3. CR parameters and Multi-Objective Fitness Function

Transcription

1 3 CR parameters and Mult-objectve Ftness Functon CR parameters and Mult-Objectve Ftness Functon 3.1. Introducton Cogntve rados dynamcally confgure the wreless communcaton system, whch takes beneft of the exstng RF envronment. The desgn of the rado lnk for a partcular network confguraton and geographc based on multple parameters that are non-lnearly lnked. For example, operatng frequency, sgnal-to-nose rato, dfferent antenna types, data rate, transmtter power, modulaton scheme and nterference levels are a few of the parameters that should be consdered whle desgnng an rado lnk. These parameters are related to each other and have non-lnear and lnear lnked relatonshps and are dependent on mult-path fadng, nterference levels, and network topology. Fgure 3.1 Drected graph ndcatng how one objectve affects another objectve.

2 3 CR parameters and Mult-objectve Ftness Functon 42 Demandng a real-tme optmal soluton for these parameter values s an extremely complcated and trcky task. The result for each of the objectve managng these parameters vares and overlaps among each other and thus one objectve (source) affects another objectve (target) as shown n Fgure 3.1. In CR system desgnng, a several parameters as nputs must be descrbed. The decsons accuracy made by an AI technque are depends upon the qualty and amount of nputs to the system. More nputs to the system formulate the rado more knowledgeable, therefore permttng the decson makng process to produce decsons that are more precse. The decson varables are () at the physcal layer: modulaton and transmsson power order for each sub-carrer; () at the MAC layer: mnmum and maxmum contenton wndows szes, frame sze; () at the network layer: ndex of the assocated access pont and varable transmsson range [Alexandre de Baynast et al., Pages ]. A goal s to defne a set of decson varables concernng the CR physcal layer only and other layers are out of scope through out n ths thess. There are two sets of nputs to the system: transmsson parameters and envronmental parameters are dscussed n followng secton Transmsson Parameters In the CR system, decson varables correspond to the transmsson parameters that can be handled by the CR system that takes beneft of the SDR that controls the parameters, whch are nput to a ftness functon along wth the objectves, and envronmental parameters. The ftness functon provdes a value that represents optmal parameters for the specfed objectves. Ftness functons to be used by CR technques need a specfc lst of transmsson parameters that should be accessble to

3 3 CR parameters and Mult-objectve Ftness Functon 43 the system. These transmsson parameters are equvalent to the parameters that are controlled by SDR mechansm. Table 3.1 Lsts of Transmsson Parameters Parameters Transmt Power (P) Modulaton Type (Mod) Modulaton order (M) Bandwdth (B) Packet Sze (L) Symbol Rate (R s ) Descrpton Raw transmsson power Type of modulaton format Number of symbols for gven modulaton format Bandwdth of transmsson sgnal n Hz Transmsson packet sze n bytes Number of symbols per second The parameters selected based on lteratures cted as transmsson or rado parameters used by CRs [J. F. Haurs, pp , T. Chrstan James Reser s Dssertaton]. The transmsson or rado/antenna parameters nclude values that affect to rado performance and the complete lst of parameters used n ths thess to create a ftness functon s shown n Table Envronmental parameters The envronmental parameters are assocated to network layout and geographc topology. Envronmental measurements update the system of the surroundng envronment characterstcs. These parameters are nformaton concernng the exstng wreless envronments that are used as nputs to the CR system. These characterstcs may nclude nternal nformaton about the rado n use state, and perpheral nformaton representng the wreless channel envronment. The envronmental

4 3 CR parameters and Mult-objectve Ftness Functon 44 varables can be dvded nto two groups. The frst envronment varables that are drectly used by the ftness functon as key parameters to the functon. For example, the parameter of nose power of the channel whch s used n the mnmze BER. These parameters drectly mpact the ftness score of the partcular objectve functon. The second envronment parameters are observed by the CR system, and decsons regardng the objectve functon depend upon ther values. Table 3.2 Lsts of Envronmental Parameters Parameters Bt-Error-Rate (BER) Sgnal-to-nose rato (SNR) Nose power (N) Battery Status Power Utlzaton Descrpton Total bts have errors relatve to transmtted bts Rato of the sgnal power to the nose power Magntude n db of the nose power Predctable energy left n batteres Power utlzaton of present confguraton. For example battery status parameter, n ths regard the system may be observng ths parameter whle s reduces below a specfc threshold, the system may alter the weghtng on the objectve functons so as to provde the mnmze power consumpton. Decson-makng n CR engne to formulate a defnte output, the exstng wreless envronment should be modeled nternally. Ths model s formed wth envronmentally sensed data receved by the CR system by a perpheral sensor. Several sensors exst to detect characterstcs of the wreless envronment. The envronmental data also used to form the transmsson parameters and the wreless channel, performance objectves. The envronmental parameters lst used are shown n Table 3.2. All parameters dscussed as above wll utlzed n mult-objectve optmzaton and ts concept s explored n next followng secton.

5 3 CR parameters and Mult-objectve Ftness Functon Mult-Objectve Optmzaton Concepts Optmzaton problems are normally stated n a sngle-objectve way. In other words, the process must optmze a sngle-objectve functon complyng wth a seres of constrants that are based on constrants gven by the real world. A sngle-objectve optmzaton problem may be stated as follows [Mult-Objectve Optmzaton n Computer Networks Usng Metaheurstcs, by Auerbach]: Optmze [mnmze/maxmze] subject to y f ( x) (3.1) H ( x) 0 G( x) 0 In ths case, the functon to be optmzed (mnmze or maxmze) s f ( x ) vector x s the set of ndependent varables. Functons H ( x ) and G( x ) constrants of the model. where are the For ths problem we can defne three sets of solutons:. The unversal set whch n ths case are all possble values of x, whether feasble or non- feasble.. The set of feasble solutons whch are all the values of x that comply wth the H ( x ) and G( x ) constrants. In the real world, these varables would be all possble solutons that can be performed.

6 3 CR parameters and Mult-objectve Ftness Functon 46. The set of optmal solutons whch are those values of x that, n addton to beng feasble, comply wth the optmal value (mnmum or maxmum) of functon ( ) f x whether n a specfc, a b nterval or n a global, context. In ths case, one says that the set of optmal solutons may consst of a sngle element or several elements, provded that the followng characterstc s met: f x f x ', where x x '. In ths case there are two optmal values to the problem when vector x { x, x '}. But n real lfe, t s possble that when we want to solve a problem, ths may need to optmze more than one objectve functon. When ths happens, ths s referred to mult-objectve optmzaton. In general, a mult-objectve ftness functon problem can be presented as tryng to determne the correct records of a set of m parameters to a set of n objectves. A mult-objectve optmzaton model may be stated as follows: Optmze [mnmze/maxmze] F( x) { f ( x), f ( x),..., f ( x)} 1 2 n (3.2) subjected to H ( x) 0 G( x) 0 x ( x, x, x,..., x ) X m

7 3 CR parameters and Mult-objectve Ftness Functon 47 In ths case, the functons to be optmzed (whether mnmze or maxmze) are the set of functons F( x ), where the vector x s the set of ndependent varables and X s the parameter space. Functons H ( x ) and G( x ) are the constrants of the model. In a mult-objectve evolutonary algorthm, each f ( x ) corresponds to the ftness functon for a sngle objectve. The purpose s to merge them to obtan a sngle ftness functon, F( X ), consderng wth all objectve and parameters. In real world, problem such optmzaton technques dscussed n ths thess, the solutons found; objectve solutons even when they are conflctng, that s, when mnmzng one functon may worsen other functons. For example, mnmzng BER and mnmzng power smultaneously generate a dvergence because of the sngle parameter.e. transmt power, whch affects each objectve n a dfferent manner. Obtanng the optmal set of decson varables for a sngle objectve as mnmze power, often outcome n a non-optmal set wth respect to other objectves, e.g. mnmze BER and maxmze throughput. The optmal set for mult-objectve functons placed s known as the Pareto optmal front [ZHOU et al., E. Ztzler and L. Thele, pp , 1999]. Ths front corresponds to the set of solutons that cannot be enhanced upon n any measurement. The results on the Pareto front are best and co-exst due to the tradeoffs among the mult-objectves. A typcal plot of a Pareto front, usng a smple CR parameter state s shown n Fgure 3.2. The y-axs represents the score of the sngle objectve ftness functon for BER n the case of several modulaton types, whle the x-axs s the score for the rato of the energy per bt (E b ) to the nose power spectral densty (N 0 ). The parameter x corresponds to the decson vector of varable used as nputs to the ftness functons.

8 3 CR parameters and Mult-objectve Ftness Functon BER QPSK BPSK QAM Eb/No (db) Fgure 3.2 Pareto Front trade-off. Here, transmt power and modulaton was used as decson parameters. For every curve, as the ftness score for BER objectve decreases, the value for the Eb / N 0 ncreases. Ths trade-off has to be made by usng mult-objectve optmzaton. The ftness functons used for ths model are derved n Secton 3.2. In ths thess, ftness functons usng the defned set of parameters has been developed, that are used by CR engnes to establsh a sngle optmal transmsson parameter result. In Fgure 3.2, some parameter sets le on the Pareto front, but the ftness functon have to provde a search drecton that drects the system to a sngle resoluton. There are several methods that can be used to solve mult-objectve problems usng sngle-objectve approxmatons. Some of them are weghted sum, ε-constrant, weghted metrcs, Benson, and mn-max, among others [Mult-Objectve Optmzaton n Computer Networks Usng Metaheurstcs by Auerbach]. All of these methods try to fnd the

9 3 CR parameters and Mult-objectve Ftness Functon 49 optmal Pareto front usng dfferent approxmaton technques. Ths thess uses a weghted sum optmzaton method, whch conssts of creatng a sngle-objectve model by weghng the n objectve functons by assgnng a weght to each the functons. Ths method appears well wth the CR development snce t provdes a sutable procedure for applyng weghts to the objectves. Through the weghted sum method, the mult-objectve model (3.3) can be restated n the followng way: Optmze [mnmze/maxmze] n F( X ) w. f ( X ) (3.3) 1 subjected to H ( X ) 0 G( X ) 0 0 w 1, {1, 2,... n} n 1 w 1 In ths case one can see that each functon s multpled by a weght ( w ) whose value must be found between 0 and 1. Also, the sum of all the weghts appled to the functon must be 1. An analyss of ths type of soluton shows that functon F( X ) obtaned from the sum s a lnear combnaton of the functons f ( X ). What the weghted sum method does exactly s fnd the ponts of the optmal Pareto front, whch conssts of all the optmal solutons n the mult-objectve optmzaton, through

10 3 CR parameters and Mult-objectve Ftness Functon 50 the combnatons gven by the weghted vector W { w1, w2,... w n }. For example, n the case of two objectve functons would have the followng equaton. F( X ) w. f w. f Once the weghtng each objectve the value of weght s nvarable, thus the search drecton of the evolutonary algorthm s fxed. Ths s the proposed to fnd a sngle optmal result for a specfed envronment. However, varyng the objectve weghtng then the ftness functon wll nstantly nvoke the evolutonary algorthm to navgate a new soluton. For example, f a rado has to operate n a mnmze BER mode. In ths mode, the ftness functon wll gve hgher value to sets of parameter provded that a hgh transmt power, because the weght on the objectve of mnmze BER s the largest as shown n Fgure 3.2. In the case when the rado detects low battery power, t swtches the objectve weghtng to reproduce a mnmzng transmtted power. Ths s made by decreasng the weghts on other assocated objectves at the same tme as ncreasng the weght of the objectve of mnmze power. Once the weghts change, the ftness functon wll mmedately start gvng hgher scores to those parameter sets, whch offer lower power transmsson. Ths s the man characterstc that allows the objectve weghtng to order the rado goal state. DSA can be acheved by nstantaneously swtch operatng goals by just modfyng the vector of objectve weghtng.

11 3 CR parameters and Mult-objectve Ftness Functon Cogntve Rado Objectves The envronment of wreless communcatons requres some desrable objectves that the rado system would lke to acheve. T. Chrstan James Reser, reports usng GA s to resolve the optmzaton of wreless channel models and certan characterstcs of the wreless communcaton system. Based on ths work t was determned that a Ftness Measure (Ftness Functon or Cost Functon) requred to be derved. Ths thess defnes four objectves for the ftness functons n order to drect the system to a best possble state are gven n Table 3.3. Nowadays, n communcaton system, mnmzng the BER s a common goal n wreless world. Ths objectve mnmzes the amount of errors wth respect to the amount of bts beng sent and mproves the communcatons sgnal of the rado. Maxmzng the throughput correspond to the system s data throughput rate, ths objectve enhanced the system throughput. Table 3.3 Objectve Functon of CR. Ftness objectve Mnmze BER Maxmze Throughput Mnmze Power Utlzaton Mnmze Interference Descrpton Recover the on the whole BER/PER of the transmsson envronment. Increase the on the whole data throughput transmtted by the rado. Reduce the amount of power utlzed by the system. Reduce the rados nterference contrbutons. Mnmze power utlzaton s easy to understand and s used to drect the CR to a stuaton of mnmal power utlzaton. Mnmzng nterference objectve are used to

12 3 CR parameters and Mult-objectve Ftness Functon 52 avod overlappng transmssons wth other users that causes nterference. The proposed CR engne model has been shown n Fgure 3.3. CR Engne Envronmental Parameters Transmsson Parameters Decson-Makng (Evaluatng Ftness Functon) Operatng Modes (.e. Emergency Mode, Multmeda Mode, Low Power Mode, DSA Mode, etc.) Fgure 3.2 Typcal CR Engne Model Trade-off analyss between maxmzng throughput, mnmzng probablty of bt error, mnmzng power utlzaton and maxmze spectral effcency has been explored n chapter-4 of ths thess. The ftness functon has to descrbe the tradeoffs between each objectve by rankng the objectves accordng to ts mportance. Ths thess uses a weghted sum technque where each objectve be gven a weght on behalf of ts mportance [Mult-Objectve Optmzaton n Computer Networks Usng Metaheurstcs by Auerbach, Cogntve Rado Technology by Bruce Fette, J. F. Haurs pp ]. Ths method s selected because of the smplcty of mplementaton of mult-objectve optmzaton wthn the GA and PSO technque. Last secton defnes four CR objectves for requred system: relablty, throughput, power consumpton and spectral nterference. Next, defnng the resultant objectve functons of base-10 GA, PSO and hybrd (of these two) mplementaton n

13 3 CR parameters and Mult-objectve Ftness Functon 53 order to drect the system to an optmal condton. In order to make easy the selecton of the weghts of the objectve functons, normalzng each objectve functon score to the range [0, 1]. The mplementatons of four objectve functons are as follows: 1) Mnmze Bt-Error-Rate: The majorty n wreless communcaton systems s to obtan an error free sgnal, or to mnmze the BER of the transmsson n order to relablty. Determnng the theoretcal BER based on numerous transmsson parameters ncludes the transmt power, bandwdth, modulaton type, modulaton ndex and nose power. The most essental thng n determnng the BER s the modulaton and channel type n use. Every modulaton and channel type combnaton uses a dfferent method to conclude the BER of the system. One more vtal factor n determnng the BER of the system s the Eb / N 0 rato. Ths rato bascally s a measure of the quantty of energy per bt to the quantty of nose power n the system, or on the SNR bass. To determne the Eb / N 0 rato, denoted as, usng the receved power of sgnal, S that s determned by the transmtted sgnal power and path loss, shadowng and mult-path fadng as descrbed n [Wreless communcatons, Anderea Goldsmth]. From S, one can get the quantty of energy per symbol S / R s (=E s ) by usng the symbol rate R s. For a alphabet of sgnalng wth M alternatve symbols, each symbol represents k = log 2 M bts. k s the modulaton effcency measured n bts/symbol or bts per channel use (bpcu ). The energy per bt (E b ) can be obtaned by dvdng by the number of bts n each symbol as S Eb (W/b) (3.4) R k s

14 3 CR parameters and Mult-objectve Ftness Functon 54 The sngle-sded nose power spectral densty (W/Hz) s calculated by Boltzmann s equaton. N k T (J) (3.5) 0 b N N B (3.6) 0 Where 23 kb J / K (Boltzmann s constant), T s the nose temperature (290K), B s bandwdth of the channel, and N s the total computed nose power. The ultmate equaton for the value of that the BER functons utlzed s gven by: E b S S B 10log10 10log10 N0 RskN0 Rsk N S B 10 log 10 log ( db) N Rsk (3.7) The followng equatons gve the BER of BPSK, M-ary PSK and M-ary by assumng an AWGN channel model wth gray-coded bt assgnment [J. G. Proaks, Dgtal Communcatons]. For a BPSK sgnal constellaton, the bt error probablty s gven as be P Q (3.8) For M-ary PSK, the bt error probablty s defned as 2 Pbe Q 2k sn k M (3.9)

15 3 CR parameters and Mult-objectve Ftness Functon 55 And M-ary QAM, the bt error probablty s gven as P be 4 1 3k 1 Q k M M 1 (3.10) Lastly, Probablty of Packet-error (PER) s gven as [ P pe 1 (1 P ) L (3.11) be Suppose that the bt errors are ndependent of each other. For small bt error probabltes, ths s approxmated as P pe ( P ) L (3.12) be Therefore, probablty of bt-error can be determned form gven probablty of packet-error usng (3.11) and (3.12). One feasble objectve functon for defnng the relablty of the system s: f mn_ ber log(0.5) 1 (3.12) log( P ) be Where P be s the average probablty of bt error (BER) for a specfed modulaton system over N c ndependent sub-carrer. Ths objectve functon, whch was orgnally proposed by [Newman et al.], however, t does not ft well wth the common QoS requrement whch s based on a maxmum acceptable BER or PER and over ths threshold, the communcaton s nterrupted. In ths concern, a objectve functon for the relablty of the transmsson ensures that PER s equal to or lower than a target

16 3 CR parameters and Mult-objectve Ftness Functon 56 PER represented as PER * [Alexandre de Baynast et al., Pages ]. However, equaton of ths objectve functon stll havng error and modfed specfcally as, f mn_ ber * log10 max( PER, PER) 1, 1 1. * log10 max( PER, PER) * log 10( PER ) 1, otherwse. * log 10( PER ) (3.13) Ths objectve functon penalzes f PER * PER and mn_ ber 0 f, f PER * PER, also guarantee that value of the f mn_ ber wll be fall n range [0, 1] and t was not n the case of paper [Alexandre de Baynast et al., Pages ] QPSK BPSK QAM PER BER Fgure 3.4 A plot of bt-error-rate vs. packet-error-rate usng (3.11).

17 3 CR parameters and Mult-objectve Ftness Functon 57 However, choose 10 5 to be the best-case BER n order to zero PER as shown n Fgure 3.4 and all nvestgatonal values seen lower ths value wll be rounded up to ) Maxmze Throughput: Ths ncreases the overall data throughput transmtted by the rado. At the physcal layer, the pulse duraton T and that ts bandwdth B s approxmately equal to the recprocal of T. Thus, B=1/T and, T=k/R b = log 2 (M)/R, t s follow that, R b B (3.14) log 2 M Therefore, as M s ncreased, the channel bandwdth requred, when the bt rate R b s fxed, decreases. For mult-carrer sgnal T can be expressed n number of bts per N c symbol perod as T log 2( M ) / N, c where N c ndcate the total number of 1 channels that SU operates on t, where = 1,... N c, and N c beng the upper lmt of channels that a SU wll be operate on, M s the order of modulaton emtted on subcarrer, M max s the maxmum modulaton order wth typcal values 64 or 256 n wreless networks. M can take values from 1 to M max wth 1 specal case occurrng when sub-carrer s shut down. M = 1 means that the rate log 2 ( M ) s equal to zero; no nformaton s transmtted. In ths partcular case, the correspondng transmsson power P s set to zero. In ths partcular, 0 T log2 M max, where the value log 2 ( M ) s acheved when all sub-carrers are loaded wth symbols modulated wth the largest avalable modulaton order. Therefore, the objectve functon for the throughput s smply:

18 3 CR parameters and Mult-objectve Ftness Functon 58 f N 1 c 1 log ( M ) (3.15) max_ throughput 2 Nc log 2 ( M max ) 1 The functon f max_throughput s equal to 0 when all sub-carrers transmt wth largest modulaton order and equal to 1 when all sub-carrers are swtched off. 3) Mnmze Power Consumpton: Ths objectve functon decreases the amount of transmsson power and gven by f mn_ power Nc 1 P N P (3.16) c max 1 Where N c ndcate the total number of channels that SU operates on t, where = 1,... N c. where N c ndcate the total number of channels that SU operates on t. P s the transmsson power on sub-carrer takes values range [P mn, P max ] and P max s the maxmum possble transmsson power for a sngle sub-carrer. P can takes values zero,.e., no transmsson on sub-carrer f the channel fadng coeffcent n ths band s smaller than a pre-determned threshold [Alexandre de Baynast et al., Pages ]. In other words, f mn_ power 1, all subcarrers are transmttng wth P max. 0, all subcarrers are transmttng wth P mn. 4) Mnmzng nterference: Ths s an essental objectve n shared frequency bands. For example, ths objectve may be gven a hgh weghtng by a SU that operates spectrum n a PU band. Here, the PU has man concern n a partcular band of frequency and on the other hand SUs are permtted to transmt n the band gven causng no nterference to the PUs. Rado parameters such as bandwdth (B) and transmt power (P) are used to determne the estmated amount of spectral nterference

19 3 CR parameters and Mult-objectve Ftness Functon 59 produced by transmsson. Overlappng transmssons wth other users causes nterference. Ideally, to compute the total nterference, ntegratng over the spectral bandwdth that transmtted, and get the total power of overlappng transmssons. In ths thess, t has been assumed unform power transmsson over the bandwdth of transmsson permttng to obtan the nterference equaton gven by, fnt erference P B (3.17) As ncrease n nterference the bandwdth ncreases and, nterference s ncreases as the transmt power of the transmtter ncreases. Thus, ncreased n spectral leakage and more power nterfere wth another system. The normalzed spectral nterference s gven by, N 1 c fmn_ nt erference ( P B) (3.18) N P B c max max 1 Ths objectve functon s defned as, f fmn_ nt 1, then subjected to maxmum erference nterference, when fmn_ nt erference 0 then, there s no nterference or mnmum nterference Mult-Objectve goals The weghted sum approach permtted to merge the sngle objectve functons nto one cumulatve mult-objectve functon. Equaton (3.19) llustrates that each objectve s multpled by a weght w and added smultaneously to gve a sngle value that are equvalent to the value of a parameter set. The weghted sum approach

20 3 CR parameters and Mult-objectve Ftness Functon 60 attempts to mnmze the sum of the absolutely normalzed, weghted, sngle objectve scores of the parameter set soluton. The mult-objectve functon for mult-carrers can be obtaned n forms of sngle objecton functon by use of weghted sum approach that provde sngle scalar value usng four objectves (3.13), (3.15), (3.16) and (3.18) as, F w f w f w f w f (3.19) 1 mn_ ber 2 max_ throughput 3 mn_ ower 4 mn_nt erference Where, w1, w2, w3, w4 are the weghtng values that decde the search drecton for the evolutonary algorthm (EA). Ths technque suts the cogntve rado state as shown by Newman et al., snce t provdes a sutable process for applyng weghts to the objectves. As the weghtng for each objectve s constant, the search drecton of the EA s unchangng as example shown n Table 3.4. Ths s the preferred property when demanded to dscover a sngle optmal soluton for a partcular envronment. Varyng the objectve drecton of the ftness functon needs just a smple change of the weghtng vector. Table 3.4 Example Weghtng Scenaros. Scenaros Weght Vector w, w, w, w Mnmze BER (Emergency Mode) [0.70, 0.10, 0.10, 0.10] Maxmze Throughput (Multmeda Mode) [0.15, 0.60, 0.10, 0.15] Mnmze Power (low power mode) [0.10, 0.20, 0.55, 0.15] Mnmze Interference (DSA Mode) [0.10, 0.20, 0.10, 0.60] Usng the weght vectors shown n Table 3.4 and CR engne has been generated base- 10 GA and PSO convergence results by use of the ftness functons and s presented n Chapter 4.

21 3 CR parameters and Mult-objectve Ftness Functon Summary Ths chapter explores a precse lst of common parameters for CR. These parameters contan envronmentally consdered parameters from sensors nsde the CR system, and operaton of nternal nformaton on condtons that measurement concernng the nternal state of the rado. Ths nformaton s used n combnaton wth the CR objectves to decde the sutable transmsson parameters to use by SU. A multobjectve problem contans complextes whle all objectves are tryng to be acheved at once upon a tme. The man complexty s to fnd the trade-offs between the parameters of the mult-objectves. Ths work defnes four performance CR objectves for a SU n whch varous objectves overlapped as consder to maxmzng ther performance. All ftness functon used n ths thess to optmze QoS performance has been lsted n the Table gven below. Ftness Functon Mnmze BER f mn_ ber Table 3.5 Ftness Functon of Cogntve Rado. * log10 max( PER, PER) Functon Dervaton * log10 max( PER, PER) 1, 1 1. * log 10( PER ) 1, otherwse. * log 10( PER ) N Maxmze 1 c fmax_ throughput 1 log 2( ) Throughput M Nc log 2 ( M max ) 1 Mnmze Nc 1 Power fmn_ power P Utlzaton NcPmax 1 Mnmze Interference Sngle Functon for mult objectve N 1 c fmn_ nt erference ( P B) N P B c max max 1 F w f w f w f w f 1 mn_ ber 2 max_ throughput 3 mn_ ower 4 mn_nt erference