Power Minimization in Uni-directional Relay Networks with Cognitive Radio Capabilities

Transcription

1 00 5th Intenational Symposium on elecommunications (IS'00) Poe Minimization in Uni-diectional Relay Netoks ith Cognitive Radio Capabilities Adalan Alizadeh Seyed Mohammad-Sajad Sadough Cognitive elecommunication Reseach Goup Depatment of Electical Compute Engineeing Shahid Beheshti Univesity GC Evin 9896, ehan, Ian Abstact In this ok, e conside a uni-diectional (one ay) elay netok ith a pai of pimay tansmitte eceive hich ae elay-assisted by multiple cognitive adio (CR) teminals A CR base station is deployed to sense the absence/pesence of the pimay use based on the eceived signal-to-noise atio (SNR) at the fusion cente he pimay netok utilizes a to-step one-ay amplify--foad (AF) elaying scheme uses the CRs as its elay nodes In the fist step of AF elaying, the pimay tansmitte sends its signal to the CRs/elays A distibuted beamfoming is then pefomed in the second step of elaying In this phase, the CR base station sets the beamfoming eights of CR teminals to satisfy the SNR equiements at the pimay tansmitte at the CR base station We aim at minimizing the poe dissipated in the cognitive (elay) nodes togethe ith ensuing an accuate spectum sensing pocess his optimization poblem is efficiently solved by using semidefinite elaxation (SDR) techniques Simulation esults ae povided to compae the elay tansmit poe in ou investigated netok ith that in a conventional AF elay netok Cognitive adio, one-ay elaying, convex optimization, distibuted beamfoming, elay netoks, semidefinite elaxation I INRODUCION Cognitive adio (CR) [] is a ne design paadigm to eliminate the poblem of scace spectum esouces in ieless communications CR netok allos a seconday (unlicensed) use to utilize a fequency b aleady allocated to some pimay uses (PU) o pevent hamful intefeence at the pimay eceive, the CR netok senses the licensed spectum constantly to detect the absence/pesence of the pimay tansmitte Recently, the hidden teminal poblem has become a geat challenge fo implementing CRs his happens hen the CR node is shadoed o is in sevee multipath fading [] Coopeation among diffeent cognitive uses is an efficient solution to ovecome the hidden teminal limitation he basic idea behind coopeative communications is pesented in many efeences []-[5] In these netoks, each teminal oks as a elay collaboates ith othe uses to incease the sensing/detection eliability In a to-step one-ay amplify-foad (AF) scheme, thee is a pai of tansmitte eceive that fom the pimay netok In the fist step, the tansmitte sends its signal toads the elays Each elay pocesses its eceived signal multiplies it by a deived beamfoming eight in the second step Recently, distibuted beamfoming has been poposed fo elaying schemes to satisfy some system equiements fo the netok Fo instance, diffeent optimal beamfoming poblems have been pesented in [6] to minimize the tansmit poe to maximize the eceived signal-to-noise atio (SNR) In this pape, e complete ou pevious ok pesented in [7] fo uni-diectional pimay elay netoks hee the main idea is to enable a CR capability fo a conventional elay netok In this model, the CR base station uses the combination of signals fom CR/elays (duing the second step) fo its sensing pupose We deive the optimal beamfoming eights so as to minimize the equied poe at the elay netok subject to SNR constaints on the pimay eceive on the cognitive base station Ou poposed scheme povides to desied featues in each CR netok: i) the SNR constaint at the CR netok ensues an accuate spectum sensing, ii) the poe dissipated at the CR netok is minimized We sho that the investigated beamfoming optimization poblem can be fomulated as a non-convex quadatically constained quadatic pogam (QCQP) [8] hen, the semidefinite elaxation (SDR) is deployed to change the poblem into a convex fom obtain an efficient solution fo the so-obtained convex poblem hen, the poblem is solved by semidefinite pogamming (SDP) II CONSIDERED SCENARIO AND SYSEM MODEL A Cognitive Relay Netok As shon in Fig, ou netok is composed of a pimay tansmitte eceive, n decentalized CR teminals (hich ae also used as elay nodes, simila to [7]) We assume that thee is no diect link beteen the pimay tansmitte eceive In this scenaio, the CR netok uses the licensed spectum oppotunistically hen the pimay netok is off We conside a to-step AF elaying scheme fo the pimay his ok is suppoted by the Ianian Education & Reseach Institute fo IC (ERIC) unde the gant numbe 8974/ /0/$ IEEE 8

2 tansmission Duing the fist step, the pimay tansmitte tansmits its signal to the CR/elays In the second step, each CR multiplies its eceived signal ith a complex eighting vecto boadcasts it to the eceive Obviously, this signal is also eceived at CR base station Duing the fist step, the eceived signal vecto x of size n at the CR teminals can be itten as: x P f s + n hee P is the tansmitted poe of pimay tansmitte, s is the infomation symbols tansmitted by pimay tansmitte, n is the n complex noise vecto at the CR uses, f f f n () f () is the vecto of the complex channel coefficients beteen the tansmitte the CR teminals, () sts fo the tanspose opeato Duing the second step, the i -th CR teminal ( i,,, n ) multiplies its eceived signal by a complex * eight i boadcasts it in the netok he n complex vecto t denotes the tansmitted signal as: t Wx () hee W * * * diag { n }, (4) hee diag{ a } is a diagonal matix ith diagonal elements equal to vecto a B Received Signals at the Pimay Netok he eceived complex signal, denoted byy, can be itten as: y f Wx + n f W P f s + n + n (5) ( ) hee n is the additive noise coesponding to the link beteen the elay the pimay eceive Note that a diag b b diag a, e can eite (5) as: since ( ) ( ) Ff Fn y P s + + n (6) hee Fk diag( f k ) fo k,, diag{ W }, () denotes emitian tanspose ee, diag{ A} is a vecto fomed by the diagonal elements of the squae matix A he eight vecto is set afte solving ou optimization poblem C Spectum Sensing Based on Received SNR he signal z eceived at the CR base station can be itten as: z f Wx + n f W P f s + n + n (7) hee ( ) f f f n f (8) Figue Achitectue of the consideed cognitive one-ay elay netok is the vecto of complex channel coefficients beteen the CR uses the CR base station, n is the eceived noise at the CR base station Simila to (6), e can eite z as:, z P F f s + F n + n (9) hee F diag ( f ) We assume that the noise pocess is zeomean spatially hite ith vaiance σ hich means that E [ nn ] σ I E[ n ] E[ n ] σ Since P is defined as the tansmit poe of pimay tansmitte, this implies that E[ s ] As shon in Fig, the enegy summation of the eceived signal z duing the sensing peiod is used as a metic fo deciding about the pesence/absence of the pimay signal [9] It can be shon that the pobability of detection inceases ith the incease of the SNR at the CR base station heefoe, e can expess the sensing hypothesis as: SNR BS γ, SNR BS < γ, 0 (0) hee SNRBS is the eceived SNR at the CR base station γ is a pedefined SNR theshold ensuing a taget detection pobability III OPIMAL DISRIBUED BEAMFORMING FOR RELAY POWER MINIMIZAION he optimization poblem that minimizes the elaying poe unde the constaints that the eceived SNR at the pimay eceive at the CR base station ae kept above a cetain theshold is stated as follos: minp SNR γ,snr γ PR BS () hee P is the tansmitted poe fom the CR/elay teminals By assuming that the infomation symbol s the elay noise n ae independent vaiables/vectos complex channel coefficients ae constant duing the elaying scheme, the total tansmitted poe of the elay teminals can be expessed as: 9

3 Figue Enegy detection metic evaluation by data fusion at the CR base station P E t t E W( P f s + n)( P f s + n ) W P E s + E FF + I Wff W W nn W ( P σ ) () In the optimization poblem (), SNR PR, SNR BS, γ γ ae the SNR at the pimay eceive CR base station, minimum equied SNR of pimay eceive CR base station, espectively Simila to (), the eceived SNR in the second tansmission step at pimay eceive CR base station can be expessed as: P hh + σ SNR PR σ D P hh + σ SNR BS σ D () (4) hee D FF, D FF, h Ff h Ff hen, the minimization of the elay tansmitted poe can be eitten as: min ( P D + σ I) P hh γ σ + σ D P hh γ σ + σ D c : c :,, (5) hee D FF o solve the poblem (5), let us ite as: / D (6) hee hen the optimization poblem can be itten as: min / / P D hh D γ / / σ + σ D DD / / P D hh D γ / / σ + σ D DD c : c :, (7) hee D PD + σ I he objective function is a convex function in quadatic fom but in geneal the constaints may be non-convex Given the natue of the ieless channels, depending on the SNR thesholds tansmit poe P, it is not guaanteed that the matices / / ( / P / γ ) A D h h D D D D B / P D h h D / γ D D D ( / / ) ae positive semidefinite hen the constaints ae geneally non-convex he optimization poblem is a quadatically constained quadatic pogam (QCQP) Since the constaints may be nonconvex, the QCQP is NP-had o ovecome this poblem, e popose to use a elaxation technique to efficiently solve this optimization poblem by convex pogamming IV CONVEX RELAXAION OF E OPIMIZAION PROBLEM In this section, the optimal solution of non-convex elay poe minimization poblem is obtained by a diect convex elaxation of (7) using semidefinite pogamming [8] By using x Mx ( M( xx )), the optimization poblem (7) becomes: min ( W ) W (( P γd ) W ) γ, (8) (( P γd ) W ) γ, W, W 0 Rank( W ), / / / / / / / / D D DD hee D h h D, D D D D D h h D, P is the elay tansmit poe sets such that the optimization poblem is feasible he poblem is elaxed into a convex SDP by elaxing 0

4 Figue Aveage minimum elay tansmit poe P vesus σf fo diffeent values of σf σ f fo the elay tansmit poe minimization method ith an initial tansmit poe equal to dbw fo γ γ 0dB the ank-one constaint It can be solved efficiently by convex optimization pogams, such as CVX [0] Note that the optimization poblem in (7) cannot alays guaantee that the optimal solution has a ank equal to one oeve, if W has a ank geate than one, the ank eduction pogam in [] can be used efficiently V SIMULAION RESULS ee, e povide some numeical esults to compae ou consideed mixed netok ith a conventional elay netok, ie, a netok ithout any cognitive capability houghout the simulations, e conside thee channel vectos f, f f ith elements distibuted as complex zeo-mean Gaussian om vaiables ith vaiances σ, σ f f σ We assume that the noise poe of the thee channels f (denoted by σ ) is equal to one We have used a numbe of 00 om channel ealizations fo aveaging the solution of ou optimization poblem Figue shos the aveage minimum elay tansmit poe P vesus σ fo diffeent values of σ f f σf fo the elay tansmit poe minimization ith a tansmitted poe of dbw fo γ γ 0dB As obseved, hen the quality of the tansmitte-cr, CR-eceive CR-base station links ae impoved, the minimum elay tansmit poe is deceased Figue 4 illustates the effect of sensing constaint on poe consumption of elays Note that, hen the equied SNR theshold at the CR base station is not vey high (5 db fo instance), the aveage CR tansmit poe is close to the aveage elay tansmit poe in a conventional netok (ie, ithout cognitive capabilities) Otheise, e obseve that the Figue 4 Aveage elay tansmit poe vesus the minimum equied SNR at the pimay eceive in db fo the conventional the cognitive elay netoks diffeent QoS equiement at the CR base station, n 0 Figue 5 Aveage elay tansmit poe vesus an equal SNR theshold at the pimay eceive CR base station fo diffeent numbe of CR/Relays CR netok equies moe poe in ode to satisfy the desied constaint to povide the taget SNR he aveage elay poe consumption fo diffeent numbe of CR/elays is pesented in Fig 5 It is obseved that hen the numbe of elays inceases, the total elaying poe is educed Fo instance, the elay poe consumption fo 0 CR teminals is appoximately equal to that equied fo 5 elays in a conventional elay netok

5 VI CONCLUSION his pape fomulated the poblem of poe minimization in a one-ay elay netok ith CR capabilities Given a set of minimum equied SNR at the eceives (constaints), an optimal beamfoming eight vecto as obtained to minimize the tansmitted poe by CRs/elays he constaints ae chosen in ode to ensue accuate spectum sensing at the cognitive base station he optimization poblem as tansfomed to a non-convex QCQP hich simply can be solved by SDP elaxation Simulation esults demonstated that the minimum elay tansmit poe is deceased hen the quality of the channels ae impoved REFERENCES [] S aykin, Cognitive adio: bain-empoeed ieless communications, IEEE Jounal on Selected Aea in Communications, vol, pp 0 0, 005 [] F Digham, M S Alouini, M K Simon, on the enegy detection of unknon signals ove fading channels, IEEE Intenational Confeence on Communications, vol 5, pp , 00 [] A Sendonais, E Ekip, B Aazhang, Use coopeation divesity pat I: System desciption, IEEE ansactions on Communications, vol 5, pp 97 98, Novembe 00 [4], Use coopeation divesity pat II: Implementation aspects pefomance analysis, IEEE ansactions on Communications, vol 5, pp , Novembe 00 [5] K B Letaief W Zhang, Coopeative communications fo cognitive adio netoks, Invited pape, Poceedings of IEEE, vol 97, no 5, May 009 [6] V avay-nassab, S Shahbazpanahi, A Gami, Z-Q Luo, Distibuted beamfoming fo elay netoks based on second-ode statistics of the channel state infomation, IEEE ansactions on Signal Pocessing, vol 56, no 9, pp , Septembe 008 [7] A Alizadeh, S M S Sadough, N Khajavi, Optimal Beamfoming in cognitive to-ay elay netoks, IEEE st Intenational Symposium on Pesonal, Indoo Mobile Radio Communications, PIMRC, 00, pp 9- [8] S Boyde L Venbeghe, Convex Optimization Cambidge Univesity Pess, 004 [9] J Ma, G Zhao, Y Li, Soft combination detection fo coopeative spectum sensing in cognitive adio netoks, IEEE ansactions on Wieless Communications, vol 7, no, Nov 008 [0] M Gant S Boyd CVX: Matlab softae fo disciplined convex pogamming, vesion Octobe 00 [] Y uang S Zhang, Ne esults on hemitian matix ank-one decomposition, Aug 009