A Thresholding-Based Antenna Switching in SWIPT-Enabled MIMO Cognitive Radio Networks with Co-Channel Interference

Transcription

1 A Threholding-Baed Antenna Switching in SWIPT-Enabled MIMO Cognitive Radio Network wi Co-Channel Interference Fatma Benkhelifa, and Mohamed-Slim Alouini Computer, Electrical and Maematical Science and Engineering CEMSE Diviion King Abdullah Univerity of Science and Technology KAUST Thuwal, Makkah Province, Saudi Arabia Abtract In i paper, we conider e imultaneou wirele power and information tranfer SWIPT for pectrum haring SS in cognitive radio CR network wi a multiple antenna SWIPT-Enabled econdary receiver SR. The SR harvet e energy from e ignal ent from e econdary tranmitter ST and e interfering ignal ent from e primary tranmitter PT. Moreover, e ST ue e antenna witching AS technique which elect a ubet of e antenna to decode e information and e ret to harvet e energy. The antenna election i performed via a reholding trategy inpired from e maimum ratio combining MRC technique wi an output rehold OT-MRC. The reholding-baed antenna election trategy i propoed in two way: one i prioritizing e information data and e oer i prioritizing e harveted energy. For e two propoed election cheme, we tudy e probability ma function of e elected antenna, e average harveted energy, and e data tranmiion outage probability. Through e analytic epreion and e imulation reult, we how at ere i a tradeoff between e outage probability and e harveted energy for bo cheme. We ee alo at e preference of one cheme on e oer i alo affected by i energy-data trade off. Inde Term Energy harveting, Simultaneou Wirele Information and Power Tranfer SWIPT, cognitive radio CR, pectrum haring SS, antenna witching AS, maimum ratio combining MRC, outage probability, average harveted energy.

2 I. Introduction Energy conumption and pectrum carcity are two major iue in wirele communication ytem. For e net generation of wirele communication ytem, it i challenging to aure e energy efficiency a well e pectrum efficiency. On e one hand, cognitive radio CR network are a promiing olution to olve e pectrum carcity. CR network allow e unlicened uer to ue e pectrum whenever e licened uer are idle [. For e pectrum haring SS in CR network, e unlicened uer and licened uer are allowed to hare e pectrum a long a e interference induced by e unlicened uer do not harm e licened uer [2. Variou work have tudied e pectrum haring in CR network wi ingle/multiple antenna at e primary and econdary network [3 [5. On e oer hand, energy harveting i a promiing olution to make e wirele communication ytem more energy efficient and elf-utainable. Among e variou energy ource, e radio frequency RF ignal are found to be a good ource for energy harveting. The proce of e imultaneou ue of RF ignal for energy tranfer and information tranfer i known in e literature a e imultaneou wirele power and information tranfer SWIPT. The SWIPT technique wa tudied in ingle-input ingle-output SISO communication ytem in [6, [7, in multiple-input multiple-output MIMO communication ytem in [8, and in MIMO relay ytem [9, [. Among e EH practical cheme tudied in e literature, we tate e power plitting PS, e time witching TS, and e antenna witching AS at eparate e information decoding ID and energy harveting EH tranfer over e power, e time, and e pace, repectively. Subequently, it i intereting to invetigate e SWIPT technique in cognitive radio network. Recently, variou reearcher have hown eir interet to tudy e SWIPT technique in CR network [ [5. In [, an opportunitic pectrum acce cheme wa conidered in CR network where econdary tranmitter ST eier harvet energy from ambient tranmiion or tranmit ignal when primary tranmitter PT are far away. In [2, [3, [6, CR relay network were conidered where e ST or e econdary relay ait e primary tranmiion while harveting e energy uing e PS or TS cheme. In [6,e joint optimization of e power plitter factor and e energy allocation over N time lot which maimize e roughput wa conidered and a uboptimal management algorim wa propoed in an amplify-and-forward AF relay cognitive network wi one primary receiver, one cognitive tranmitter-receiver, and one EH relay. The EH relay harvet e energy from e received ignal uing e PS cheme. In [2, e primary and econdary outage probability and e rate-energy tradeoff between e maimum ergodic capacity and e maimum harveted energy in e econdary

3 network were analyzed in amplify-and-forward AF cognitive relay network where e ST and e SR have energy harveting capabilitie uing e PS cheme. Moreover, ST act a a relay for e primary tranmiion, harvet e energy from e primary ignal, and forward e primary ignal and tranmit to it receiver imultaneouly. In [3, e optimal cooperation trategy, e time allocation and e power allocation were invetigated in non-cooperation and cooperation mode to maimize e econdary uer achievable roughout in a CR network ytem where e ST act a a decode-and-forward DF baedrelay for e primary tranmiion. The ST i elf-powered and harvet e energy from e ambient tranmitter uing e ave-en-tranmit protocol. In [4, [5, an underlay CR network i tudied where e ST i elf-powered and harvet e energy from e primary tranmiion. In [4, e online optimal time allocation between e EH phae and ID phae i propoed which maimize e average achievable rate of e cognitive radio ytem, ubject to e ɛ-percentile protection criteria for e primary ytem where e ST harvet e energy from e primary tranmiion. In [5, a channel quality baed rehold and opportunitic cheduling were eploited in CR network wi one ST and multiple EH SR under e peak interference power contraint of e PR and e ST maimum tranmit power limit. Each SR i cheduled to harvet energy if e channel condition i above e rehold or to decode information if e channel condition i below e rehold. In i contet, e analytical epreion of e econdary ergodic capacity, ymbol error rate SER, roughput, and energy harveting were invetigated. In line wi e reearch cope, we propoe to invetigate e SWIPT for pectrum haring in MIMO CR network where e SR harvet e energy from e primary and econdary tranmiion uing e antenna witching technique. The antenna election i baed on a reholding technique baed on e maimum ratio combining MRC wi an output rehold OT-MRC. The OT-MRC combining technique wa tudied before in [7 where e co-channel interference CCI wa not conidered. In i paper, we propoe two antenna election cheme employing a reholding technique baed on OT-MRC wi CCI: one cheme i prioritizing e information data and e econd i prioritizing e harveted energy. For e two election cheme, we derive e analytical epreion of e probability ma function PMF of e elected number of antenna connected to e ID circuit at SR, e average of e harveted energy, and e data tranmiion outage probability and we how at ere i an energy-data tradeoff for e two cheme. II. Sytem Model We conider a cognitive network coniting of a primary tranmitter PT, a primary receiver PR, a econdary tranmitter ST and a econdary receiver SR. While e PT, PR and ST are battery powered, e

4 SR i elf-powered by it harveted energy from e RF ignal ent from ST and PT. All e node are equipped wi ingle antenna, ecept e SR which i equipped wi multiple antenna N 2. The channel between e PT and e PR, e channel between e PT and e j antenna of SR, e channel between e ST and e j antenna of SR, and e channel between e ST and e PR are denoted by h pp, h p j, h j, and h p, j,..., N 2. A. SWIPT-Enabled Secondary Receiver The SR harvet energy uing e antenna witching AS technique. In fact, e AS technique aign a ubet of e multiple antenna to harvet energy and e remaining to decode e received data information. Let K 2 be e number of antenna connected to e ID circuit and N 2 K 2 be e number of antenna connected to e EH circuit, wi K 2 N 2. How to chooe K 2 will be dicued later. For a given K 2, e combined ignal-to-interference ratio SIR at e SR i given by ID K 2 P K2 j h j 2 P K2 p j h p j Γ K 2 2 Γ p K 2, where P i e tranmit power at ST, P p i e tranmit power at PT, σ 2 i e variance of e additive white Gauian noie AWGN at e PR, Γ K 2 P K2 j h j 2 and Γ p K 2 P p K2 j h p j 2. The harveted energy at SR i given by Γ K 2 Γ p K 2, if K 2 < N 2, Q K 2, if K 2 N 2, N 2 jk 2 P h j 2 P p h p j 2, if K 2 < N 2, if K 2 N 2, where Γ K 2 P N2 K 2 h j 2 and Γ p K 2 P p N2 K 2 h p j 2 are e harveted energy from ST and PT, repectively, and i e converion efficiency. Now, e quetion to ak i how to chooe K 2. For at, we preent two election cheme baed on a reholding technique inpired from e OT-MRC technique tudied in [ B. Threholding-Baed Antenna Selection Technique In order to elect e number of antenna K 2, we ue a reholding technique inpired from e OT-MRC technique in e preence of e co-channel interference CCI from PT. Note at e OT- MRC technique wa previouly conidered only in e no CCI cae [7. In order to derive e OT-MRC technique wi CCI, we will follow e ame tep in [7.

5 Let ΓK 2 be e combined utility function to be pecified depending e election cheme conidered. Wi OT-MRC, e number of antenna K 2 i elected o at e choen combined utility function ΓK 2 above a certain predefined rehold. Starting from e ingle-antenna cae, e OT-MRC combiner gradually raie e number of antenna in a way to raie ΓK 2 above e rehold. For more detail about OT-MRC, pleae refer to [7. In what follow, we conider two election cheme baed on different combined utility function. Prioritizing Data Selection Scheme SC : ΓK 2 tand for e received power at ID circuit at SR from e deired tranmitter ST, i.e. ΓK 2 Γ K 2. K 2 correpond to e cae where Γ K 2 i greater an e rehold. Prioritizing Energy Selection Scheme SC 2 : ΓK 2 tand for e received power at EH circuit at SR proportional to e harveted energy from e deired tranmitter ST, i.e. ΓK 2 Γ K 2. K 2 correpond to e cae where Γ K 2 i greater an e rehold. C. Performance Metric In order to evaluate e performance of e conidered election cheme, we propoe to tudy e performance metric uch a e PMF P K2 k 2 of K 2, e epected value of e harveted energy, and e data tranmiion outage probability. The epected value of e harveted energy i defined a 2 Q E [Q E [Qk 2 K 2 k 2 P K2 k 2 4 k 2 2 E [ Γ k 2 Γ p k 2 K 2 k 2 PK2 k 2. 5 k 2 In addition, e data tranmiion outage probability at SR i defined a 2 P D,out P ID < P ID k 2 < & K 2 k k 2 k 2 Γ k 2 P Γ p k 2 < & K 2 k 2, 7 where X 2 R and R i e tranmiion rate at ST. If e election of K 2 i independent of Γ K 2 and Γ p K 2, en P D,out 2 k 2 Γ k 2 P Γ p k 2 < K 2 k 2 P K2 k 2. 8

6 III. Prioritizing Data Selection Scheme SC A. Mode of Operation The prioritizing data election cheme SC elect e antenna K 2 in a way to aure at e received power from e deired tranmitter ST at e information decoding receiver at SR i above a certain predefined rehold. Here, e utility combined function tand for e received power at ID circuit at SR from e deired tranmitter ST, i.e. ΓK 2 Γ K 2. The elected number of antenna K 2 correpond to e cae where Γ K 2 i greater an e rehold. For SC, e reholding procedure i a follow: Start wi j and Γ,. If Γ j <, update Γ j Γ j, j and j j. Repeat until Γ j or j N 2. At e end, K 2 will be equal to j. Remark : Note at e elected number of antenna K 2 cannot be equal to zero or to N 2 in a way to avoid e two wore cae when all e receiving antenna are ued for harveting energy and no antenna are ued for decoding information K 2, i.e. no data and when all e receiving antenna are ued for decoding information and no antenna are ued for harveting energy K 2 N 2, i.e. no energy. Same remark hold for e election cheme SC 2. B. PMF of K 2 Baed on e election cheme SC, e PMF of K 2 i given by: P K 2 k 2 P Γ, if k 2, P Γ k 2 < Γ k 2, if k 2 2,..., N 2 2, 9 P Γ N 2 2 <, if k 2 N 2. F, if k 2, F k 2 F N 22 f zf k 2 z dz, if k 2 2,..., N 2 2,, if k 2 N 2. where f k 2 and F k 2 are e PDF and CDF of Γ k 2, repectively, for k 2,..., N 2.

7 C. Average of Harveted Energy The average harveted energy at SR i given by Q 2 N 2 k 2 P E [ h j 2 P p E [ h p j 2 P K 2 k 2. k 2 D. Data Tranmiion Outage Probability The outage probability at SR i given by P D,out P Γ Γ p < & Γ 2 2 Γ k 2 P Γ k 2 2 p k 2 < & Γ k 2 < Γ k 2 Γ N 2 P Γ p N 2 < & Γ N 2 2 < where I, 2 2 k I k2, I N2,, 3 Γ I, P Γ p < & Γ, 4 Γ k 2 I k2, P Γ p k 2 < & Γ k 2 < Γ k 2, 5 Γ N 2 I N2, P Γ p N 2 < & Γ N 2 2 <, 6 which were hown in Appendi B to be given by [ I, y f p y dy F and I k2, [ I N2, F [ y F k 2 F k 2 [ y F k 2 y z y f F N 22 y [ y F N 22 F N 22 F k 2 F z dz f k 2 y dy z f z dz, 7 F y f k 2 y dy, 8 z y f z y f z dz z dz f N 2 y dy f N 2 y dy F y f N 2 y dy. 9 Conequently, e outage probability i given by 2, where f k 2 and F k 2 are e PDF and CDF of Γ p k 2, repectively, for k 2,..., N 2.

8 P D,out 2 k 2 2 [ F y f p y dy F [ y F N 22 F k 2 z y f z dz F f N 2 y dy 2 [ y F k 2 k 2 2 y 2 2 [ F k 2 k 2 2 z f z y f z dz z dz f k 2 y dy F y f k 2 y dy. 2 f k 2 y dy E. Eample: Rayleigh Fading Special Cae Let u aume at all e channel h pp, h p j, h k j, and h kp are modeled a flat fading wi Rayleigh ditribution wi variance λ pp, λ p, λ and λ p, repectively. PMF of K 2 : The PMF of K 2 can be written a P K 2 k 2 e k 2, Γk 2 e Γk 2, if k 2, e u k 2, u du, if k 2 2,..., N 2 2, ΓN 2 N 2 2 2,, if k2 N 2, where Γ and, are e Gamma function and e lower incomplete Gamma function [8, repectively. Uing a k, t et dt ea k Subequently, we deduce at P K 2 k 2 2 k, a which wa proven in Appendi A-A, it can be hown at: k2 e u k 2, u du e P k 2, λ k Γk 2 k2 e, if k 2,..., N 2 2, ΓN 2 N 2 2 2,, if k2 N 2, where Γ and, are e Gamma function and e lower incomplete Gamma function [8, repectively. 2 Average of Harveted Energy: For e Rayleigh fading channel, e average harveted energy at SR can be written a 25, where Γ, i e upper incomplete gamma function [8. Note at 25 wa obtained uing m [8, and e correponding derivative m kk e Γ,. Γk Γ Γ 3 Data Tranmiion Outage Probability: k e Γ, Γk Γ For e Rayleigh fading channel, we have hown in Appendi B at I,, I k2, and I N2, 23 in

9 Q [ 2 2 P p λ p e N 2 k 2 k 2 P p λ [ p N 2 Γ N 2 2 k2 Γk 2 Γ N 2 2, ΓN 2 2 N 2 2, N2 2 e N 2 2, 24, 25 P D,out P pλ p e P p λ p Ppλp 2 2 k 2 2 k2 e Γk 2 2 N2 2 Γ N2, P p λ p Ppλp [ e Γ k 2, P p λ p P p λ p k 2 Γ N 2 2 N 2 2, ΓN 2 2 P pλ p N 2 ΓN 2 2 N 2, u P pλ p u N 2 2 e u Γ N2, k 2, P p λ p P p λ p ΓN 2 2 du. 29 are given by and I, I k2, e P p λ p e P p λ p k2 Γk 2 2 e Γ k 2, k2 Pp λ p N 2 2, Γ N2, I N2, Γ N 2 2 Γ N 2 N2 2 Γ N2, Γ N 2 2 N2 P p λ p ΓN 2 2 Ppλp Conequently, e outage probability i given by Remark and Aymptotic Reult: [ Γ k 2, Ppλp P p λ p P p λ p k2 P p λ p P p λ p P p λ p, 26 P p λ p N2 N 2, u P pλ p, 27 u N 22 e u du. 28 When, we can ee at K 2, Q N 2 q, and P D,out P p λ p e P p λ p Ppλp, 3

10 where q P p λ p P K 2 P p λ p e. When, we can ee at K 2 N 2, Q q 2, and P D,out N2 2, Γ N2, P p λ p Γ N 2, Γ N 2 2 Γ N 2 where q 2 P p λ p P K 2 N 2 P p λ p P p λ p Γ N 2 ΓN 2 N 2 2 2,., 3 IV. Prioritizing Energy Selection Scheme SC 2 A. Mode of Operation By contrat to e prioritizing data election cheme SC, e prioritizing energy election cheme SC 2 elect e antenna K 2 in a way to aure at e received power from e deired tranmitter ST at e EH receiver at SR i above a certain predefined rehold. Hence, e utility combined function tand for e received power at EH circuit at SR proportional to e harveted energy from e deired tranmitter ST, i.e. ΓK 2 Γ K 2. The elected number of antenna K 2 correpond to e cae where Γ K 2 i greater an e rehold. For SC 2, e reholding procedure i a follow: Start wi j N 2 and Γ N 2 N2. If Γ j <, update j j and Γ j Γ j, j. Repeat until Γ j or j. At e end, K 2 will be equal to j. B. PMF of K 2 The PMF of K 2 i given by: P 2 K 2 k 2 P Γ 2 <, if k2, P Γ k 2 < Γ k 2, if k 2 2,..., N 2 2, P Γ N 2, if k2 N 2. F N 22, if k 2, F N 2k 2 f zf N 2k 2 z dz, if k 2 2,..., N 2 2, F, if k 2 N 2, where f N 2k 2 and F N 2k 2 are e PDF and CDF of Γ k 2, repectively, for k 2,..., N 2.

11 N2 D,out P 2 [ F N 2k 2 k 2 Γ k 2 P Γ p k 2 < K 2 k 2 P K2 k 2 f yf y dy f F N k 2 2 [ 2 k 2 f k 2 [ yf k 2 [ zf N 2k 2 z dz f k 2 yf k 2 y dy y dy f N 2 yf N 2 P K2 k 2 35 y dy F. 36 Q 2 [ N 2 P p λ p ΓN 2 2 N 2 2, P p λ [ p N 2 N 2 2, Γ N e k 2 2 Γ N 2 k 2 N 2 2, N2 k 2 ΓN 2 k 2 38 N2 2 e, 39 C. Average of Harveted Energy The average harveted energy at SR i given by Q 2 2 N 2 k 2 P E [ h j 2 P p E [ h p j 2 P 2 K 2 k k 2 D. Data Tranmiion Outage Probability The outage probability at SR i given by 36. E. Eample: Rayleigh Fading Special Cae PMF of K 2 : Similarly to P K 2 k 2, we can how at ΓN 2 N 2 2 2, P 2 K 2 k 2 2 Average of Harveted Energy: ΓN 2 k 2, if k2, N2 k 2 e, if k 2 2,..., N 2. For e Rayleigh fading channel, e average harveted energy at SR can be written a 39, which wa obtained in a imilar way a

12 P 2 D,out P p λ p N2 2, e P p λ p ΓN 2 2 P p λ p 2 F, 2k 2 ; k 2 ; P p λ p 2 Γ2k 2 P p λ p k2 N2 k 2 k 2 2 Γk 2 2 k 2 ΓN 2 k 2 2k2 P p λ p Data Tranmiion Outage Probability: For e Rayleigh fading channel, we can write f k 2 yf k P 2 p λ p y dy, 4 P p λ p f k 2 yf k 2 y dy Γk 2 2 k2 y k2 e y y Ppλp k 2, dy 4 P p λ p Γ2k k2 2 Pp λ p P λ P p λ p Γk 2 2 k 2k2 2F, 2k 2 ; k 2 ;, 42 2 P λ P p λ P p λ p p where 42 wa obtained uing [8, and 2 F a, b; c; z i e Gauian hypergeometric function. Hence, we deduce at e outage probability can be written a in Remark and Aymptotic Reult: Firt, we can ee at P 2 K 2 k 2 P K 2 N 2 k 2 if SC and SC 2 ue e ame predefined rehold. When P 2 D,out e When, we can ee at K 2 N 2, Q 2 q, and N2 Γ2N 2 Pp λ p P p λ p ΓN 2 2 N 2 2N2 P λ P p λ 2 F, 2N 2 ; N 2 ; P p λ p p, we can ee at K 2, Q 2 N 2 q 2, and P 2 D,out P p λ p N2 2, P λ P λ P p λ p ΓN2 2 P p λ p. 45 P p λ p V. Simulation Reult In i ection, we preent ome elected imulation to how e accuracy of e obtained analytical epreion and to compare e two election cheme SC and SC 2. In all e figure, e channel follow e Rayleigh ditribution. The number of imulation i N im 4. The tranmit power at PT i equal to P p dbm. The variance of e channel are choen equal to λ pp λ p 3 dbm. The noie variance at PR and SR are bo equal to σ 2 p σ 2 dbm. The converion efficiency of e EH circuit at PR i 6%. The tranmiion rate at ST i choen equal to 2 bp/hz.. 44

13 PDS: KN - PES: K PDS: K PES: KN - PMF of K Analytic epreion o Monte Carlo imulation.3 PDS K3 PES K.2 PDS K2 PES K2. PDS K PES K Tranmit Power at ST in PdBm Figure : The probability ma function of K 2 veru e tranmit power at SR P in dbm, wi N 2 4, λ λ p 3 dbm, and dbm for e two election cheme SC and SC 2. In Fig., we plotted e PMF of K 2 veru e tranmit power P at ST in dbm, repectively, for N 2 4, λ λ p 3 dbm, and dbm for e two election cheme SC and SC 2. We can ee at for e low power regime, K 2 goe to N 2 for SC and goe to for SC 2. However, for e high power regime, K 2 goe to for SC and goe to N 2 for SC 2. Outage Probability - PES N PES N 6 PES N 2 4 PDS N PDS N 6 PDS N Tranmit Power at ST P in dbm PDS PES N Analytic epreion o Monte Carlo imulation Average Harveted Energy PES N PES N 6 PES N 4 PDS N PDS N 6 PDS N 4 N Tranmit Power at ST P in dbm PDS N PES Analytic epreion o Monte Carlo imulation a b Figure 2: a The outage probability P D,out and b e average harveted energy Q veru e tranmit power at SR P in dbm, wi λ λ p 3 dbm, dbm and different value of N 2 for e two election cheme SC and SC 2.

14 In Fig. 2a and 2b, we plotted e outage probability and e average harveted energy veru e tranmit power P at ST in dbm, repectively, for λ λ p 3 dbm, dbm and different value of N 2 for e two election cheme SC and SC 2. On e one hand, from an outage probability tand point, we can ee at S C outperform SC 2 for a tranmit power contraint P 5 dbm, while for P 5dB, S C 2 outperform SC. On e oer hand, in term of e average harveted energy, S C 2 outperform SC for P 2dBm, while S C outperform SC 2 for P dbm. Thi obervation can be eplained by e fact at, when e ratio become very large low SNR regime, e number of elected antenna K 2 of SC converge to N 2, while it goe to for SC 2. Hence, for SC, more antenna are ued to decode information and le are ued to harvet energy. However, for SC 2, le antenna are ued to decode information and more are ued to harvet energy. Subequently, e outage probability of SC i better an e one of SC 2, while e average harveted energy of SC 2 i better an e one SC. However, when e ratio become mall high SNR regime, e number of elected antenna K 2 for SC converge to, while it goe to N 2 for SC 2. For SC, only one antenna i ued to decode e information and all e oer are ued to harvet energy. However, for SC 2, only one antenna i ued to harvet energy and all e oer are ued to decode e information. Subequently, e outage probability of SC 2 i better an e one of SC, while e average harveted energy of SC i better an e one SC 2. At i point, we can ee at ere i a trade off between e outage probability and e average harveted energy when we ue SC or SC 2. In addition, we can ee at e outage probability of SC i almot e ame, a we increae e number of receiving antenna at ST. For e high SNR regime, i behavior i epected from 3. For e low SNR regime, i behavior i due to e fact at e ratio P p λ p i of e order of 5 dbm, o 3 converge to. However, e outage probability of SC 2 increae for P 5 dbm, while it decreae for P > 5 dbm, a N 2 increae. On e oer hand, a N 2 increae, e average harveted energy of SC increae for P 25 dbm and i almot contant oerwie, while e average harveted energy of SC 2 increae for P dbm and i almot contant oerwie. Thi contant behavior of e average harveted energy wi repect to N 2 i due to e fact at K 2 i equal to when SC i in e high SNR regime and when SC 2 i in e low SNR regime.

15 Outage Probability Analytic epreion o Monte Carlo imulation PES λ p 3 dbm, λ 2 dbm PES λ p 3 dbm, λ 3 dbm PES λ p 2 dbm, λ 3 dbm PDS λ p 3 dbm, λ 2 dbm PDS λ p 3 dbm, λ 3 dbm PDS λ p 2 dbm, λ 3 dbm λ p 3 dbm, λ Tranmit Power at ST P in dbm λ p, λ 3 dbm λ p 3 dbm, λ λ p, λ 3 dbm Average Harveted Energy PES λ p 3 dbm, λ 2 dbm PES λ p 3 dbm, λ 3 dbm PDS λ p 3 dbm, λ 3 dbm PDS λ p 3 dbm, λ 2 dbm PES λ p 2 dbm, λ 3 dbm PDS λ p 2 dbm, λ 3 dbm λ p 3 dbm, λ λ p 3 dbm, λ Analytic epreion o Monte Carlo imulation Tranmit Power at ST P in dbm λ p, λ 3 dbm λ p, λ 3 dbm a b Figure 3: a The outage probability P D,out and b e average harveted energy Q veru e tranmit power at SR P in dbm, wi N 2, dbm and different value of λ and λ p for e two election cheme SC and SC 2. In Fig. 3a and 3b, we plotted e outage probability and e average harveted energy veru e tranmit power P at ST in dbm, repectively, for N 2, dbm and different value of λ and λ p for e two election cheme SC and SC 2. We can ee at e outage probability of SC and SC 2 improve wi λ while it woren wi λ p, which i an epected reult ince we know at e interference harm e data tranmiion. On e oer hand, e average harveted energy of SC and SC 2 improve wi λ p, if we compare e cae when λ p 2 dbm and λ p 3 dbm, while λ 3 dbm. But, when λ increae, e average harveted energy of SC improve. However, for SC 2, e average harveted energy improve for P > 5 dbm. Moreover, we can ee at e average harveted energy i highly affected by λ p at low SNR regime while it i highly affected by λ at high SNR regime.

16 Outage probability - -2 SC 2 dbm SC 2 - dbm SC dbm SC - dbm Analytic epreion o Monte Carlo imulation Tranmit Power at ST P in dbm a Average Harveted Energy - -2 SC 2 dbm SC 2 dbm SC 2 - dbm SC - dbm SC dbm SC dbm Analytic epreion o Monte Carlo imulation Tranmit Power at ST P in dbm b Figure 4: a The outage probability P D,out and b e average harveted energy Q veru e tranmit power at SR P in dbm, wi N 2, λ λ p 3 dbm and different value of for e two election cheme SC and SC 2. In Fig. 4a and 4b, we plotted e outage probability and e average harveted energy veru e tranmit power P at ST in dbm, repectively, for N 2, λ λ p 3 dbm and different value of for e two election cheme SC and SC 2. We can ee at a increae, e outage probability of SC improve, while it lighly increae for SC 2 for high P. On e oer hand, e average harveted energy decreae for SC and increae for SC 2. Thi obervation can be eplained by e fact at a e rehold increae, more antenna are allocated to decode information for SC while le antenna are allocated to harvet energy. However, for SC 2, a increae, more antenna are ued to harvet energy and le antenna are ued to decode information. VI. Concluion In i paper, we invetigate e SWIPT for pectrum haring in MIMO CR network where e SR harvet e energy from e primary and econdary tranmiion uing e antenna witching technique. We propoe a reholding-baed antenna election trategy inpired from OT-MRC technique. We tudy two election cheme: e firt i e prioritizing data election cheme SC and e econd i e prioritizing energy election cheme SC 2. For bo cheme, we derive e PMF of K 2, e average harveted energy, and e data tranmiion outage probability and we how e energy-data trade off for bo cheme.

17 Appendi A A. Proof of a k, t et dt ea k, a k a k, t e t dt a a y k2 e y dy e t dt 46 [ a y k2 e y e t dt dy 47 [ t a e a y k2 e y dy y a e a k, a ak k y k2 dy ea k, a. 5 k B. Proof of a t k, t et dt aea ak k, a k kk a t k, t e t dt a a y k2 e y dy te t dt 5 [ a y k2 e y te t dt dy 52 [ t a a e a y k2 e y dy y a y y k2 dy 53 a e a k, a ak k ak k 54 a ea k k, a a k kk. 55

18 A. Epreion for I, Appendi B Epreion for I,, I k2, and I N2, Firt, let u tart wi I, : Γ I, P Γ p < & Γ P Γ < Γ p & Γ P Γ < Γ p & Γ p [ F y F f p y dy 6 P Γ < y f p y dy 59 F y f p y dy F For e Rayleigh fading channel, I, i equal to I, P p λ e y p P p λ p e P p λ p B. Epreion for I k2, [ F e y Ppλp dy e Ppλp Then, let u compute I k2, : Γ k 2 I k2, P Γ p k 2 < & Γ k 2 < Γ k 2, 6 e Ppλp P Γ k 2,k2 < Γ p k 2 & Γ k 2 < Γ k 2,k2 [ y F k 2 z y f z dz f k 2 y dy y [ F k 2 F k 2 z f z dz F k F y f k 2 y dy. 66

19 For e Rayleigh fading channel, I k2, can be hown equal to I k2, Γk 2 k2 P p λ p Γk 2 [ y z y k 2, e z dz y k2 e y Ppλp dy y Γ k 2, P p λ p k 2, z e z dz Γk 2 Γk 2 k 2, P λ Γk 2 Γk 2 k2 e y P p λ p e Γk 2 2 k2 k 2, y k2 e y Ppλp dy P p λ P λ p k 2, Γ k2, P p λ p k2, [ Γ k Γk 2 2 2, Γk 2 Γk 2 P p λ p e k2 Pp λ p k2 Γ k 2, P p λ p P p λ p e k2 Γk 2 2 k2 Pp λ p C. Epreion for I N2, e [ Γ k 2, P p λ p k2 Γ k 2, P p λ p y k 2 e y Ppλp dy 67 P p λ p Finally, let u compute I N2, : Γ N 2 I N2, P Γ p N 2 < & Γ N 2 2 < P Γ N 2 2,N2 < Γ p N 2 & Γ N 2 2 < [ y z y f z dz f N 2 y dy F N 22 y [ y F N 22 F N 22 z y f z dz f N 2 y dy F y f N 2 y dy. 72

20 For e Rayleigh fading channel, I N2, can be hown equal to I N2, ΓN 2 N2 P p λ p ΓN 2 2 [ y z y N 2 2, e z dz y N22 e y Ppλp dy P λ p y ΓN 2 N2 P p λ p [ y N 2 2, z y e ΓN 2 N2 FN22 P p λ p e y N 2 2, Γ N2, Γ N 2 2 Γ N 2 N2 2 Γ N2, Γ N 2 2 N2 P p λ p Ppλp ΓN 2 2 ΓN 2 2 z dz y N22 e y Ppλp dy y N 22 e y Ppλp dy 73 P p λ p P p λ p P p λ p N2 N 2, u P pλ p u N 22 e u du. 74 where 74 wa obtained uing a t k, t et dt aea ak k, a which wa proven in Appendi k kk A-B. Or, we can write: ΓN 2 2 ΓN 2 Ppλp N 2 2 ΓN 2 m ΓN 2 N 2 2 ΓN 2 m Ppλp N 2, u P pλ p u N22 e u du u N 22 e u du Pp λ p m Ppλp Γm N 2, P p λ p Pp λ p m N2 m, e u Ppλp u N2m2 du 75 P p λ p Pp λ p Γm P p λ p N 2 m. 76

21 Conequently, we obtain: Γ N 2 2, Γ N2, I N2, Γ N 2 2 Γ N 2 N2 2 Γ N2, Γ N 2 2 N2 P p λ p N 2 2 ΓN 2 m P p λ p P p λ p P p λ p N2 Pp λ p m N2 m, Appendi C PDF and CDF of Q k 2 for k 2,..., N 2 Recall, for k 2,..., N 2, e harveted energy at SR i given by P p λ p Pp λ p Γm P p λ p N 2 m. 77 Q k 2 Γ k 2 Γ p k 2, 78 where Γ k 2 P N2 k 2 h j 2, Γ p k 2 P p N2 k 2 h p j 2 are e harveted energy from ST and PT, repectively. The PDF and CDF of Γ k 2 are denoted a f N 2k 2, F N 2k 2, repectively. In addition, e PDF and CDF of Γ p k 2 are denoted a f N 2k 2, F N 2k 2, repectively. We can write e PDF and CDF of Q k 2 a and repectively. F Q k 2 f Q k 2 q f Γ k 2 Γ p k 2 q 79 q f Γ k 2 Γ p k 2 8 q q q q q q q f Γ k 2 f Γ p k 2 q d 8 f N 2k 2 f N 2k 2 q d, 82 f N 2k 2 f N 2k 2 q f N 2k 2 [ q f N 2k 2 F N 2k 2 q d dq 83 f N 2k 2 q dq d 84 d, 85

22 For e Rayleigh fading channel, we have f N 2k 2 N 2k 2 ΓN 2 k 2 N 2k 2 e F N 2k 2 ΓN 2 k 2 N 2 k 2, f N 2k 2 y N 2k 2 y ΓN 2 k 2 N2 k 2 e y Pp λ p F N 2k 2 y ΓN 2 k 2 y N 2 k 2, P p λ p for, and y. Then, e PDF of Q k 2 i written a f Q k 2 q e q Ppλp ΓN 2 k 2 2 N 2k 2 Pp λ p N2 k 2 q N 2k Ppλp 88 N2 k q 2 e For P p λ p e q [ Ppλp π q f Q k 2 q ΓN 2 k 2 2 N N2 k 2k 2 2 Pp λ p e q 2 Ppλp q Γ N 2 k 2 I N2 k 2 /2 2 P p λ p πe q 2 Ppλp N2 k Γ N 2 k 2 q 2 /2 N 2k 2 /2 P p λ p P p λ p P p λ p N 2 k 2 /2 I N2 k 2 /2 Ppλp 89 d 9 9 q, 2 P p λ p where I n i e modified Beel function of e firt kind. 94 wa obtained uing [8, For P p λ p f Q k 2 q e q ΓN 2 k 2 2 2N 2k 2 e q ΓN 2 k 2 2 2N 2k 2 q q N 2k 2 q 2N2 k 2 q N2 k 2 92 d 93 B N 2 k 2, N 2 k 2 94 q 2N 2k 2 e Γ 2 N 2 k 2, 95 2N 2k 2 where B, i e Beta function. 94 wa obtained uing [8, At e end, we have q πe 2 Ppλp f Q k 2 q ΓN 2 k 2 N 2 k 2 /2 P p λ p q 2N 2 k2 e q Γ2N 2 k 2 2N 2 k 2, q N2 k 2 /2 q IN2 P p λ p k 2 /2 2 P p λ p, if P λ P p λ p if P λ P p λ p 96

23 Correpondingly, e CDF of Q k 2 i given by q N q 2k 2 q ΓN 2 k 2 2 N 2k 2 e N 2 k 2, P p λ d 97 p e q q N2 k 2 q ΓN 2 k 2 2 N 2k 2 u e u u N 2 k 2, du 98 P p λ p e q [ q N2 k 2 q ΓN 2 k 2 N 2k 2 u e u du N 2 k 2 q N2 k 2 u m q Γm P m m p λ m p u e u Ppλp du 99 e q [ q ΓN 2 k 2 N 2k 2 e q t N 2k 2 e t dt N 2 k 2 q N2 k 2 u m q Γm P m m p λ m p u e u Ppλp du e q [ ΓN 2 k 2 N 2k 2 e q P λ N 2k 2 q N 2 k 2, N 2 k 2 q N2 k 2 u m q Γm P m m p λ m p u e u Ppλp du [ e q P λ N 2k 2 N 2 k 2, F Q k 2 e q ΓN 2 k 2 N 2 k 2 N 2 k 2 m e q ΓN 2 k 2 N 2 k 2 N 2 k 2 m e q ΓN 2 k 2 N 2 k 2 N 2 k 2 m e q ΓN 2 k 2 N 2 k 2 N 2 k 2 m ΓmP m p λ m p q q u m q u N 2 k 2 du, if P p λ p, [ e q P λ N 2k 2 N 2 k 2, ΓmP m p λ m p q u m q u N 2 k 2 u e [ e q P λ N 2k 2 N 2 k 2, ΓN 2 k 2 ΓN 2 k 2 mp m p λ m p q Ppλp q du, if P p λ p, 2 q N2 k 2 m, if P λ P p λ p, [ e q P λ N 2k 2 N 2 k 2, ΓN 2 k 2 ΓN 2 k 2 mp m p λ m p q q N2 k 2 m F m ; N2 k 2 m ; q P p λ p, if P λ P p λ p, 3 where F a; b; z i e Kummer confluent hypergeometric function. 3 wa obtained uing [8, 3.9. and [8, Reference [ J. Mitola and J. Maguire, G.Q., Cognitive radio: Making oftware radio more peronal, IEEE Peronal Communication, vol. 6, no. 4, pp. 3 8, Augut 999.

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