equivalent iruit model given in (4), if the loaded apaitor is smaller than the parasiti apaitane, it annot effetively ontrol the resonant frequeny. Instead, the parasiti apaitane would determine the resonant frequeny. Therefore, to keep the resonant frequeny under ontrol, the bottom line is to that the loaded apaitor should be larger than the parasiti apaitane. In this paper, our objetive is to maximize the MI hannel apaity and we want the smallest path loss and the largest bandwidth. Therefore, we let the loaded apaitor have a value on par with the parasiti apaitane. As a result, the path loss of the MI waveguide an be minimized while we an still tune the value of the loaded apaitor to assign optimal resonant frequeny to eah MI oils. Based on the above disussion, we an alulate the reeived power P r with mathed load as follows: P r 4 Z n,n + R ( jωl + jωc n + Z n,n + R ) () U s M jωm L Z, + jωl + ( jωc + R )... jωm n Z n,n + jωl + (, jωc n + R ) In (), Z i,i and Z i,i are the oupled impedane that the adjaent oils put on eah other. Z i,i and Z i,i have signifiant effets only if the oils are losely plaed (i.e. the interval r i between adjaent oils is small enough). However, one of the design objetives is to use as few relay oils as possible to redue the deployment and maintenane ost. Aording to the numerial alulations using (4), Z i,i and Z i,i an be safely negleted if the ratio of the oil interval and the oil size (radius) r i a is larger than, whih is appliable in most envisioned appliations. Hene, by using () while ignoring the oupled impedanes, the path loss of the MI waveguide system under the SR strategy an be alulated: L p (ω) 4 R ( jωl + jωc n +R ) M jωm L jωl + ( jωc +R )... jωm n jωl + ( () jωc n + R ). It should be noted that the transmission power P t used for alulating the MI path loss is the maximum power at the transmitter, i.e., Pt max = U s R. The reason is that the atual transmission power of the MI ommuniation systems dereases as the transmission distane inreases. Less power an be emitted as the MI oils are plaed further to eah other. Hene, using the atual transmission power results in an unrealistially small value for the path loss, whih annot haraterize the MI hannel. By using the maximum transmission power, the path loss annot be underestimated.

6 3948 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 6, NO. 9, SEPTEMBER 3 In SR strategy, the bandwidth of the MI waveguide is determined by how widely the resonant frequeny is spread: B = n Δ f. () Flutuations may exist inside the bandwidth sine the path loss reahes its loal minima at eah resonant frequeny of the MI oils, whih an be eliminated by hannel equalizations. Then, by substituting () and () into (), the MI hannel apaity an be alulated. To avoid the integral in the optimization, we selet a single frequeny, i.e. f = f n Δ f, in alulating the path loss L p (π f ) in (3). At suh frequeny, the MI waveguide system ahieves maximum in-band path loss due to the following two reasons: ) MI waveguide path loss ahieves its loal maxima at the frequeny in the middle of two adjaent resonant frequenies; and ) the overall path loss inreases as the signal frequeny deviates from the entral operating frequeny. Therefore, all the path loss inside the bandwidth is guaranteed to be lower than the path loss at f n Δ f. Due to this reason, the atual system hannel apaity an be slightly higher than theoretial one derived in this paper. Moreover, to guarantee orret demodulation, the signal to noise ratio is expeted to be suffiiently large. Hene, the onstant inside the logarithm funtion an be negleted. Then, the MI hannel apaity in () an be dedued as [ P t L p π( f C MI n Δ f log n Δ f ) ] (3) N ambient [ ( P t R ) n = n Δ f log + log N ambient 4ωL ωm i i= n log jωl + + R ] jωc i ; i= where ω = π( f n Δ f ); C i is set to the value to ahieve the resonant status at the frequeny f + (i n ) Δ f,i.e. j4π[ f + (i n ) Δ f ] C + jπ[ f + (i n i ) Δ f ] L = ; (4) Then the MI hannel apaity an be further developed as: [ ( P t R ) n C MI =nδ f log + log N ambient 4ωL ωm i (5) i= n log jπ i= [ f + (i + n)δ f ] ( i)δ f L f n + R ] Δ f ; Sine the resonant frequeny deviation i Δ f, (i =,,...,n) is muh smaller than entral operating frequeny f, the hannel apaity formula an be further developed as ( P t R C MI nδ f [log ) n + log N ambient 4ωL (π f M i ) i= n log jπ ( i)δ f L + R ] ; (6) i= As mentioned in Setion III-C, the mutual indutions M i between the MI oils are random variables sine the position and the diretions of eah MI oils may vary in different loations as time elapses. Therefore, the MI hannel apaity is also a random variable. In the optimization problem addressed in this paper, we aim to maximize the ε-outage hannel apaity Outage ε [C MI ], whih is the hannel apaity that the MI ommuniation system an ahieve with a probability ε. Sine the oils are supposed to be deployed in dense medium like underground soil medium, it is unlikely that the oils an be shifted a distane longer than the dimension of the oil one the oils are deployed. Moreover, the oil interval length is muh longer than the oil size in MI ommuniation systems. Therefore, within the deviation limit, the influene of the deviations of the intervals r i an be negleted. However, the diretions of the oils an be highly random in some speifi appliations, suh as the oil reservoir monitoring. Assuming eah MI oil has an independent and identially distributed (i.i.d) diretion, the MI hannel apaity an be approximately viewed as a Gaussian random variable, whih an be proven as follows. Aording to (6), only the seond term in the MI hannel apaity formula is a random variable. This term is the sum of the logarithm funtions of the mutual indution of eah MI oil. Sine the value of the mutual indution of eah oil is i.i.d and the MI waveguide usually onsists of many relay oils, the term n i= log [ π f M i ] approximately follows the normal distribution aording to the entral limit theorem [37]. Sine the other two terms in (6) are not random variables, the total MI hannel apaity also follows the normal distribution. The mean value of the MI hannel apaity an be approximately expressed as ( P t R E[C MI ]=nδ f [log ) ( +nlog N ambient 4ωL π f M ( f ) ) n i= log jπ ( i)δ f L + R ] ; (7) where M ( f ) is the initial diretion or the designed diretion of eah oil. There two types of the designed diretions of MI oils: the axial alignment and the planar alignment. In the axial alignment, θ i t = andθ i r = ; while in the planar alignment, θ i t = π and θi r = π. It should be noted that M ( f ) is still a funtion of the entral operating frequeny f sine the skin depth takes effet at any diretions of the oils. The variane of the MI hannel apaity Var[C MI ] annot be analytially alulated sine it depends on the speifi appliations and environments, whih an be dramatially different from ase to ase. Therefore, in this paper, we set the variane of the MI hannel apaity as q% of the mean apaity, where the value of q defines how severely the oil diretions may deviate from the designed value. Then, the ε- outage hannel apaity Outage ε [C MI ] an be alulated as Outage ε [C MI ] = E[C MI ] + erf (ε ) Var[C MI ]. (8) Now the optimization problem given in (3) an be realized: Find : f, Δ f Maximize : Outage ε [C MI ] S ub jet to : f + n Δ f < π L C p (9) where C p is the lumped model of the parasiti apaitane, whih is given by (5). The onstraints in (9) are due to the

7 SUN et al.: INCREASING THE CAPACITY OF MAGNETIC INDUCTION COMMUNICATIONS IN RF-CHALLENGED ENVIRONMENTS 3949 fat that the loaded apaitor should be larger than the parasiti apaitane, as disussed previously. Although the problem in (9) is a nonlinear programming, it an be solved by the onvex optimization methods [38], espeially the Lagrange multiplier, due to the following reasons: ) the ε-outage hannel apaity Outage ε [C MI ] is a onave funtion of the entral frequeny f and the spread intensity Δ f ; and ) the onstraint set f + n Δ f < π L C p is onvex. Hene, the optimal entral operating frequeny f and the optimal spread intensity Δ f in the SR strategy an be derived by solving the onvex programming problem defined in (9). Sine (9) is already the standard form of a onvex programming problem, it would be trivial to show the detailed proedure of lassi Lagrange multiplier method to solve the onvex programming problem in this paper. In next setion, we will disuss the optimization results in details based on the numerial evaluations. IV. Numerial Evaluation In this setion, the performane of the SR strategy is evaluated by Matlab numerial results. The effets of the transmission distane, the parasiti apaitane, the skin depth, and the oil diretion rotations on the maximum MI hannel apaity, the optimal operating frequeny, and the intensity of the spread resonant frequeny are quantitatively aptured. The MI hannel apaity optimized by the SR strategy is also ompared with the apaity of the original MI waveguide ommuniation system, whih validates the dramati apaity inrease of the proposed strategy. We use the -db bandwidth to alulate the hannel apaity of the original MI waveguide. It should be noted that the apaity ontribution from the signal that has a reeived power more than db lower than the power at the entral frequeny an be negleted. In the evaluations, exept studying the effets of ertain parameters, the default values are set as follows: The MI waveguide onsists of MI oils with the radius of.5 m.the number of turns of eah oil is N =. The oils are deployed every r = 5 m. The total number of oils n are determined by the transmission distane d, i.e., n = d r. The oils are made of ooper wire with 4 mm diameter and mm thik oating material. The unit resistane of suh opper wire is.5 Ω/km. The relative permittivity of the oating material is. The parasiti apaitane of suh MI oil an be alulated by (5), whih is 5 pf. As disussed in the beginning, the permeability of the transmission medium is the same as that in the air, i.e. μ = 4π 7 H/m. The ondutivity of the transmission medium σ =.5 S/m. The transmission power is set as dbm ( mw) and the bakground noise level is 5 dbm. As disussed in the last setion, the effet of the random oil diretion is haraterized by the ratio of the apaity variane and the apaity mean value, whih is set to % as the default value in the analysis. In Fig. 3, the %-outage hannel apaity is given as a funtion of the entral operating frequeny f and the spread intensity of the resonant frequeny Δ f. As expeted, the MI hannel apaity is a onave funtion of f and Δ f, whih justifies the effetiveness of the Lagrange multiplier optimization method. As shown in Fig. 3, the spread intensity % Outage Capaity (bit/s/hz).5.5 x 6 x 4.5 Operating Frequeny f (Hz) Δ f (Hz) f (MHz) Spread Intensity Δ f (Hz) Fig. 3. The %-Outage hannel apaity as a funtion of the entral operating frequeny and the spread intensity of the resonant frequeny. Fig. 4. % Outage Capaity (bit/s/hz) 4 x SR Strategy (no deviation) Original (no deviation) Original (% deviation) SR Strategy (% deviation) TX distane (m) (a) The optimal %-outage apaity with/without oil diretion deviations as a funtion of transmission distane. Spread Intensity Δ f (Hz) TX Distane (m) (b) The optimal spread intensity of the resonant frequeny as a funtion of transmission distane. Effets of transmission distane and random oil diretions. Δ f ranges from to Hz. There is an optimal intensity for eah entral operating frequeny that an maximize the MI hannel apaity. The entral operating frequeny f ranges from 5 KHz to the maximum operating frequeny, whih is onstrained by the parasiti apaitane as shown in (9). The MI hannel apaity in Fig. 3 is a monotonially inreasing funtion of f in this range. The reason for the monotoni inrease is that the medium ondutivity is not very high in Fig. 3. Hene, the skin depth effet is not signifiant for the oil interval length. As a result, the onstraint only omes from the parasiti apaitane in this senario.

8 395 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 6, NO. 9, SEPTEMBER 3 In Fig. 4(a), the %-outage hannel apaity with and without oil diretion deviations is given as a funtion of transmission distane. The apaity of the original MI waveguide ommuniation with the same parameters is also plotted for omparison. As shown in Fig. 4(a), the SR strategy ahieves a MI hannel apaity that is muh higher than the original MI waveguide system, espeially in the far region. The reason for the signifiant apaity inrease an be explained as follows. If the MI oils are deployed lose enough to maintain suffiient oupling, the path loss an be ontrolled in a low level even the transeivers are hundreds of meters apart from eah other. However, in the original MI waveguide system, the system bandwidth dramatially dereases as the number of relay oils inreases. The SR strategy solves this problem by assigning unique and optimal resonant frequeny for eah MI oil to tradeoff the low path loss and the high bandwidth, whih results in a muh higher hannel apaity. An interesting phenomenon is that the MI hannel apaity under SR strategy inreases as the transmission distane inreases at first. This is due to the fat that more relay oils are used when the distane inreases. More relay oils means that the resonant frequenies are spread more widely. However, after a ertain distane, the MI hannel apaity starts to derease. This is due the reason that the system path loss inreases dramatially when the transmission distane is larger than a threshold. Fig. 4(a) also indiates that the random diretions of the MI oils signifiantly affet the MI hannel apaity, espeially in the SR strategy that highly depends on the mutual indution between adjaent oils. In Fig. 4(b), the optimal spread intensity of the resonant frequeny is given as a funtion of transmission distane. As expeted, the optimal spread intensity dereases as the transmission distane inreases, whih an lower the path loss in the far region. As disussed previously, when the medium ondutivity is low, it is always optimal to hoose the maximum entral operating frequeny no matter how large the transmission distane is. In Fig. 5, the effets of the parasiti apaitane on the SR strategy are investigated. Fig. 5(a) shows the optimal %- outage hannel apaity as a funtion of parasiti apaitane; Fig. 5(b) gives the optimal frequeny spread intensity as a funtion of parasiti apaitane; and Fig. 5() provides the optimal entral operating frequeny as a funtion of parasiti apaitane. As the parasiti apaitane inreases, the allowed maximum operating frequeny also dereases. Sine the medium ondutivity is not very high, the optimal operating frequeny equals the maximum operating frequeny, whih dereases as the parasiti apaitane inreases. Lower operating frequeny auses weaker mutual magneti oupling and smaller optimal frequeny spread intensity. Therefore, the optimal MI hannel apaity also dramatially dereases as the parasiti apaitane inreases. In Fig. 6, the effets of the medium ondutivity or the skin depth on the SR strategy is analyzed. Fig. 6(a), Fig. 6(b), and Fig. 6() give the optimal %-outage hannel apaity, the optimal frequeny spread intensity, and the optimal entral operating frequeny as funtions of the medium ondutivity, respetively. As the medium ondutivity inreases, the mutual indution between adjaent oils is weakened due to the smaller skin depth. Hene, the optimal frequeny spread inten- Fig. 5. % Outage Capaity (bit/s/hz) 4 x Parasti Capaitane (pf) (a) The optimal %-outage hannel apaity as a funtion of parasiti apaitane. Spread Intensity Δ f (Hz) Parasti Capaitane (pf) (b) The optimal spread intensity of the resonant frequeny as a funtion of parasiti apaitane. Central Operating Freq (Hz) 6 x Parasti Capaitane (pf) () The optimal entral operating frequeny as a funtion of parasiti apaitane. Effets of parasiti apaitane. sity dereases aordingly to ompensate the weakened mutual indution. The optimal MI hannel apaity also dereases as the medium ondutivity inreases. To ahieve the optimal MI hannel apaity, the maximum entral operating frequeny is seleted when the medium ondutivity is smaller than a threshold, sine the higher operating frequeny enhanes the indued voltage U MI at eah MI oil while the skin depth is still not too small. However, when the medium ondutivity is larger than the threshold, higher operating frequeny auses muh smaller skin depth. As a result, the optimal operating frequeny is smaller than the maximum operating frequeny. V. Conlusion In this paper, we propose the Spread Resonane (SR) strategy to inrease the hannel apaity of the MI waveguide ommuniation systems in RF-hallenged environments. Unique resonant frequeny is optimally alloated for eah MI relay oils and transeiver oils. As a result, the reeived power is not onentrated at the single entral operating frequeny but is spread among the multiple resonant frequenies. We formulate an optimization problem for the resonant frequeny alloation to maximize the MI hannel apaity, whih an be solved by the Lagrange multiplier method. Multiple unique MI effets are analytially aptured in the optimization, inluding the parasiti apaitor in eah MI oil, the skin depth in various transmission media with limited ondutivities, and the random diretion of eah oil. Through the theoretial analysis and numerial evaluations, we find signifiant hannel apaity improvements in the

9 SUN et al.: INCREASING THE CAPACITY OF MAGNETIC INDUCTION COMMUNICATIONS IN RF-CHALLENGED ENVIRONMENTS 395 Fig. 6. % Outage Capaity (bit/s/hz).5 x Medium Condutivity (S/m) (a) The optimal %-outage hannel apaity as a funtion of medium ondutivity. Optimal Spread Intensity Δ f (Hz) Medium Condutivity (S/m) (b) The optimal spread intensity of the resonant frequeny as a funtion of medium ondutivity. Optimal Operating Freq f (Hz). x Medium Condutivity (S/m) () The optimal entral operating frequeny as a funtion of medium ondutivity. Effets of medium ondutivity and skin depth. MI waveguide ommuniation system if the proposed SR strategy is applied. Sine the adjaent oil in the MI waveguide ommuniation system is very weakly oupled to minimize the number of relay oils, there exists a tradeoff between larger bandwidth and lower MI path loss. The SR strategy utilizes this tradeoff and find the optimal balane by letting eah MI oils working at different pre-designed resonant frequenies. Despite the advantages, the system omplexity is signifiantly inreased sine eah relay oil in a MI waveguide is different from eah other now. The system deployment also beomes more diffiult due to the non-homogeneous MI waveguide. To solve this problem in the future, more advaned MI waveguide strutures other than simple resonant oils need to be investigated. For example, the thin-film MI waveguide [] provided an improved struture to enhane both the MI bandwidth and reeived signal strength in the strong mutual oupling appliations. It remains an open researh issue to find out advaned MI waveguide struture to improve the performane of the MI-based wireless ommuniations where the mutual oupling is very weak. Aknowledgment This work was supported by the German Researh Foundation (Deutshe Forshungsgemeinshaft, DFG) under Grant No. GE 86/4- and the Start-up Grant from the Shool of Engineering, State University of New York at Buffalo. Referenes [] I. F. Akyildiz, Z. Sun, and M. C. Vuran, Signal propagation tehniques for wireless underground ommuniation networks, Physial Commun. J., vol., no. 3, pp , Sep. 9. [] Z. Sun and I. F. Akyildiz, Key ommuniation tehniques for underground sensor networks, Foundations and Trends in Networking, vol. 5, no. 4, pp 38 83,. [3] Z. Sun, et al., BorderSense: border patrol through advaned wireless sensor networks, Ad Ho Networks J., vol. 9, no. 3, pp , May. [4] Z. Sun, et al., MISE-PIPE: magneti indution-based wireless sensor networks for underground pipeline monitoring, in Ad Ho Networks J., vol. 9, no. 3, pp. 8 7, May. [5] Z. Sun and I. F. Akyildiz, Magneti indution ommuniations for wireless underground sensor networks, IEEE Trans. Antennas Propag., vol. 58, no. 7, pp , July. [6] Z. Sun and I. F. Akyildiz, Underground wireless ommuniation using magneti indution, in Pro. 9 IEEE ICC. [7] J.J. Sojdehei, P. N. Wrathall, and D. F. Dinn, Magneto-indutive (MI) ommuniations, in Pro. MTS/IEEE Conferene and Exhibition. [8] R. 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10 395 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 6, NO. 9, SEPTEMBER 3 [6] R. R. A. Syms, L. Solymar, and I. R. Young, Broadband oupling transduers for magneto-indutive ables, J. Physis D: Applied Physis, vol. 43, no. 8,. [7] S. Kisseleff, W. Gerstaker, R. Shober, Z. Sun, and I. F. Akyildiz, Channel apaity of magneti indution based wireless underground sensor networks under pratial onstraints, in Pro. 3 IEEE WCNC. [8] Z. Sun and I. F. Akyildiz, Deployment algorithms for wireless underground sensor networks using magneti indution, in Pro. IEEE Globeom. [9] M. Dionigi and M. Mongiardo, Multi band resonators for wireless power transfer and near field magneti ommuniations, inpro. IEEE MTT-S, pp [3] M. Dionigi and M. Mongiardo, A novel resonator for simultaneous wireless power transfer and near field magneti ommuniations, in Pro. IEEE MTT-S. [3] C. E. Shannon, The Mathematial Theory of Communiation University of Illinois Press, 949. [3] H. Lu, J. Zhu, and S. Y. R. Hui, Experimental determination of stray apaitanes in high frequeny transformers, IEEE Trans. Power Eletron., vol. 8, no.5 pp. 5, 3. [33] A. Massarini and M. K. Kazimierzuk, Self-apaitane of indutors, IEEE Trans. Power Eletron., vol., no. 4 pp , 997. [34] L. Li, M. C. Vuran, and I. F. Akyildiz, Charateristis of underground hannel for wireless underground sensor networks, in Pro. 7 Med- Ho-Net. [35] J. R. Wait, Criteria for loating an osillating magneti dipole buried in the earth, Pro. IEEE, vol. 59, no. 6 pp , 97. [36] D. R. Frankl, Eletromagneti Theory. Prentie-Hall, 986. [37] P. Billingsley, Probability and Measure, 3rd ed. John Wiley & Sons, 995. [38] S. Boyd and L. Vandenberghe, Convex Optimization Cambridge University Press, 4. Zhi Sun (M ) reeived the B.S. degree in Teleommuniation Engineering from Beijing University of Posts and Teleommuniations (BUPT), and the M.S. degree in Eletroni Engineering from Tsinghua University, Beijing, China, in 4 and 7, respetively. He reeived the Ph.D. degree in Eletrial and Computer Engineering from Georgia Institute of Tehnology, Atlanta, GA. in. Currently, he is Assistant Professor in the Eletrial Engineering Department at State University of New York at Buffalo, Buffalo, NY. Prior to that, he was a Postdotoral Fellow at Georgia Institute of Tehnology, Atlanta, GA. Dr. Sun has won the Best Paper Award in the IEEE Global Communiations Conferene (Globeom). He reeived the BWN researher of the year award at Georgia Institute of Tehnology in 9. He was also given the outstanding graduate award at Tsinghua University in 7. His expertise and researh interests lie in wireless ommuniations, wireless sensor networks, and yber physial systems in hallenged environments. He is a member of the IEEE. Ian F. Akyildiz (M 86-SM 89-F 96) reeived the B.S., M.S., and Ph.D. degrees in Computer Engineering from the University of Erlangen-Nürnberg, Germany, in 978, 98 and 984, respetively. Currently, he is the Ken Byers Chair Professor with the Shool of Eletrial and Computer Engineering, Georgia Institute of Tehnology, Atlanta, the Diretor of the Broadband Wireless Networking Laboratory and the Chair of the Teleommuniations Group at Georgia Teh. In June 8, Dr. Akyildiz beame an honorary professor with the Shool of Eletrial Engineering at Universitat Politènia de Catalunya (UPC) in Barelona, Spain. He is also the Diretor of the newly founded N3Cat (NaNoNetworking Center in Catalunya). He is also an Honorary Professor with University of Pretoria, South Afria, sine Marh 9. He is the Editor-in-Chief of Computer Networks (Elsevier) Journal, and the founding Editor-in-Chief of the Ad Ho Networks (Elsevier) Journal, the Physial Communiation (Elsevier) Journal and the Nano Communiation Networks (Elsevier) Journal. Dr. Akyildiz serves on the advisory boards of several researh enters, journals, onferenes and publiation ompanies. He is an IEEE FELLOW (996) and an ACM FELLOW (997). He reeived numerous awards from IEEE and ACM. His researh interests are in wireless sensor networks, ognitive radio networks, and nanonetworks. Steven Kisseleff reeived his Dipl.-Ing. degree in Information Tehnology with fous on Communiation Engineering from Tehnial University of Kaiserslautern, Germany in. Currently, he is a PhD student at Institute for Digital Communiations (IDC) at Friedrih-Alexander University of Erlangen-Nuremberg, Germany. His researh interests lie in wireless ommuniations, magneti indution based signal transmissions, and wireless sensor networks in hallenged environments. He is a student member of the IEEE. Wolfgang Gerstaker (M 98-SM ) reeived the Dipl.-Ing. degree in eletrial engineering from the University of Erlangen-Nuremberg, Erlangen, Germany, in 99, the Dr.-Ing. degree in 998, and the Habilitation degree in 4 from the same university. Sine, he has been with the Chair of Mobile Communiations (now renamed to Institute for Digital Communiations) of the University of Erlangen-Nuremberg, urrently as a Professor. His urrent researh interests inlude digital transmission, wireless ommuniations and statistial signal proessing. For work on single antenna interferene anellation for GSM, he was a reipient of the EEEfCOM Innovation Award 3 and of the Vodafone Innovation Award 4. In 6, he reeived a best paper award for a publiation in EURASIP Signal Proessing. In, he reeived the Mobile Satellite & Positioning trak paper award of VTC-Spring. He is a Member of the Editorial Boards of IEEE Transations on Wireless Communiations and Elsevier Physial Communiation (PHYCOM), serves as a Lead Guest Editor of the Speial Issue on Broadband Single-Carrier Transmission Tehniques in 3, and is a Co-Chair of the Cooperative Communiations, Distributed MIMO and Relaying Trak of VTC3-Fall. He has served as a Member of the Editorial Board of EURASIP Journal on Wireless Communiations and Networking (JWCN) from 4 to.