Mitigation of Channel Diversity and Indoor Channel Modeling for Remote Patient Monitoring Systems

Transcription

1 Mitigatio of Chael Diversity ad Idoor Chael Modelig for Remote Patiet Moitorig Systems Amit Sehgal, Rajeev Agrawal G. L. Bajaj Istitute of Techology ad Maagemet Sweta Seha Computer Sciece & Iformatio Systems Departmet, Keesaw State Uiversity, Keesaw, GA 344 ABSTRACT The cotiuously icreasig demad for better healthcare services has added aother applicatio to the sphere of remote moitorig services. This extesio to e-health ad Telecare services is kow as Remote Patiet Moitorig (RPM). The direct impact of this applicatio o huma life has made it a missio critical applicatio. The radomess ad diversity i locatio ad movemet profile of patiets ad Doctors further complicates the modelig ad aalysis of this system. This paper cocetrates o the mitigatio of the diversity i commuicatio liks ivolved i the etire system ad a decisio rule based adaptive idoor chael model. This paper highlights the diversity modelig of wireless chaels due to variatios i locatio pheomeo alog with movemet of the user through a four state Markov Model. From this model, oe state correspodig to idoor chael (represetig pre or post hospital moitorig) has bee aalyzed. It suggests the use of a adaptive model with correspods to a decisio rule as per the local coditios of the user ad the best suited value represetig a model is selected to capture the radomess of the received sigal. It is established that the proposed techiques predicts more real values of QoS parameters such as Bit Error Rate (BER) ad Outage probability, leadig to a higher reliability of wireless chaels. It is also show that the proposed model ca be a best fit for this missio critical applicatio - remote patiet moitorig - through wireless commuicatio Keywords: wireless chael diversity, adaptive fadig model, decisio rule, patiet moitorig, bit-error-rate, age probability. INTRODUCTION With the advaces i sesor ad commuicatio techology, the sphere of applicatio areas for remote moitorig has several iclusios to it e.g. vehicle moitorig, terrai moitorig, machie moitorig etc. A curret developmet i wireless commuicatios itegrated with ew research i pervasive ad wearable biomedical sesor techologies has a radical impact o future healthcare services. Some of the major challeges i implemetig these services are access to the service for large segmet of populatio, cotiuous healthcare cost iflatio, ad demad for sustaied quality beyod geographic distributio. From this domai, aother remote moitorig system called Remote Patiet Moitorig (RPM) is uder developmet for social ad commercial acceptace by various etities ivolved. Fig. shows oe such proposed system. The body sesor etworks deployed for patiet moitorig assist the healthcare professioals i maagig ad providig their expertise durig chroic or critical illess []. It beig a missio critical applicatio, a certai set of QoS requiremets o etwork performace must be satisfied which demads high level of reliability, guarateed badwidth, short ed-to-ed delay ad miimum bit or packet error rate. Curret health care system focuses o the work towards developig a structured ad optimized system for reactig to crisis ad maagig illess. I [], a prototype of 3G wireless etwork based mobile teletrauma system was developed. The system uses a desktop istalled i a ambulace ad the patiet iformatio e.g. video/medical images like ultrasoud, electrocardiogram (ECG) sigals, blood pressure etc. ca be trasmitted simultaeously through a cellular Volume 7 Number 4 Page 77

2 etwork. This system was developed with the objective to assist healthcare cetres, providig prehospital care for the patiets preset at remote locatios. Schedulig of data trasmissio with differet QoS requiremets is doe usig a softwareradio based approach. A similar system to provide commuicatio betwee a ambulace ad the hospital was preseted i [3]. This system was however, based o Uiversal Mobile Telecommuicatio System (UMTS). I [], the complexities associated with the process of ubiquitous patiet moitorig through emergig techologies were explored. The key cotributio of this work is a framework, that captures the complex processes, the parameters ivolved, ad the decisio criteria for ubiquitous patiet moitorig. A coceptual model of ubiquitous patiet moitorig was developed by leveragig the proposed framework, the same was validated by a usage sceario. The opportuities ad challeges of ubiquitous patiet moitorig were also detailed i this publicatio []. Wearable itelliget sesors ad systems for e-medicie (WISSE) Figure : Wireless etwork based remote patiet moitorig system (Source: Guest Editorial Itroductio to the Special Sectio o M-Health: Beyod Seamless Mobility ad Global Wireless Health-Care Coectivity by Robert S. H. Istepaia, Emil Jovaov, Y. T. Zag) I [4], a Global System for Mobile Commuicatio (GSM) for -of-hospital follow-up service was proposed, specifically for cardiac patiets. This service was desiged to facilitate moitorig of data trasmissio betwee the patiets ad the healthcare professioals. The measuremet devices were coected to the GSM etwork through mobile equipmets. The wireless data trasmissio was doe usig Wireless Applicatio Protocol (WAP). I [5], the implemetatio ad validatio of a prototype of a Remote Patiet Moitorig (RPM) system based o wireless techology usig a pervasive device (such as a cellular phoe) was described to sed a SMS (Short Message Service) to the medical staff. The proposed system provides a easy, viable, cheap ad effective way for trasmittig vital iformatio to the healthcare providers. It also moitors patiet's health status, such as SpO (oxyge percetage i blood), heart rate, ad temperature. This system combies Global System for Mobile (GSM) ad Global Positioig System (GPS) for health moitorig. Aother architecture of remote patiet moitorig was preseted i [6], with a provisio of help at home with wearable devices ad wireless trasmissio methods. The work was based o the icreasig eed for efficiet maagemet of emergecy messages, origiatig from portable ad wearable devices as well as demad for such a efficiet maagemet scheme for mobile uits which provide help at home. Major cotributio of this work was to provide help at home i a efficiet maer, miimizig the service time while maitaiig high availability for the high priority calls. A algorithm to eable the maagemet of such prioritized messages, maagig the mobile uits providig assistace at home i a efficiet maer was also proposed i this work. Suil Kumar, Kashyap Kambhatla et al. i [7] provided a overview of a architecture ad QoS characteristics of the telecardiology systems via mobile techologies. The challeges faced were highlighted i this work while implemetig such a itegrated system viz.. The hardware must be wearable ad reliable as it will be wor for log periods of time i various eviromets.. As the iterferece from multiple sesors will be radom. Therefore, Sesor commuicatio to a basestatio eeds to be aalyzed/modeled. 3. The commuicatio from base-statio to doctor must traverse through multiple etworks (3G, WiFi, 4G, Bluetooth, etc.) with differet packet size requiremets ad data loss parameters. I [8], various challeges issues ad implemetatio strategy of Wireless Sesor Networks for Persoal Health Moitorig were discussed. Further, the use of Wearable Wireless Body Area Networks as a key ifrastructure eablig uobtrusive, cotiual, ambulatory health moitorig was demostrated. A geeral Wearable Wireless Body/Persoal Area Network (WWBAN) architecture was also described alog with importat implemetatio issues, ad a prototype WWBAN based o off-the-shelf wireless sesor platforms ad custom-desiged ECG ad motio sesors was also itroduced. Several key techical issues such as sesor ode hardware architecture, software architecture, etwork time sychroizatio, ad eergy coservatio were addressed. Aspects like improvemet of QoS of wireless commuicatio, reliability of sesor odes, security, ad stadardizatio of iterfaces ad iteroperability were left utouched i the work. Volume 7 Number 4 Page 78

3 Due to the wide diversity of the eviromet ad terrai profiles ad severe costraits o supportig techologies i remote/rural areas, it becomes a challege to evaluate the etwork performace. Uder such coditios, ay better model which ca provide a effective alterative approach to the desig ad aalysis of the etworks will ehace the use of wireless techologies i the field of patiet moitorig. Further, the radio lik is highly dyamic due to radom ature of the received sigal, as a result of the effect of shadowig ad fadig which eeds probabilistic framework. This makes modelig of wireless chael, a more complex task. I cotext to remote patiet moitorig, the diversity of these chaels is further icreased due to the movemet ad diverse locatio of the patiet. I the proposed work, a decisio rule has bee defied to obtai a adaptive idoor chael model which models all possible wireless lik characteristics ragig from Lie-of-Sight (LOS) to No-Lie-of-Sight (NLOS) coditios. Figure : Framework of patiet moitorig system. I previous works, the framework for wireless patiet moitorig system proposed by Sweta Seha ad Upkar Varshey [] ivolves two differet types of wireless liks. Fig. shows these liks viz. (i) Lik : betwee body sesors ad patiet device (coordiator) e.g. PDA ad (ii) Lik : betwee coordiator device ad healthcare professioal. The Lik is a case of short term chael modelig sice the patiet device is assumed to be preset close to the patiet, wearig the sesors. The Lik is a case of log term chael modelig ad icludes a wide diversity due to variable local features ad distace. I additio to this, the complexity of both the liks is further added by the presece of huma body i close proximity of the coordiator device, almost always, which leads to body shadowig effect [9]. Sice the overall lik betwee the body sesors ad healthcare professioal is closely depedat o the locatio of the patiet which is highly diverse ad dyamic, a decisio rule based adaptive chael modelig is required to capture the pheomeo of sigal variatio for such systems.. MODELING MOVEMENT/LOCATION OF THE PATIENT To capture the movemet of a patiet, we have used a three state Markov model show i fig. 3 represetig the movemet profile of the patiet. These states ad their correspodig chael models represetig the locatio of the patiet (State A, State B ad State C) viz. (i) State A - patiet preset i a room ad movemet is restricted to withi the room, (I-chael model), (ii) State B - patiet preset i a partially ope area like balcoy of the house or buildig, (Partial I-chael model) ad (iii) State C - patiet preset i wide ope area, (Outchael model). The possible state trasitios cosidered i our model is: B Figure 3: Markov s Model represetig movemet of the patiet The trasitio probability matrix of sigle trasitio from oe state to aother state as per fig.. ca be obtaied as: C A Volume 7 Number 4 Page 79

4 / / P Trasitio / 3 / 3 / 3 () / / I state B, the patiet is assumed to be preset just side the room ad is i a partially ope area. This state ca further be decomposed ito two sub states viz State B ad State B. State B represets the situatio where the patiet moves of the room with carryig the coordiator device. Whereas, State B represets the coditio whe the patiet has moved of the room ad is carryig his/her device. The Markov s model ca ow be represeted as show i fig. 4: C B Figure 4: Modified Markov s model The trasitio probability matrix for all possible sigle step state trasitio is give as: / 3 / 3 / 3 / 3 / 3 / 3 P Tras () / / / / I trasitio matrix P, the probability of Tras trasitio betwee some states is zero as i case of trasitio from state A to state C there is o direct path however, it is possible oly through itermediate state B. A two step trasitio matrix ca be calculated usig Chapma Klomogrov (C- K) Equatio [] give as: P (+m) P ().P (m) where P () deotes the matrix of -step trasitio probabilities P ij. Usig this equatio the two step trasitio matrix ca obtaied as:. P P P P + Tras Tras Tras Tras P Tras represets the two step trasitio probability from state A to state C via state B which is 5/8 ad B A for the reverse trasitio from state C to state A via state B is /6. / 3 / 3 / 3 / 3 / 3 / 3 / 3 / 3 / 3 / 3 / 3 / 3 P Tras / / / / (3) / / / / 7 /8 / 9 5/8 / 9 / 9 7 /8 / 9 5/8 5/ / 6 5/ / 6 5/ 5/ Similarly, the two step trasitio probability from state B to B is /6 ad the reverse is /9. The probability of trasitio from state B to state C is still zero sice it is assumed here that the patiet will always carry the co-ordiator device with him/her, while goig to regios represeted by state C. So, as show i figure., he/she must go back to state A from B ad the through B the patiet ca go to state C. Similarly, the probability of trasitio from state C to state B i oe or two trasitios is zero. Therefore, we ow calculate three step trasitio probability matrix usig C-K equatio. P P P P 3 + Tras Tras Tras Tras 7/8 /9 5/8 / 9 / 3 / 3 / 9 7/8 /9 5/8 / 3 / 3 / 3 5/ /6 5/ / / / 6 5/ 5/ / / (4) Fially from the matrix P, we get a o-zero 3 Tras probability of trasitio from state B to C ad reverse trasitio i three steps which was zero i iitial two steps. 3. CHANNEL MODELING I this sectio, we will aalyze the lik betwee body sesor odes ad coordiator device represetig the sceario whe both the patiet ad the coordiator device are preset iside a room. It is iterestig to ote that the presece of the patiet ad the coordiator device i the same room does ot guaratee the availability of LOS sigal, the chael characteristics will chage with movemet of the patiet withi the room. Assumig that all the sesors are deployed o the frot of the body ad the coordiator device is also preset i frot of the patiet, a strog LOS compoet will be available with various multipath compoets. I such sceario assumig that the sigal variatio follows Nakagami- Volume 7 Number 4 Page 8

5 distributio havig pdf p ( x) give as []: p N N ( + ) e x ( + ) x ( x) exp( ) y y + Io( x ) y (5) where is the Nakagami- fadig parameter, which rages from to. This parameter is related to the Ricia K factor by K which correspods to the ratio of power of LOS compoet to the average power of multipath compoets. Replacig (+ )/y by d, Eq. (5) ca, ow, be re-writte as: N o p ( x) de x exp( dx ) I ( x d ) (6) The modified Bessel fuctio I v (z) ca is represeted as [3]: k ( z / ) Iv ( z) (7) ( k!) k o For v ad z (x(d) ), eq. (7) ca be rewritte as: I ( x d ) k ( x d ) (8) k o ( k!) Substitutig eq. (8) i eq. (6), we get: k ( x d ) pn ( x) de x exp( dx ) k o ( k!) (9) Whe the patiet chages directio or positio withi the room, the coordiator device may ow be preset o the side or back of the patiet. The sigal compoet chages gradually from LOS to NLOS. I the later case, there is o or small LOS compoet however, various multipath compoets reach the coordiator device through reflectio, diffractio ad/or scatterig. The sigal variatio, i the extreme NLOS case follows Nakagami-m distributio, with m, havig pdf p ( x). The pdf of geeral N mln Nakagami-m distributed variate X coditioed o radom variable Y represetig average power is expressed as [4]: m m m x m pn m( x Y y) exp( x ), x > m Γ( m) y y () where Γ ( m) is the gamma fuctio. For the NLOS propagatio, m so that Nakagami distributio closely follows Rayleigh distributio which is the widely accepted distributio for NLOS idoor propagatio. 3. Decisio Rule A simple two states (with ad with LOS) model ca be represeted as a covex combiatio of LOS multipath ad NLOS multipath fadig which is characterized by a time sharig factor A. The factor A takes biary values ( ad ) based o the put of a comparator which compares age probability of LOS multipath fadig ( P preset value ( P th LOS ) with a ). This factor A also represets the coditio for trasitio from LOS chael model to NLOS chael model. The comparator works accordig to the followig rule: LOS th A, if P < P LOS chael model (eq. 6) LOS th, if P P NLOS chael model (eq. 7) () The resultig combied pdf is give by: p( x) ( A) pn ( x) + A pn m ( x) () where pn ( x) is give by eq. (9) whereas p ( ) N m x is give by eq. (). 4. QoS PARAMETER ESTIMATION FOR THE PROPOSED MODEL 4.. Outage Probability: The age probability is a importat performace criterio for the diversity systems operatig over fadig chaels. It correspods to the probability that the sigal evelope or the SNR falls below a pre-determied threshold value. I terms of SNR, it ca be calculated as: p th P p ( ) d where ( ) is the probability distributio fuctio (pdf) of SNR. We, ow, preset a closed form solutio of the age probability for LOS chael represeted by P. LOS Usig variable trasformatio give i [], eq. (6) will have a form: p N ( + ) e ( + ) ( ) exp( ) ( + ) I o ( ) (3) where is istataeous SNR ad is average SNR. For Nakagami- distributio, the age probability ca be calculated usig eq. (3): Volume 7 Number 4 Page 8

6 a LOS ( + ) e ( + ) ( + ) P exp( ) Io( ) d Let a ( + ) e ( + ) ( + ) exp( ) Io( ) d + ( ( + ) λ I ) o ( b ) ( k ) k! (4) b. The modified Bessel fuctio k [4]. Now, LOS P ca be calculated as: ca be writte as k a LOS ( b) k P be exp( b ) d k ( k!) k a ( b) k k t be b t e dt k ( k!) 4.. BER estimatio: (5) BER is the practical equivalet term for Probability of Error (P e ) ad represets chael performace as a fuctio of available (C/N) ratio. BER f(c/n) ad/or BER f(e b /N o ) where E b is average eergy of modulated bit ad N o is oise power spectral desity. To aalyze the performace of the proposed model we have calculated BER performace of liearly amplified ad coheretly modulated Quadrature Phase Shift Keyig (QPSK) system for a statioary AWGN chael which is widely used modulatio scheme for wireless commuicatio. The probability of error for QPSK is Eb expressed as Pe erfc [5]. N I the above expressio, oise desity N o does ot chage with fadig ad E b is costat i a statioary AWGN eviromet. To obtai the BER i a faded eviromet, we defie a radom variable which follows fadig distributio. The modified expressio for BER is: Eb Pe ( ) erfc where α (6) No Probability of bit error (P e ) for a faded chael havig P() as pdf of fadig ca be calculated as: o Pe erfc P( ) d (7) For a chael havig fadig pdf give by eq. (3), probability of bit error or BER ca be writte as: P e + Let ( + ) e ( + ) erfc exp( ) ( + ) Io ( ) d (8) g. Now, eq. (8) ca be writte as: Pe erfc ge exp( g ) Io( g ) d (9) ge erfc exp( g ) Io ( g ) d () k ( g ) ge erfc exp( g ) d ( k!) k k () k ( g ) k ge erfc exp( g ) d ( k!).5e g k ( ) () k k g ( g) * Γ [ + k] 3/ g g π k! 3 Γ + k 3 3 F, + k,, g (3) Back-substitutig g i eq. (3), we get the expressio for BER i terms of ad. For ay particular value of oe these two parameters, the effect of variatio of the other ca be observed. 5. DECISION RULE BASED PERFORMANCE MODELING For the performace aalysis of a remote patiet moitorig system uder proposed model, we have take Quadrature Phase Shift Keyig (QPSK), a widely accepted modulatio techique for wireless commuicatio, to calculate the QoS parameters. Volume 7 Number 4 Page 8

7 Bit Error Rate (BER) ad Outage Probability for the lik (discussed i sectio II) are umerically calculated usig expressios obtaied i the previous sectio. For sceario (a) which is a complete idoor eviromet (described i sectio II), we iitially assume the positio of the patiet such that there is a strog LOS path available betwee the o-body sesors ad coordiator device. I this case, fig. 5 ad fig. 6 preset the plots of BER ad Outage Probability vs. E b /N o usig Nakagami-. To represets presece of strog LOS compoet, we have take 7 where is the ratio of LOS compoet to multipath compoet. For values of E b /N o above the threshold value of 5, the age probability is almost zero. The BER also decreases as the value for E b /N o icreases. For, BER distributio matches closely with Nakagami-m for m. Based o this plot, threshold values ca be set for various values of E b /N o for a gradual chage i the value of from LOS case to NLOS case. The two state adaptive model based o decisio rule give by eq. () i sectio II ca ow be expaded to multiple states, each correspodig to a particular directio of the patiet w. r. t. the coordiator device ad modeled by a particular value of. For example, for a seve state model, various positios of the patiet are quatized ito 7 levels, each represeted by a value of from the set i {,7}. Figure 7: Outage probability of QPSK for various values of Nakagami- chael model parameter takig th 5 ad avg. E b /N o 5. Figure 5: Bit Error Rate of QPSK for Nakagami- chael model for various values of E b /N o takig 7 Figure 6: Outage Probability of QPSK for akagami- chael model for various values of E b /N o takig 7 ad th 5 Now, as the patiet moves iside the room or chages directio from the assumed iitial positio, the fractio of LOS compoet reduces as compared to multipath compoet. This chage is represeted by chage i value of from iitial assumed value of 7 towards. The BER ad age probability also icrease with reductio of LOS compoet as show i fig. 7 ad fig. 8 ad fially matches with NLOS chael model which is best represeted by Nakagami-m chael model for m. Fig. 8 gives a comparative study of BER for various values of. From fig. 5, for E b /N o 5, decisio rule to select a particular value of i ca be defied as: 7, BER.897E- 6,.897E- < BER 3.46E-9 i : (4) :, 9.894E-4 < BER.58 The adaptive model ca ow be writte as: k ( ) i ix d pn ( x) de x exp( dx ) i k o ( k!) (5) Nakagami- is a geeralized case which leads to both NLOS (Rayleigh distributio) ad LOS (Rice distributio) chael model for differet values of. Usig the proposed decisio rule, we are able to achieve a more geeralized or a better represetatio of the wireless fadig chael model. The QoS parameters like age probability ad BER ca ow be estimated for almost all the positios ad locatios of the patiet iside the room usig this sigle model. Volume 7 Number 4 Page 83

8 Figure 8: BER of QPSK for various values of (Nakagami- parameter) ad for m (Nakagami-m parameter) 6. CONCLUSION I this paper, a ovel way to mitigate chael diversity has bee preseted for the missio critical applicatio of remote patiet moitorig. A four state Markov model has bee used to represet various chael coditios based o the locatio of the patiet. A adaptive models ad its QoS parameter based decisio rule has bee proposed for the idoor chael i cotext to this applicatio. The objective is to capture the highly dyamic ad radom coditios of locatio of patiets ad healthcare professioals. A geeralized Nakagami- model with a variable parameter has bee show to capture the etire variatio i sigal stregth ad other effects. The suitability of the proposed model is judged by obtaiig the expressios for age probability ad BER estimate ad has bee used for the performace aalysis of the wireless chael. A decisio rule based o BER estimatio has also bee suggested selectig the value of variable parameter i. Future work will focus o applyig the proposed techique to cliical RF data, ad to extedig the approximatios to also estimate other chael characteristics. ACKNOWLEDGEMENT The work of the third author was sposored i part by the Computer Sciece & Iformatio Systems Departmet, Keesaw State Uiversity, Keesaw, GA 344. REFERENCES [] Sweta Seha, Upkar Varshey, Eablig ubiquitous patiet moitorig: Model, decisio protocols, opportuities ad challeges, Decisio Support Systems, Volume 46, Issue 3, February 9, Pages [] Y. Chu ad A. Gaz, A moble Teletrauma System Usig 3G Networks, IEEE Tras. Iform. Tech. Biomed., vol.8, o. 4, Dec. 4, pp [3] J. R. Gallego et al., Performace Aalysis of Multiplexed Medical Data Trasmissio for Mobile Emergecy Care over the UMTS Chael, IEEE Tras. Ifo. Tech. Biomed., vol. 9, o., March 5, pp. 3-. [4] C. H. Salvador et al., Airmed-cardio: a GSM ad Iteret Services Based System for Out-of- Hospital follow-up of Cardiac Patiets, IEEE Tras. Ifo. Tech. Biomed.., vol. 9, o., March 5, pp [5] Mudasser F. Wye, Vamsi K. Vitla et al., Remote Patiet Moitorig Usig GSM ad GPS Techologies, Joural of computig scieces i colleges, volume 4, issue 4, April 9, pp [6] G. Patziou, P. Belsis et al., A scheme for osite service provisio i pervasive assistive eviromets, Proceedigs of the d Iteratioal Coferece o Pervasive Techologies Related to Assistive Eviromets, Greece, 9. [7] Suil Kumar, Kashyap Kambhatla et al., Ubiquitous Computig for Remote Cardiac Patiet Moitorig: A Survey, Iteratioal Joural of Telemedicie ad Applicatios, Volume 8, Article ID Volume 7 Number 4 Page 84

9 [8] Aleksadar Milekovi, Chris Otto, Emil Jovaov, Wireless Sesor Networks for Persoal Health Moitorig: Issues ad a Implemetatio, Computer Commuicatios, Vol. 9, 6, pp [9] Kashiwagi, I. Taga, T. Imai, T., Time-Varyig Path-Shadowig Model for Idoor Populated Eviromets,IEEE Trasactios o Vehicular Techology, Volume: 59 Issue:, Ja, pp [] Sheldo Ross, Itroductio to Probability Models, Academic Press, Teth Editio, Dec. 9, pp. 45. [] Marvi K. Simo ad Mohamed-Slim Alouii, Digital Commuicatio over Fadig Chaels, Joh Wiley & Sos, Secod Editio, pp. 3 (4). [] Marvi K. Simo ad Mohamed-Slim Alouii, Digital Commuicatio over Fadig Chaels, Joh Wiley & Sos, pp., Secod Editio, (4). [3] Abramowitz ad Stegu, Hadbook of Mathematical Fuctios with Formulas, Graphs, ad Mathematical Tables, Joh Wiley & Sos Teth Pritig (97). [4] Karmeshu, Rajeev Agrawal, Study of ultrasoic echo evelope based o Nakagami-iverse Gaussia distributio, Ultrasoud i Medicie ad Biology, Vol. 3, Issue 3, pp (6). [5] Kamilo Feher, Wireless Digital Commuicatios, Pretice Hall of Idia (4). Volume 7 Number 4 Page 85