Algorithm for Re-use of Shadowed CRs as Relays for Improving Cooperative Sensing Performance Dinh Thi Thai Mai, Nguyen Quoc Tuan, Lam Sinh Cong Dinh-Thong Nguyen University of Engineering and Technology, Vietnam National University, Hanoi - Vietnam Faculty of Engineering and Information Technology, University of Technology, Sydney – Australia Email: dinh-thong-nguyen@eng.uts.edu.au Email: dttmai@vnu.edu.vn, tuannq@vnu.edu.vn reporting channels, are assumed free of loss and fading In reality, when these channels are of significant distances in suburban macrocells or under shadowing in urban microcells, loss and fading is a significant issue In this case, cooperative diversity relaying may be necessary to improve the performance of the reporting wireless channels The cooperative diversity relay can process the information it receives from the source and forward the information to the destination using either amplify-and-forward (AF) or decodeand-forward (DF) protocols Abstract – In cooperative spectrum sensing, information from deeply faded local cognitive radios (CRs) needs to be eliminated from contributing to the fusion pool at the fusion center Most current works on the subject unrealistically assume that the reporting channels between the CRs and the fusion center are free of loss and fading In order not to waste those deeply faded CRs, this paper proposes an efficient algorithm to re-use them by reassigning them to act as cooperative diversity relays to assist the surviving CRs in combatting outages due to Suzuki fading in the reporting channel The algorithm involves the pairing of a surviving CR to a relay CR so as to select the lowest outage probability of the resulting cooperative diversity relaying network The paper proposes a closed-form and accurate approximation for the outage probability of such a network in the composite Rayleigh-lognormal fading channel, thus rendering fast and simple execution of the pairing algorithm In an earlier paper [6], we proposed an innovative, albeit simple, re-use of those CRs under deep fading of the sensing channels by re-assigning them to act as diversity relays to their more healthy peers in the reporting channels, thus improving the global detection reliability of the fusion center Signal-tonoise ratio in the sensing channels was used as a sole parameter in deciding which shadowed relay was to assist which surviving CR However, in realistic radio propagation scenarios, the fading characteristics in the reporting channels are different from those in the sensing channels, thus SNRs from the latter channels cannot usually be used as valid parameters for calculating the outage probability of the resulting cooperative diversity relaying networks in the reporting channels Also, in [6] the fading mechanism in the reporting channels is assumed to be Rayleigh distributed, which is rather simplistic in urban and suburban areas In this paper, we propose a more sophisticated and more reliable algorithm to select ‘surviving-rejected’ CR pairs to form cooperative diversity relaying networks in a composite Rayleigh-lognormal environment, also known as the Suzuki fading channel [7] The proposed pairing algorithm involves searching for pairs that produce lowest outage probabilities of the resulting networks However, it is well known that the infinite integral in the probability density function (pdf) of the Suzuki fading distribution makes it difficult to derive a closedform expression for channel outage probability, thus preventing any efficient and fast search Another mathematical complexity arises in the calculation of the pdf of the sum of two lognormal random variables [8] [9] at the FC destination of the resulting cooperative diversity AF relaying network - one directly from the surviving CR and the other forwarded from the relay This pdf can be calculated using the moment generating function (MGF) technique [8] [10] followed by the inverse Laplace Transform (ILT) [10] In this paper, using a similar approach as in [10] we derive a closedform and accurate approximation for the outage probability of Keyword – cognitive radio, Suzuki fading, relay network I INTRODUCTION Cooperative spectrum sensing using cognitive radios (CRs) has proved to be a reliable technique for combating deep fading during the sensing a primary user [1] [2] The sensing is carried out in two phases: in the sensing phase, the CRs independently measure and process the signal from the primary user, and in the reporting phase the CRs independently report the processed information to a fusion center (FC) which is usually a cognitive base station, to make the final global sensing decision as to whether the primary user is present or absent In many standard fusion rules, it is easy to see that the inclusion of deeply faded CRs, i.e with low SNRs, in the decision fusion at the FC diminishes the reliability of the cooperative detection of the primary user Thus by discarding the detection contribution from shadowed CR sensors, the detection probability of the cooperative sensing network can be improved However, by doing so the CRs under shadowing are wasted Signal-to-noise ratio (SNR) is a dominant metric of transmission quality affecting the detection performance of a CR sensor and can be used by the FC to decide if a CR should be rejected [4] Various techniques are available to date in wireless communications for a CR to efficiently estimate the SNR directly from its sensing energy samples without the knowledge of the transmitted signal power or the noise variance, e.g [5] In most research papers in the literature to date on cooperative spectrum sensing using CRs, the wireless links between individual CRs and the fusion centre, i.e the the cooperative diversity AF relaying network, and therefore can significantly speed up the proposed pairing search While the main motivation of our paper is clearly to re-use the shadowed sensing CRs which otherwise will be wasted, its main contribution is more towards the mathematical and computational advance for cooperative diversity relaying using AF protocol Therefore spectral sensing and detection decision fusion are not issues in this paper where λ is the power detection threshold, Γ(.) and Γ(.,.) are complete and incomplete gamma functions, respectively PD in fading conditions is obtained by averaging its value in the AWGN case over the SNR fading distribution f(γ), while PF remains the same under all fading conditions since it is calculated under Η hypothesis, i.e no signal, hence independent of SNR, i.e The rest of the paper is organized as follows In Section II, we summarize briefly the principle of cooperative spectrum sensing and present a novel and accurate closed-form expression for the approximation of probability of detection of CR in a Suzuki fading channel Similarly, in Section III we summarize the essence of a cooperative diversity AF relaying network and present a novel and accurate closed-form approximation for the calculation of probability of outage of the network using moment generating function (MGF) and inverse Laplace transform (ILT) techniques In Section IV, a ‘pairing’ algorithm is presented for efficient re-use of shadowed CRs as relays Finally in Section V, results and conclusions are presented ∞ PD, fading = f (γ )Qm ( 2γ , Gm−1 ( PF ))d γ where γ is the SNR, Qm(.,.) is the generalized Marcum’s Q function of 2m degree of freedom In a Rayleigh fading channel with average SNR γ , the probability of detection of a local CR is given in [3] as P (γ ) = D, Rayleigh Γ( m − 1, λ / 2) λ + exp(− )× Γ( m − 1) 2(1 + mγ ) 1 + mγ II COOPERATIVE SPECTRUM SENSING A Sensing Network Definition Figure shows a cooperative spectrum sensing CR network in which local CRs detect signals from the primary user, perform local processing, then send information to the fusion centre (FC) for the latter to make the final global sensing decision as to whether the primary user is absent (H0) present (H1) In many applications, the CRs report their local binary decision {ui} together with associated parameterssignal to noise ratio {SNRi}, probability of detection{PDi} and probability of false alarm {PFi} to the fusion centre via the reporting wireless channels These parameters adequately characterize the reliability or the trustworthiness of the local binary decision In this paper, we assume that while both sensing and reporting networks are subject to composite Rayleigh-lognormal fading, a CR can be deeply shadowed in the sensing network, e.g by an obstacle, but still is clear in the reporting network (3) fading channel with power gain YR-Ln=eZ where Z is a Gaussian RV with distribution N (µz, σz2) The pdf of its power gain is (ln x − μ ) p Z f R − Ln ( p ) = ∞ exp( − ) exp − dx x x xσ π Z 2σ Z (4) Thus by inserting (4) into (2), it can be shown that the probability of detection in the composite Rayleigh-lognormal (also known as Suzuki) fading channel, can be approximated in terms of its corresponding probability of detection in a Rayleigh channel, is [10] PD ,Suzuki ≈ Np wn PD ,Rayleigh (γ = e π n=1 in which wn abscissas of ( μ z + anσ z ) ) (5) and an are, respectively the weights and the the Gauss-Hermite polynomial The approximation becomes more and more accurate with increasing approximation order Np, and high accuracy is Probabilities of false alarm is given in [1] as Γ(m, λ / 2) = Gm (λ ) Γ ( m) λ mγ ) m −1 Γ( m − 1, 2(1 + mγ ) 1 − Γ( m − 1) In this paper we consider a composite Rayleigh-lognormal B Detection and False Alarm Probabilities over Fading Channels There are two probabilities that are most commonly used as performance metrics for spectrum sensing: probability of a false alarm PF which is the probability that a signal is detected while it does not exist, and probability of detection PD which is the probability that the presence of a signal is correctly detected PF = P Y > λ Η = (2) achieved for Np > [8][9] (1) The behavior of the curve of PD in (5) versus PF in (1) represents the receiver operating characteristics (ROC) in a Suzuki fading channel the FC and a Relay is an unreliable CR being reused The relay is assumed to use the amplify-and-forward (AF) protocol and operates in the time division mode having two phases: the relay-receive phase and the relay-transmit phase; each phase or sub-block is of duration T/2 In the relay-receive phase, the source transmits the complete message to both the destination and the relay (broadcast mode), and the received signal at the relay and at the destination, respectively is C Cooperative Spectrum Sensing Let ui = [0,1], i=1,2,…,n, denote the 1-bit decision from the ith CR There are many different decision fusion rules, but if the individual measurements are mutually independent, then the k-out-of-n rule is most popular by which hypothesis Η1 is chosen if k or more individual decisions are 1, and Η is chosen otherwise Under this rule the global average probabilities are n QF = n u 1−u ∏ ( PFi ) i (1 − PFi ) i y sr (t ) = (6) j = k ui = j i =1 Ps hsr x s (t ) + nsr (t ) ysd (t ) = Ps hsd xs (t ) + nsd (t ) (8a) (8b) and QD = n n ∏ ( PDi )u (1 − PDi )1−u i In the relay-transmit phase, the relay with power Pr sends a signal xr and the destination receives (7) i j = k ui = j i =1 y rd (t + T / 2) = (9a) which is an amplified version of the signal it receives in (11a) to the destination, i.e Phenomenon yrd (t + T / 2) = hrd α r { Ps hsr x s (t ) + nsr (t )} + nrd (t + T / 2) {H , H1} Sensing channel Pr hrd xr (t + T / 2) + nrd (t + T / 2) (9b) dsr By equating the expectations of (9a) and (9b), we obtain CR1 PD1 Reporting channel CR2 CRN PD2 … PDN dsd αr = drd Pr 2 Ps E[ hsr ] + σ sr (10) Fusion Center δ i = ( PD , PF , SNRi ) i i u0 {0,1} Figure : A decentralized cooperative spectrum sensing network with the Nth CR sensor eliminated from the fusion process III COOPERATIVE DIVERSITY RELAYING Figure 2: Diagram of an M-relay cooperative diversity relaying network A AF Cooperative Relaying Protocol Definition Figure shows a simple cooperative diversity relay network using M relaying branches, where xs, Ps, yij, hij and nij, are, respectively the normalized transmit signal, the power from the source, i.e E x = , the received signal, the From (9b) the SNR at the destination of the relayed signal can be obtained with αr from (10), as ( ) α r hsr hrd Ps γ sr γ rd = 2 α r hrd σ sr + σ rd γ sr + γ rd + 2 hrd Pr h sr Ps where γ = , γ rd = sr 2 σ sr σ rd γR = channel gain (or loss), and the additive noise on the channel link from i to j The additive noise is modeled as a circularly symmetric complex Gaussian random variable with zero mean and variance σ2 at the receiver, i.e n ~ N(0,σ2) In the application for CR reuse in this paper we use only one relay (M=1); the Source is a reliable CR, the Destination is (11) For simplicity we assume that unfaded SNR is the same on all channels, i.e P/σ2=SNRo, then the power gain of the relay channel corresponding to (11) is hR = h sr h sr 2 + h rd h rd Therefore f (12) 2 2 ( SNRo , Rth ) = Pr ( hij < μ th ) = F hij ( μ th ) ( M +1) Rth − SNRo (e − p/k [k (s) n, sd − e n, sd k m ,R ( a m ; μˆ R , σˆ R ) = 10 ( (.) − k (17) − p/k m, R m, R ) (.)] 2σ sd an + μ sd ) / 10 2σˆ R am + μˆ R ) / 10 = exp( = exp( 2σ sd a n + μ sd ξ 2σˆ R a m + μˆ R ξ ) ) Therefore the outage probability of the AF cooperating diversity relaying network is out PAF ( μth ) = μth (14) Np N f hAF ( p ) dp wn wm k [ (.) π m=1n=1 n ,sd − k m ,R (.)] − p / kn ,sd − p / km ,R ( k n ,sd (1 − e ) − k m , R (1 − e )) = where F (.) is the cdf of the fading distribution and the channel gain threshold is defined as μth = Np h AF k n ,sd ( a n ; μ sd , σ sd ) = 10 ( (13) between two points i and j having instantaneous channel gain hij for a given outage information rate threshold, Rth is defined as hij where t The outage probability, Phou ( μt h ) of the wireless channel ij P ( p ) = InvLaplace M w w π m = 1n = n m B System Outage Definition out Np + / SNRo Finally, the end-to-end power gain of the AF relay wireless network is hAF = hsd + hR h AF p (18) (15) and M is the number of relays which is in this paper C AF Cooperative Relaying Outage Calculation Since the end-to-end power gain in (13) is a continuous function, the outage probability of an AF cooperative diversity relaying network is defined simply as out PAF ( μ th ) = Pr( h AF < μ th ) == F h AF ( μ th ) To calculate (16), we require the pdf of has been justified that the power gain (16) hAF In [10] it hR in (12) of the diversity relaying channel can be represented by a single Suzuki RV with estimated Gaussian distribution parameters ( μˆ R , σˆ R ) Thus, 2 hAF in (13) can be considered Figure 3: Probability of outage versus given channel power gain threshold defined in (15) for an AF cooperative diversity relay network as the power sum of two Suzuki RVs, and in [10] an elegant method is presented to calculate its pdf using moment generating function (MGF) and inverse Laplace transform (ILT) The result given in [10] is M h AF Figure confirms the accuracy of the closed form expression for the probability of outage in (18) ( s) = IV N N w w 1 p p n m 1 − − π n = k (.)[ s + k n, sd (.)] m = k (.)[ s + k m, R (.)] n, sd m, R ALGORITHM FOR RE-USE OF SHADOWED CRs In this section we propose a method that utilizes eliminated CRs by assigning them to act as cooperative diversity relays for the surviving CRs that still stay in the fusion pool In Figure we illustrate an example in which { CRN suffers from deep fading and its reported information is discarded by the fusion center The FC then reassigns CRN to act as a relay for CR1 to improve the transmission reliability of the CR1-to-FC reporting channel, thus forming a 3-terminal relay network with the surviving CR1 as the source (S), the eliminated CRN as the relay (R), and the FC as the destination (D) where PDj is probability of detection from (5) and P (j) is the outage probability of the channel between the jth CR and the FC either with (using (18)) or without (when all terms involving m are omitted) diversity relaying It can be easily observed that the outage probability in (18) is lower with the use of the relay compared to that without the relay, hence improving the local effective probability of detection in (19) received by the fusion center A Eliminating Algorithm • Step 1: Local CRs calculate the SNR {SNRi;i=1,2, N } from their respective raw sensed signal {yi}from the primary user and calculate the probability of detection {PDi}using (5) Step 2: The fusion center receives the processed information in Step from the local CRs Note that having received individual SNRs (of the sensing channels) from the CRs, the FC can evaluate the individual PDs instead of the CRs However, such evaluated PDs will be unreliable due to fading in the reporting channels Step 3: The FC ranks the CRs in the descending order of their SNR and eliminates those CRs with lowest SNR • From these simulation data, the Gaussian parameters ( μˆ Rji , σˆ Rji ) are found for each cooperative diversity relay network (Sj,Ri,D) The outage probability of all the networks (Sj,Ri,D) required to complete Table for rate threshold μth=0.1 and Table for rate threshold μth=0.5 is calculated from (18) • Table 1: Matrix of Probability of Outage of Cooperative Relay Network (Sj,Ri,D) with µth = 0.1 S1 0.0182 0.0154 0.0122 S2 0.0198 0.0182 0.0154 S3 0.0182 0.0198 0.0182 S4 0.0154 0.0182 0.0198 S5 0.0122 0.0154 0.0182 Table 2: Matrix of Probability of Outage of Cooperative Relay Network (Sj,Ri,D) with µth = 0.5 CR R1 R2 R3 S1 0.1262 0.1152 0.0963 S2 0.1296 0.1262 0.1152 S3 0.1262 0.1296 0.1262 S4 0.1152 0.1262 0.1296 (19) out Figure below represents the simulation model used in this paper for the reporting network to illustrate the proposed pairing algorithm to select which relay (eliminated CR) to assist which source (CR retained in the fusion pool) We assume that Suzuki fading channels all have σ =8dB and that µ is proportional to a negative exponent of the propagation distance, d-α In the simulation we normalize µsd=µrd=5dB, then µs1r1=2dB, µs1r2=4dB, µs1r3=6dB, similarly for other values of μsjri Relative values are important but precise values of µ are not important for the objective of this paper CR R1 R2 R3 } PDe ( j ) = PDj − P out ( j ) S5 0.0963 0.1152 0.1262 B Pairing Algorithm The pairing algorithm is based on the minimum probability of outage of the entire reporting network • Step 1: Calculate PAFjout (μth), (j=1,2,3,4,5; i=1,2,3) using (18) of the resulting cooperative diversity relay networks using AF protocol, and complete Table (or Table 2) • Step 2: Rank and select three pairs (i=1,2,3) with lowest PAFjout (μth) from Table (or Table 2) as the optimal solution for pairing The pairing result is shown in red V RESULTS AND CONCLUSIONS The paper has successfully presented an accurate analysis of the proposed strategy for the re-use of discarded CR sensors as diversity relays to improve the performance of surviving peers against Suzuki fading in the reporting network The most significant contribution of this paper is the derivation of closed-form and accurate expressions for the probability of detection PD of the primary user and the probability of outage Pout of the resulting three-terminal cooperative diversity relaying wireless network These closed-form and accurate expressions greatly speed up the execution of the proposed reuse algorithm, giving us the incentive to research into a more sophisticated and efficient algorithm The effectiveness of the strategy was judged on the basis of resulting global ROC curves, i.e global probability of detection, QD, versus global probability of false alarm, QF Figures 5a and 5b show the simulation results of the receiver operating characteristic (ROC) curves of the Figure 4: Simulation model of reporting network to illustrate the proposed pairing algorithm Because the reporting channels between the CRs and the FC are subjected to fading and hence link outages, the reported parameters received at the FC are usually deteriorated The effective probability of detection received from the jth CR by the FC is ACKNOWLEDGEMENTS cooperative sensing network in three operating environments: transparent reporting channels (no fading), Suzuki fading reporting channels without re-use of eliminated CRs as diversity relays, and Suzuki fading reporting channels with reuse of eliminated CRs as diversity relays All ROC curves are for the simulation model in Figure The outage power gain threshold µth is much lower, i.e much healthier SNR, in Figure 5a than in Figure 5b giving much higher global probability of detection, and therefore the benefit of re-use of deeply faded CRs is not as pronounced in Figure 5a compared to Figure 5b However, in both cases the benefit of the proposed re-use of poor sensing CRs as diversity relays is very convincing This work was supported by research grants from QG.2012 (Projects of the University of Engineering and Technology, Vietnam National University Hanoi) and NAFOSTED (National Foundation for Science and Technology Development) REFERENCES [1] A Ghasemi and E.S Sousa, “Collaborative Spectrum Sensing for Opportunistic Access in Fading Environments,” Proc IEEE 1st Symposium on Dynamic Spectral Access Networks (DySPAN’05), pp 131-136, Baltimore, November 2005 [2] A Ghasemi and E.S Sousa, “Opportunistic Spectrum Access in Fading Channels Through Collaborative Sensing,” Journal of Communications, vol 2, No 2, pp 71-82 , March 2007 [3] F.F Digham, M.S Alouini and M.K Simon, “On the energy detection of unknown signals over fading channels,” Proc IEEE Int Conf on Coms ICC’03, pp.3575-3579, May 2003 [4] Yi Zheng et al “Cooperative Spectrum Sensing Based on SNR Comparison in Fusion Center for Cognitive Radio,” Proc International Conference on Advanced Computer Control, ICACC’2009, pp 212-216, 22-24 Jan 2009 [5] T Cui et al “Blind Spectrum Sensing in 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spectrum sensing network under fading with and without re-use of poor CRs as diversity relays, (a) Outage threshold µth =0.1 and (b) Outage threshold µth= 0.5 ... propose a method that utilizes eliminated CRs by assigning them to act as cooperative diversity relays for the surviving CRs that still stay in the fusion pool In Figure we illustrate an example... “Efficient Re-use of CRs under Deep Fading for Improving Cooperative Sensing Performance, ” Proc IEEE International Conference TENCON 2011, Bali, Indonesia, 21-24 November, 2011 [7] H Suzuki, “A statistical... probability of detection, and therefore the benefit of re-use of deeply faded CRs is not as pronounced in Figure 5a compared to Figure 5b However, in both cases the benefit of the proposed re-use of poor