Jont Spectrum Sensng and Resource Allocaton for OFDM-based Transmsson wth a Cogntve Relay S. Eman Mahmood 1 K.P. Subbalakshm 1 R. Chandramoul 1 Bahman Abolhassan 1 Department of Electrcal and Computer Engneerng Stevens nsttute of Technology Hoboken NJ USA Department of Electrcal Engneerng ran Unversty of Scence and Technology Tehran ran Abstract n ths paper we nvestgate the ont spectrum sensng and resource allocaton problem to maxmze throughput capacty of an OFDM-based cogntve rado lnk wth a cogntve relay. By applyng a cogntve relay that uses decode and forward (D&F we acheve more relable communcatons generatng less nterference (by needng less transmt power and more dversty gan. n order to account for mperfectons n spectrum sensng the proposed schemes ontly modfy energy detector thresholds and allocates transmt powers to all cogntve rado (CR subcarrers whle smultaneously assgnng subcarrer pars for secondary users (SU and the cogntve relay. Ths problem s cast as a constraned optmzaton problem wth constrants on (1 nterference ntroduced by the SU and the cogntve relay to the PUs; ( mss-detecton and false alarm probabltes and (3 subcarrer parng for transmsson on the SU transmtter and the cogntve relay and (4 mnmum Qualty of Servce (QoS for each CR subcarrer. We propose one optmal and two suboptmal schemes all of whch are compared to other schemes n the lterature. Smulaton results show that the proposed schemes acheve sgnfcantly hgher throughput than other schemes n the lterature for dfferent relay stuatons. Receved on 11 November 013; accepted on 15 March 014; publshed on 11 Aprl 014 Keywords: cogntve rado power allocaton spectrum sensng subcarrer parng cogntve relay OFDM. Copyrght 014 S. Eman Mahmood lcensed to CST. Ths s an open access artcle dstrbuted under the terms of the Creatve Commons Attrbuton lcense (http://creatvecommons.org/lcenses/by/3.0/ whch permts unlmted use dstrbuton and reproducton n any medum so long as the orgnal work s properly cted. do:10.4108/ws.1.1.e4 between PUs and the CR was calculated for power 1. ntroducton allocaton assumng OFDM for the PU transmsson Cogntve rado networks (CRNs have been envsoned to provde effcent utlzaton of spectra for the secondary (unlcensed users(sus wthout affectng the performance of the prmary users (PUs who as well. Also n [6] a new opportunstc scheme for resourceallocatonwasexpressedbasedonnterference cancellaton.nourprevouswork[7]wedervedthe transmtpowerallocatonswthouttheassumptonsof are the prmary lcensees of the spectrum [1]. perfect knowledge of nterference ntroduced by the Orthogonal Frequency Dvson Multplexng (OFDM s consdered the most approprate modulaton scheme for secondary users [] [3]. Power allocaton for PUs to the SUs. Also several pror works n ths area [4-7] assumed perfect channel sensng whch also s not guaranteed n practce. n [8] by adustng the capacty maxmzaton of an OFDM based CRN sensngthresholdontsensngandresourceallocaton whle keepng the nterference from the cogntve rado (CR to the PUs below a gven threshold was consdered n [4]. n [5] the mutual nterference power s performed. There s a trade-off between achevng maxmum throughput of the CRN and guaranteeng the qualty-of-servce (QoS of the PUs. By accessng more OFDM subchannels the CRN obtans hgher Correspondng author. smahmood@stevens.edu throughput and also ntroduces nterferences caused 1
by the mss-detecton. So ont resource allocaton and sensng thresholds selecton s needed to acheve optmum performance. However [8] assumed that both PUs and the CR use OFDM and that the transmt power levels for spectrum sensng at each of the OFDM subchannels are known. n ths paper we allocate transmt power under more practcal consderatons where the sensng mechansms may lead to false alarms and mss probabltes. Decode and Forward (D&F relayng has been shown to acheve more relable transmssons even at lower transmt power levels thereby allowng for less nterference to the PUs [9]. n ths paper we show that by applyng D&F relay we can acheve hgher precson n spectrum sensng and we call such a relay cogntve relay. Here spectrum sensng s performed by the cogntve relay and the sensng thresholds are updated n the frst tme slot transmsson [10]. A cogntve relay network under fadng channels has been proposed [11] where better spectrum opportunty utlzaton has been acheved va hgher dversty gan (and therefore hgher system complexty although under the assumptons of perfect spectrum sensng results. A two pronged approach where mperfect soft sensng and a sensng update has been used to allevate the problem of sensng errors n [1] and [13]. n [1] the SU adapts the transmt power based on the detecton and false alarm probabltes. n our prevous work [13] we maxmzed throughput of the CRN by consderng constrants on nterference and total power for multuser CRN under mperfect sensng condtons characterzed by false alarm probabltes. Management of CR subcarrers s another problem n the cogntve relay transmsson. The cogntve relay can decode and forward data on the same CR subcarrer used by the secondary node [14-16]. However a more effcent soluton s to reconsder throughput capacty maxmzaton of the CRN by CR subcarrer allocaton for the cogntve relay. Ths means that the cogntve relay may not apply the same CR subcarrer as the SU transmtter (TX [17]. Thus two OFDM subcarrers are pared n the frst and second tme slot durng the transmsson by the SU TX and the cogntve relay respectvely. The goal of ths paper s to maxmze the throughput capacty of the CRN by ontly allocatng transmt power levels sensng spectrum (updatng the values of energy detector thresholds and parng CR subcarrers to the SU TX and cogntve relay. Constrants of ths optmzaton problem are: keepng the total nterference ntroduced by the SU and cogntve relay below a gven threshold keepng mss-detecton and false alarm probabltes n each CR subcarrer below a specfed threshold consderng subcarrer parng for subcarrer pars of the SU and cogntve relay and provdng a lower bound on transmt power levels for CR subcarrers. Frst convexty of ths optmzaton problem s verfed. Then usng Lagrange formulaton constrants dualty [18] takng subgradent method [19] and applyng a greedy method ths problem wll be solved. We wll then propose low complexty suboptmal schemes and evaluate them. The rest of ths paper s organzed as follows. Secton descrbes the system model. Secton 3 formulates the optmzaton problem by nterference modelng. Secton 4 proposes the man scheme for ont power allocaton spectrum sensng and subcarrer parng. Secton 5 ntroduces the suboptmal and other schemes comparable to the man proposed scheme. Secton 6 dscusses smulaton results by comparng fve schemes wth each other. Fnally Secton 7 concludes the paper and the expected future works are expressed.. System Model n ths paper we consder a two tme slot D&F relay CRN consstng of a SU transcever and a cogntve relay both of whch coexst wth a number of PUs. n addton to relayng transmtted data streams the cogntve relay also performs wdeband spectrum sensng wth N energy detecton thresholds for the N OFDM subcarrers. Fg. 1 depcts the system model. n the frst tme slot we observe that the SU TX sends data on subcarrer whle the cogntve relay and SU recever (RX receves the data. Then the cogntve relay whch employs D&F transmts decoded data n the second tme slot on subcarrer whle the SU RX receves data. Snce data transmsson of the SU TX and cogntve relay occurs n dfferent tme slots there
s no nterference between them. The SU RX apples Maxmum Rato Combnng (MRC to obtan data by explotng spatal dversty. The cogntve relay must decde whch subcarrer to use for data transmsson based on ts channel sensng results. So the cogntve relay may not transmt data n the same subcarrer that the SU TX used. We assume the tme slots are of the same duraton and the coherence tme of channels are much longer than the tme between CS updates hence channel gans (h (ab m n subcarrer m between TX a and RX b n Fg. 1 do not change whle data transmsson perod once t s measured. Also we assume that the sensng perods are smaller than the swtchng tme of the PUs actvtes. n ths paper we mprove the relablty of spectrum sensng results along wth power allocaton and subcarrer parng. To perform wdeband spectrum sensng energy detectors are used for each CR subcarrer. Energy detecton thresholds (λ 1 λ λ N are appled on each of the N CR subcarrers for spectrum sensng [0]. Let the fadng channel gan between the prmary TX and cogntve relay n subcarrer be h (pr. As shown n [0] based on Neyman- Pearson crteron the probabltes of false alarm and detecton n subcarrer are respectvely gven by p f (λ Q( λ Mσn Mσ and p d (λ Q( n λ M(σ n + h (pr Mσ n (σ n + h (pr where M denotes the number of prevous receved samples taken n the cogntve relay for spectrum sensng and σn represents the varance of Addtve Whte Gaussan Nose (AWGN channel. Let the rato of channel gan to nterference power ntroduced by L OFDM subchannels of PUs n subcarrer m from TX a atrxb beγ m (ab. Then γ (sr h (sr σ s + L l1 J (pr(l γ (ss h (ss σ s + L l1 J (ps(l γ (rs h (rs σ s + L l1 J (ps(l where we assume the same AWGN varance σs for all three lnks and L denotes the number of OFDM subchannels occuped by PUs. The nterference power ntroduced by PU s subchannel l to the CR subcarrer s gven by J (ps(l h (ps l Δ l + Δf Φ Δ l Δf PER (wdw [1] where the expected perodogram s Φ PER (w 1 +π πk π φ(l PU (ew ( sn((w νk/ sn((w ν/ dν K s the Fast Fourer Transform (FFT sze of the perodogram w s the normalzed frequency Δ l s the spectral dstance between Secondary transmtter th Prmary transmtter 1 st tme slot nterference to PUs 1 st tme slot (sr Cogntve Relay nd tme slot nterference to PUs Secondary recever th Prmary recever Fgure 1. System Model of the CRN n Two Tme Slot Transmsson. CR subcarrer and PU s subchannel l and φ (l PU s the power spectrum densty (PSD of PU s subchannel l. The achevable weghted rate wth an deal codng scheme for subcarrer par SP( can be expressed as R Δfρ log (1 + γ P where Δf and ρ are the frequency space of OFDM subcarrers and weght factor for subcarrer respectvely [14]. The weght factors are taken nto consderaton to reflect dstnct QoS requrements for each subcarrer n the CRN. Note that ρ s dependent only on CR subcarrer whch s used by the SU TX. γ s the equvalent channel gan of SP( and P s the sum of two powers: the transmt power of SU TX n subcarrer when the cogntve relay s transmttng n subcarrer (P (1 and the transmt power of the cogntve relay n subcarrer when the SU TX s transmttng n subcarrer (P ( P P (1 + P (. The communcatons n our model can ether follow the drect mode or relay mode dependng on whether the channel gans to nose rato (γ s s favorable (relay or not (drect. As n [] the power levels and equvalent channel gan to nose plus nterference rato for SP( n the relay lnk (f γ (sr γ (ss & γ (rs γ (ss are formulated by P (1 P ( γ γ (sr γ (sr γ (sr γ (rs +γ (rs γ (sr γ (ss +γ (rs γ (sr γ (rs +γ (rs P γ (ss γ (ss γ (ss. P (1 3
Otherwse for the drect lnk transmsson we have P (1 P P ( 0 γ γ (ss. 3. nterference Modelng and Problem Formulaton We defne an obectve functon for the transmsson lnk on SP( as A B that gves us a sense of both the throughput (A and the capacty (B where A (1 p f (λ (1 p f (λ and B Δf ρ log (1 + γ P. A ncreases as the false alarm decreases ust as we would expect the throughput of the system to do. So n a sense A s related to the throughput. B s a measure of the capacty of the system n transmsson of SP(. Hence the obectve functon for SP( s defned as: C q (1 p f (λ (1 p f (λ Δfρ log (1 + γ P (3 where q s an ndcator functon takng on a value 1 when the SP( s used and zero otherwse. Note that Eqn. (3 has three sets of unknown parameters: the equvalent transmt power levels (P subcarrer parng ndcators (q and energy detector thresholds (λ 1... N. The obectve functon s dscrete because the selecton of subcarrer pars s dscrete. n order to deal wth ths we apply contnuous relaxaton to ths bnary constrant (q by wrtng the obectve functon for SP(as C q (1 p f (λ (1 p f (λ Δfρ ( log (1 + γ P q (4 where the bnary constrant changes to: q 0 0 1...N [3]. As llustrated n Fg. 1 the nterference s ntroduced to the PUs by each secondary node transmsson (ether the th subcarrer of the SU TX or the th subcarrer of the cogntve relay. These nterference power levels can be calculated as P (s Ll1 N1 P (1 φ(l s and P(r L N1 l1 P ( φ(l r respectvely. The nterference power spectral denstes ntroduced by CR subcarrer on the prmary subchannel l s gven by φ (l s h(sp l Δl +B T l / s df φ (l r Δ l B l / ( sn(πf T s πf T s h (rp l Δl +B T l / s Δ l B l / ( sn(πf T s πf T df can be calculated assumng deal Nyqust transmtted pulse [1] and OFDM s symbol duraton T s. One of the man constrants n ths optmzaton problem s to keep the nterference power ntroduced by SU and the cogntve relay below the specfed nterference power threshold (P (th. So we consder P (s P (th and P (r P (th whch can be rewrtten as a functon of P by where N1 Ll1 { N 1 P Φ s(l N1 Ll1 { N 1 P Φ r(l Φ s(l Φ r(l γ (sr γ (sr } P (th } P (th. γ (rs +γ (rs γ (ss γ (sr γ (ss +γ (rs γ (ss φ (l s (5 φ (l r. (6 The obectve functon whch s called throughput capacty n ths paper s maxmzed over P q λ: max N1 N1 Δfρ q P qλ (1 p f (λ (1 p f (λ ( P log 1+γ q subect to the connectons n Eqn (5 and: (7 1 p d (λ α 1.. N (8 p f (λ β 1.. N (9 N q 1 1.. N (10 1 N q 1 1.. N (11 1 P ν 1.. N P 0 (1 q 0 1.. N (13 λ 0 1.. N. (14 n Eqn (7 P and q are (N N matrces wth entres (P q 1... N and λ [λ 1 λ...λ N ]. The constrants n Eqns (8 and (9 show that the mssdetecton and false alarm probabltes for each CR subcarrer by the assgned energy detector thresholds 4
4.1. The Dual Problem Precse Spectrum Sensng ntal Spectrum Sensng Applyng Channel Condtons for Relayng Subcarrer Parng Fgure. Flowchart of the proposed scheme. Power Allocaton should be kept below gven thresholds to provde both effcent performance of the CRN and convexty of the problem. Also Eqns (10 and (11 respectvely denote that for each of the N number of CR subcarrers allocated to the cogntve relay only one CR subcarrer can be used for the SU TX and for each of CR subcarrers allocated to the SU TX only one CR subcarrer can be used for the cogntve relay. We know that each of P s should be nonnegatve but the constrant n Eqn (1 s used to the convexty of the problem. The proof of the convexty of ths optmzaton problem wth all ts constrants s gven n the Appendx. 4. Jont Subcarrer Parng Power Allocaton and Spectrum Sensng Our obectve s to maxmze throughput capacty (gven by Eqn (7 of the cogntve relay network by ont power allocaton on the qualfed subcarrer parng and spectrum sensng. Fg. llustrates a flowchart of the communcaton procedure from the vew pont of TX to provde an effcent transmsson. Frst the CR obtans an ntal spectrum sensng output from the cogntve relay to know whch OFDM subchannels are dle. Then usng the channel nformaton and applyng Eqns (1 and ( the decson on whether to take a drect lnk or a relay lnk s made. The optmzaton problem s then solved for the optmum transmt power levels energy detector thresholds and subcarrer pars. By applyng Karush-Kahn-Tucker (KKT condtons n the convex optmzaton takng subgradent method n the dual problem and usng an teratve algorthm the optmzaton problem can be solved. We frst obtan Lagrangan formulaton of the obectve functon gven by Eqn (7 and normalzed to the bandwdth as C(P q ληκτ μ δ 1 N1 N1 {ρ q (1 p f (λ (1 p f (λ log (1 + γ q P } + η(p (th + κ(p (th L l1 N1 N1 P Φ s(l L l1 N1 N1 P Φ r(l N 1 τ (1 N 1 q + N 1 μ (β p f (λ + N 1 δ (p d (λ 1+α. (15 where ηκ are Lagrange multplers for the constrant n Eqn (5 and τ μ δ are Lagrange vectors for the constrants n Eqns (10 (9 and (8 respectvely. For convenence we assume the same threshold for mss detecton and fales alarm probabltes n each subcarrer (α α and β β. The constrant n Eqn (11 s studed n the proposed algorthm n Subsecton 4. whch smultaneously consders the satsfacton of ths constrant wth the other constrants. To maxmze the throughput capacty for each SP( gven by Eqn (4 wth respect to transmt power levels we equate C 0: P C P ρ γ (1 p f (λ (1 p f (λ 1+( γ η( L q P l1 Φ s(l κ( L l1 Φ r(l 0. (16 We see that effect of the constrant n Eqn (11 s not consdered n ths formulaton and the obectve functon s maxmzed by optmzng over two Lagrange varables. We solve the dual optmzaton problem wth respect to Eqn (1 and smplfyng Eqn (16 toget P q [ν ρ (1 p f (λ (1 p f (λ η( L l1 Φ s(l +κ( L l1 Φ r(l 1 γ ] + (17 where [x y] + max(x y. Snce the power s dependent on the energy detector thresholds and the subcarrer par selecton we ontly optmze these parameters. Also accordng to Eqn (1 the power may be zero for some subcarrer pars. From Eqn (17 we see that ths occurs when q 0. 5
S.E.Mahmoodetal. For spectrum sensng we acheve the values of energy detector thresholds over N CR subcarrers whch are used ether by SU TX or the cogntve relay n transmsson. So the obectve functon gven by Eqn (3 s consdered for one set of N CR subcarrers (for 1... N. Then smplfed formulaton for Eqn (15 s wrtten as C 1 N1 (1 p f (λ log (1 + γ P +η(p(th L N1 N1 l1 P +κ(p (th Φs(l L l1 N1 N1 P Φr(l + N 1 τ (1 N 1 q + N 1 μ (β p f (λ + N 1 δ (p d (λ 1+α. (18 Then to obtan λ wehave C (μ + R e x δ λ 4πMσ + e y n 4πMσn (σn +E( s h (pr (19 where x λ Mσ n Mσ n y λ M(σn +E( s h (pr Mσn (σn +E( s h (pr the normalzed rate of CR subcarrer ; R Δ 1 log (1 + γ [ e 1 1 γ η L l1 Φ s(l +κ L l1 Φ r(l By settng Eqn (19 to zero we have y x and Eqn (1 smplfes to ( λ M(σn +E( s h (pr Mσn (σn +E( s h (pr ln( σ n ξ σ n +E( s h (pr ( λ Mσ n Mσ n and R 1 γ ] +. s (0 ( where the two Lagrange multplers δ and μ are combned and gven by ξ δ.we set μ μ + R 0 n Eqn (3 and by settng a lower bound to satsfy the false alarm constrant gven by Eqn (9 we obtan λ max((q 1 (β M + Mσn λ. (4 We now obtan the optmal subcarrer par ndcators (q s. By substtutng the allocated transmt power levels gven by Eqn (17 nto Eqn (15 we have where C N N1 1 q Ω +((η + κp (th + N 1 τ + N 1 μ (β p f (λ + N 1 δ (p d (λ 1+α (5 Ω ρ log (1 + γ [ν τ η L l1 Φ s(l [ν κ L l1 Φ r(l [ν ρ (1 p f (λ (1 p f (λ η L l1 Φ s(l +κ L l1 Φ r(l ρ (1 p f (λ (1 p f (λ η L l1 Φ s(l +κ L l1 Φ r(l ρ (1 p f (λ (1 p f (λ η L l1 Φ s(l +κ L l1 Φ r(l 1 γ ] + 1 γ ] + 1 γ ] +. (6 As can be seen from Eqn (5 to maxmze throughput capacty of the CRN over subcarrer pars Ω (for 1... N 1... N should be maxmzed. So q s assgned as δ ln( μ + R q ln( 1 arg max Ω 1... N (7 4πMσn (σn +E( s h (pr 4πMσ 0 otherwse 1... N. n (1 However the subcarrer pars obtaned by Eqn (7 do not necessarly satsfy the constrant n Eqn (11 n whch only one CR subcarrer could be allocated for the cogntve relay n each par. Ths problem wll be solved n the followng secton by applyng a greedy method n the proposed algorthm. where ξ δ. By solvng Eqn (14 two values for μ + R λ are obtaned and only one of them s nonnegatve (Constrant (19 and acceptable whch s gven by λ [ Mσ n s h (pr M s h (pr {(σ4 n +σn s h (pr 8σn ln( σnξ σ n + s h(pr Mσ 6 n (σ n + s h (pr ] 1/ + s h (pr } (3 4.. Algorthm Desgn n the prevous subsecton all optmal transmt power levels and subcarrer pars were allocated and energy detector thresholds were obtaned by maxmzng the throughput capacty gven by Eqn (7 subect to constrants expressed n Eqns (6 and (8 to (14 except (11. The constrant n Eqn (11 specfes that each subcarrer should be allocated to one subcarrer par for the cogntve relay transmsson. n order 6
to obtan optmal values for transmt power levels and energy detector thresholds as well as optmally par subcarrers and also satsfy Constrant (11 and explot approprate Lagrange multplers we propose an teratve algorthm whch s shown n by Algorthm 1. Algorthm 1 Proposed ont sensng subcarrer parng and power allocaton. 1: ntalze Lagrange multplers (for teraton: k1 : whle all Lagrange multplers have hgher errors than ɛ do 3: compute λ s by Eqn. (4 4: compute Ω s by Eqn. (6 5: compute q s by Eqn. (7 6: codfy q s by Greedy method 7: compute P s by Eqn. (17 8: modfy the values of Lagrange multplers by 9: η (k+1 η (k ε (k N1 Ll1 { N 1 P (k 10: κ (k+1 κ (k ε (k N1 Ll1 { N 1 P (k τ (k ε (k 11: τ (k+1 1: μ (k+1 13: δ (k+1 14: k k +1 15: end whle 1 (P(th Φ s(l } 1 (P(th Φ r(l } (1 N 1 q (k 1... N μ (k ε (k 3 [β p f (λ (k ] δ (k ε (k 4 [p d(λ (k 1+α] Algorthm Greedy method to acheve q by satsfyng constrant (11. 1: t( N 1 q 1... N : for u 1:N do 3: f t(u > 1 then b arg max bu b q bu 1 4: end f 5: whle t(u > 1 do 6: arg mn u τ c arg t(0 7: t(u t(u 1t( t(+1 8: q(c u 0q(c 1 9: end whle 10: end for max b q cu 1 cb Ω c n the proposed algorthm we apply a greedy method smlar to [17 4] for satsfyng Eqn (11 whch s shown by Algorthm. n summary to maxmze Eqn (7 the greedymethodfndsthe columnsofq wth total value of more than one. Then t places ones to the columns wth sum value of zero whle the mnmum devaton to Lagrange multpler τ (for 1.. N s generated. Through ths process we acheve the mnmum decrease n Ω (for 1.. N n the throughput capacty (Eqn (7 of the CRN. 4.3. Complexty Analyss By applyng the above algorthm we ontly optmze the spectrum sensng power allocaton and subcarrer parng n the cogntve relay network. We now compare the complexty of ths algorthm wth that of exhaustve search. Exhaustve search for subcarrer parng has a complexty O(N! and for each fx subcarrer par the complexty of power allocatons accordng to Eqn (17 and energy detector thresholds s O(NlogN. Hence the complexty for exhaustve search s O(N.logN.N! whch could be smplfed to O(N.N!. However by applyng the proposed algorthm the complexty s O(N.logN per teraton. The number of teratons on the algorthm wll depend on the value of ε. Total complexty of ths algorthm wll be O(N.logN (number of teratons. Clearly ths s much smaller than the exhaustve search method. 5. Suboptmal and Classcal Schemes n ths secton we propose a suboptmal scheme (n subsecton 5.1 and ntroduce three classcal schemes (n subsectons 5. 5.3 and 5.4 for the throughput capacty maxmzaton of the CRN whch s gven by Eqn (7 wth lmted nterference threshold on PUs. All these schemes are compared usng smulatons. 5.1. Alternate Suboptmal Scheme n ths scheme we propose a suboptmal soluton by smplfyng the method of fndng the Lagrange multplers η and κ to calculate energy detector thresholds. To do ths we consder a fxed Lagrange multpler denoted by η and κ and then compute the energy detector thresholds for spectrum sensng. Usng these thresholds transmt power levels and subcarrer pars are calculated. Fnally energy detector thresholds are modfed wth correspondng updated Lagrange multpler for power allocaton (η and κ. Although ths could cause a loss n the throughput capacty the number of smultaneous varables to be calculated 7
S.E.Mahmoodetal. decreases and therefore the system complexty reduces. For explotng the normalzed rate we frst consder a unform power dstrbuton and accordng to Eqn (5 we fnd η and κ for subcarrer pars wth nonzero powers. Then by consderng the boundary condtons n Eqn (5 and replacng P wth RHS of Eqn (17 and assumng p f (λ p f (λ 0 we wrte N1 Ll1 { N 1 ( N1 Ll1 { N 1 ( ρ η ( L l1 Φ s(l +κ ( 1 L l1 Φ r(l γ } P (th Φ s(l ρ η ( L l1 Φ s(l +κ ( 1 L l1 Φ r(l γ } P (th Φ r(l (8 and from Eqn (8 η andκ are obtaned. As well ntal energy detector thresholds are calculated by ths η and κ based on Eqn (4. Then resource allocaton s performed by one teraton of step up to step 7 shown n Algorthm 1. Fnally modfed energy detector thresholds are calculated by new updated η and κ obtaned by one teraton of the algorthm. 5.. Fxed Subcarrer Parng (SCP based Scheme Lke [14] we consder a fxed assgnment for subcarrer parng n ths scheme. n ths scheme the assgned subcarrer for the frst tme slot wll be also used n the second tme slot. So we allocate power levels as P P [ν X 1 γ ] + (9 where X s the water level and t s based on the Lagrange multplers η and γ and the false alarm probablty over CR subcarrer. So t s gven by X ρ (1 p f (λ η( L l1 Φ s(l +κ( L l1 Φ r(l. (30 5.3. Resource Allocaton Based on ntal Spectrum Sensng (SS n ths suboptmal scheme we consder that spectrum sensng s performed by ntal sensng results wthout updatng the energy detector thresholds to obtan false alarm probabltes p f (λ 1...N for each CR subcarrer based on [0]. Then we ontly allocate transmt power levels usng Eqn (17 and manage subcarrer pars usng Eqn (7. 5.4. Classcal Scheme Wthout use of the Cogntve Relay (WCR Eventually we compare the proposed schemes wth a classcal scheme wthout use of the cogntve relay. n ths scheme transmt power s dstrbuted accordng to the waterfllng scheme [5]. Based on Eqn (5and wth regards to the gven nterference power threshold the water levels are obtaned. The power allocated to CR subcarrer s gven by and ϖ s found by solvng L l1 1 P [0 1 ϖ 1 N [0 1 ϖ 1 γ (ss γ (ss ] + (31 ] + φ (l s P(th. (3 So the nterference constrant for the CRN s satsfed. By consderng ths constrant the soluton whch has been obtaned n [4] s acheved. Note that spectrum sensng s performed lke the prevous scheme and false alarm and mss detecton probabltes are obtaned usng [0]. 6. Smulaton Results n ths secton smulaton results are presented and dscussed. The performance of the man proposed scheme ntroduced n Secton 4 s compared wth those of the other four schemes descrbed n Secton 5. We assume that the number of CR subcarrers (N PU occuped channels(l and prevous receved samples taken n the cogntve relay for spectrum sensng (M are 16 48 and 3 respectvely. n ths system model we consder an OFDM-based CR wth cogntve relayng whch coexsts wth three PUs. Also the CRN uses the ntal soft sensng results as the three PUs occupy 0 1 and 16 subchannels. Note that n each run of the smulaton these three frequency bands of PUs are randomly dstrbuted through OFDM subchannels. For the OFDM based CRN we assume the OFDM frequency spacng (Δf and symbol duraton (T s to be 0.1565 8
Fgure 3. Throughput capacty of the CRN versus nterference ntroduced to the PUs by several schemes wth E[ γ (sr ]8 E[ γ (ss ]3 and E[ γ (rs ]8. MHz and 7 μs respectvely. AWGN varance n all the channels s assumed to be 10 5 Watts. The PU s transmt power (P PU s consdered to be 5 10 3 Watts. n the proposed algorthm ntal values of δ and τ for each CR subcarrer are randomly dstrbuted between 0.01 and wth step sze of 0.05/ k where k s the teraton ndex. The ntal value for η s randomly dstrbuted between 100 and 00 and ε s assumed to be 10 5. All the communcaton lnks are ndependent of each other n two tme slots and ther channel gans have Raylegh dstrbutons wth gven average channel gans. Except for three channels of h (ss h (rs and h (sr whch have dfferent average channel gans through smulatons the rato of average channel gans to nose plus nterference n other lnks are set to 3. At frst we compare fve schemes n a geographcal stuaton where the cogntve relay s located between the SU TX and RX. So we consder E[ γ (sr ]8 E[ γ (ss ]3 and E[ γ (rs ]8 n Fgs. 3 to 7. Fg. 3 shows the throughput capacty n bts/slot whch s defned n Eqn (7 n terms of nterference power ntroduced to the PUs by the SU TX and the cogntve relay n Watts. n ths fgure α and β are assumed to be 0. and 0.3061 respectvely. As we can see the proposed scheme acheves the hghest throughput for a gven nterference threshold. We also Fgure 4. Maxmum achevable sum rate of the CRN versus nterference ntroduced to the PUs by several. observe that Alternate scheme where the sensng and the ont power allocaton and subcarrer parng are done n two excessve phases performs close to the man proposed scheme. Ths scheme s able to acheve throughout capactes very close to the man proposed scheme but wth more teratons. However decrease of the system complexty n ths scheme s an advantage but should be consdered because t makes the precson of the approach lower. Note that by ncrease of teratons Alternate scheme obtans the throughput close to the man proposed scheme but the system complexty ncreases. The fxed subcarrer parng (SCP based scheme and the scheme based on ntal spectrum sensng (SS acheve less throughput than the proposed scheme and the proposed alternate scheme but acheve more throughput than the scheme wthout use of cogntve relay (WCR. Note that false alarm probablty n SS and WCR based schemes are fxed and assumed to be 0.. We observe that for the nterference equal to 10 3 Watts the man proposed alternate fxed SCP and SS schemes have respectvely 441% 363% 313% and 13% hgher throughput capacty n comparson to WCR. n Fg. 4 we plot the achevable total rate for the CRN versus nterference power ntroduced to the PUs by the SU TX and the cogntve relay. As 9
S.E.Mahmoodetal. Fgure 5. Weghted throughput capacty of the CRN versus nterference ntroduced to the PUs by several schemes. Fgure 6. Throughput capacty of the CRN versus probablty of false alarm threshold by several schemes. expected snce qualty of spectrum sensng (false alarm probablty s not consdered for the achevable total rate performance of the man proposed scheme alternate scheme and SS scheme are very close to each other. However as can be understood from Fg. 3 spectrum sensng results are dfferent n these schemes. We also observe that the fxed SCP and WCR acheve smaller rates compared to those of the other schemes. n Fg. 5 we present the weghted throughput capacty gven by Eqn (7 versus nterference power Fgure 7. Average transmt power of the cogntve relay versus nterference ntroduced to the PUs by CRN by several schemes. ntroduced to the PUs by the SU TX and the cogntve relay. So far we consdered ρ (for all 1...N as unty. However n ths fgure we consder weghted rates such that ρ 1+(-1/(N-1. Ths dstrbuton s only an example for the weghted subcarrers n order to satsfy the QoS requrements n each one. n ths condton we observe that our man proposed scheme acheves hgher throughput capacty for weghted CR subcarrers compared wth those of the other schemes. Moreover we observe that all of the schemes have smulaton results smlar to the smulaton results shown n Fg. 3. n Fg. 6 we plot the throughput capacty n terms of probablty of false alarm threshold. Here th and α are assumed to be 10 3 Watts and 0. respectvely. We see that the throughput of the CRN decreases by ncreasng the false alarm probablty. Fg. 7 presents the total transmt power of the cogntve relay for all CR subcarrers versus the nterference ntroduced to PUs by the SU TX and cogntve relay. We see that by subcarrer parng the man proposed alternate and SS schemes allow for hgher transmt power than that of the fxed SCP scheme for a gven nterference threshold. The fxed SCP does not take dynamc subcarrer parng nto account for the system. Therefore ths scheme allocates lower transmt power to the cogntve relay and acheves less total rate for the CRN. 10
Fgure 8. Throughput capacty of the CRN versus nterference ntroduced to the PUs by several schemes wth E[ γ (sr ]8 E[ γ (ss ]3 and E[ γ (rs ]8 Fgure 9. Throughput capacty of the CRN versus nterference ntroduced to the PUs by several schemes wth E[ γ (sr ]3 E[ γ (ss ]3 and E[ γ (rs ]8 n Fg. 8 we consder the case where the cogntve relay s located close to the SU TX. So we consder E[ γ (sr ]8 E[ γ (ss ]3 and E[ γ (rs ]3. However n Fg. 9 we assume a stuaton n whch the cogntve relay s close to the SU RX and we have E[ γ (sr ]3 E[ γ (ss ]3 and E[ γ (rs ]8. Both of these fgures show optmalty of the proposed schemes. However comparng Fgs 3 8 and 9 we see that the throughput capacty s lower f the cogntve relay s located close to ether the SU transmtter or recever. 7. Concluson and Future Works n ths paper we optmzed the throughput of a CRN wth cogntve relayng by ont spectrum sensng and resource allocaton under OFDM transmsson. An optmzaton problem was formulated and solved whle meetng constrants such as the nterference power ntroduced by the SU and cogntve relay to the prmary system subcarrer parng the mss-detecton and false alarm probabltes n each CR subcarrer. By solvng the optmzaton problem a new teratve algorthm was proposed to obtan energy detector thresholds subcarrer parng and the transmt power levels of the SU and the cogntve relay. Moreover an alternate low complexty suboptmal scheme was also proposed whch acheves a performance close to the man proposed scheme accordng to the smulatons. Smulaton results llustrate that the proposed schemes acheve sgnfcantly hgher throughput capacty and achevable total rate than those of exstng schemes such as fxed subcarrer parng the scheme based on ntal spectrum sensng results and the classcal scheme wthout use of the cogntve relay as presented quanttatvely n Secton 6. The extenson of ths work can be consdered for multple relays wth consderng relay selecton. Then the work should be on the cogntve mult-relay network envronment whle ont optmzaton of power allocaton subcarrer allocaton subcarrer parng and relay selecton s consdered. Furthermore the purpose s to maxmze the weghted sum rate of the network under mutual nterference constrants. Appendx Verfyng the Convexty of Optmzaton Problem For the obectve functon whch s expressed n (7 f C<0 then C s convex and ts Hessan s not postve sem-defnte. We rewrte the obectve functon as C f 1 (P f (λ λ (33 where f 1 (P log (1 + θ P (34 11
S.E.Mahmoodetal. f (λ λ (1 Q( λ Mσ n Mσ n (1 Q( λ Mσ n Mσ n (35 whle θ γ q. As shown n [6] to provde the concavty for f 1 we have γ P > 1.7183 and by followng Eqn (1 ν 1.7183/γ. Also Hessan determnant of f s Δ H f (λ f (λ f (λ f (λ (f (λ f (λ 1 1 +x π x x e x ( 1 +x x +x π e π x x e x {[1 Q(x ][1 Q(x ] 1 πx x e x +x }. (36 We assume that x and x are postve and so the frst term n RHS of Eqn (36 s postve. Snce n ths scenaro we want to obtan the values of energy levels whch are derved from the same where we assgn x x. Ths means that we ontly restrct the value of energy detector thresholds n the SU TX and cogntve relay whle n the case where both of them apply one CR subcarrer {[1 Q(x ] 1 e x πx } s ncreasng and so we can set the possble least value for x to satsfy postvty of the Hessan whch s obtaned by x 0.507. So p f (λ β 0.3061. We see that the result of ths s approxmately the same as the one n [6] whch consders a CR wth no relayng. So by the obtaned values for β and ν the concavty of the obectve functon s acheved. Also for Eqn (8 f α 0.5 snce Q(x s convex then ths constrant s convex. We see that both of the obtaned values for α and β ( are reasonable bounds n practce. Acknowledgment Ths work was supported n part by NSF #0917008 and #0916180. References [1] Haykn S. Cogntve rado: Bran-empowered wreless communcatons. EEE J. Sel. Areas n Commun. 005 Feb; 3(: 01-0. [] Wess S. and Jondral F. K. Spectrum poolng: an nnovatve strategy for the enhancement of spectrum effcency. EEE Commun. Mag. 004 Mar; 43(3: S8-S14. [3] Setoodeh P. and Haykn S. Robust transmt power control for cogntve rado. Proceedngs of the EEE 009 May; 97(5: 915-939. [4] Bansal G. and Hossan M. J. and Bhargava V. K. Optmal and suboptmal power allocaton algorthms for OFDM-based cogntve rado systems. EEE Trans. Wreless Commun. 008 Nov; 7(11: 4710-4718. [5] Zhao C. and Kwak K. Power/bt loadng n OFDM-based cogntve networks wth comprehensve nterference consderatons: The sngle-su case. EEE Trans. Vehcular Tec. 010 May; 59(4: 1910-19. [6] Maham B. Popovsk R. Zhou X. Houngnes A. Cogntve multple access network wth outage margn n the prmary system. EEE Trans. Wreless Commun. 011 Oct; 10(10: 3343-3353. [7] Mahmood S. E. and Abolhassan B. Two new power allocaton schemes for an OFDM cogntve rado wth no knowledge on prmary users nterference. nt. J. Commun. Syst. n Wley 01 Oct; do: 10.100/dac.443. [8] Lm H. and Seol D. and m G. Jont sensng adaptaton and resource allocaton for cogntve rado wth mperfect sensng. EEE Trans. Commun. 01 Apr; 60(4: 1091-1100. [9] Hossan E. and Km D. and Bhargava V. K. (011 Cooperatve Cellular Wreless Communcatons (Cambrdge Unversty Press 1st ed. [10] Zou Y. and Yao Y. and Zheng B. Cogntve transmssons wth multple relays n cogntve rado networks. EEE Trans. Wreless Commun. 011 Feb; 10(: 648-659. [11] Letaef K. B. and Zhang W. Cooperatve communcatons for cogntve rado networks. Proc. EEE. 009 May; 97(5: 878-893. [1] Kang X. B. and Lang Y. and Garg H. K. and Zhang L. Sensng-based spectrum sharng n cogntve rado networks. EEE Trans. Vehcular Tec. 009 Oct; 58(8: 4649-4654. [13] Mahmood S. E. and Kordan S. B. and Abolhassan B. A new algorthm for ont sensng and power allocaton n multuser cogntve rado networks. Proc. EEE Wreless Personal Multmeda Commun. (WPMC. 011 Oct; Brest- France. 41-45. [14] Yng W. and Xn-chun Q. and Tong W. and Bao-lng L. Power allocaton and subcarrer parng algorthm for regeneratve OFDM relay system. Proc. EEE Vehcular Tec. Conf. (VTC 007 Apr; Dubln-reland. 77-731. [15] Wang S. and Huang F. and Ge M. and Wang W. Optmal power allocaton for OFDM-based cooperatve relay cogntve rado networks. EEE nternatonal Conf. Commun. (CC 01 Jun; Ottawa-Canada. 1651-1655. 1
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