Energy efficiency in cognitive radio network: study of cooperative sensing using different channel sensing methods

Transcription

1 Graduate Teses and Dissertations Graduate College 2015 Energy efficiency in cognitive radio network: study of cooperative sensing using different cannel sensing metods Cenxuan Cui Iowa State University Follow tis and additional works at: ttp://lib.dr.iastate.edu/etd Part of te Electrical and Electronics Commons, and te Oil, Gas, and Energy Commons Recommended Citation Cui, Cenxuan, "Energy efficiency in cognitive radio network: study of cooperative sensing using different cannel sensing metods" (2015). Graduate Teses and Dissertations ttp://lib.dr.iastate.edu/etd/14749 Tis Tesis is brougt to you for free and open access by te Graduate College at Iowa State University Digital Repository. It as been accepted for inclusion in Graduate Teses and Dissertations by an autorized administrator of Iowa State University Digital Repository. For more information, please contact

2 Energy efficiency in cognitive radio network: Study of cooperative sensing using different cannel sensing metods by Cenxuan Cui A tesis for Master submitted to te graduate faculty in partial fulfillment of te requirements for te degree of MASTER OF SCIENCE Major: Electrical Engineering Program of Study Committee: Sang W. Kim, Major Professor Amed El-Sayed Kamal Natan Neiart Iowa State University Ames, Iowa 2015 Copyrigt Cenxuan Cui, All rigts reserved.

3 ii DEDICATION I dedicate my tesis work to my loving family, especially to my mom Ke Cen and my dad Jiancun Cui, wo ave been loving and supporting me since te beginning of my life. I dedicate my tesis work to all of my friends, we togeter ave created our best memories and we ave taken care of eac oter in ard times. I also dedicate my tesis work to my professor Sang Kim, wo as given me knowledge and always been patient wit me in my difficult time. Last but not least, I dedicate my tesis work to you, because someow we are all connected.

4 iii TABLE OF CONTENTS Page NOMENCLATURE AND NOTATION... ABSTRACT.... iv vi CHAPTER 1 INTRODUCTION... 1 CHAPTER 2 LITERATURE REVIEW ON CR ENERGY EFFICIENCY... 2 CHAPTER 3 SENSING SINGLE CHANNEL OF VARYING BANDWIDTH.. 5 Energy Detection Sceme and Error Probabilities... 5 Network Cannel Capacity and Energy Efficiency... 7 Cooperative Sensing and Data Fusion Rules... 9 Study on AND Fusion Rule wit Constrain on Misdetection Probability Case Study: Maximal Energy Efficiency Using AND Fusion Rule wit Misdetection Tresold CHAPTER 4 SENSING MULTIPLE CHANNELS OF SAME BANDWIDTH. 21 One Cognitive Radio wit Two Primary Users Cannel Capacities and Energy Efficiency wit Two PUs One Cognitive Radio wit Multiple Primary Users Cannel Capacities and Energy Efficiency wit Multiple PUs Setting Misdetection Tresold on CRs OR Fusion Rule wit k CRs and S PUs Case Study: AND Fusion Rule wit k CRs and S PUs CHAPTER 5 CONCLUSION AND FUTURE RESEARCH DIRECTIONS REFERENCES... 39

5 iv NOMENCLATURE AND NOTATION ADC CR FC PU SINR SNR SR SU Analog to Digital Converter Cognitive Radio Data Fusion Center Primary Users Signal to Interference plus Noise Ratio Signal to Noise Ratio Secondary Receiver Secondary User H 0 Hypotesis Test 0 H 1 Hypotesis Test 1 s(t) n(t) σ n 2 T s B λ γ P CS P P C ave E total Primary Signal Noise Signal Noise Variance Sensing Time Sensing Bandwidt Detection tresold SNR from PU and Measured at CR Signal Power Transmitted from CR and Measured at SR Signal Power Transmitted from PU and Measured at CR Average CR Cannel Capacity CR Network Total Energy Consumption

6 v P T P S T T T S E d E C K D FC P e P f n S k P m P m,r,k P m,r Q f Q m Q f,r Q m,r,k m m,cr CR Transmission Power CR Sensing Power CR Tranmission Time CR Sensing Time CR Decision Report Signal Energy Consumption CR Circuit Energy Consumption Number of Cooperative Sensing CR Sum of Decision Bits from CR to DFC Average Reporting Cannel Error Probability False Alarm Probability at Eac CR Decision Tresold Sensed Cannels Number of PU Tat Are Active (Transmitting) Misdetection Probability Misdetection Probability for r PUs Wen k of Tem Are Active Total Misdetection Probability for r PUs at CR Network False Alarm Probability Network Misdetection Probability Network False Alarm Probability for r PUs Network Misdetection Probability Wen k out of r PUs Are Active Network Misdetection Tresold Misdetection Tresold on Eac CR

7 vi ABSTRACT Wen cognitive radio (CR) operates, it starts by sensing spectrum and looking for idle bandwidt. Tere are several metods for CR to make a decision on eiter te cannel is occupied or idle, for example, energy detection sceme, cyclostationary detection sceme and matcing filtering detection sceme [1]. Among tem, te most common metod is energy detection sceme because of its algoritm and implementation simplicities [2]. Tere are two major metods for sensing, te first one is to sense single cannel slot wit varying bandwidt, wereas te second one is to sense multiple cannels and eac wit same bandwidt. After sensing periods, samples are compared wit a preset detection tresold and a decision is made on eiter te primary user (PU) is transmitting or not. Sometimes te sensing and decision results can be erroneous, for example, false alarm error and misdetection error may occur. In order to better control error probabilities and improve CR network performance (i.e. energy efficiency), we introduce cooperative sensing; in wic several CR witin a certain range detect and make decisions on cannel availability togeter. Te decisions are transmitted to and analyzed by a data fusion center (DFC) to make a final decision on cannel availability. After te final decision is been made, DFC sends back te decision to te CRs in order to tell tem to stay idle or start to transmit data to secondary receiver (SR) witin a preset transmission time. After te transmission, a new cycle starts again wit sensing. In tis tesis, we find metods to maximize total energy efficiency of te cognitive radio network using closed form expressions, and wit te consideration on misdetection tresold on eac CR or te CR network in order to protect PU. Furtermore, we derives te

8 vii optimal fusion rule for DFC in order to maximize energy efficiency in a cooperative sensing environment. Finally compare between two difference sensing scemes and find te one wic furter maximize te energy efficiency. Tis tesis report is organized as followed: Capter II review some of te papers on optimizing CR energy efficiency. In Capter III, we study ow to acieve maximal energy efficiency wen CR senses single cannel wit canging bandwidt and wit constrain on misdetection tresold in order to protect PU; furtermore, a case study is given and we calculate te energy efficiency. In Capter IV, we study ow to acieve maximal energy efficiency wen CR senses multiple cannels and eac cannel wit same bandwidt, also, we preset a misdetection tresold and calculate te energy efficiency. A comparison will be sown between two sensing metods at te end of te capter. Finally, Capter V concludes tis tesis.

9 1 CHAPTER I INTRODUCTION Te Federal Communication Commission as allocated radio spectrum from 9 KHz to 275 GHz [3], and wit increasing amount of wireless transceiver devices and networks, we will encounter difficulties in assigning and licensing new wireless users due to scarcity in available spectrum in te near future. On te oter and, according to a survey done in Dublin Ireland [14], more tan 80 percent of spectrum is underutilized, and similarly for some major cities in te United States. Terefore, tere is a low spectrum utilization rate. Josep Mitola III, from Stevens Institute of Tecnology, foresaw tis problem and developed te concept of cognitive radio in te late 1990s and tis tecnology as since attracted muc attentions among scolars all around te world. CR does not ave a license for any radio frequency band. It accesses to cannels opportunistically wen te licensed user (PU) is not transmitting its signal. And jumps out from tat cannel in 2 seconds (IEEE ) after PU restarts to transmit its signal. A similar scenario is tat imagine you are at a movie teatre on your own and you forget to purcase a ticket. You want to sit down to watc te movie but te teatre is full. One way to watc te movie wile sitting down is to wait by te entrance door until someone stands up to go to use te restroom or answer an important pone call. Ten you can run to is or er seat and sit for a wile until e or se comes back, and you ave to leave te seat and wait by te entrance for te next opportunity. Besides alleviating spectrum scarcity issue, CR can be used for secured communication, since CR searc for available spectrum on itself and it is a type of frequency opping radio, we can apply tis tecnology for secured communication suc as on te battlefields.

10 2 CHAPTER II LITERATURE REVIEW ON CR ENERGY EFFICIENCY In tis capter, we coose and review some of te papers [4] [5] [6] [7] on optimizing energy efficiency in cognitive radio network. Some papers are on optimizing energy efficiency in sensing period [4] [5], some on energy efficiency optimization in transmission period [6], and finally a paper on CR overall circuit energy consumption by studying te tradeoff between sensing and transmission of te cognitive radio [7]. Paper [4] proposed a metod on optimizing te energy efficiency (or opportunity cost, as described in te paper) in sensing period of te cognitive radio network. In te paper, sensing period is divided into R rounds, and at eac round, CR is able to make a local decision on eiter te PU is transmitting or in idle for a specific cannel. Eac round is consisted of tree parts, spectrum sensing, decision report, and cannel switcing. Terefore, CR is able to sense R cannels during sensing period. After all CRs report teir decision to DFC, te DFC use a specific data fusion rule to produce a final decision on eiter PU is transmitting or not. Te sensing energy efficiency is described using total energy consumption (sum of energy consumption in spectrum sensing, decision report and cannel switcing) divides te amount of available bandwidt found in R rounds. Te metrics of energy efficiency is in Joule per Hz. Te paper later optimized suc energy efficiency wit te consideration of preset misdetection and false alarm probability. Anoter paper to mention on sensing energy efficiency is [5]. Te autors proposed an energy efficiency sensing sceme by using adaptive spectrum sensing algoritm and sequential sensing policy [5]. Te adaptive spectrum sensing algoritm was introduced since PU s active and idle probability and periods can be studied [5], in order to allow CR to limit

11 3 sensing time and give more opportunity for transmission and reduce missed spectrum opportunities. On te oter and, sequential sensing policy is to constrain two error probability, namely false alarm probability and misdetection probability. Te autors set two tresold for detection, λ1 and λ2. If received signal energy is greater tan λ2, ten CR decides tat PU is transmitting, wereas if received signal energy is less tan λ1, CR decides PU is not transmitting. And finally if received signal energy is between two tresolds, CR will collect more signal samples. By optimizing tese two tresold, te paper sows tat we can minimizing false alarm probability, wic allow more transmission opportunities for CR, and minimizing misdetection probability below a certain tresold in order to protect PU. Paper [6] introduced a metod to optimize transmission energy efficiency by optimizing transmission duration and power allocation to eac cannel. First, te autors sowed te model for energy efficiency for CR in a frame cycle, and it was a function of transmission duration. Ten tey derived te derivative of suc energy efficiency wit respect to transmission time and set te function equals to zero to find te optimal transmission duration. Next, te autors moved to te oter topic, wic is to find te optimal power allocation for K cannels under a preset transmission power budget. By using gradient assisted binary searc and binary searc assisted ascent [8], te autors sowed tat tere exist an optimal power allocation in transmission period for cognitive radio. Last but not least, Paper [7] maximize te overall energy efficiency of cognitive radio (bot in sensing and transmission periods). Te autors assumed power consumption during sensing period is mainly caused by low noise amplifier and analog to digital converter. Power amplifier, low noise amplifier and analog to digital converter contributes to te power consumption in transmission periods. Later on, te autors sowed tat in order to maximize

12 4 energy efficiency, one sould maximize sensing time, te ratio of te power consumption for power amplifier and analog to digital converter, bit resolution of te ADC and te input backoff of te power amplifier [7]. Since tere is no close form expression for teir energy efficiency expression. Te autors used numerical simulation to find te maximal energy efficiency. In general, tis literature review sows tat on te topic of energy efficiency maximization for cognitive radio network, some researc as been done on energy efficiency maximization in sensing period, transmission period and overall energy efficiency wit te consideration in misdetection probability but witout close form expression for maximal energy efficiency. In tis tesis work, we analyze two different sensing metods for CR at eac sensing period: sensing single cannel wit canging bandwidt and sensing multiple cannels eac wit same bandwidt. After tis, we find te optimal fusion rule wit constrain on misdetection probability using misdetection tresold for eac sensing case. And finally, we simulate te performance of energy efficiency. Terefore, compare wit oter works on energy efficiency in cognitive radio network, wic only maximize sensing or transmission energy efficiency, or maximize overall energy efficiency but witout a close form expression; te contribution of tis work is to find metods to maximize total energy efficiency of te cognitive radio network using closed form expressions wit a misdetection tresold on eac CR or te CR network in order to protect PU. Furtermore, we derives te optimal fusion rule for DFC wic elps CR network to maximize its energy efficiency, and finally we compare between two difference sensing scemes and analyze teir performance on maximizing energy efficiency.

13 5 CHAPTER III SENSING SINGLE CHANNEL OF VARYING BANDWIDTH Energy Detection Sceme and Error Probabilities In tis section, we first derive te pdf and CDF of received input samples. Assume ypotesis test 1 (H 1 ) is wen PU is transmitting its signal, ypotesis test 0 (H 0 ) is wen PU is not transmitting its signal. Assume CR receives inputs witout PU signal (H 0 ) are Gaussian random process wit zero mean, x(t) = n(t): N (0, σ 2 n ). And Assume CR received inputs wit PU signal (H 1 ) present is Gaussian random process wit nonzero mean x(t) = α s(t) + n(t): N (μ s, σ 2 n ). Wit some cannel fading factor α. x(t) = { α s(t) + n(t) H 1 n(t) H 0 (1. 1) According to Claude Sannon s sampling teorem [9], for a signal wit bandwidt B and is sampled in a time T s, we need 2T s B samples in order to acquire knowledge of te received signal completely. Te sampled signals are: 2T s B x(t) = (α s i (t) + n i (t)) H 1 i=1 2T s B n i (t) { i=1 H 0 (1. 2) Assume noise is additive wite Gaussian noise wit zero mean and variance σ n 2, and eac sample is a random variable wit zero mean and variance σ 2 i,n = σ 2 n, we divide every samples by noise standard deviation σ n ; ten te normalized noise sample as distribution of N (0,1). For energy detection, we square and sum eac received signal sample wit unit variance, and result a sum of te squares of 2T S B i.i.d random variables:

14 6 y(t) = { 2T s B ( α s 2 i(t) + n i (t) ) σ n i=1 2T s B ( n i(t) ) 2 σ n i=1 H 1 H 0 (1. 3) For H 0, we ave squares of 2T s B standard normalized Gaussian random variables, eac wit zero mean and unit variance. Terefore, it follows central ci-squared distribution wit 2T s B degrees of freedom. Te pdf of suc distribution according to reference [10] is: f Y (y, H 0 ) = 1 2 TsB Γ(T S B) ytsb 1 e y 2 (1. 4) Te complimentary CDF of te distribution at point λ is te false alarm probability [10] : P f = 1 F Y (λ, H 0 ) = Γ(T sb, λ 2 ) Γ(T s B) (1. 5) In wic Γ(. ) is gamma function and Γ(., b) is upper incomplete gamma function at point b. In te case of PU transmitting, Assume primary signal and noise are independent. Sampled normalized signals ave means of μ s = μ s,i = 1 2T 2T s B (α s i (t) s B ) σ n 1 and variances of 0. Ten te received inputs are normal distributed N (μ s, 1). Wic follows non-central ci-squared distribution wit 2T s B degrees of freedom. And te pdf of suc distribution is: f Y (y, H 1 ) = 1 2 e y+φ 2 ( y T s B 1 φ ) 2 I Ts B 1( φy) (1. 6) In wic φ is te non-centrality parameter and I a 1 ( b c) is te modified Bessel s function. We ave te misdetection probability (P m ) of eac CR according to reference [10] : P m = 1 Q Ts B( 2γ, λ) (1. 7) In wic Q a ( b, c) is Marcum-Q function and γ is SNR from PU and measured at CR. For now, we ave derived pdf and CDF of received input samples. In detection teory,

15 7 we always measure te performance of detector using false alarm probability (probability of CR decides PU is transmitting, given PU is actually not transmitting: P f = P(H H 1 0 ); and misdetection probability (probability of CR decides PU is not transmitting, given PU is actually transmitting: P m = P(H H 0 1 )). Accordingly, given a preset detection tresold λ for 2T s B samples, wic CR decides PU is transmitting if te sum of received signal power is above te tresold, and decides PU is idle if te sum is below λ, we can easily find out P f and P m for eac CR using CDF derived in equations (1.5) and (1.7). P f = P(y > λ H 0 ) = 1 F Y (λ, H 0 ) = Γ(T sb, λ 2 ) Γ(T s B) { P m = P(y < λ H 1 ) = 1 Q Ts B( 2γ, λ) (1. 8) Network Cannel Capacity and Energy Efficiency In tis section, we want to finally derive energy efficiency (bits per Joule) of te CR network. But first, we calculate transmission capacity of CR under correct detection (H 0, H ) 0 and misdetection (H 1, H ); 0 given sensing bandwidt W, detection tresold λ, amount of CRs and oter parameters. Assume te signal power transmitted to SR from CR, and measured at SR is P CS wit cannel gain. Assume sensing bandwidt is B and noise spectrum power is N 0. CR transmission cannel capacity of correct detection is: C d = Blog 2 (1 + P CS N 0 B ) Given te probability of CR transmission under tis condition is P(H 0, H ) 0 = P(H H 0 0 )P(H 0 ), te weigted transmission capacity of correct detection is terefore:

16 8 C d(weigted) = Blog 2 (1 + P CS N 0 B ) P(H H 0 0 )P(H 0 ) (1. 9) Similarly, te transmission capacity of misdetection is: C md = Blog 2 (1 + P CS N 0 B + P ) P In wic P P is signal power from PU measured at secondary network (CR-SU network) and g is te cannel gain from PU to secondary network. Probability of transmission under misdetection is P(H 1, H ) 0 = P(H H 0 1 )P(H 1 ). Te weigted transmission capacity of misdetection is: C md(weigted) = Blog 2 (1 + P CS N 0 B + P ) P(H H 0 1 )P(H 1 ) P (1. 10) Assume in cooperative sensing case, Q f is network false alarm probability and Q m is network misdetection probability, we ave P(H H 0 0 ) = (1 Q f ), and P(H H 0 1 ) = Q m, and te average CR cannel capacity is: C ave = B [log 2 (1 + P CS N 0 B ) (1 Q P f)p(h 0 ) CS + log 2 (1 + N 0 B + P ) Q mp(h 1 )] P (1. 11) Next, we give te energy consumption of CR network. Te total energy consumption of te network in one frame cycle is: E total = P T T T + (P S T S + E d + E C )K (1. 12) Equation (1.12) sows te total energy consumption of cooperative sensing CR network, P S is sensing power; T S is sensing time; P T T T is transmission energy from CR to SR. E d is one bit decision report signal energy from every CR to DFC; and finally E C is circuit energy consumption of CR. Hence; average energy efficiency in bits per watt is: Average energy efficiency = T TC ave E total (1. 13)

17 9 In te next section, we look at some famous data fusion rules suc as AND fusion rule and OR fusion rule; ten we sow te fusion rule tat can acieve maximal energy efficiency given preset misdetection tresold, in order to protect PU. Cooperative Sensing and Data Fusion Rules In te first section, we derived probability of false alarm and misdetection of eac CR during sensing period. Next, we discuss about different data fusion rules and network false alarm and misdetection probability. Assume tere are K CRs nearby wic are able to join cooperative sensing network (Fig.1), and eac CR sends one bit decision K i (i = 1,2,, K; K i = 0 or 1) to DFC. Te DFC receives Kk binary decisions and ten make a final decision using tese binary data. Assume decision tresold is n, and summation of received bits add up to be D FC. If te summation of te received bits is less tan decision tresold n, DFC decides PU is not transmitting. If te summation of te received bits is greater tan or equals to decision tresold n, te DFC decides PU is transmitting. We ave: K K i < n, H 0 i=1 D FC = K (1. 14) K i n, H 1 { i=1 Figure 1.1 a: CR Cooperative Sensing Network Diagram

18 10 Figure 1.1 b: CR Cooperative Sensing Network Scematics From previous studies on data fusion rules introduced in [10] and [11], we generalize following commonly used fusion rules: OR Fusion Rule Te one bit data sent from eac CR to DFC can be eiter 0 (PU idle) or 1 (PU transmitting). OR fusion rule allows DFC to make final decisions of PU is transmitting if one or more CR out of Kk CRs decide(s) PU is transmitting [10]. Assume Q f and Q m are te false alarm and misdetection probability in DFC s final decisions; we ave: K Q f = 1 (1 P f,i ) = 1 (1 Γ (T sw, λ 2 ) Γ(T s W) ) i=1 K K Q m = (P m,i ) = (Q Ts W( 2γ, λ )) { i=1 i=1 K i=1 (1. 15) Assume reporting cannel from eac CR to DFC is also fading cannel wit error probability P e,i (imperfect reporting cannel), and reporting errors in all cannels are identical and independent. Ten we ave P e,i (for i = 1,2,, K) = P e (Average reporting cannel error probability) and assume eac CR as same P f and P m : let { P f e = P f (1 P e ) + P e (1 P f ) P m e = P m (1 P e ) + P e (1 P m )

19 11 we ave { Q f = 1 (1 P f e ) K Q m = (P m e ) K { Q f = 1 [ (1 P f ) ( Q m = [ P m (1 P e ) + AND Fusion Rule AND fusion rule allows DFC to make final decisions of PU is transmitting if and only if all of te CRs decide(s) PU is transmitting. If even one CR decides PU is idle, te DFC will make a final decision tat PU is idle [10]. AND fusion rule is described below: { Q f = (P f e ) K Q m = 1 (1 P m e ) K { Q f = [ P f (1 P e ) + P e (1 P f )] k Q m = 1 [ (1 P m ) (1 P e ) + P e P m ] k n Out of K Fusion Rule Wen te amount of CRs tat join cooperative sensing is K, and decision tresold is n, we ave te general expression of te network false alarm and misdetection probability for n out of K fusion rule as described in equation (1.18): { K Q f = K ( l ) l=n K (P f e ) l (1 P f e ) K l Q m = 1 K ( l ) e l (1 P m) (P e K l m) l=n (1. 18) Wic OR fusion rule is equivalent as letting n = 1 in equation (1.18), and AND fusion rule is same as letting n = K in equation (1.18). Study on AND Fusion Rule wit Constrain on Misdetection Probability Among above fusion rules, we want to find te one wic gives maximal energy efficiency. According to equation (1.13), given te number of coop CR, we want to minimize false alarm probability wile maximize misdetection probability in order to maximize energy efficiency. According to te general equations for Q f and Q m given in equation (1.18), we ave:

20 12 K Q f,(n=k) = ( K l ) (P e f ) l (1 P e f ) K l = (P e f ) K l=k K 1 Q f,(n<k) = (P e f ) K + ( K { l ) (P e f ) l (1 P e f ) K l l=n for n = K for n < K (1. 19) Clearly, Q f,(n<k) is always greater tan Q f,(n=k), since te second term on te rigt side of equation for Q f,(n<k) is always greater tan 0 (for nonzero false alarm probability at eac CR). Terefore, for given K, in order to minimize false alarm probability, we sould use AND fusion rule, in wic decision tresold is equal to number of coop CRs. Next, we want to maximize misdetection probability: Q m,(n=k) = 1 (1 P e m ) K for n = K K 1 { Q m,(n<k) = 1 (1 P e m ) K ( K l ) (1 P e m ) l (P e m ) K l for n < K l=n (1. 20) Clearly, Q m,(n<k) is always less tan Q m,(n=k), since te tird term on te rigt side of equation for Q m,(n<k) is always greater tan 0 (for nonzero misdetection probability at eac CR). In conclusion, for given K, in order to maximize misdetection probability, we sould let n = K, wic is equivalent as using AND fusion rule. Furtermore, Figure 1.2 below sows te decrease of false alarm probability and increase of misdetection probability as te number of CRs increase; by setting P e m = P e f = In real applications, we want to transmit using maximal energy efficiency wit preset tresold for misdetection probability m, in order to protect PU. Next, we study ow to acieve maximal energy efficiency using AND fusion rule given m.

21 13 Figure 1.2: False Alarm Probability and Misdetection Probability According to equation (1.17), in order to let te network misdetection probability less tan or equal to m, misdetection probability at eac CR sould satisfy: { m Q m = 1 (1 P m e ) K P m e 1 (1 m ) (1 K ) (1. 21) From page 8 we ave: P m = P m e P e 1 (1 m) ( 1 K ) P e (1. 22) 1 2P e 1 2P e And also from equation (1.7), we ave P m = 1 Q Ts B( 2γ, λ) = ncx2cdf(λ, T S B, T S Bγ) (1. 23) In wic ncx2cdf(a, b, c) = j=0 j ( (1 2 c) e c 2 2) Pr[x j! b+2j x] (1. 24)

22 14 Equation (1.24) computes te non-central ci square cumulative distribution function at a, using degrees of freedom b and non-centrality parameter c [12]. And P m increases as λ increases. Next, according to [13] we ave: λ = ncx2inv(p m, T S B, T S Bγ) (1. 25) Wic ncx2inv(p m, T S B, T S Bγ) is inverse non-central ci square cumulative distribution function. Notice tat λ increases as P m increases. Terefore; by substituting P m wit rigt and side of equation (1.18) we ave: λ ncx2inv ( 1 (1 m) ( 1 K ) P e, T 1 2P S B, T S Bγ) (1. 26) e Furtermore, in equation (1.5), false alarm probability decreases as detection tresold λ increases (in wic 1 P f increases as λ increases). Terefore, in AND fusion rule, in order to minimize false alarm probability and maximize misdetection probability at eac CR wile ensuring misdetection probability is below preset misdetection tresold m, we sould maximize detection tresold λ and te maximal value is: λ max = ncx2inv ( 1 (1 m) ( 1 K ) P e, T 1 2P S B, T S Bγ) (1. 27) e For now, we ave learned ow to maximize energy efficiency, wic is to use AND fusion rule, and derived te optimal detection tresold in order to maximize energy efficiency wile ensuring misdetection probability is below misdetection tresold, in order to protect PUs. Next, we provide a case study and calculate te maximal energy efficiency. Figure 1.3: Flow Cart on Steps to Calculate Energy Efficiency

23 15 Case Study: Maximal Energy Efficiency Using AND Fusion Rule wit Misdetection Tresold Setting-up te Parameters Table 1.1: Spectrum Occupancy in Dublin, Ireland [14] Table 1.1 is from te survey of spectral occupancy in Dublin, Ireland [14]. In te survey, te available bandwidt is divided into 31 slots, from 30MHz to 3GHz. According to te data, we first calculate te average spectral occupancy and set 1MHz as one unit of cannel bandwidt and unit increment: 31 i=1(bandwidt i %occupancy i ) total scanned bandwidt(mhz) = 14.47% (1. 28)

24 16 Terefore, te average 1MHz spectral active probability P(H 1 ) is 14.47%, and spectral idle probability P(H 0 ) is 85.53%. Assume noise spectrum power N 0 = Watt/Hz, received PU power P P = 10 6 Watt. Assume BPSK modulation is used for decision reports from eac CR to DFC, and we coose to implement a low power consumption XTend transceiver [15] for CR to transmit its signals. Tis type of transceiver operates at frequency range of MHz, and it is compatible for DigiMesTM networking topology. We set 9.6Kb/s as transmission rate in order to minimize reporting cannel error probability since it is te minimal transmission rate, and set transmission power from CR to FC (P d ) and transmission power from CR to SR to be 1W, or 30dBm. Terefore, we ave bit energy E D = 0.104mJ. Furtermore, according to survey on pat loss in German cities sown in Figure 1.4, we coose te pass loss exponent to be 2.7. Assume all te CRs are at 50 meters away from FC, and SR is 200 meters away from CR. we ave decision report error probability as: P e = Q ( 2 P d N 0 W ) = Q ( 2 P d distance 2.7 ) (1. 29) N 0 W = Q( ) ,000 According to Figure 1.5 from [16], wic sows te relation between power consumption and sampling rate of analog to digital converter (ADC), and since most of te sensing power is consumed by ADC, we can approximate sensing power consumption using power consumption of ADC. Wen samples are in N bits and f S = 2B, Sensing power can be terefore described as: P S = N ( 2B 10 3) (μw) (1. 30)

25 17 Figure 1.4: Pat Loss vs Distance in German Cities [17] Figure 1.5: ADC Power Consumption vs Sampling Rate [16] Simulation Results Using AND Fusion Rule wit Different Misdetection Tresold All simulations and plots in te tesis use te parameters given below, unless oterwise mentioned in te plots caption.

26 18 Table 1.2: Summary of Parameters Parameters Parameter Value Note P(H 0 ) P(H 1 ) P e N 0 Pat Loss Exponent P P P CS P S 85.53% Average spectral idle probability in Dublin Ireland [11] 14.47% Average spectral occupied probability in Dublin Ireland [11] Reporting cannel error probability (from CR to DFC) Noise power spectral density 2.7 Found in pat loss vs distance in German cities [17] Watt Received PU signal power measured at CR 1 Watt CR transmission power to DFC and SR (30dBm) ( 2B 10 3) CR sensing power consumption (ADC power consumption) T s 10µS CR sensing time T T 1 T s CR transmission time 100KHz Bandwidt for eac cannel wen CR senses multiple cannels B0 E d E C d CS N 104µWatt Decision report transmission energy consumption CR circuit energy consumption in one frame cycle 200 meters Distance between CR and secondary receiver (SR) 12 Number of bits for ADC to scale te samples As sown above in Figure 1.6 a, X-axis is te number of cooperative sensing CRs, Y- axis is sensing bandwidt in ertz, and Z-axis (illustrated in color) is energy efficiency. Tere exist maximal energy efficiency in AND fusion rule wit a preset misdetection tresold (labeled in eac subplot). In te simulation, we found out as we increase misdetection tresold, we can acieve iger maximal energy efficiency. Te optimal number of CR decreases and optimal sensing bandwidt increases as misdetection tresold increases.

27 19 Figure 1.6 a: Energy Efficiency (Z-axis) vs Number of CR (X-axis) vs Sensing Bandwidt (Yaxis) Using AND Fusion Rule wit Different m Figure 1.6 b: Energy Efficiency vs Number of CR Using AND Fusion Rule (B=1MHz)

28 20 Next, we let te primary user active probability P(H 1 ) as a variable, and find optimal number of coop CR for given different P(H 1 ). Finally, we plot te relation between P(H 1 ) and optimal number of coop CR. We set misdetection tresold to 0.1 and sensing bandwidt to 1MHz. Figure 1.6 c: Energy Efficiency vs Number of CR wit Canging P(H 1 ) ( m = 0.1) As we can see from above, energy efficiency increases as we decreases P(H 1 ).

29 21 CHAPTER IV SENSING MULTIPLE CHANNELS OF SAME BANDWIDTH In tis capter, we study energy efficiency in CR networks wen CR senses multiple cannels and eac cannel wit same bandwidt. We can visualize tis problem by assuming tere are several PUs nearby and eac of tem uses its own cannel wit no overlap wit eac oter. CR senses multiple cannels eac wit same bandwidt instead of single cannel wit canging bandwidt. For simplicity, we assume eac cannel as same bandwidt. One Cognitive Radio wit Two Primary Users Assuming tere are 2 PUs nearby, and eac wic probability of transmission P(H 1 ) = and probability of idle (no transmission) P(H 0 ) = 1 P(H 1 ) = Figure 2.1: CR Network wit 1 CR and 2 PUs Te tradeoff between number of PUs and CR transmission bandwidt can be described as below: wen CR increases its sensing and transmission bandwidt, te network will ave an increase of data transmission rate as described in paper [18]. However, increasing CR bandwidt will inevitably causing collision wit PU s transmission. Figure 2.2 illustrated tis scenario:

30 22 Figure 2.2: CR Transmission Interfere wit Primary Transmissions As sown in Fig.2, assume PU use different cannels and as CR transmission bandwidt increases, te transmission bandwidt of CR intersects (overlaps) wit primary transmission bandwidt. Next, we look at misdetection probability. In general, we ave misdetection probability described as: P m = P(H 0 H 1 ) = P(H 0, H 1 ) P(H 1 ) (2. 1) As sown in equation (2.1), H 0 is wen PU is inactive (idle) and H 1 is wen PU is active (busy). Ten, we extend tis representation for 2 PUs present: H 00 means wen PU1 and PU2 are bot idle, H 01 is wen PU1 is idle wile PU2 is active. And so on for S PUs, in wic te representation of teir activity is described in form of H 01 10, as we will discuss in te next section. Wen tere are two PUs, we ave misdetection probability: P m,2 = P(H 0 H 1 ) = P(H 0, H 1 ) P(H 1 ) = P(H 0 H 1 ) = P(H 0 (H 01 H 10 H 11 ) P(H 1 ) P(H 1 ) = P(H 0 H 01 ) + P(H 0 H 10 ) + P(H 0 H 11 ) P(H 0 H 01 H 10 ) P(H 1 ) P(H 0 H 01 H 11 ) + P(H 0 H 10 H 11 ) P(H 0 H 01 H 10 H 11 ) P(H 1 ) (2. 2a)

31 23 We assume primary users transmissions are independent from eac oter s wit disjoint cannels and same bandwidt B 0 ; and since H 01, H 10 and H 11 are mutually exclusive events, we ave: P(H 01 H 10 ) = P(H 01 H 11 ) = P(H 10 H 11 ) = 0, and eventually P m,2 = P ((H 0 H 01 ) + (H 0 H 10 ) + (H 0 H 11 )) P(H 1 ) P(H 0 H 01 ) = P(H 0 H 01 )P(H 01 ) Furtermore, we ave: { P(H 0 H 10 ) = P(H 0 H 10 )P(H 10 ) P(H 0 H 11 ) = P(H 0 H 11 )P(H 11 ) and we adopt following (2. 2b) notations: P(H 0 H 01 ) = P m,01 { P(H 0 H 10 ) = P m,10 P(H 0 H 11 ) = P m,11 misdetection probability wen PU1 is idle and PU2 is active misdetection probability wen PU1 is active and PU2 is idle misdetection probability wen PU1 and PU2 are bot active In wicp m,01 means PU 1 is idle and PU 2 is active. Ten te misdetection probability wen tere are 2 PU can be expressed as: P m,2 = P(H 0 H 01 )P(H 01 ) + P(H 0 H 10 )P(H 10 ) + P(H 0 H 11 )P(H 11 ) P(H 01 ) + P(H 10 ) + P(H 11 ) = P m,01p(h 01 ) + P m,10 P(H 10 ) + P m,11 P(H 11 ) P(H 01 ) + P(H 10 ) + P(H 11 ) (2. 2c) For misdetection probability, we ave from equation (1.7) wit bandwidt B 0 : P m = 1 P d = 1 Q TS B 0 ( 2γ, λ) (2. 3) In wic γ is SNR from primary user and received at CR; λ is detection tresold and T S is sensing time. In te case wen tere are 2 PUs, we ave different SNR from PU to CR, depend on ow many of te PU is active:

32 24 P P γ PC01 = (SNR from PU, received by CR; wen PU1 is idle and PU2 is active) 2N 0 B 0 P P γ PC10 = (SNR from PU, received by CR; wen PU1 is idle and PU2 is active) 2N 0 B 0 γ { PC11 = 2P P (SNR from PU, received by CR; wen bot PU are active) 2N 0 B 0 In wic P P is transmission power from PU and measured at CR. Te misdetection probability described in equation (2.2) can be detailed into: P m,2 = P m,01p(h 01 ) + P m,10 P(H 10 ) + P m,11 P(H 11 ) P(H 01 ) + P(H 10 ) + P(H 11 ) = P(H 0)P(H 1 )(P m,01 + P m,10 ) + P(H 1 ) 2 P m,11 1 P(H 0 ) 2 = P(H 0)P(H 1 )[1 Q 2TS B 0 ( 2γ PC01, λ) + 1 Q 2TS B 0 ( 2γ PC10, λ)] + P(H 1 ) 2 (1 Q 2TS B 0 ( 2γ PC11, λ)) 1 P(H 0 ) 2 And false alarm probability P f for 2 PU is: (2. 4) P f,2 = Γ(2T sb 0, λ 2 ) Γ(2T s B 0 ) (2. 5) Cannel Capacities and Energy Efficiency wit Two PUs Total Cannel Capacity can be derived as below: Cannel Capacity = 2B 0 log(1 + γ CS00 ) (1 P f,2 )P(H 0 ) + 2B 0 log(1 + γ CS01 ) P m,01 P(H 0 )P(H 1 ) + 2B 0 log(1 + γ CS10 ) P m,10 P(H 1 )P(H 0 ) + 2B 0 log(1 + γ CS11 ) P m,11 P(H 1 )P(H 1 ) (2. 6) Note tat in te first term of equation (2.6), te probability of correct sensing is P(H 0 ), since te idle probability for single cannel is P(H 0 ), and te average amount of

33 25 cannel available given te S cannels is SP(H 0 ). Notations γ CSxx are te signal to noise ratio from CR and received at secondary user (SU), x can to replace by digit 0 (PU inactive) or 1 (PU active). And te descriptions for SINR from CR to SR are sown below: P CS γ CS00 = (SNR from CR to SU wen bot PUs are idle) 2N 0 B 0 P CS γ CS01 = (SINR from CR to SU, interfered by te first PU. ) 2N 0 B 0 + P P P CS γ CS10 = (SINR from CR to SU, interfered by te second PU. ) 2N 0 B 0 + P P P CS γ CS11 = (SINR from CR to SU, interfered by 2 PU) { 2N 0 B 0 + 2P P Te first term on te rigt and side of equation (2.6) is te trougput under correct detection given bot PUs are idle. Te second term is te trougput under misdetection given PU1 is idle and PU2 is active. Te tird term is te trougput under misdetection given PU1 is active and PU2 is idle. And te last term is te trougput under misdetection given bot PUs are active. Assume frame time (T F ) is 1 second, and sensing time plus transmission time equals frame time: T F = T S + T T. Te energy efficiency wen tere are 2 PUs is: Energy Efficiency = transmission time cannel capacity energy consumption in one frame = T T (2B 0 log(1 + γ CS00 ) (1 P f,2 )P(H 0 ) + 2B 0 log(1 + γ CS01 ) P m,01 P(H 0 )P(H 1 )) P s T S + P T T T + P C (T S + T T ) + T T(2B 0 log(1 + γ CS10 ) P m,10 P(H 1 )P(H 0 ) + 2B 0 log(1 + γ CS11 ) P m,11 P(H 1 ) 2 ) P s T S + P T T T + P C (T S + T T ) (2. 7)

34 26 One Cognitive Radio wit Multiple PUs Wen tere are S PUs nearby and all PU uses disjoint cannel wit same bandwidt B 0. Ten in te case of misdetection, te status of PUs can be from one of tem is active to all of tem are active. Wic can be described as: H PU(1) PU(S 1) are idle, only PU(S) is active (1 PU active) H PU(1) PU(S 2), PU(r) are idle, only PU(S 1) is active (1 PU active) H PU(1) PU(S 2) are idle, PU(S 1) and PU(S) are active (2 PUs active) { H PU(1) PU(S)are all active (all PUs active) In general, te total amount of 1 PU active cases is ( S 1 ) = S! (S 1)!1! = n; in wic (a b ) represents b -combinations of a set n. Similarly, te total amount of 2 PUs active cases is ( S 2 ) = S! (S 2)!2!. And so on for n PUs are active, wic is (S S ) = 1. Next, we derive misdetection probability wen tere are S PUs nearby. Te general expression for misdetection probability wen tere are r PUs is: P m,s = P(H 0 H 1 ) = P(H 0,H 1 ) P(H 1 ), and for te numerator: P(H 0, H 1 ) = P(H 0 (H 0 01 H 0 11 H 1 11 )) = P[(H 0 H 0 01 ) + + (H 0 H 0 11 ) + + (H 0 H 1 11 )] Since te rest of te term contains mutually exclusive events, we ave (H 0 H 0 01 H 0 11 ) = = (H 0 H 0 01 H 0 11 H 1 11 ) = Tere are ( S 1 ) = S cases wen 1 PU is active, (S ) cases wen 2 PUs are active and in 2 general, ( S ) cases wen k PUs are active. We ten ave for k PUs active: k P (H 0 H 0 1 ) = (P (H 0 H P (H 0 k 1s k 1s) H k 1s )) P(H 0 ) S k P(H 1 ) k

35 27 Note tat: P (H 0 H = = P (H 0 k 1s) Terefore, we ave: H k 1s ) = 1 Q STS B 0 ( 2 kp P SN 0 B 0, λ) P (H 0 H 0 1 ) k 1s = P(H 0 ) S k P(H 1 ) k [ ( 1 Q STS B 0 ( 2 kp P SN 0 B 0, λ) ) + + ( 1 Q STS B 0 ( 2 kp P totally ( S ) terms and eac term is identical wit one anoter k SN 0 B 0, λ) ) ] = ( S k ) P(H 0) S k P(H 1 ) k [1 Q STS B 0 ( 2 kp P SN 0 B 0, λ)] Hence, wen tere are S PUs nearby, te numerator of equation (2.1) is: P(H 0, H 1 ) = ( S 1 ) P(H 0) S 1 P(H 1 ) [1 Q STS B 0 ( 2, λ)] SN 0 B 0 P P + ( S 2 ) P(H 0) S 2 P(H 1 ) 2 [1 Q STS B 0 ( 2 2P P SN 0 B 0, λ)] ( S S ) P(H 0) S S P(H 1 ) S [1 Q STS B 0 ( 2 P P N 0 B 0, λ)] S = ( S k ) P(H 0) S k P(H 1 ) k [1 Q STS B 0 ( 2 kp P k=1 SN 0 B 0, λ)]

36 28 We let: P m,s,k = 1 Q STS B 0 ( 2 kp P wen k out of S PU is (are) active. And Let: SN 0 B 0, λ), wic is te misdetection probability P(H 0, H 1,k ) = ( S k ) P(H 0) (S k) P(H 1 ) k [1 Q STS B 0 ( 2 kp P, λ)] SN 0 B 0 We ten ave for S PUs, misdetection probability can be described as: P m,s = P(H 0, H 1 ) = P(H 0, H 1,1 ) + P(H 0, H 1,2 ) + + P(H 0, H 1,S ) P(H 1 ) 1 P(H 0 ) S = S k=1 ( S k ) P m,s,kp(h 0 ) (S k) P(H 1 ) k 1 P(H 0 ) S (2. 8) Similarly to Equation (2.5), false alarm probability for r PUs is: P f,s = P(H 1 H 0 ) = Γ(ST sb 0, λ 2 ) Γ(ST s B 0 ) (2. 9) Cannel Capacities and Energy Efficiency wit Multiple PUs According to Equation (2.6) and Part 4, te total Cannel Capacity wen tere are S PUs is sown below: Cannel Capacity (S PUs) = SB 0 (log (1 + P CS ) (1 P SN 0 B f,s )P(H 0 ) 0 + ( S 1 ) log (1 + P CS SN 0 B 0 + P ) P m,s,1p(h 0 ) S 1 P(H 1 ) P + ( S 2 ) log (1 + P CS SN 0 B 0 + 2P ) P m,s,2p(h 0 ) S 2 P(H 1 ) 2 + P + ( S S ) log (1 + P CS S(N 0 B 0 + P P ) ) P m,s,sp(h 0 ) S S P(H 1 ) S )

37 29 = SB 0 (log (1 + P CS ) (1 P SN 0 B f,s )P(H 0 ) 0 S + ( S k ) log (1 + P CS SN 0 B 0 + kp ) P m,s,kp(h 0 ) S k P(H 1 ) k ) (2. 10) P k=1 In general, wen CR transmission time is T T, energy efficiency of te CR network, wen tere are S PUs, is: Energy Efficiency = = T T SB 0 ( T T cannel capacity power consumption of one frame P CS log (1 + SN 0 B ) (1 P f,s )P(H 0 ) + S ( S 0 l ) log (1 + P CS l=1 SN 0 B 0 + lp ) P m,s,lp(h 0 ) S l P(H 1 ) l P P s T S + P T T T + P C (T S + T T ) (2. 11) ) Setting Misdetection Tresold on CRs In order to protect PU transmission and avoid excessive interference by CR transmission, we need to set a misdetection tresold ε m. Wen tere are S PUs in te sensing environment, te misdetection tresold sould be able to protect eac PU, and we assume eac are protected wit same misdetection tresold. Terefore, we ave to make sure tat te no matter ow many PUs are active, misdetection probability as to always less tan or equals to te preset misdetection tresold ε m. Or: P m,s,1 ε m P { m,s,2 ε m P m,s,s ε m Next, we look at te misdetection for S PUs wen k of tem are active P m,s,k :

38 30 P m,s,k = 1 Q STS B 0 ( 2 kp P SN 0 B 0, λ) (2. 12) As we can see from above, wen te number of active PU (k) increases, term increases and Q SN 0 B STS B 0 ( 2 kp P, λ) increases, wic leads to decrease in 0 SN 0 B 0 2 kp P misdetection probability. Terefore; misdetection probability decreases as te amount of active PU increase: P m,s,k P m,s,k+1. Intuitively tinking, as more PU are active, CR will receive a stronger signal wic leads to a decrease in sensing error probability. Moreover, we can see tat for given S PUs, we can assure misdetection probability is below preset misdetection tresold ε m if te misdetection probability of 1 PU active is below ε m : ten: if: P m,s,1 = 1 Q STS B 0 ( 2 P P P m,s,k = 1 Q STS B 0 ( 2 kp P SN 0 B 0, λ) ε m SN 0 B 0, λ) ε m for k 1,2,..., S Next, we look at te simulation of ε m, wic is te misdetection probability of one PU active wile te rest are idle: As we can see from Figure 2.3 below, for given amount of PUs, misdetection probability increases as preset detection tresold of eac sample since it is more understandable, for example, λ 2T s B λ increases (we use λ 2T s B 2T s B = 1.5 means we set detection tresold to be 1.5 times noise power). Intuitively tinking, te decrease of detection tresold is equivalent to increase CR sensing sensitivity.

39 31 Figure 2.3: Misdetection Probability vs Detection Tresold of Eac Sample Next, we derive te relation between misdetection and detection tresold of eac sample. Following Capter II section 4 and considering cannel error probability, we ave: P P λ ncx2inv (ε m, ST S B, ST S B ) SN 0 B 0 (2. 13) Note tat K is te number of CR and k is te number of active PU. According to equation (2.9) and (2.11), for a given false alarm probability, in order to increase cannel capacity and energy efficiency, we need to increase misdetection probability. Furtermore, for a fixed misdetection probability, in order to increase cannel capacity and energy efficiency, we sould decrease false alarm probability. From equation (2.9), we can easily see tat in order to decrease false alarm probability, we sould maximize λ. Terefore, λ sould be maximized in order to maximize energy efficiency (in te meanwile, misdetection probability, as a function of λ, sould also equals to or less tan preset misdetection tresold ε m ).

40 32 In general; for a given number of PUs, maximal energy efficiency is acieved wen P P λ opt = ncx2inv (ε m, ST S B, ST S B ) SN 0 B 0 (2. 14) Figure 2.4: Misdetection Tresold vs Detection Tresold of Eac Sample Next, we generate and plot maximal energy efficiency for given misdetection tresold wit different number of sensing cannels (eac cannel wit 100 KHz bandwidt). As sown in Fig.8 below, we calculated maximal energy efficiency given numbers of PUs under te constraint of preset misdetection tresold, in order to protect PU.

41 33 Figure. 2.5: Maximal Energy Efficiency vs Sensing Bandwidt (single CR) Figure 2.5 above sows acievable Maximal Energy Efficiency for different amount of PUs. Furtermore, te figure sows tat amount 0 to 10 PUs, global maximal energy efficiency point is at wen tere are 4 PUs, wit igest misdetection tresold (in tis case, ε m = 0.4) OR Fusion Rule wit K CRs and S PUs Wen tere are K CRs in te network, assume tey are all identical and ave same misdetection and false alarm probability given in te same sensing environment, for OR rule we ave: Q f,s = 1 (1 P e f,s ) K (2. 15) e Q m,s,k = (P m,s,k ) K ϵ m

42 34 e e In wic P f,s is false alarm probability and P m,s,k is misdetection probability wen k out of S PU are active, and superscript e means we are considering reporting cannel error probability. In wic: { P f,s e = P f,s (1 P e ) + P e (1 P f,s ) e P m,s,k = P m,s,k (1 P e ) + P e (1 P m,s,k ) (2. 16) Correspondently, Q f,s is network false alarm probability; Q m,s,k is misdetection probability at DFC wen k out of S PU are active. ϵ m is misdetection tresold. Next, we ave te expression for energy efficiency of 1 PU under cooperative sensing environment: And te energy efficiency for suc network is: Energy Efficiency = = T T SB 0 ( P CS T T cannel capacity power consumption of one frame S l=1 log (1 + ) (1 Q SN 0 B f,s ) P(H 0 ) + ( S 0 l ) log (1 + P CS SN 0 B 0 + lp ) Q m,s,l P(H 0) S l P(H 1 ) l P P T T T + (P s T S + P C (T S + T T )) K Note tat sensing power in tis case is calculated using equation (2.18) below: (2. 17) ) P S = N ( 2SB ) (μw) (2. 18) Case Study: AND Fusion Rule wit k CRs and S PUs Similar as OR fusion rule, for AND fusion rule wit K CRs and S PUs, we ave: { Q f,s = (P e f,s ) K e Q m,s,k = 1 (1 P m,s,k ) K (2. 19) ϵ m And te energy efficiency expression for AND fusion rule is same as te energy efficiency for OR fusion rule.

43 35 Note tat wen we are using cooperative sensing, we only need to ensure tat te network misdetection probability to be equal or less tan misdetection tresold: Q m ϵ m, since te final decision is given by DFC. Refer to section 5 from tis capter, we ave: if: P m,s,1 = 1 Q STS B 0 ( 2 P P SN 0 B 0, λ) ε m ten: P m,s,k = 1 Q STS B 0 ( 2 kp P SN 0 B 0, λ) ε m for k 1,2,..., S e Similarly for cooperative sensing case, since Q m,s,k monotone increases as P m,s,k increases, we ave: ten: e if: Q m,s,1 = 1 (1 P m,s,1 ) K ε m e Q m,s,k = 1 (1 P m,s,k ) K ε m for k 2,..., S By using misdetection tresold on eac CR instead of for te network, we ave: P m,s,1 = P e m,s,1 P e 1 (1 m) ( 1 K ) P e (2. 20) 1 2P e 1 2P e In wic te rigtmost term is misdetection tresold at eac CR. And as we described above, by maximizing detection tresold λ, we can maximize misdetection probability wile minimize false alarm probability. In cooperative sensing case, we ave: λ opt = ncx2inv ( 1 (1 m) ( 1 K ) P e, ST 1 2P S B, ST S B P P ) e SN 0 B 0 (2. 21) After finding te optimal detection tresold, we can calculate network false alarm and misdetection probability using equation (2.9), (2.12), (2.16), and (2.19); and use equation (2.17) to calculate energy efficiency of te CR network.

44 36 By using te same parameters presented in capter II, we can plot energy efficiency vs number of sensing cannels vs number of coop CR in Figure 2.6 a and b: Figure 2.6a: Energy Efficiency vs Number of Sensing Cannels vs Number of CRs Figure 2.6b: Energy Efficiency vs Number of CRs (AND Fusion Rule, 10 cannels)

45 37 Figure 2.6 c: Energy Efficiency vs Number of CR wit Canging P(H 1 ) ( m = 0.1, S = 5) Note tat sensing bandwidt equals to number of cannels times 100 KHz, in wic eac cannel is 100 KHz. By comparing figure 2.6 a and b above wit figure 1.5 a and b from capter 2, we can see tat cannel sensing metod does affects overall energy efficiency of te network. Te comparison sows tat sensing single cannel wit canging bandwidt can acieve iger energy efficiency tan sensing multiple cannels tat eac wit same bandwidt. Moreover, as we increase misdetection tresold, bot sensing metod sows tere is an increase in energy efficiency. In Capter II and III, we studied different fusion rules, different sensing metods and focused more on AND fusion rule for its ability to maximize misdetection probability wile minimizing false alarm probability for a given amount of CR. Also, we studied on setting misdetection tresold in order to protect PU from CR transmission interference. Te case study sows tat we can acieve maximal energy efficiency wile ensuring te protection of PU in a given environment.

46 38 CHAPTER V CONCLUSION AND FUTURE RESEARCH DIRECTIONS CR network can uses radio spectrum more efficiently because of its ability to searc for idle spectrum and access it opportunistically in order to transmit its own data Te study in tis tesis was to explore te metods to maximize energy efficiency of te CR network in order to enable green wireless network; Terefore, we can make CR network bot spectrum efficient and energy efficient. In Capter II, we proved tat for a given number of CR, AND fusion rule can maximize energy efficiency. And in Capter II and III, two different sensing scemes are presented, te first one is to sensing single cannel wic te bandwidt can be varied, and te next sensing sceme is to sense multiple cannels and assume eac cannel as same bandwidt. Furtermore, we studied about setting misdetection tresold on eac CR in order to protect primary user from excessive interference by CR. Te case study results sow tat by presetting misdetection probability and sensing bandwidt, tere exist a maximal energy efficiency point. And sensing single cannel wit varying bandwidt can be more energy efficient tan sensing multiple cannel slots eac wit same bandwidt. Future study on tis topic can be to find te optimal sensing time, transmission time or CR transmission power. In addition, more spectrum survey can be conducted in oter cities all around te world.