Cooperative Cognitive Radio Networks: Spectrum Acquisition and Co-Channel Interference Effect

Transcription

1 Cooperative Cognitive Radio Networks: Spectrum Acquisition and Co-Channel Interference Effect by Ala Abu Alkheir A thesis submitted to the Department of Electrical and Computer Engineering in conformity with the requirements for the degree of Doctor of Philosophy Queen s University Kingston, Ontario, Canada January 23 Copyright c Ala Abu Alkheir, 23

2 Abstract Cooperative Spectrum Sensing (CSS) allows Cognitive Radio Networks (CRNs) to locate vacant spectrum channels and to protect active Primary Users (PUs). However, the achieved detection accuracy is proportional to the duration of the CSS process which, unfortunately, reduces the time of useful communication as well as increases the Co-Channel Interference (CCI) perceived by an active PU. To overcome this, this thesis proposes three CSS strategies, namely the Dual-Threshold CSS (DTCSS), the Maximum CSS (MCSS), and the Max-Min CSS (MMCSS). These strategies reduce the number of reporting terminals while maintaining reliable performance and minimal CCI effect. The performance of these three methods is analyzed, and the numerical and simulations results illustrate the accuracy of the derived results as well as the achieved performance gains. The second part of this thesis studies the impact of CCI on the performance of a number of transmission techniques used by CRNs. These are Chase combining Hybrid Automatic Repeat Request (HAQR), Fixed Relaying (FR), Selective Relaying (SR), Incremental Relaying (IR), and Selective Incremental Relaying (SIR). The performance of these techniques is studied in terms of the average spectral efficiency, the outage probability, and the error probability. To obtain closed forms for the error probabilities, this thesis proposes a novel accurate approximation of the exponential integral function using a sum of exponentials. i

3 List of Publications Chapter 3. Ala Abu Alkheir and Mohamed Ibnkahla, Maximum Cooperative Spectrum Sensing Based on the Energy Detection for Cognitive Radio Networks Submitted to the IEEE Communications Letters, November Ala Abu Alkheir and Mohamed Ibnkahla, Selective Cooperative Spectrum Sensing Strategies Based on the Energy Detection for Cognitive Radio Networks Submitted to the IEEE Transactions on Wireless Communications, October Ala Abu Alkheir and Mohamed Ibnkahla, Selective Cooperative Spectrum Sensing in Cognitive Radio Networks, In proceedings of the IEEE Global Communications Conference, Huston, USA, 5-9 December 2. Chapter 4. Ala Abu Alkheir and Mohamed Ibnkahla, An Accurate Approximation of the Exponential Integral Function using a Sum of Exponentials, Submitted to IEEE Communications Letters, October 22. Chapter 5 ii

4 . Ala Abu Alkheir and Mohamed Ibnkahla, Outage Performance of Decode and Forward Incremental Relaying in an Overlay Spectrum Sharing Environment, The 26th Biennial Symposium on Communications, May 28-29, 22, Kingston, Canada. 2. Ala Abu Alkheir and Mohamed Ibnkahla, Performance Analysis of Decode and Forward Incremental Relaying in the Presence of Multiple Sources of Interference, IEEE VTC-Fall 22, 3-6 Sep. 22, pp Ala Abu Alkheir and Mohamed Ibnkahla, Impact of Co-Channel Interference and Imperfect Channel Estimation on the Performance of Regenerative Cooperative Diversity Protocols, Submitted to the IEEE Transactions on Wireless Communications, November Ala Abu Alkheir and Mohamed Ibnkahla, Error Probability Analysis of Regenerative Selection Incremental Relaying in the Presence of Co-Channel Interference and Imperfect Channel Estimation, Submitted to the IEEE Communications Letters, November 22. iii

5 Acknowledgments All praise and blessings be due to the All-Mighty Lord, the Lord of heavens and earth, the one who gave me the ability and the strength to finish this thesis and to be a step away from earning my degree. When I look back, I find so many people, without whose help, I would have never reached this point in my life. My supervisor, Professor Mohamed Ibnkahla, who was always there for me with his guidance and help, Professor Il-Min Kim who taught me to enjoy wireless communications, my colleagues and friends, Basil Alnabulsi, Abdallah Alma itah, and Amr Almougy, who helped me by every means possible. For all these people I say Thank you, I am deeply grateful to each and everyone of you. I should also mention that this work would have never been completed without the support of each and every member of my family here in Canada and back home. With your support and believe I have reached this point, so thank you all for believing in me and for being always by my side. iv

6 Contents Abstract List of Publications Acknowledgments Contents List of Figures Abbreviations i ii iv v vii x Chapter : Introduction. Motivation and Thesis Overview Organization of the Thesis Chapter 2: Background 5 2. Spectrum Sensing Cooperative Spectrum Sensing (CSS) Decision-Based CSS Using Energy Detection Performance Analysis Transmission Techniques Chase Combining HARQ Cooperative Diversity Chapter 3: Selective CSS Strategies Dual-Threshold Selective CSS (DTCSS) Strategy Performance Analysis Results and Discussion The Maximum CSS (MCSS) Strategy Performance Analysis Results and Discussion v

7 3.3 The Maximum-Minimum CSS (MMCSS) Strategy Performance Analysis Results and Discussion Comparison and Discussion Conclusions Chapter 4: Mathematical Tools The Proposed Approximation Mathematical Applications Integrations Involving E x Integrations Involving E 2 x Integrations Involving ln x Exponential Integral Function with Negative Argument Chapter 5: Transmission Techniques in the Presence of CCI 7 5. Chase Combining HARQ System Model Performance Analysis Results and Discussion Regenerative Cooperative Diversity System Model Performance Analysis Results and Discussion Conclusions Chapter 6: Conclusions and Future Work 2 6. Conclusions Future Work References 5 vi

8 List of Figures 2. Flow diagram of an arbitrary spectrum sensing method Performance of the energy detector for a number of ϑ values using u = Performance of the energy detector for a number of u values using ϑ = 5dB A block diagram of CSS The three parts of the CSS process P fa,css and P d,css using different decision thresholds Flow diagram of FR Flow diagram of SR Flow diagram of IR Flow diagram of SIR P fa,dt,k and P d,dt,k for different values of Kr,H PU and K r,h PU as functions of P fa P fa,dtcss and P d,dtcss as functions of P fa M,DTCSS and M,DTCSS as functions of P fa P fa,mcss, and P d,mcss, as functions of P fa assuming different numbers of network terminals, K vii

9 3.6 P fa,mcss and P d,mcss as functions of P fa assuming different numbers of network terminals, K M,MCSS and M,MCSS as functions of P fa assuming different numbers of network terminals, K P fa,mmcss, and P d,mmcss, as functions of P fa assuming different numbers of network terminals, K P fa,mmcss and P d,mmcss as functions of P fa assuming different numbers of network terminals, K M,MMCSS and M,MMCSS as functions of P fa assuming different numbers of network terminals, K Detection and False Alarm probabilities for DTCSS, MCSS, and MM- CSS strategies using Θ th = and Average number of retransmission requests of the DTCSS, MCSS, and the MMCSS strategies A plot of E x using exact and approximate values for x 3, 2 using n k = n i = A plot of Υ 7 η; α, τ using exact and approximate values for τ = 3, α =.5, and M = 3, 6,, A two terminal network with N sources of CCI P out for HARQ as a function of SNR using K =,, P out for HARQ as a function of SNR using K = 2 and N =,,..., P e for HARQ as a function of SNR using BPSK modulation for K =, 3, 6 and N = viii

10 5.5 P e for HARQ as a function of SNR using BPSK modulation for K = and N =,, 3, 6, Three terminal relay network with K sources of CCI Q as a function of the transmission SNR in the presence and absence of CCI effect P out,sir, P out,ir, P out,sr, and P out,fr in the presence and absence of CCI effect P e,sir, P e,ir, P e,sr, and P e,fr in the presence of CCI P e,sir along with its three constituting components, the direct-transmission, the relay-assisted transmission, and the retransmission-assisted.... ix

11 Abbreviations ACK AF AWGN CCI CDF CR CRN CSS DF DTCSS FC FR HARQ INR IR MCSS Acknowledgment Amplify and Forward Additive White Gaussian Noise Co-Channel Interference Cumulative Distribution Function Cognitive Radio Cognitive Radio Network Cooperative Spectrum Sensing Decode and Forward Dual-Threshold Cooperative Spectrum Sensing Fusion Center Fixed Relaying Hybrid Automatic Repeat Request Interference to Noise Ratio Incremental Relaying Maximum Cooperative Spectrum Sensing x

12 MGF MMCSS MRC NACK PDF PU SINR SIR SNR SR TV WRAN Moment Generating Function Maximum-Minimum Cooperative Spectrum Sensing Maximum Ratio Combining Negative Acknowledgment Probability Density Function Primary User Signal to Interference plus Noise Ratio Selection Incremental Relaying Signal to Noise Ratio Selection Relaying Television Wireless Regional Area Network xi

13 Chapter Introduction Over the past decade, Cognitive Radio (CR) technology has emerged as powerful means to enhance the spectrum utilization efficiency of certain underutilized spectrum bands, including the Television (TV) bands. This is facilitated through allowing secondary access to these bands by license-exempt users such that licensed users experience no harmful interference thereof. In particular, this is implemented through either, controlling, mitigating, or avoiding the potential interference to licensed users. These three options have emerged as three possible scenarios for implementing CR technology. While interference mitigation and control requires close collaboration between the licensed and the unlicensed users; mitigating the interference through opportunistic spectrum access requires little or even no such collaboration. As a result, this last scenario, often referred to as spectrum interweave, has found its way to practical implementations and was thus adopted by a number of spectrum regulatory agencies worldwide, 2. In an interweave spectrum sharing scenario, secondary users, also referred to as CR users, exploit the instances of silence of licensed users, also referred to as Primary

14 .. MOTIVATION AND THESIS OVERVIEW 2 Users (PUs), to transmit their signals. However, as these instances are unpredictably random; CR users are required to employ agile spectrum managers to oversee spectrum access. These spectrum managers are responsible for choosing operating channels to be used as well as evacuating those channel claimed by PUs. To achieve this, a CR user needs to sense the spectrum in order to locate vacant channels as well as to detect the occupancy of operating channels. The output of this sensing process does not necessarily entail evacuating the operating channel even if it is deemed busy because other CR users may concurrently be using the channel. In this case, the CR user needs to examine the quality of communication supported by this channel, and hence, quantity the possible impact of Co-Channel Interference (CCI) to decide whether to evacuate the channel or not.. Motivation and Thesis Overview Despite the ever growing CR literature, the need for agile spectrum sensing remains persisting. Cooperative Spectrum Sensing (CSS) has been shown to enhance the performance of an arbitrary sensing channel through allowing different terminals to share their local sensing information. However, this collaboration requires a nonnegligible reporting duration that should be accounted for when designing the CSS process. Most of the proposed methods in the literature assume the presence of a common control channel for reporting, or that reporting does not cause a significant reduction to the effective throughput perceived by the network terminals. However, when the network population grows, this duration becomes a bottleneck to the amount of achievable throughput. Consequently, regardless of the advantages of collaboration, if the network cannot reduce the reporting time, the achieved throughput will be 2

15 .. MOTIVATION AND THESIS OVERVIEW 3 reduced. In this thesis, we revise the reporting aspect of CSS and propose three novel selective reporting strategies to reduce the duration of the reporting phase while maintaining an acceptable level of performance. In the first strategy, the Dual-Threshold Cooperative Spectrum Sensing (DTCSS), network terminals whose local energy estimates fall within a preset no-decision region are not allowed to report to the FC. Hence, reducing the amount of CCI perceived by an active PU. However, this does not reduce the duration of the reporting process since the identity of the silent terminals cannot be known a priori. To overcome this, the Maximum Cooperative Spectrum Sensing (MCSS) and the Maximum Cooperative Spectrum Sensing (MMCSS) strategies are proposed. In these two strategies, we limit the number of reporting terminals to one. This single terminal is chosen according to either a maximum energy estimate criterion, in the MCSS case, or according to the maximum-minimum criterion for the MMCSS case. In this latter case, the qualities of the sensing and reporting channels are accounted for in the selection criterion. Hence, MMCSS is able to reduce the number of potential retransmission requests. These three reporting strategies are presented in Chapter 3. In Chapters 4 and 5, we study the impact of CCI on the performance of a number of transmission techniques used in Cognitive Radio Networks (CRNs). These are Chase combining Hybrid Automatic Repeat Request (HARQ), Fixed Relaying (FR), Selection Relaying (SR), Incremental Relaying (IR), and Selection Incremental Relaying (SIR). This study is motivated by the spectrum sharing nature of CRNs and the fact that a number of CRNs will be sharing the limited number of vacant channels on an interference tolerance basis. Hence, it is of the interest of these networks to 3

16 .2. ORGANIZATION OF THE THESIS 4 quantify the impact of potential CCI on their performance. In Chapter 4, we propose a number of novel approximations for the exponential integral functions that help studying the error probability of the aforementioned protocols. These approximations are then used in Chapter 5 to obtain the desired closed form expressions..2 Organization of the Thesis The remainder of this thesis is organized as follows. Chapter 2 gives a background about spectrum sensing using energy detection. It also presents decision-based CSS which is the basis for the three strategies proposed in Chapter 3. Chapter 2 also reviews Chase combining HARQ along with the four regenerative cooperative diversity, FR, SR, IR, and SIR. Chapter 3 presents the three selective CSS strategies, the DTCSS, the MCSS, and the MMCSS. Each of these strategies is described and its performance is analyzed. A comparative study is also conducted where it is shown that MMCSS strikes an attractive balance between MCSS and DTCSS in terms of detection performance and average number of retransmission requests. The second part of the thesis studies the performance of a number of communication protocols in the presence of CCI. In Chapter 4, we present three novel approximations for the exponential integral functions. These functions are encountered while analyzing the error probability in the presence of CCI. In Chapter 5, these approximations are used to obtain closed form expressions for the error probability of Chase combining HARQ, FR, SR, IR, and SIR. Finally, conclusions and future work are given in Chapter 6. 4

17 Chapter 2 Background 2. Spectrum Sensing The ability to detect the activity of PUs without direct collaboration, known as spectrum sensing, has been identified as one of the core functionalities of CR technology. Since the early days of CR, numerous spectrum sensing methods have been proposed, including the energy detector, the cyclostationarity detector, the covariance and eignevalue based detectors, the matched filer and many other spectrum sensing methods 3 8. While these methods are different in terms of the detection principle, most of them are based on the binary hypothesis testing principle. In other words, most spectrum sensing methods observe the sensed channel for a particular period of time, calculate a particular decision metric, and compares this metric to a preset decision threshold. If the threshold is exceeded, the channel is deemed busy, otherwise, it is deemed idle. A flow diagram of an arbitrary spectrum sensing method is shown in Figure 2.. During the observation window, multiple antenna techniques 9 2 and relaying techniques 3 5 can be used to collect as much evidence as possible about the status 5

18 2.. SPECTRUM SENSING 6 Observation Window Calculate Decision Metric Comparator Final Decision Figure 2.: Flow diagram of an arbitrary spectrum sensing method of the sensed channel. This collected information is then used to calculate a decision metric which is then compared to a threshold. While this threshold can be obtained analytically for some sensing methods, e.g., the energy detection 6; most sensing methods use empirically evaluated thresholds. Out of all available sensing methods, energy detection was studied the most. Due to its simplicity and ease of implementation, this method has been deployed in a number of CR testbeds 7 9 and its performance has been analyzed over a wide range of fading circumstances As the name indicates, an energy detector estimates the energy present in the sensed channel over a particular period of time and compares it to a preset threshold. Mathematically speaking, let the received signal during the sensing period be denoted by yn, which can be written as hnxn + wn, yn = wn, H PU H PU (2.) where hn is the coefficient of the sensing channel, i.e., the channel between the PU and the CR user, wn is the zero mean Additive White Gaussian Noise (AWGN) with variance σ 2, while xn is the transmitted signal of the PU modeled as a zero mean complex valued Gaussian process with variance of E p, E p being the transmission energy. Finally, the status of the PU is captured using the two hypotheses H PU and 6

19 2.. SPECTRUM SENSING 7 H PU which stand for PU active and PU inactive, respectively. In this thesis, the sensing channel is assumed constant during the sensing period. Furthermore, hn is modeled as a zero mean complex-valued Gaussian random variable corresponding to a Rayleigh fading channel with an average channel gain of Ω. The energy of yk is accurately estimated by summing the energies of 2u 2W T samples of yk over the sensing period T where W is the channel bandwidth 2. Consequently, the decision metric φ is calculated as φ 2u i= y i 2, (2.2) where y i is the i th sample of yn taken at time i/2w, i.e., y i y ( i/2w ). Next, this decision metric is compared to a decision threshold λ and a final decision about the status of the channel is made according to the rule φ H CR H CR λ, (2.3) which means that the channel is deemed busy, denoted by H CR, if φ λ and is deemed idle, denoted by H CR, otherwise. Since φ is a summation of 2u random variables, the detection performance of (2.3) can be evaluated using the detection and false alarm probabilities. The detection probability, denoted by P d, is defined as the probability of detecting the presence of an active PU while the false alarm probability, denoted by P fa, is the probability of mistakenly assuming the presence of an active PU. Accordingly, these two probabilities are given by P d Pr φ λ H PU P fa Pr φ λ H PU = Fφ H PU(λ), = Fφ H PU(λ), (2.4a) (2.4b) 7

20 2.. SPECTRUM SENSING 8 where Pr is the probability operator while F φ H PU (φ) and F φ H PU (φ) are the Cumulative Distribution Functions (CDFs) of φ under H PU and H PU, respectively. It was shown in 2 that F φ H PU (φ) is given by ( ) γ u, φ 2 F φ H PU (φ) =, (2.5) Γ(u) where γ(, ) x e t t α dt is the lower incomplete Gamma function 23, Eqn while Γ( ) e t t α dt is the Gamma function 23, Eqn On the other hand, under H PU, φ follows a non-central Chi-squared distribution with 2u degrees of freedom and a non-centrality parameter of 2ϑ, where ϑ is the Signal to Noise Ratio (SNR) of the sensing channel defined as ϑ E p hn 2 /σ 2. Consequently, this SNR is exponentially distributed with a mean value of ϑ E p Ω/σ 2. After averaging the CDF of the non-central Chi-squared distribution over the exponential Probability Density Function (PDF) of ϑ, the CDF F φk H PU (φ) can be written as F φ H PU (φ) = e φ 2 u 2 i= φ i 2 i i! u { + ϑ ϑ e φ 2(+ ϑ) e φ 2 u 2 i= i! φ ϑ 2( + ϑ) i }. (2.6) By looking at P fa and P d, it can be seen that the performance of the energy detector can be adjusted using u and λ. In particular, for a given u, the energy detector can be tuned to operate at a certain P fa by controlling the decision threshold λ. This adjustment is known as the Neyman-Pearson criterion 6. As a result, the corresponding P d can be written as P d = F φ H PU (λ) where λ = F φ H PU ( P fa ), (2.7) 8

21 2.. SPECTRUM SENSING 9 F φ H PU ( ) being the the inverse function of F φ H PU ( ). Having said this, it can be concluded that the performance of the energy detector depends on the number of samples, u, the operating P fa, which specifies λ, the average SNR, ϑ, and the noise variance, σ 2. Of these four parameters, the CR user can directly control u and P fa, while ϑ can be controlled by changing the location of the CR user relative to the PU and σ 2 can be controlled by redesigning the CR transceiver. The performance for a number ϑ and u values is shown in Figures 2.2 and 2.3, respectively. As these figures show, the performance degrades when ϑ decreases or when u increases. While the first observation is expected, the second one can be easily explained by knowing that increasing u increases λ for a given P fa, and hence decreases P d. Figure 2.2 shows that while decreasing ϑ from db to 5dB causes a significant P d 2 ϑ = db Sim ϑ = db Ana ϑ = 5dB Sim ϑ = 5dB Ana ϑ = db Sim ϑ = db Ana ϑ = 5dB Sim ϑ = 5dB Ana ϑ = db Sim ϑ = db Ana P fa Figure 2.2: Performance of the energy detector for a number of ϑ values using u = 8. 9

22 2.. SPECTRUM SENSING performance loss, decreasing it from 5dB to db causes almost no difference. In fact this suggests that P d P d, as ϑ, i.e., lim P d = P d,, (2.8) ϑ where P d, can be obtain as (after applying L Hpital s rule 24, Ch.4.4 a few times) P d, = e λ 2 u i= λ i 2 i i! = P fa. (2.9) This result should not be surprising, but rather expected since decreasing ϑ means that the mean values of the 2u random variables constituting φ under H PU are vanishing and thus F φ H PU (φ) F φ H PU (φ). The performance of the energy detector, similar to any other spectrum sensing method, fails to mitigate certain channel impairments, like deep fading, shadowing, and hidden terminal problem. In fact, these limitations cannot be mitigated without exploiting diversity. In other words, the CR user needs to get additional information about the status of the channel. This information can be collected at different times or at different locations. Intuitively speaking, collecting this information at different times prolongs the sensing duration and cannot fully mitigate the shadowing effect. On the other hand, collecting it at different locations preserves the sensing duration and mitigates shadowing. For this reason, CSS has been proposed and studied since the early days of CR technology 25, 26.

23 2.2. COOPERATIVE SPECTRUM SENSING (CSS) P d 2 u = Sim u = Ana u = Sim u = Ana u = 25 Sim u = 25 Ana u = 75 Sim u = 75 Ana u = 3 Sim u = 3 Ana u = Sim u = Ana P fa Figure 2.3: Performance of the energy detector for a number of u values using ϑ = 5dB. 2.2 Cooperative Spectrum Sensing (CSS) The diversity gain achieved through using multiple signals collected at different locations or transmitted through different paths has always been the motive behind innovative ideas. These include diversity combining techniques 27, space-time coding 28, cooperative diversity 29, Coordinated Multipoint techniques 3 and many other techniques. So, when the need to enhance the performance of spectrum sensing methods appeared, the solution was readily found in CSS. Through combining the sensing results of a number of dispersed CR users, a central terminal, referred to as the Fusion Center (FC), can make an accurate decision about the vacancy of a particular channel.

24 2.2. COOPERATIVE SPECTRUM SENSING (CSS) 2 Figure 2.4 shows a network consisting of K CR users performing CSS under the Cognitive Radios(CRs) R K h K g K R 2 h 2 g 2 h R g PU Primary User(PU) h R Fusion Center(FC) Figure 2.4: A block diagram of CSS coordination of a CR FC. The CSS process consists of three stages as illustrated in Figure 2.5. These are sensing period, reporting period, and broadcast period. During Duration of the CSS process Sensing Period Reporting Period Broadcast Period Time Figure 2.5: The three parts of the CSS process. the sensing period, every network terminal, including the FC itself, senses the examined channel using some sensing method, like the energy detector. At the end of this period, every terminal sends a local report to the FC in a round robin manner, i.e., every terminal has a preset time slot to report. The content of the local reports can 2

25 2.2. COOPERATIVE SPECTRUM SENSING (CSS) 3 be either the local decision metric, which is the energy estimate in the energy detector case, or a binary local decision. Choosing between these two options is subject to the performance/overhead tradeoff 3, 32. While sending the decision metrics requires significant reporting overhead, it can help the FC achieve superior detection reliability compared to the low overhead decision based reporting 33. In practice, however, the reporting overhead shares the data transmission due to the absence of dedicated control channels 34. Consequently, decision based CSS is more appealing especially for highly populated networks Decision-Based CSS Using Energy Detection At the end of the sensing period, every terminal makes a local decision according to the decision rule in (2.3). Accordingly, if we denote the local decision of terminal R k, k =,,..., K, by d k {, }, then we can write H CR, if φ k λ d k = H CR, if φ k < λ, (2.) where we have assumed that all terminals operate at the same P fa. This assumption helps the FC treat the decisions of the various terminals equally. These local decisions are sent to the FC to make the final decision about the channel. When R k sends d k at time slot t k, the FC receives g k t k x k t k + w t k, r k t k = g k t k x k t k + h t k x p t k + w t k, H PU, H PU (2.) 3

26 2.2. COOPERATIVE SPECTRUM SENSING (CSS) 4 where g k t k is the coefficient of the R k -FC reporting channel and x k t k is the signal of R k with energy E k. Assuming that the FC perfectly knows g k t k, and hence uses coherent detection, the received SNR and Signal to Interference plus Noise Ratio (SINR) from R k under H PU and H PU is given by H PU : ψ k E k g k t k 2, (2.2a) σ 2 H PU : ψ k E k g k t k 2. (2.2b) E p h t k 2 + σ 2 Furthermore, assuming that all reporting channels experience flat Rayleigh fading, the CDFs of ψ under H PU and H PU can be written as F ψk H PU (x) = e x/ ψ,k, F ψk H PU (x) = (2.3a) µ k µ k + x e x/ ψ,k, (2.3b) where µ k ψ,k / ϑ, ψ,k E k G k /σ 2, and G k is the mean value of the channel gain g k t k 2. Due to the imperfectness of the reporting channels, the decoded versions at the FC are subject to non-negligible decoding errors. In particular, if ˆd k denotes the decoded version of d k, then we can write Pr ˆdk = d k H PU = BER,k and Pr ˆdk = d k H PU = BER,k, where BER,k and BER,k are the decoding error probabilities experienced by d k under H PU and H PU, respectively. To calculate these probabilities, assuming BPSK modulation, we need to average the conditional error probability Q ( 2ψ k ) 35, Eqn.8.9 over the PDFs fψk H PU (x) and f ψk H PU (x), i.e., we 4

27 2.2. COOPERATIVE SPECTRUM SENSING (CSS) 5 need to solve BER,k = BER,k = Q ( 2x ) f ψk H PU (x)dx = 2 π Q ( 2x ) f ψk H PU (x)dx = 2 π e x e x x F ψk H PU x F ψk H PU (x)dx, (x)dx, (2.4a) (2.4b) using the CDFs in (2.3). The second equation in each integration follows after applying integrals by parts and observing that Q( ) = and F ψk H PU () = F ψk H PU() =. After some mathematical manipulations, these integrals yield ψ,k BER,k =, (2.5a) 2 ψ,k + BER,k = 2 µ k π exp (µ k + ) Q (2µ k + ), (2.5b) ψ,k ψ,k At the end of the reporting phase, the FC uses the set of decoded reports, { ˆd k } K k= and its own decision, d, to calculate the decision metric Θ as Θ d + K ˆd l = K ˆd l, (2.6) l= l= where, for mathematical convenience, we have defined ˆd = d. The FC chooses either H FC or H FC by comparing Θ to a decision threshold, Θ th according to the rule Θ H FC H FC Θ th. (2.7) 5

28 2.2. COOPERATIVE SPECTRUM SENSING (CSS) Performance Analysis If we denoted the FC decision by D {, }, then the detection and false alarm probabilities at the FC side are defined as P d,css Pr D = H PU and Pfa,CSS Pr D = H PU, respectively. These two probabilities can be calculated using the total probability theorem as P d,css = P fa,css = K+ l=θ th Pr Θ = l H PU, (2.8a) K+ l=θ th Pr Θ = l H PU, (2.8b) where Pr Θ = l H PU and Pr Θ = l H PU are the probabilities that a total of l out of the K + decoded decisions, ˆdk, equal one. However, since { ˆd k } K k= is a set of independent random variables, then Pr ˆdi =, ˆd j = H PU Pr ˆdi =, ˆd j = H PU = Pr ˆdi = H PU Pr ˆdj = H PU, (2.9a) = Pr ˆdi = H PU Pr ˆdj = H PU, (2.9b) for i, j {, K} and i j. Furthermore, the probabilities, Pr ˆdk = H PU and Pr ˆdk = H PU can be written by exploiting the independence between the sensing and reporting processes, i.e., the independence between φ k and ψ k. Accordingly, we 6

29 2.2. COOPERATIVE SPECTRUM SENSING (CSS) 7 can write Pr ˆdk = H PU = Pr φk λ H PU ( BER,k ) + Pr φk < λ H PU BER,k ( ) ( ) = P d,k BER,k + Pd,k BER,k, (2.2a) Pr ( ) ˆdk = H PU = Pr φk λ H PU BER,k + Pr φk < λ H PU BER,k = P fa ( BER,k ) + ( Pfa ) BER,k. (2.2b) Observe that for k =, BER, = BER, =, and thus Pr ˆd = H PU = Pd, and Pr ˆd = H PU = Pfa. Finally, P d,css and P fa,css can be written in a compact form as P d,css = P fa,css = K+ M l l=θ th m= K+ M l l=θ th m= U,m V,m, U,m V,m. (2.2a) (2.2b) where M l = ( ) K+ l = (K+)! is the number of possible permutations of K + (K+ l)!l! elements taken l at a time. These elements are taken from the sets Pr ˆdk = H PU and Pr ˆdk = H PU under H PU and H PU, respectively. Under H PU, U,m is the product of the l elements in the m th permutation, while V,m is the product of the complements of the remaining K + l elements. Similarly, under H PU, U,m is the product of the l elements in the m th permutation, while V,m is the product of the complements of the remaining K + l elements. The performance of this CSS strategy was thoroughly studied in the literature 32, 36, 37. It was shown that the best performance is achieved when Θ th = while the worst occurs at Θ th = K + as Figure 2.6 shows. In this figure, we consider a 7

30 2.2. COOPERATIVE SPECTRUM SENSING (CSS) 8 K = 6 network sensing a particular channel where an active PU transmits at 2dBs, while reports are sent using 5dBs. The average gains of the sensing and reporting channels of R k are written as (D ref /D PU,k ) 4 and (D ref /D k,fc ) 4, respectively, where D ref is a reference distance at which the channel gain is unity and 4 is the path loss exponent. Accordingly, the network terminals are randomly distributed within a range of D ref, 2D ref from the PU and, D ref from the FC. 2 4 P fa,css Θ th = Sim Θ th = Ana Θ = 4 Sim th Θ = 4 Ana th Θ th = 6 Sim Θ th = 6 Ana 3 2 P fa P d,css 2 Θ th = Sim Θ = Ana th Θ = 4 Sim th Θ = 4 Ana th Θ th = 6 Sim Θ = 6 Ana th 3 2 P fa Figure 2.6: P fa,css and P d,css using different decision thresholds. The value of Θ th gives the FC the ability to control the level of protection given to the PU. By increasing Θ th, the FC requires more evidence to claim the presence of a PU, and hence, increases the chances of missing to detect an active PU. On the other hand, having a low Θ th means that the FC claims the presence of a PU even if the 8

31 2.2. COOPERATIVE SPECTRUM SENSING (CSS) 9 evidence is mild or even low 37. Despite the simplicity of this CSS strategy and the low overhead requirement, it suffers from a few downsides. First, the duration of the reporting phase increases linearly with the number of network terminals. While this may not be a problem for low populated networks, it becomes a performance bottleneck for highly populated networks. Second, this strategy is prone to the faulty reporters problem which results due to decoding errors. Third, the amount of CCI affecting an active PU during the reporting phase can be non-negligible. Over the past few years, these downsides has been addressed in a number of publications. In particular, the faulty reporters problem has been mitigated in 38 4 using clustering techniques, and in 36 using space-time coding and relaying. However, these techniques resulted in longer reporting time, which only worsens the other downsides. An attempt to reduce the CCI effect on an active PU was made in 42 where only terminals that claim the absence of the PU are allowed to report to the FC. However, since the identity of these terminals cannot be known beforehand, the duration of the reporting period cannot be reduced. On the opposite side, 43 observed that when the FC sets Θ th =, only a single transmission is needed to claim the presence of the PU. Hence, the authors proposed that all terminals that decide the presence of the PU transmit at the same time such that the FC will enjoy spacial diversity. While this limits the duration of the reporting phase, it causes more CCI to a potentially active PU. 9

32 2.3. TRANSMISSION TECHNIQUES Transmission Techniques In the absence of PUs, the CRN uses the vacant channels as if they were the PUs. This means that any communication technique can be used, including multiple antenna techniques, relaying techniques, coordinated multipoint techniques, etc. However, as some of these techniques cannot be used in certain situations, the network terminals need to make intelligent decisions about the deployed transmission techniques. For instance, TV bands are known to have long wavelengths, and thus render using multiple antenna techniques infeasible 44. Also, due to the diversity of PUs in these bands, CRNs operating over these bands have to minimize their transmission power as much as possible and have to keep it below a preset threshold. For these two reasons, it is envisioned that CRNs operating over TV bands will rely on cooperative diversity techniques to extend their transmission range and to achieve spatial diversity. They will also use HARQ to achieve time diversity 45. In the sequel, these transmission techniques shall be revised Chase Combining HARQ ARQ is an error control protocol that enhances the communication reliability by using acknowledged transmissions. According to this protocol, the transmitting terminal expects a reception acknowledgment for every transmitted packet. If this Acknowledgment (ACK) is not received during a preset timeout, the packet is retransmitted. This process is repeated until an ACK is received or until a maximum number of retransmissions is reached. A combination of an error correction code and ARQ is referred to as a HARQ protocol. Unlike ARQ, this protocol gives the receiver the ability to correct some of 2

33 2.3. TRANSMISSION TECHNIQUES 2 the detected errors. In HARQ, the receiver sends an ACK if the channel is good and a Negative ACK (NACK) if the channel is bad. The channel quality is measured by comparing the instantaneously received SNR (in a CCI-free environment) or the SINR (in a CCI environment) to a preset quality threshold. If this threshold is exceeded, the channel is deemed good, otherwise, it is deemed bad. When the retransmitted signals contain the same amount of information; the receiver can use Maximum Ratio Combining (MRC) to combine the replicas. This allows the receiver to maximize the SNR (or the SINR). This type of HARQ is referred to as Chase combining HARQ 46. On the other hand, incremental redundancy is another HARQ protocol wherein every retransmission contains a different set of coding bits. Hence, giving the receiver additional evidence about the transmitted packet. Intuitively, a Chase combiner, which resembles a repetition encoder, is easier to implement 47, Ch Cooperative Diversity Cooperative diversity has been proposed in the pioneering works of A. Sendonaris and J. Laneman 29,48,49 as means to enhance the performance of cellular networks through user cooperation. In particular, this family of protocols allow single antenna terminals to experience the virtues of space-time diversity through relaying. This notion has stimulated a tremendous number of researchers to investigate almost all aspects of these protocols, and to propose a countless number of ideas suiting a wide range of wireless applications. In general, cooperative diversity protocols can be classified based on the underlying relaying protocol into transparent protocols, e.g., Amplify and Forward (AF), and 2

34 2.3. TRANSMISSION TECHNIQUES 22 regenerative protocols, e.g., Decode and Forward (DF). They can also be classified based on the number of hops into dual-hop protocols and multihop protocols 5. Recently, the impact of CCI on a number of cooperative diversity protocols have been investigated. In particular, the performance of a dual-hop relay network was studied in The extension to the multi-hop where CCI affects all relays and the destination was studied in The DF dual-hop case in the presence of multiple relays was considered in Another group of researchers have focused on proposing protocols for CCI environments. These works have exploited the abundance of relay terminals in certain environments to propose relay selection strategies that account for the CCI effect. For instance, 7 proposed a modified version of the max-min relay selection criterion (see 72) where a single relay is chosen based on the SINR of the source-relay link and the SNR of the relay-destination link. On the other hand, 73 proposed a selection strategy that allows the network to use relaying only when the relay path is better than direct transmission while 74 proposed a relay selection criterion when AF is used in two adjacent cells. Fixed Relaying (FR) This primitive protocol allows the destination to enjoy spatial diversity at the cost of halving the throughput. A source terminal, S, communicates with a destination terminal, D, through the assistance of an intermediate relay terminal, R. Every transmission consumes two consecutive time slots. In the first slot, S broadcasts the signal to R and to D, while in the second slot, R forwards a regenerated replica of this signal. Consequently, D combines the two replicas and achieves a better performance. Figure 2.7 shows a flow diagram of this protocol. 22

35 2.3. TRANSMISSION TECHNIQUES 23 n n S transmits xn ˆ R sends xn Figure 2.7: Flow diagram of FR. This relaying protocol suffers from error propagation and throughput reduction. Error propagation results from the fact that R has to regenerate the signal before forwarding it. While this may not be a problem when the S-R channel is good, it becomes a performance bottleneck when this channel is poor. Mathematically, analyzing error propagation probability is an involved process especially for high-constellation modulation techniques, e.g., 8 PSK. For the BPSK case, however, 75 were able to obtain an accurate closed form expression for this probability by comparing the SNRs of the R-D and S-D channels. A widely used remedy for error propagation problem is threshold-based relaying where R uses DF only if the S-R channel is in a good condition 29,75,76. While this does not totally eliminate error propagation; it significantly reduces it. When the S-R channel is poor, R can still use AF 77, or it can remain silent while S retransmits the signal. A protocol that uses this latter option is studied next. Selection Relaying (SR) This protocol measures the quality of the S-R channel by comparing the instantaneously received SNR/SINR to a preset quality threshold, λ r. The S-R channel is considered good only if this condition is met or is exceeded. When this is not the case, 23

36 2.3. TRANSMISSION TECHNIQUES 24 R remains silent and S intervenes by retransmitting the signal in the following time slot, assuming the channel condition changes, 29. Figure 2.8 shows a flow diagram of this protocol. This protocol suffers from a minimal error propagation effect while enjoying diversity gain at all times. As a result, it still suffers from a 5% throughput loss. This loss can be mitigated by extending the decision-based relaying to the destination side. S transmits xn n n? sr r R sends xn ˆ YES NO S retransmits xn Figure 2.8: Flow diagram of SR. Incremental Relaying (IR) This protocol waives diversity gain when the S-D channel is in a good condition. In this case, D is likely to successfully decode the signal, and hence, assistance is not needed. Similar to the SR, IR measures the quality of the S-D channel by comparing the instantaneously received SNR/SINR to a preset threshold λ d. When this threshold is met or exceeded, D sends an ACK asking for a new transmission. Otherwise, it sends a NACK asking R for assistance 78. Figure 2.9 shows a flow diagram of this protocol. The original proposal of this protocol, made in 29, suffered from error propagation 24

37 2.3. TRANSMISSION TECHNIQUES 25 as it did not adopt decision-based relaying. Recently, 79 and 8 combined IR and SR into a SIR protocol. S transmits xn n n YES sd? d R sends xn ˆ No Figure 2.9: Flow diagram of IR. Selection Incremental Relaying (SIR) By combining decision-based relaying to decision-based assistance, SIR achieves a good balance between throughput reduction and performance gain. Figure 2. shows a flow diagram of this protocol. Obviously, this protocol encompasses the previous S transmits xn n n YES sd? d NO R sends xn ˆ YES? sr r S retransmits xn NO Figure 2.: Flow diagram of SIR. three protocols as special cases. In particular, when λ d = and λ r =, the SIR reduces to FR, while when λ d = and < λ r <, the SIR reduces to SR, and finally when < λ d < and λ r =, the SIR reduces to IR. 25

38 Chapter 3 Selective CSS Strategies In this chapter, we present three selective CSS strategies that reduce the duration of the reporting phase of CSS and the CCI experienced by a potentially active PU. These strategies are the DTCSS strategy, the MCSS strategy, and the MMCSS strategy. The performance of these strategies is analyzed in terms of the achievable detection probability, false alarm probability, and the average number of retransmissions. It is shown that while these strategies reduce the CCI effect and the duration of the reporting phase, they achieve a performance comparable to, and sometimes superior to, the performance of the conventional CSS strategy studied in Chapter Dual-Threshold Selective CSS (DTCSS) Strategy Consider the K terminal CRN shown in Figure 2.4. At the end of the sensing period, the local decisions d k s are forwarded to the FC in a round robin manner to make the final decision D. However, to reduce the CCI effect to a potentially active PU, a modified version of the energy detector is used. In particular, the local energy estimates φ k are compared against two decision thresholds λ U and λ L, where λ L λ U, 26

39 3.. DUAL-THRESHOLD SELECTIVE CSS (DTCSS) STRATEGY 27 such that, φ k λ L ; d k =, φ k λ U ; No Decision, λ L < φ k < λ U. (3.) After this comparison, only terminals with local decisions, i.e., d k = or, report to the FC while those with no-decision remain silent 8. The width of the no-decision region, λ U λ L, is inversely proportional to the amount of CCI affecting an active PU. Hence, the wider this region is the smaller the amount of CCI. However, this also reduces the number of reports transmitted to the FC, which lowers the detection capability. Hence, the width of this region should be chosen to strike a balance between these two conflicting objectives. In general, we set λ U and λ L to be functions of the Neyman-Pearson threshold value, λ, such that λ L = f L (λ) and λ U = f U (λ), where f L (λ) and f U (λ) are two arbitrary functions that satisfy λ L (, λ and λ U λ, for arbitrary λ, respectively. If we denote the set of terminals with local decisions by C r, then the FC receives a total of K r K local decisions, where K r is the number of elements in C r. These local decisions will be sent over imperfect reporting channels, and hence will be subject to non-negligible decoding errors. To reduce the impact of these errors, the FC eliminates the reports whose instantaneous SINR, or SNR, falls below a preset threshold of τ th. While this threshold can be arbitrarily chosen to meet a certain performance level, its value is lower bounded by the outage threshold of 2 Q, where Q is the spectral efficiency in bits per second per Hertz (bps/hz). At the end of the reporting phase, the FC will have a total of K d reliably decoded 27

40 3.. DUAL-THRESHOLD SELECTIVE CSS (DTCSS) STRATEGY 28 local decisions. These decisions form the decoding set C d which is a subset of C r, i.e., C d C r. With the aid of these K d reports, the FC calculates the decision metric Θ as Θ = K d + l= ˆd k, (3.2) and compares it to the decision threshold Θ th to make the final decision as Θ H FC H FC Θ th. (3.3) Let us next look at the performance of this strategy at both, the terminal level and FC level. In particular, we are interested in the following performance metrics. Detection and false alarm probabilities of R k, 2. The average number of reporting terminals in the presence and the absence of a PU, 3. The detection and false alarm probabilities of the FC, and 4. The average number of retransmission requests in the presence and the absence of a PU. 28

41 3.. DUAL-THRESHOLD SELECTIVE CSS (DTCSS) STRATEGY Performance Analysis Detection and False Alarm Probabilities of R k According to the decision rule in (3.), the probabilities of detection and false alarm are given by P d,dt,k Pr φ k λ U H PU, and Pfa,DT,k Pr φ k λ U H PU, respectively. Using the CDFs in (2.6) and (2.5), these two probabilities become P d,dt,k = F φk H PU (λ U ), (3.4a) P fa,dt,k = F φk H PU (λ U ). (3.4b) Average Number of Reporting Terminals Next, let us look at the average number of reporting terminals under H PU and H PU. According to (3.), R k C r only if φ k λ U or φ k λ L. Consequently, we can write Pr R k C r H PU = + F φ H PU (λ L ) F φ H PU (λ U ), (3.5a) Pr R k C r H PU = + F φ H PU (λ L ) F φ H PU (λ U ). (3.5b) With the aid of these probabilities, the average number of reporting terminals is calculated as K r,h PU = K r,h PU = K k= K k= Pr R k C r H PU, (3.6a) Pr R k C r H PU. (3.6b) 29

42 3.. DUAL-THRESHOLD SELECTIVE CSS (DTCSS) STRATEGY 3 Observe that by setting λ U = λ L = λ, the width of the no-decision region vanishes, and hence Pr R k C r H PU = Pr R k C r H PU =, which makes K r,h PU = K r,h PU = K. Detection and False Alarm Probabilities at the FC At the FC side, the detection and false alarm probabilities, P d,dtcss and P fa,dtcss, are written similar to P d,css and P fa,css in (2.2). However, the changes made to the decision-making process reflect on the probabilities Pr ˆdk = H PU and Pr ˆdk =. In particular, these two probabilities can be written as H PU Pr ˆdk = H PU Pr ˆdk = H PU ( ) = Pr φk λ U H PU BER,k Prψk τ th H PU + Pr φ k < λ L H PU BER,k Prψ k τ th H PU, { = P d,dt,k ( BER,k ) + Fφk H PU } (λ L )BER,k Fψk H PU (τ th ), ( ) = Pr φk λ U H PU BER,k Prψk τ th H PU + Pr φ k < λ L H PU BER,k Prψ k τ th H PU, { = P fa,dt,k ( BER,k ) + Fφk H PU (3.7a) } (λ L )BER,k Fψk H PU (τ th ), (3.7b) where P d,dt,k and P fa,dt,k are as given in (3.4) while F ψk H PU (ψ) and F ψk H PU (ψ) are = as given in (2.3). For the FC local decision, i.e., k =, we have Pr ˆd = H PU = Pfa,DT,. Unlike the case studied in chapter 2, BER,k P d,dt, and Pr ˆd = H PU 3