Adaptation to the Primary User CSI in Cognitive Radio Sensing and Access

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1 Adaptation to e Priary User CSI in Cognitive Radio Sensing and Access Yuan Lu, Alexandra Duel-Hallen Departent of Electrical and Coputer Engineering Nor Carolina State University Raleigh, NC, 2766 {ylu8, sasha}@ncsu.edu Abstract In Cognitive Radio (CR) networks, ultiple secondary network users (SUs) attept to counicate over wide potential spectru wiout causing significant interference to e Priary Users (PUs). A spectru sensing algori is a critical coponent of any sensing strategy. Perforance of conventional spectru detection eods is severely liited when e average SNR of e fading channel between e PU transitter and e SU sensor is low. Cooperative sensing and advanced detection techniques only partially reedy is proble. A key liitation of conventional approaches is at e sensing reshold is deterined fro e iss detection rate averaged over e fading distribution. In is paper, e reshold is adapted to e instantaneous PU-to-SU Channel State Inforation (CSI) under e prescribed collision probability constraint, and a novel sensing strategy design is proposed for overlay CR network where e instantaneous false alar probability is incorporated into e belief update and e reward coputation. It is deonstrated at e proposed sensing approach iproves SU confidence, randoizes sensing decisions, and significantly iproves SU network roughput while satisfying e collision probability constraint to e PUs in e low average PU-to-SU SNR region. Moreover, e proposed adaptive sensing strategy is robust to isatched and correlated fading CSI and iproves significantly on conventional cooperative sensing techniques. Finally, joint adaptation to PU channel gain and SU link CSI is explored to furer iprove CR roughput and reduce SU collisions. Keywords-CSI; Channel State Inforation; Cognitive Radio; Sensing Strategy; Mediu Access Control; Ad-Hoc Network; Multiuser Diversity; Multichannel Diversity; Sensing Reliability; Adaptive Threshold Control I. INTRODUCTION Cognitive radio (CR) is an eerging technology at can potentially iprove spectru utilization and has drawn broad interest fro researchers in recent years. In CR networks, secondary users (SUs) attept to counicate over a set of channels wiout severely liiting activities of e priary users (PUs). The SUs eploy a sensing strategy, or a ediu access control (MAC) algori, to ake sensing and access decisions. A spectru sensing eod is an integral coponent of any sensing strategy. Classical sensing approaches include atched filtering and energy detection []. To provide sufficient protection to e PU receivers, a constant detection rate (CDR) of e PU signals [2] is required. To avoid e hidden node proble and to protect e PUs, it is desirable to aintain sensing accuracy even when e signal fro e PU transitter to e SU detector is weak (low PU-to- SU SNR) [ 3 ]. However, individual SU sensing decisions This research was supported by e NSF grant CNS SU(Tx) PU(Tx) SU(Rx) SU-to-SU CSI PU-to-SU CSI PU-to-PU CSI SU-to-PU CSI SU(Rx) SU(Tx) PU(Rx) Fig. : Types of CSI in a typical CR Scenario. becoe unreliable for fading PU-to-SU channels wi low average SNR. To reedy is proble, cooperative spectru sensing approaches [4] and feature-based sensing [] were proposed, but e gain of ese approaches is liited for realistic CR networks. Related work: In [5], PU-to-SU channel gain (see Fig. ) is eployed as a criterion in choosing channels for sensing. However, unifor PU activity across a wide band of channels was assued. Moreover, a fixed reshold based on e false alar rate constraint was eployed alough in practice e reshold should be chosen to satisfy a iss detection rate constraint [2]. Sensing reshold adaptation for single channel CR networks was investigated based on SU transission power [6], e Channel State Inforation (CSI) between SU pairs [7], e aount of interference caused to PUs in case of issed detection [ 8 ], and e sensed SNR [ 9 ]. However, reshold adaptation has not been incorporated into sensing strategy design for ultichannel CR networks. Contribution: We design a sensing strategy for overlay CR networks at adapts to e instantaneous SNR of e signal between e PU transitter and e SU sensor, i.e. PU-to-SU CSI illustrated in Fig.. To e best of our knowledge, only [9] has explored such reshold adaptation. However, in [9], only one PU pair, one SU pair, and one channel were assued, and unrealistic constraints at require e knowledge of e PU-to- PU SNR statistics and e instantaneous channel gain between e SU transitter and e PU receiver at e SU (SU-to-PU CSI in Fig. ) was eployed. We consider ultiple SU pairs at copete for available channels under e hardware constraints. To offer sufficient protection to e priary network, we ipose a constraint on e instantaneous iss detection probability at each SU. The resulting instantaneous false alar probability is incorporated into e belief update and reward coputation of e sensing strategy. By selecting to sense channels wi high instantaneous PU-to-SU SNR, e

2 proposed policy reduces false alar rate, iproves sensing decisions, and increases e CR network roughput. Since e PU range is often uch larger at e SU range, SUs converge to siilar sensing decisions and suffer fro network congestion when e yopic, or greedy, strategy is used []. The proposed adaptive sensing strategy randoizes sensing decisions of different SU detectors and helps to resolve SU collisions since e received channel gain fro e PU transitter varies over SU locations and frequencies. Thus, e proposed detection eod converts e conventional yopic strategy into a randoized sensing strategy. Moreover, we cobine e proposed sensing reshold adaptation wi e channel-aware yopic sensing strategy in [] at adapts e reward to e CSI of e SU link. We also investigate practical feasibility of adaptive sensing reshold control. First, is policy requires e knowledge of e PU-to-SU channel gain prior to sensing, which can be obtained directly fro a channel gain ap [2] if available. Oerwise, such inforation can be acquired fro previous spectru sensing or during e "silence" phase [3] when an SU does not have data to transit and/or has sensed a channel at is occupied by a PU. This CSI is likely to be noisy and outdated, will require estiation and prediction, and CSI isatch at e sensor is likely. To aintain e iss detection rate constraint, we incorporate e CSI error into e sensing strategy design and investigate robustness to CSI isatch. Second, we validate perforance of e proposed strategy for ultipa and correlated shadow fading channel odels. Finally, adaptive reshold control is copared wi cooperative sensing detection for realistic network scenarios. The rest of is paper is organized as follows. In section II, we forulate e proble and discuss sensing reshold adaptation. Myopic PU-to-SU CSI-aided sensing strategy is described and cobined wi reward adaptation to e CSI of e SU link in section III. Nuerical results are presented in section IV. Finally, we draw conclusions in section V. II. ADAPTIVE SENSING THRESHOLD CONTROL. In is paper, we consider an overlay CR network [] wi M SU transitter-receiver pairs and N orogonal channels. The SUs can only access spectru when active PUs are not detected in e neighborhood and are required to sense e spectru before accessing any channel. All SUs ake eir own sensing and access decisions autonoously wiout e coordination of a central controller. Suppose y = [ y,..., yν ] is e signal received by e sensor of e SU on e n channel at e tie slot t, where ν is e nuber of collected saples. The coponents yi contain independent and identically distributed (i.i.d) Gaussian noise ters wi unit variance. If e PU transitter is active, ey also contain e PU signal. The instantaneous PU-to-SU SNR per saple λ has e distribution f λ ( λ ). Assue energy detection [4]. If e PU signal is not present during e sensing period (null hypoesis H ), e output decision statistic S( y ) follows a central Chi-square distribution wi 2ν degrees of freedo. If e PU signal is present (alternative hypoesis H ), S( y ) follows a non-central Chi-square distribution wi 2ν degrees of freedo and a non-centrality paraeter 2 νλ. If e decision statistic S( y ) is larger an e detection reshold τ, e spectru sensor accepts e alternative hypoesis H and vice versa. The instantaneous iss detection probability p ( ) t and e false alar probability p ( ) FA t are given by and p = Pr[ y < τ H ] = Q ( 2 νλ, τ ), ν p = Pr[ y > τ H ] FA Γ = ( ν τ t ), ( ) 2, Γ( ν ) where Q ν (, ) is e generalized Marcu Q-function, Γ(, ) and Γ( ) are e upper incoplete gaa function and e coplete gaa function, respectively. Conventionally e reshold is fixed, so τ = τ. In is case e probability of iss detection is given by e expectation () (2) p = ( 2, ) Q νλ τ f ( λ ) dλ, (3) and e probability of false alar is λ ν p FA Γ = ( ν τ ) λ, 2. Γ( ν ) We propose to adjust e reshold according to e instantaneous PU-to-SU CSI. Assuing e ideal CSI knowledge, e detector eploys e instantaneous false alar and iss detection probabilities (,2) instead of averaging ese probabilities over e fading distribution. Bo e conventional and e adaptive detectors ust satisfy e iss detection rate constraint p. The detection reshold is coputed by inverting e iss detection probability: where (4) τ = p ( p ), (5) p is given by (3) for e traditional energy detector and by p ( ) t in () for e adaptive reshold selection. Since e range of e PUs is usually uch larger an e range of e SUs, all SUs in e neighborhood have siilar PU SNR statistics. Thus, in e fixed reshold case, e false alar probability and e reshold are tie-invariant and are likely to take on e siilar values for neighboring SUs. However, for e proposed eod, ese paraeters are tievariant and will have different values across e CR spectru for different SUs due to spatial and frequency diversity in fading scenarios. Moreover, fro (,2) and (5), p ( t ) FA decreases wi λ given p. Thus, as e received power at e SU sensor increases, at SU can raise e

3 Avg p FA Adaptive Threshold Fixed Threshold Avg p Fig. 2: Coparison of ROC curves for energy detection wi fixed vs. adaptive reshold selection; Rayleigh fading; λ = db; ν =. detection reshold while aintaining a certain collision probability constraint. As a result, abrupt fluctuations in e received power caused by noise or interference will not be isidentified as PU signals, resulting in fewer wasted spectru opportunities relative to e conventional detector case. The receiver operating characteristic (ROC) curves of e energy detector wi fixed and adaptive reshold selection under Rayleigh fading are copared in Fig. 2. The average PU-to-SU SNR λ = db. When e prescribed probability of iss detection is under.3, coputing e reshold adaptively provides a lower average false alar probability and us iproves sensing reliability. III. MYOPIC SENSING STRATEGIES WITH ADAPTIVE THRESHOLD SELECTION The PU traffic is odeled as a stationary Markov process wi known transition probabilities evolving independently on each channel. For channel n at e SU location, p denotes e probability of transition fro state i to state j, where i, j {(busy), (idle)}. All PUs and SUs share e sae slotted structure and are perfectly synchronized []. We assue at each SU can sense and en access only one channel at each tie slot due to e hardware constraints. The belief vector θ = [ θ,..., θ,..., θ N ] is eployed by e SUs to infer e current state of e PU traffic, where θ is e conditional probability at channel n is available at tie t for e SU pair based on past sensing history [ 4 ]. The sensing result a ( t ) = if a spectru opportunity is correctly detected or if a issed detection occurs, and a ( t ) = if a PU activity is correctly detected or when a false alar occurs. In is paper we consider yopic, or greedy, sensing policies where each SU akes sensing decisions selfishly wiout taking into account possible collisions wi oer CR users. Suppose e reward for SU on channel n is R ( t ). At e first tie slot t =, e initial belief vector is given by e stationary probabilities of e Markov process. Then at each tie slot t >, SU chooses to sense e channel n ( ) t by ij axiizing e expected reward E[ R ( t )] : n = arg ax θ R. (6) n In e equations below, e false alar and e probability of iss detection ters are given by (,2) for e proposed adaptive reshold and (3,4) for e conventional fixed reshold energy detection, respectively. After sensing, e belief is corrected by e reliability of e spectru sensor [5], n = n, =,... M, ( pfa ) ( FA ) θ θ, a = p + p ( θ ) (7) θr = pfaθ, a = pfaθ + ( p )( θ ) and en updated according to e Markov chain, ( ) ( ( )),if ( ) p θr t + p θr t n t = n θ ( t + ) = (8) p θ + p ( θ ),if n n where e process is repeated over e tie horizon t [, T ]. When e instantaneous reliability paraeter p ( ) FA t is eployed in (7,8) instead of e average p, FA ore accurate estiation of e current PU traffic states results. Finally, e reward is odified by e instantaneous probability of false alar in e proposed policy. Suppose e reward for a fixed reshold strategy is given by R ( ). FT t The corresponding sensing strategy wi adaptive reshold update eploys e reward R = ( p ) R. (9) AT FA FT Thus, R ( t ) in (6) is given by R ( ) FT t when e conventional sensing eod is eployed and by (9) for adaptive reshold selection. By taking into account e sensing reliability when selecting channels to sense, SUs will favor stronger PU-to-SU channels since p ( ) FA t decreases wi λ. This approach increases SU confidence relative to e conventional sensing eod where e individual SU roughput is sacrificed to protect e PUs. Moreover, due to geographical separation at provides spatial and frequency diversity, SUs perceive distinct sensing reliabilities on each channel, resulting in different sensing decisions. Thus, e proposed policy randoizes sensing decisions and reduces SU congestion. Conventionally e reward is given by e channel bandwid, i.e., R n FT B. = () However, when is reward is eployed in e yopic policy, it results in severe CR network congestion and poor roughput. To reduce congestion, several strategies in e literature, e.g. [4], randoize sensing decisions or use negotiation while retaining e reward given by e channel bandwid. However, e gains of ese strategies are liited. In [], we proposed to adapt e reward to e axiu achievable rate of e SU link, i.e.,

4 R = C = B log ( + γ ), () FT n 2 where γ is e instantaneous SNR of e SU pair on e n channel, and C ( t ) is e channel capacity. This sensing strategy exploits spatial and frequency diversity, randoizes sensing decisions, and boosts e network roughput. It significantly outperfors oer randoized strategies even when ey eploy adaptive transission. This gain is due to adaptiation to e SU link CSI prior to sensing. We showed at is approach is robust to CSI isatch and fading correlation and retains its gain when e reward is coputed using realistic adaptive odulation []. In practice, sensing errors significantly degrade e roughput of all strategies in e literature under a realistic collision probability constraint, especially in e low PU-to-SU SNR region [3]. To reedy is proble, we can eploy adaptive reshold control. These two types of adaptation, i.e. adaptation to PU-to-SU and SU-to-SU CSI, are tested individually and jointly in e nuerical results below. Thus, we evaluate e benefits of adaptive reshold control for bo conventional and channel-aware yopic strategies and e gain of cobined adaptation to e PU-to-SU and e SU-to- SU link CSI. IV. NUMERICAL RESULTS Consider a CR network wi M = 2 SU pairs and N = 4 channels wi e sae bandwid B =. The transition probabilities of e PU traffic on all channels at all SU locations are [ p p ] = [.2.8]. All SU-to-SU, PUto-SU, and PU-to-PU channels are subject to independent Rayleigh fading unless stated oerwise. All SU-to-SU links are identically distributed on all channels wi e average SNR γ. Siilarly, at all SU sensors e average PU signal SNR λ is e sae on all channels. In is paper we focus on low average SNR fro e PU transitter to e SU sensor (PU-to-SU SNR in Fig. ). Note at e PU receiver can be closer to e sensor an e PU transitter, so e interference to e PU network (SU-to-PU SNR) can still be significant. We assue an overlay scenario where a iss detection results in a collision between e SU and e PU transissions. We eploy a MAC schee siilar to [6] where an SU will transit over a channel if it is sensed idle or go to sleep during e current tie slot if it is sensed busy. If ultiple SU pairs choose to sense e sae channel and if at channel is idle, only one of e can transit successfully. Moreover, we assue at SUs always have data to transit. Finally, e SU network roughput for any sensing strategy in is paper is coputed under e assuption at adaptive transission is eployed after sensing wi e accuulated reward given by e channel capacity. Since e generalized Marcu Q-function in () and its inverse in (5) are very coputationally coplex, we eploy e Gaussian approxiation at holds for ν []. A. Throughput gain of PU-to-SU CSI Adaptation We copare e average secondary network roughput (noralized by M ) and e priary network roughput (noralized by N ) assuing average PU-to-PU SNR=dB SU Network Average Noralized Max Achievable Throughput PU Network Max Achievable Average Noralized Throughput (bits per slot per Channel) Fig. 3: Throughput vs. over T = 2 tie slots, as a function of p in Fig. 3(a) and Fig. 3(b), respectively, for four sensing policies. The first two policies eploy fixed reshold selection in (3,4): e conventional yopic sensing policy wi e bandwid reward in () (yopic, iperfect) [] and e yopic sensing policy at adapts to SU link SNR wi e reward () (SU-SU CSI-aided, iperfect) []. The oer two policies eploy adaptive reshold selection (2,5) and e reward (9), where R ( ) FT t is given by () for e yopic PU-SU CSI aided policy and () for e cobined PU-SU and SU-SU CSI-aided yopic sensing policy. Moreover, e roughputs of e conventional and SU-SU CSI-adaptive strategies under perfect sensing are also plotted in e Fig. 3. Due to e iss detection rate constraint our proposed policy offers e sae long-ter protection to e PUs as conventional sensing strategies as deonstrated by overlapped PU perforance curves in Fig. 3(b). The roughput of e PU network is coproised severely when P > and approaches its optial value as e prescribed collision 2 probability tends to. However, fro Fig. 3(a), e SU network roughput degrades rapidly for P when conventional fixed reshold detection is eployed. The proposed reshold adaptation results in.4- bit per slot per SU roughput gain over e fixed reshold policy in e sall (a) (b).5 Myopic (Iperfect) Myopic (PU-SU CSI-aided,Iperfect) Myopic (SU-SU CSI-aided,Iperfect) Myopic (SU-SU & PU-SU CSI-aided,Iperfect) Myopic (Perfect) Myopic (SU-SU CSI-aided,Perfect) Prescribed collision probability p for (a) SU network; (b) PU network; 2 SU pairs; 4 channels; i.i.d Rayleigh fading; PU-to-SU SNR=SU-to-SU SNR γ = db; PU-to-SU SNR λ = db; T = 2; ν =. The legend for bo is in (b).

5 P region. Bo strategies converge to eir ideal counterparts as e prescribed collision probability increases. The cobined adaptation provides up to.4 bits additional gain relative to adaptive sensing reshold selection alone for P. Since bo policies eploy adaptive transission, is gain is due to adaptation to SU link CSI prior to sensing. However, in e low p region adaptive reshold selection is ore beneficial for e conventional yopic strategy an for e strategy at also adapts to e CSI of e SU link. First, e forer strategy reaches e ideal sensor case for p as sall as. while e latter converges to e 2 ideal case only for p =. Moreover, at p =, e roughput gain provided by reshold adaptation is about 75% of e ideal roughput for e conventional yopic policy and is only 43% for e SU-to-SU CSI adaptive strategy. The lower relative gain in e latter strategy is due to reward adaptation at randoizes sensing decisions, so additional ultiuser and ultichannel diversity provided by sensing reshold adaptation has lower ipact an for e conventional yopic strategy. In Fig. 4 we evaluate e yopic policy using two spectru detection approaches: sensing reshold adaptation and cooperative sensing. In e latter eod, we assue ORrule hard decision cobining [4] where a fusion center collects independent individual sensing decisions fro L SUs and decides H if any of e L local decisions is H. The probability of iss detection and e probability of false alar L L of e final decisions are P = p and PFA = ( pfa ), respectively, where p and p FA are given by (3,4), and e reshold can be deterined by inverting P, i.e., τ = P SU Network Average Noralized Max Achievable Throughput Myopic (Perfect) Myopic (PU-SU CSI-Aided) Myopic (Iperfect,L=2).2 Myopic (Iperfect,L=8) Myopic (Iperfect,L=36) Prescribed collision probability Fig. 4: Throughput of adaptive reshold selection and of cooperative sensing; yopic strategy; 2 SU pairs; 4 channels; i.i.d Rayleigh fading; γ = db; p = ; λ = db; T = 2; ν =.. ( p ). Cooperative sensing has lower roughput an e proposed PU-to-SU CSI-aided yopic policy unless e nuber of diversity branches is very large. We found at at least L=3 independent sensing observations are required to atch e roughput of adaptive reshold selection at a single SU detector. Thus, roughput iproveent and ultiuser SU Network Average Noralized Max Achievable Throughput Myopic Myopic (PU-SU CSI-aided) Myopic (SU-SU CSI-aided) Myopic (SU-SU & PU-SU CSI-aided) ρ Fig. 5: Throughput vs. spatial correlation ρ ; 2 SU pairs; 4 channels; lognoral fading; µ = db; µ = db; σ = σ = 5 db; Average Noralized Throughput.5.5 diversity gain of e proposed eod outweigh e benefits of cooperative sensing for realistic CR networks. B. Ipact of Correlated Shadow Fading and CSI Error We explore adaptation to e log-noral shadow fading where e short-ter (ultipa) fading is reoved using diversity techniques. While estiation and tracking of shadow fading CSI is sipler and ore practical an for short-ter fading CSI for high speeds, e shadow fading signals fro e PU transitter to different SU sensors are likely to be correlated. We eploy e correlated lognoral shadowing odel [ 7 ] for e network wi one PU transitter and M = 2 equally spaced SU detectors placed on a linear track. The shadow fading coefficients are assued uncorrelated across different channels and for all SU-to-SU links. For each channel, e correlation coefficient between any two PU-to-SU links observed at detectors and is given by ρ = ρ, where ρ is e shadow fading correlation at two adjacent detectors. Each channel is odeled using e We assue at SU transitter is responsible for spectru sensing. In practice, sensing can also be carried out at e receiver side or at bo ends of e SU link (equivalent to cooperative sensing wi L=2). p =.; T = 2; ν =. Myopic Myopic (PU-SU-CSI-aided, Perfect) Myopic (PU-SU-CSI-aided, Iperfect) NMSE Fig. 6: Throughput vs. NMSE of CSI estiation; 2 SU pairs; 4 channels; i.i.d Rayleigh fading; γ = db; λ = db; p =.; T = 2; ν =.

6 lognoral distribution wi average db-scale SNR µ = db, µ = db, and e db-spread σ = σ = 5 db. The ipact of different values of ρ is shown in Fig. 5. Note at e roughput of e proposed PUto-SU CSI-aided sensing strategy degrades as e correlation ρ increases alough significant ultiuser diversity gain is observed even for relatively high values of ρ. These results show at e proposed eod is useful in practical shadow fading scenarios [7, 8]. As discussed in e introduction, estiated PU-to-SU channel gain will result in CSI isatch, and CSI estiation errors can also degrade perforance of proposed sensing reshold adaptation. We assue at e detector eploys e Miniu Mean Square Error (MMSE) estiate of e actual PU-to-SU SNR λ conditioned on its isatched observation ˆ. λ (We oit e indexes, n and t for siplicity.) The reshold is calculated using e expected iss detection rate, + pˆ ( ) ( ˆ = p t f λ λ) dλ, (2) ˆ( τ t) = pˆ ( p ), (3) where p ( t ) is given by () and ˆ f ( λ λ ) is e conditional probability density function (pdf) of λ given ˆ, λ e.g. [9]. The false alar probability is coputed using e reshold (3), and e reward is coputed using (9) where R ( ) FT t is given by (). We illustrate e roughput vs. noralized eansquare-error (NMSE) of SNR estiation for e yopic strategy wi adaptive reshold selection in Fig. 6. We observe at e proposed approach approxiates e ideal PU-to-SU CSI case when NMSE. and degrades gracefully to e conventional yopic policy wi fixed reshold when e PU-to-SU CSI becoes unreliable. Note at NMSE. corresponds to severely degraded CSI prediction accuracy in conventional counication systes [2]. Thus, we conclude at e proposed schee is robust to PU-to-SU CSI isatch. V. CONCLUSION Adaptation of e detection reshold to e instantaneous SNR of e PU signal was proposed for CR spectru sensing. The instantaneous iss detection probability constraint was iposed, and e resulting tie-variant false alar probability was incorporated into e sensing strategy design. It was deonstrated at e proposed sensing strategy randoizes sensing decisions and provides.4- bit per slot per SU roughput gain over e fixed reshold policy for sall prescribed collision probabilities wi e PU network and low average PU-to-SU SNR. Additional.4 bits can be gained by cobined adaptation to PU-to-SU and SU-to-SU CSI. Moreover, cooperative sensing wi at least 3 independent sensing results is necessary to atch e roughput of proposed reshold adaptation at a single detector. Finally, it is shown at e proposed adaptive strategy is robust to shadow fading correlation and to CSI isatch for practical CR network paraeters. REFERENCES [] Z. Quan, S. Cui, H. Poor and A. 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