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1 Middlesex University Research Repository An open access repository o Middlesex University research Vien, Quoc-Tuan and Nguyen, Huan X. and Trestian, Ramona and Shah, Purav and Gemikonakli, Orhan 014) Perormance analysis o cooperative spectrum sensing or cognitive wireless radio networks over Nakagami-m ading channels. In: 014 IEEE 5th Annual International Symposium on Personal, Indoor, and Mobile Radio Communications PIMRC), 0-05 Sep 014, Washington DC, DC, USA. Final accepted version with author's ormatting) Available rom Middlesex University s Research Repository at Copyright: Middlesex University Research Repository makes the University s research available electronically. Copyright and moral rights to this thesis/research project are retained by the author and/or other copyright owners. The work is supplied on the understanding that any use or commercial gain is strictly orbidden. A copy may be downloaded or personal, non-commercial, research or study without prior permission and without charge. Any use o the thesis/research project or private study or research must be properly acknowledged with reerence to the work s ull bibliographic details. This thesis/research project may not be reproduced in any ormat or medium, or extensive quotations taken rom it, or its content changed in any way, without irst obtaining permission in writing rom the copyright holders). I you believe that any material held in the repository inringes copyright law, please contact the Repository Team at Middlesex University via the ollowing address:

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3 Perormance Analysis o Cooperative Spectrum Sensing or Cognitive Wireless Radio Networks over Nakagami-m Fading Channels Quoc-Tuan Vien, Huan X. Nguyen, Ramona Trestian, Purav Shah, and Orhan Gemikonakli School o Science and Technology, Middlesex University, The Burroughs, London NW4 4BT, UK. {q.vien; h.nguyen; r.trestian; p.shah; o.gemikonakli}@mdx.ac.uk. Abstract This paper is concerned with cooperative spectrum sensing CSS) in cognitive wireless radio networks CWRNs). A practical scenario is investigated where all channels suer rom Nakagami-m ading. Speciically, we analyse the probabilities o missed detection and alse alarm or two CSS schemes where the collaboration is carried out either at usion centre FC) only or at both the FC and secondary user SU). By deriving closed-orm expressions and bounds o these probabilities, we not only show that there are signiicant impacts o the m-parameter o Nakagami ading realisation or dierent channel links on the sensing perormance but also evaluate and compare the eectiveness o the two CSS schemes with respect to various ading parameters and the number o SUs. Finally, numerical results are provided to validate the theoretical analysis and indings. I. INTRODUCTION Cognitive radio has been proposed as an emerging technology to cope with the scarcity o spectrum resource by implementing dynamic spectrum access [1]. In cognitive wireless radio networks CWRNs), unlicenced users or secondary users SUs)) can opportunistically exploit unused licenced requency bands o licenced users or primary users PUs)). Thus, the SUs should continuously sense the spectrum to check its availability. However, the implementation o spectrum sensing at SUs is limited or hidden terminal problems caused by shadowing and ading eects. Recently, relay-assisted communications has been incorporated in various wireless systems e.g. [] [4]). Data transmission rom senders to receivers is carried out with the aid o relay terminals. The relays help improve service quality or near-by users and extend coverage region or ar-end users. Adapting relaying techniques into CWRNs, cooperative spectrum sensing CSS) has been then proposed not only to help the shadowed SUs detect the licenced requency bands but also to improve sensing reliability o the SUs [5] [7]. Speciically, a CSS scheme can be divided into three phases e.g. in [7]) consisting o sensing SS) phase, reporting RP) phase, and backward BW) phase. In the SS phase, every SU perorms local spectrum sensing LSS) to determine the availability o the licenced spectrum. Then, all SUs orward their local decisions to a common receiver, namely usion centre FC), in the RP phase. At the FC, a global spectrum sensing GSS) is carried out to make a global decision on the spectrum availability, which is then broadcast back to all the SUs in the BW phase. In this paper, we analyse the perormance o CSS over Nakagami-m ading channels in terms o the probabilities o missed detection and alse alarm. Given the LSS and GSS decisions available at the SUs, we consider two CSS schemes as ollows: i) Scheme 1: The GSS decision is the inal spectrum sensing FSS) decision at the SUs e.g. [6]) and ii) Scheme : Both the LSS and GSS decisions are taken into account to make the FSS decision at the SUs e.g. [7]). Particularly, we investigate a practical scenario where all the SS, RP and BW channels suer rom ading and noise. This work is dierent rom the published work which assumes either the RP or the BW channels are error-ree [5], [6] or suered rom Rayleigh ading [7]. In this work, the ading channels are characterised by Nakagami-m distribution, which is used or modelling landmobile and indoor-mobile multipath propagation [8], [9]. By deriving closed-orm expressions o missed detection probability MDP) and alse alarm probability FAP), we irst compare the sensing perormance achieved with the above CSS schemes. It is shown that the combination o GSS and LSS in scheme results in a lower MDP compared to scheme 1, while it causes a higher FAP. Secondly, the eects o the number o SUs and the ading channel parameters are evaluated. Speciically, we derive the bounds o MDP and FAP when the number o SUs is large. Both schemes are shown to approach the same FAP and the bounds o MDP also show an improved perormance achieved with scheme. Furthermore, the ading parameters o RP and BW channels are shown to have a signiicant impact on the sensing perormance over those o SS channels. II. SYSTEM MODEL &COOPERATIVE SPECTRUM SENSING A. System Model The system model o a CWRN under investigation is illustrated in Fig. 1 consisting o PU, {SU 1, SU,...,SU N } and FC. We assume there are K non-overlapping licenced requency bands 1,,..., K. For convenience, let us deine a spectrum indicator vector SIV) o length K in bits) to report the availability o the licenced spectrum [7] where the unavailable and available requency bands are represented by bits 0 and 1, respectively. The channel or a link A!B,

4 PU SU 1 SU SU N... FC SS phase RP phase BW phase Fig. 1: System model o cognitive wireless relay network. where {A, B} {PU, SU 1, SU,...,SU N, FC} and A6= B, is denoted by h AB 1 and assumed to suer rom quasi-static slow Nakagami-m ading. B. Cooperative Spectrum Sensing CSS) In this subsection, let us briely introduce three phases o CSS as ollows: 1) Sensing SS) Phase - Local Spectrum Sensing LSS): Over the SS channel, the signal sensed at SU i, i,,...,n, at the k-th requency band, k,,...,k, can be expressed as r SS) h PSi x[k]+n SS) i [k], H 1,k, i [k] = 1) n SS) i [k], H 0,k, where x[k] is the transmitted signal rom PU and n SS) i [k] is complex Gaussian noise at SU i having zero mean and variance o 0. Here, H 1,k and H 0,k denote the two hypothesis that the k-th requency band is occupied and unoccupied, respectively, by PU. Then, SU i detects the availability o the k-th requency band by comparing the energy o the received signal in 1) with an energy threshold denoted by " i [k]). Let s L) i [k] denote the local SIV o the k-th requency band estimated at SU i and [ ] denote the energy measurement o a signal. We have s L) i [k] = 0, i [r SS) i [k]] > " i [k], 1, otherwise. ) Reporting RP) Phase - Global Spectrum Sensing GSS): In RP phase, the received signal at FC rom SU i, i = 1,,...,N, at the k-th requency band, k,,...,k, can be written by r RP ) i [k] = p i h SiF x LSS) i [k]+n RP ) i [k], 3) where i is the transmission power o SU i, x L) i [k] is the binary phase shit keying BPSK) modulated version o s L) i [k] see )) and n RP ) i [k] is complex Gaussian noise at FC having zero mean and variance o 0. Then, FC decodes and combines all the decoded SIVs denoted by {s RP ) i [k]}) rom all {SU i } to make a global decision in terms o a global SIV as ollows : s G) FC [k] = 0, i P N i srp ) i [k] <N, 4) 1, otherwise. 1 For brevity, A and B correspond the irst letter o PU, SU i and FC i.e. P, S i, F ). The OR rule is used since it was shown to give the best CSS perormance compared to other rules [10]. ) 3) Backward BW) Phase - Final Spectrum Sensing FSS): The received signal at SU i, i,,...,n, rom FC with respect to the k-th requency band, k,,...,k, can be written by r BW) i [k] = p FC h FSi x G) FC [k]+nbw) i [k], 5) where FC is the transmission power o FC, x G) FC [k] is the BPSK modulated version o s G) FC [k] see 4)) and nbw) i [k] is complex Gaussian noise at SU i over the BW channel having zero mean and variance o 0. Then, SU i decodes the received signal as s BW) i [k]. Let us denote s Fj) i [k] as the inal SIV o the k-th requency band, k,,...,k, at SU i, i,,...,n, using scheme j, j, as described in Section I). Scheme 1 - Non-combined scheme: In this scheme, the GSS decision received rom FC is also the inal decision at SU i. Thus, we simply have s F1) i [k] =s BW) i [k]. 6) Scheme - Combined scheme: In this scheme, SU i combines its local SIV with the global SIV received rom FC as ollows [7]: s F) i [k] = 0, i s L) i [k]+s BW) i [k]) <, 1, otherwise. III. PERFORMANCE ANALYSIS In this section, we derive closed-orm expressions and bounds or the alse alarm probability FAP) and the missed detection probability MDP) o CSS schemes in CWRNs over Nakagami-m ading channels. Deinition 1. The FAP and MDP o the k-th requency band i.e. k ), k,,...,k, at node A, A {SU i, FC}, i = 1,,...,N, using scheme j, j,, are deined as,j m,j respectively, where M {L, G, F }. 7), Pr{s Mj) i [k] =0 H 0,k }, 8), Pr{s Mj) i [k] H 1,k }, 9) The Nakagami ading parameters o the SS, RP and BW channels are denoted by, m rp and m bw, respectively. For simplicity, let us assume that the RP and BW channels o the same link have the same Nakagami ading parameters i.e. m rp = m bw ) and all the SUs have the same energy threshold or detection o the k-th requency band i.e. " i [k] = "[k] 8i,,...,N) 3. Without loss o generality, we analyse the perormance or a speciic requency band and thus the index o the requency band i.e. k) is omitted in the rest o the paper. Let us irst consider the LSS at SU i, i,,...,n. Deine, "/ 0), i, 0 / 0 + PSi ), where PS i is the average signal-to-noise ratio SNR) at SU i over h PSi. The FAP and MDP o the LSS are given by [11] =Pr{s L) i =0 H 0 } = u, ), 10) 3 The perormance analysis or the general scenario o various ading parameters and energy thresholds can be easily extended by aggregating the perormance achieved at SUs over the associated RP and BW links. )

5 where SUi) =Pr{s L) i H 1 } # i,1 # i,, 11) i # i,1 = e mss m [ ss 1 i L mss 1 1 i)) mx ss j +1 i) i L j 1 i))], # i, = mss i X 1 e j j=0 1) j j! 1 F 1 ; j + 1; 1 i)), 13) denotes the time-bandwidth product o the energy detector, ) is the gamma unction [1, eq )], u, ) is the upper incomplete gamma unction [1, eq )], 1 F 1 ; ; ) is the conluent hypergeometric unction [1, eq )] and L i ) is the Laguerre polynomial o degree i [1, eq )]. Note that over a Nakagami-m ading channel h AB, the average bit error rate BER) or BPSK modulation with respect to the average SNR o AB is obtained as in [13] and given below mab P b E AB )= 1+ AB mab +1/) m AB p m AB + 1) 14) F 1 m AB, 1/; m AB + 1; 1/1 + AB /m AB )), where F 1, ; ; ) is the Gauss hypergeometric unction [1, eq )]. For brevity, let us deine a unction m AB, AB) or AB in short) as the RHS o 14). Considering the GSS at FC over the RP channels suered rom Nakagami-m ading, we have the ollowing inding: Lemma 1. The FAP and MDP o the GSS are determined by 1 [ )] N [ l, )1 SiF )+ u, ) SiF ], i 15) FC) = [1 # i,1 # i, )1 SiF )+# i,1 + # i, ) SiF ], i 16) where SiF is given by 14) and l, ) is the lower incomplete gamma unction [1, eq )]. by m Proo: From 4), the FAP and MDP at FC can be given = Pr{s G) FC =0 H 0} = Pr{s G) FC H 1} = i i Pr{s RP ) i x=0}, 17) Pr{s RP ) i x 6= 0}, 18) where x is the transmitted signal rom PU. Thus, over the Nakagami-m ading channels {h SiF }, i,,...,n, with BER o SiF see 14)), we have m = i [1 )1 SiF )+ SiF ], 19) i [ m 1 SiF )+1 SUi) ) SiF ]. 0) Substituting 10) and 11) into 19) and 0) with the act u, ) + l, ) = ) [1, eq )], the lemma is proved. In the BW phase, the FSS at SU i, i = 1,,...,N, is carried out using either o two schemes, namely non-combined and combined schemes see Sect. II-B.3). We then have the ollowing indings: Lemma. The FAP and MDP o the FSS at SU i, i = 1,,...,N, using scheme 1 are determined by,1 [1 )1 FSi )+ FSi ], 1) m,1 = m 1 FSi )+1 m ) FSi, ) where FSi, 16), respectively. and m are given by 14), 15) and Proo: In scheme 1, the FSS at SU i, i,,...,n, is also the GSS eedback rom FC over the Nakagami-m BW channels {h FSi }. Following the same approach as in the proo o Lemma 1,,1 and m,1 can be calculated by 1) and ), respectively. Lemma 3. The FAP and MDP o the FSS at SU i, i = 1,,...,N, using scheme are determined by 1, ) [ l, )1 FSi )+ u, ) FSi ] [1 )1 FSi )+ FSi ], 3) m, =[1 # i,1 # i, )1 FSi )+# i,1 + # i, ) FSi ] where FSi, 16), respectively. [ m 1 FSi )+1 m ) FSi ], and m 4) are given by 14), 15) and Proo: In scheme, the FSS at SU i, i,,...,n, is obtained by combining both the GSS rom FC and the LSS. From 7),, and m, can be given by, = Pr{s F) i =0 H 0 } Pr{s L) i m, = Pr{s F) i H 1 } = Pr{s L) i x =0}Pr{s BW) i x=0}, x 6= 0}Pr{s BW) i x 6= 0}. 5) 6) where x is the transmitted signal rom PU. Thus, over the Nakagami-m BW channels h FSi with BER o FSi,, and m, can be obtained by 3) and 4), respectively. Remark 1 Lower FAP with Scheme 1 and Lower MDP with Scheme ). From 1), ), 3) and 4) in Lemmas and 3, it can be easily shown that,1 <, and m,1 > m,, i,,...,n. This accordingly means a lower FAP is achieved with scheme 1 compared to scheme, while scheme achieves a lower MDP than scheme 1. Remark Lower MDP but Higher FAP with Increased Number o SUs). Both CSS schemes improve the MDP but

6 cause higher FAP at SUs when the number o SUs increases. From 15) and 16) in Lemma 1, it can be seen that and FC) monotonically increase and decrease, respectively, over N. Thus, rom 1), ), 3) and 4), the increased number o SUs helps both CSS schemes improve the MDP, however, causing a higher FAP. Remark 3 Impact o Nakagami-m Fading Parameters on MDP and FAP). Both the MDP and FAP decrease when the ading parameters o RP and BW channels increase, while only MDP is improved with increased ading parameters o SS channels. In act, it is known that the BER o a Nakagami-m ading channel h AB monotonically decreases as m AB increases see 14)). Thus, rom 1), ), 3) and 4), it can be proved that,j and m,j, i,,...,n, j,, monotonically decrease as either m rp or m bw increases. Additionally, as shown in 10) and 11),, i,,...,n, o the LSS is independent o, while a lower SUi) is achieved as increases. This accordingly results in an invariant inal FAP,j, i,,...,n, j,, over, but a lower inal MDP m,j is achieved with the increased. Bounds o FAPs and MDPs: According to Remark, there is a signiicant impact o the number o SUs on FAPs and MDPs o two CSS schemes in CWRNs. For the sake o providing insightul meanings o the above derived expressions or the FAPs and MDPs o the two CSS schemes, let us investigate a speciic scenario o identical channels, i.e. PS i, ss, S if, rp, FS i, bw, 8i = 1,,...,N. Thus, rom 1) and 13), we can rewrite # i,1 = # 1 and # i, = #. We then have the ollowing indings: Lemma 4. When the number o SUs is very large, i.e. N!1, FAP and MDP o scheme 1 approach,1 N1 and, respectively, where,1 N1 bw, 7) = bw. 8) Proo: As N!1, rom Lemma 1, it can be seen that! 1 and FC)! 0. Substituting into 1) and ), we obtain,1 N1 and as shown in 7) and 8). Lemma 5. When the number o SUs is very large, i.e. N!1, FAP and MDP o scheme approach, N1 and m, N1, respectively, where l, ) u, ) l, ), N1 bw ) ) bw, 9) m, N1 =1 # 1 # ) bw 1 # 1 # ) bw. 30) Proo: Similar to the proo o Lemma 4, we substitute! 1 and FC)! 0 into 3) and 4), and thus obtain, N1 and m, N1 as shown in 9) and 30). Remark 4 Lower MDP Bound with Scheme and Approximately Similar FAP Bounds). In act, rom 8) and 30), it can be easily shown that m, N1 <, which means a lower MDP bound is achieved with scheme. Considering the FAP bound, it is noted that l, ) ) as = "/ 0)!1. Also, we have bw bw < 1. Thus, rom 9), we have, N1 1 bw =,1 N1. This accordingly means that both schemes approach the same FAP bound as the number o SUs is very large. IV. NUMERICAL RESULTS In this section, we evaluate the FAP and MDP perormance o CSS schemes in CWRNs, including Scheme 1 - Non-combined scheme: There is no combination o decisions at the SUs over BW links. Scheme - Combined scheme: There is a binary combination o decisions at the SUs over BW links. Speciically, the analytical ormulations derived or the FAP and MDP o the above two CSS schemes as well as observations deduced in the previous section are now discussed and validated =3,m rp Scheme 1 simulation),m rp Scheme 1 analysis) Scheme simulation) Scheme analysis) P Fig. : Perormance comparison o two CSS schemes. Fig. shows the MDP against the FAP o two CSS schemes with respect to various ading parameters and various values o the energy threshold. We assume there are 10 SUs i.e. N = 10) and the time-bandwidth product o the energy detector is =5. The SNRs o the channels are set as ollows: { PSi } = {10, 8, 9, 1, 5, 7, 8, 4,, 6} db, { SiF } = {8, 7, 10, 4, 6, 8, 9, 11, 8, 10} db and { FSi } = {10, 11, 13, 9, 8, 14, 11, 10, 1, 7} db. Two Nakagami-m ading scenarios NFSs) are considered: i) =3, m rp = m bw and ii), m rp = m bw. It can be observed in Fig. that, at a given energy threshold in either NFS, scheme achieves a lower MDP than scheme 1, while a lower FAP is achieved with scheme 1 compared to scheme. This observation conirms the statement in Remark 1 regarding the lower FAP with scheme 1 and the lower MDP with scheme. Additionally, in Fig., the analytical results o the FAP and MDP or both CSS schemes derived in Lemmas and 3 are shown to be consistent with the simulation results. Investigating the impact o Nakagami-m ading parameters on the sensing perormance o the CSS, Fig. 3 plots the MDP versus FAP o scheme with respect to various NFSs 4 : NFS1):, m rp = m bw NFS):, m rp = m bw NFS3):, m rp = m bw 4 The impact o the ading parameters on the sensing perormance o scheme 1 can be similarly observed, and thus is omitted or brevity.

7 ,m rp,m rp,m rp,m rp =4 =4,m rp Increased Increased m rp or m bw ) P Fig. 3: Perormance o CSS scheme with various NFSs. NFS4):, m rp = m bw =4 NFS5): =4, m rp = m bw A total o 10 SUs is considered and the SNRs o the SS, RP and BW channels are similarly set as in Fig.. Let us irst evaluate the impact o RP and BW channel parameters. As shown in Fig. 3, given ixed e.g. NFS1) vs NFS) or NFS3) vs NFS4)), both the MDP and FAP are improved as m rp or m bw ) increases. Considering the scenario o ixed m rp and m bw e.g. NFS1) vs NFS3) or NFS) vs NFS5)), it can be observed that only a lower MDP is achieved as increases, while the FAP is unchanged or all values o the energy threshold. These above comparisons veriy the statement in Remark 3 regarding the impact o the Nakagami-m ading parameters o the SS, RP and BW channels on the sensing perormance. P Upper bound Scheme 1 with,m rp Scheme with,m rp = Scheme 1 with,m rp Scheme with,m rp N Fig. 4: FAP o CSS schemes over the number o SUs Lower bounds Scheme 1 with,m rp Scheme with,m rp Scheme 1 with,m rp Scheme with,m rp N Fig. 5: MDP o CSS schemes over the number o SUs. Taking into consideration the impact o the number o SUs on the sensing perormance o various CSS schemes, as shown in Figs. 4 and 5, the FAP and MDP o the two aorementioned CSS schemes are plotted as unctions o the number o SUs i.e. N). The SNRs o the SS, RP and BW links are set as 8 db, 10 db and 1 db, respectively. We consider two NFSs: i), m rp = m bw and ii), m rp = m bw. It can be observed in Figs. 4 and 5 that both schemes approach the similar FAP upper bound as N is large, while the MDP o scheme approaches a lower MDP bound in both NFSs. This accordingly veriies the statements in Remarks and 4 about the MDP lower bound and the FAP upper bound with a large number o SUs. Additionally, the FAP and MDP o the two CSS schemes are shown to approach the bounds given by 7), 8), 9) and 30) in Lemmas 4 and 5. V. CONCLUSIONS In this paper, we have analysed the sensing perormance o two CSS schemes or CWRNs considering the practical scenario where all SS, RP and BW channels suer rom Nakagami-m ading and background noise. The combined CSS scheme scheme ) has been shown to achieve an improved MDP while causing a higher FAP when compared to the noncombined CSS scheme scheme 1). As the number o SUs is very large, the perormance bounds have shown that both schemes approach the similar FAP upper bound and the MDP lower bound o the combined scheme is still smaller than that o the non-combined scheme. Furthermore, the derived expressions relect well the impact o the Nakagami-m ading parameters o various links on the sensing perormance. Both the MDP and FAP are improved as the ading parameters o the RP and BW channels increase, while the increased ading parameters o SS channels only results in a lower MDP. REFERENCES [1] S. Haykin, Cognitive radio: brain-empowered wireless communications, IEEE J. Sel. Areas Commun., vol. 3, no., pp. 01 0, Feb [] K. Loa, C.-C. Wu, S.-T. Sheu, Y. Yuan, M. Chion, D. Huo, and L. Xu, IMT-advanced relay standards [WiMAX/LTE update], IEEE Commun. Mag., vol. 48, no. 8, pp , Aug [3] S. Sharma, Y. Shi, Y. Hou, and S. Kompella, An optimal algorithm or relay node assignment in cooperative ad hoc networks, IEEE/ACM Trans. Netw., vol. 19, no. 3, pp , Jun [4] Q.-T. Vien, H. X. Nguyen, O. Gemikonakli, and B. Barn, Perormance analysis o cooperative transmission or cognitive wireless relay networks, in Proc. IEEE GLOBECOM 013, Atlanta, Georgia, USA, Dec. 013, pp [5] G. Ganesan and Y. Li, Cooperative spectrum sensing in cognitive radio, part I: Two user networks, IEEE Trans. Wireless Commun., vol. 6, no. 6, pp , Jun [6] W. Zhang and K. Letaie, Cooperative spectrum sensing with transmit and relay diversity in cognitive radio networks, IEEE Trans. Wireless Commun., vol. 7, no. 1, pp , Dec [7] Q.-T. Vien, H. Tianield, and B. G. Stewart, Eicient cooperative spectrum sensing or cognitive wireless relay networks over Rayleigh lat ading channels, in Proc. IEEE VTC 01-Spring, Yokohama, Japan, May 01, pp [8] W. Braun and U. Dersch, A physical mobile radio channel model, IEEE Trans. Veh. Technol., vol. 40, no., pp , May [9] A. Sheikh, M. Abdi, and M. Handorth, Indoor mobile radio channel at 946 MHz: Measurements and modeling, in Proc. IEEE VTC 93, Secaucus, NJ, USA, May 1993, pp [10] A. Ghasemi and E. S. Sousa, Opportunistic spectrum access in ading channels through collaborative sensing, J. Commun., vol., no., pp. 71 8, Mar [11] F. F. Digham, M.-S. Alouini, and M. K. Simon, On the energy detection o unknown signals over ading channels, IEEE Trans. Commun., vol. 55, no. 1, pp. 1 4, Jan [1] I. S. Gradshteyn and I. M. Ryzhik, Table o Integrals, Series, and Products, 7th ed. Academic Press, 007. [13] H. Shin and J. H. Lee, On the error probability o binary and M-ary signals in Nakagami-m ading channels, IEEE Trans. Commun., vol. 5, no. 4, pp , Apr. 004.