Analytic Performance Evaluation of Underlay Relay Cognitive Networks with Channel Estimation Errors

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1 Analytic Performance Evaluation of Underlay Relay Cognitive Network with Channel Etimation Error Khuong Ho-Van, Pachali C. Sofotaio, Son Vo Que, Tuan Dang Anh, Thai Pham Quang, Lien Pham Hong 3 arxiv: v [c.it] 9 Dec 6 Department of Telecommunication Engineering, HoChiMinh City Univerity of Technology, HoChiMinh City, Vietnam. khuong.hovan@yahoo.ca, {onvq, datuang}@hcmut.edu.vn, pqthai.hcmut@gmail.com School of Electronic and Electrical Engineering, Univerity of Leed, LS 9JT, Leed, United Kingdom. p.ofotaio@leed.ac.uk 3 Department of Electrical and Electronic Engineering, Univerity of Technical Education, HoChiMinh City, Vietnam. Abtract Thi paper evaluate the bit error rate (BER) performance of underlay relay cognitive network with decodeand-forward (DF) relay in arbitrary number of hop over Rayleigh fading with channel etimation error. In order to facilitate the performance evaluation analytically we derive a novel exact cloed-form repreentation for the correponding BER which i validated through extenive comparion with reult from Monte-Carlo imulation. The propoed expreion involved well known elementary and pecial function which render it computational realization rather imple and traightforward. A a reult, the need for laboriou, energy exhautive and timeconuming computer imulation can be ultimately omitted. Numerou reult illutrate that the performance of underlay relay cognitive network i, a expected, ignificantly degraded by channel etimation error and that i highly dependent upon of both the network topology and the number of hop. Index Term Multi-hop communication, channel etimation error, underlay cognitive radio. I. INTRODUCTION It wa recently pointed out by a pectrum uage urvey from the Federal Communication Commiion (FCC), that the current licened pectrum ituation i ignificantly underutilized []. Contrary to that, the current availability of pectrum reource for mot emerging wirele application uch a video calling, online high-definition video treaming, high-peed Internet acce through mobile device, etc. are particularly carce. In an attempt to improve the pectrum utilization in wirele communication ytem, cognitive radio (CR) technology wa propoed a a promiing technology [] [8]. In cognitive radio, econdary uer-su (or unlicened uer) are generally allowed to ue the licened band primarily allotted to primary uer-pu (or licened uer), unle their operation interfere with the etablihed communication of PU. Thi operation can be realized in three ditinctive mode: underlay, overlay and interweave [9]. In the underlay mode, SU are allowed to ue the pectrum when the interference caued by SU on PU i within a tolerated range by PU. Thi mode i more preferable than it two counterpart thank to it low implementation complexity []. phamhonglien5@gmail.com Due to the interference power contraint impoed on SU operating in the underlay mode, their tranmit power i limited and a uch, their tranmiion range i reduced ubtantially. To overcome thi contraint, SU can apply relaying technique, which take advantage of horter range communication that reult to lower path lo effect. Among variou relaying technique, decode-and-forward (DF) and amplify-andforward (AF) deployment have been extenively invetigated []. In DF, each relay decode information from the ource, re-encode it, and forward it to the detination. In AF, each relay imply amplifie the received ignal and forward it to the detination. Due to it capability of regenerating noie-free relayed ignal, DF i employed in thi paper. Thi paper invetigate underlay DF multi-hop cognitive network with arbitrary number of hop. Mot relevant work conidering uch network deployment focu in outage probability analyi [9], [] [7], and BER analyi [8] [] auming perfect channel etimation and two-hop communication. It i alo recalled here that channel tate information (CSI) i eential for coherent detection; neverthele, exiting channel etimator are unable to provide and guarantee perfect CSI. A a conequence, the impact of imperfect CSI on the ytem performance hould be conidered realitically. In [], the BER analyi for ingle-hop cognitive network i preented under the aumption of imperfect CSI only for SU-PU link. In [], an exact outage probability expreion wa propoed for AF dual-hop cognitive network. However, to the bet of our knowledge, the exact BER analyi for underlay DF N-hop cognitive network, with N being arbitrary integer, and imperfect CSI on all wirele channel, ha not been addreed in the open technical literature. Motivated by thi, thi paper i devoted to an analytic invetigation of thi topic by deriving a correponding exact cloed-form BER expreion. The derived expreion i validated by extenive computer imulation and i utilized in evaluating the correponding ytem performance. The work in [] derive an approximate cloed-form BER expreion.

2 The tructure of thi paper i a follow: The next ection preent the ytem model and the CSI imperfection model. The BER analyi i dicued in Section III while imulated and analytical reult are preented in Section IV for derivation validity and performance evaluation. Finally, the paper i concluded in Section V. II. SYSTEM MODEL The underlay cognitive DF multi-hop network model under conideration i depicted in Fig., where N econdary relay (SR) numbered from to N ait the tranmiion of the econdary ource (SS) to the econdary detination (SD) N. The SS and SR ue the ame pectrum a a primary uer P. The direct communication between SS and SD i bypaed, which i conidered reaonable in cenario where SS and SD are too far apart or their communication link i blocked due to evere hadowing and fading. We aume that the channel between any pair of tranmitter and receiver experience independent block frequency-flat Rayleigh fading i.e., frequency-flat fading i invariant during one phae but independently changed from one to another. Therefore, the channel coefficient between the tranmitter t {,,...,N } and the receiver r {,,...,N,P} i h tr CN (,η tr = d α ) tr, where d tr i the ditance between the two terminal and α i the path-lo exponent [3]. h P R e () h P h P R e () h Fig.. h P Sytem model. h (N-)P N- R e (N) h (N-)N N An N-hop communication time interval conit of N phae. In the firt phae, SS tranmit a equence of K modulated ymbol x = [x (),x (),...,x (K)] with the ymbol energy, B i.e., E{ x (k) } = B where E{ } denote the expectation and k i the time index. SR demodulate the received ignal from SS and re-modulate the demodulated ymbol a x = [x (),x (),...,x (K)] with the ymbol energy, B, before forwarding to SR in the econd phae. The proce continue until the ignal reache SD N. Without the notation confuion, the time index i omitted in the equel h CN(m,v) denote an m-mean circular ymmetric complex Gauian random variable with variance v. and hence, the received ignal through the hop r can be expreed a y tr = h tr x t +n tr, () wherey tr denote a ignal received at the noder from the node t = r and n tr CN(,N ) i additive white Gauian noie at the node r. In the underlay relay cognitive network (e.g., [6], [4]), the SU t tranmit power i limited uch that the interference impoed on PU i under control. Without CSI error, thi interference contraint can be addreed a B t I T / h tp where I T i the maximum interference level that PU till operate reliably. For the maximum tranmiion range, B t = I T / h tp i et. Following [5] [8], we chooe the CSI imperfection model a h tr = ĥtr +ε tr, () where ĥtr i the etimate of the t r channel and ε tr i the CSI error. We aume that h tr and ĥtr are jointly ergodic and tationary Gauian( procee. Therefore, ) ε tr CN (,σ tr ) and ĥtr CN, λ tr = η tr σ tr with σ tr repreenting the quality of the channel etimator. For example [5], for the linear-minimum-mean-quare-error (LMMSE) etimator, { σ tr = E h tr } E{ ĥ tr } = /(L p γ tr,training +) where L p i the number of pilot ymbol, γ tr,training = E{γ tr,training } = B t,training η tr /N i the average SNR of pilot ymbol for the t r channel, and B t,training i the pilot power. III. ERROR PROBABILITY ANALYSIS Due to CSI error, the tranmit power of the node t i modified a B t = I T/ ĥtp. Then, there are two poibilitie: ĥtp h tp and ĥtp > h tp. Setting the tranmit power a B t = I T / ĥtp meet the interference power contraint for h tp ĥtp, ince thi cae reult in the interference power a B t h tp = I T h tp / ĥtp I T, but not for h tp > ĥtp, ince thi cae reult in the interference power a B t h tp = I T h tp / ĥtp > I T. Given that E{ ĥ tp } { E h tp } where the equality hold for no CSI error, on average uch tranmit power etting may not meet the interference power contraint i.e., the interference at P i greater than I T. Therefore, the primary ytem performance may be everely degraded if the channel etimator i not efficient. Conequently, in order to propoe olution to interference reduction on primary ytem, tatitic of interference at the PU receiver hould be analyzed. The mot important tatitic i the probability that the interference exceed I T, namely the interference probability P I a ued in []. It i noted that P I i derived for underlay AF dual-hop cognitive network [] and for underlay ingle-hop cognitive network [] with the CSI imperfection model lightly different 3. Due 3 The CSI imperfection model in [] and [] i ĥtr = ρtrhtr + ρ trεtr where ρtr i the correlation coefficient between ĥtr and htr.

3 to the pace limitation, the interference probability analyi i deferred to the journal verion of thi paper. Intead, we focu on the BER analyi for underlay relay cognitive network. To thi effect, uing the CSI imperfection model in (), we rewrite () a, y tr = ĥ tr x }{{} t + ε tr x t +n tr. (3) }{{} deired ignal effective noie According to (3), the effective SNR of the t r channel taking CSI error into account i expreed a, ĥtr E { x t } γ tr = E { ε tr x t +n tr } = = B t ĥtr B tσ tr +N σ tr + ĥtr ĥtp /µ = z tr, (4) d tr where z tr = ĥtr, d tr = σ tr + ĥtp /µ, and µ = I T /N. The average BER at the node r for quare M-QAM with M = q (q even) and rectangular M-QAM with M = q (q odd) modulation cheme 4 i expreed in (5) which i cited from [9, eq. (6)] and [9, eq. ()], correpondingly. In (5), we define g = u = 3 (M ), (6) 6 (I +J ), (7) I = (q )/, (8) J = (q+)/, (9) and ψ(,v,m;γ) in () in which Q(.) i the Q-function [3, eq. ()], [33, eq. ()]. Next, we derive f γtr (γ) in order to enable the derivation of an explicit expreion for (5). Since ĥtr CN and ĥtp CN ( ), λ tr (, λ tp ), the probability denity function (pdf ) of z tr and d tr are f ztr (x) = λ tr e λtrx and f dtr (x) = λ tp µe λtpµ(x σtr), repectively. A a reult, the pdf of γ tr = z tr /d tr in (4) i given a [3, eq. (6-6)] f γtr (x) = yf ztr (yx)f dtr (y)dy = κ trµe λtpµσtr (x+κ tr µ), () 4 The average BER of other modulation cheme uch a M-PSK can be derived in the ame approach. where κ tr = λ tp /λ tr. Inerting () into (5) yield, { θ(i,u,wtr ( )+θ(j,u,w tr ),q odd R e (r) = M,g,Wtr ) θ,q even () where W tr = {M,κ tr,µ,λ tp,σ tr } i a et of parameter and θ(,v,w tr ) i defined in (3). Alo, ζ(β,a) in (3) i defined a ζ(β,a) = Q ( βx ) dx. (4) (x+a) Applying the integration by part, we obtain the cloed-form of ζ(β,a) a follow, ζ(β,a) = a β π = βa βe a π = βπ a a x where erf (x) = π a e βa e βx (x+a) x dx e βy y y a dy [ ( )] βa erf, (5) e t dt i the error function [37, eq. (8.5.)] and the cloed-form expreion of the integral in the econd equality i deduced with the aid of [37, eq. (3.363.)]. Given the et of the average BER of all hop {R e (),,R e (N)}, the exact cloed-form average BER of the underlay DF multi-hop cognitive network i expreed a [35, eq. (9)] N N R e = R e (n) ( R e (j)). (6) n= j=n+ IV. NUMERICAL RESULTS For illutration purpoe, we arbitrarily elect uer coordinate a hown in Fig. : P at (.7,.5), SS at (,), SR at (.6,.), SR at (.8,.3), SD 3 at (,). SS, SD 3, and P are alway fixed and thu, for -hop cae only SR i conidered. Alo, the number on the line i the ditance between two correponding terminal. The network topology in Fig. i applied to all following reult. We conider the path-lo exponent of α = 3 and the CSI error variance ofσ tr = /(L p B t,training η tr /N +), [5]. The value of B t,training i elected uch that the average received power at P doe not exceed I T (i.e., B t,training η tr I T ) 5. A a reult, for illutration purpoe we elect B t,training = I T /η tp. 5 The tudy of channel etimator i outide the cope of thi paper. Therefore, the election of B t,training in thi paper i jut an example to demontrate the effect of CSI imperfection on the BER of underlay relay cognitive network.

4 R e (r) = {ψ(i,u,m;γ)+ψ(j,u,m;γ)}f γtr (γ)dγ,q odd ( M,g,M;γ ) ψ f γtr (γ)dγ,q even. (5) ψ(,v,m;γ) = log M log k= ( k ) i= ( ) ( ) i k Q (i+) vγ ( ). () k i + θ(,v,w tr ) = log M log k= ( k ) i= ( ) i k ( κ tr µe λtpµσtr ζ ( k i k + ) (i+) v,κ tp µ ). (3) (.7,.5) (.6,.) P.. (.8,.3) BER hop Perfect CSI (Analyi) Perfect CSI (Simulation) Imperfect CSI (Analyi) Imperfect CSI (Simulation) 3 hop (,) (,) Fig.. Network topology. Fig. 3 and 4 compare imulated and numerical reult for two typical modulation level, namely, -QAM for odd q and 4-QAM for even q, N = {,3}, and different degree of CSI availability - perfect CSI and imperfect CSI with L p =. It i een that analytical reult are well matched with imulated one, validating the derived expreion. Additionally, the BER performance i improved with repect to the increae in I T. Thi i obviou ince I T impoe a contraint on the tranmit power and the higher I T, the higher the tranmit power, eventually enhancing communication reliability. Moreover, the BER performance i deteriorated with the lack of CSI. Fig. 5 invetigate the impact of the quality of the channel etimator on the BER. The quality of the channel etimator can be enhanced by increaing the number of pilot ymbol L p at the cot of the bandwidth lo due to increaed overhead. The reult are reaonable ince the BER performance i improved with the increaed L p. Furthermore, for the elected channel etimator model, the performance i aturated at L p = 4. Given the pecific network topology in Fig., the reult in 5 5 I /N (db) T Fig. 3. BER veru I T /N (-QAM). Fig. 3, 4, and 5 illutrate that 3-hop communication i wort than -hop communication for any et {L p,α,i T,M}. Thi mean that in underlay DF multi-hop cognitive network the advantage of the 3-hop communication over -hop communication in term of the path lo reduction, e.g., the ditance from the lat relay to the detination in the 3-hop cae (SR ) i maller than that in the -hop cae (SR ), can not ometime turn into the performance improvement. Thi i becaue the lat relay in the 3-hop cae i cloer to the primary uer than in the -hop cae, cauing higher interference. Thu, the lat relay in the 3-hop cae hould utilize lower tranmit

5 BER BER hop Perfect CSI (Analyi) Perfect CSI (Simulation) Imperfect CSI (Analyi) Imperfect CSI (Simulation) 3 hop 5 5 I /N (db) T Fig. 4. BER veru I T /N (4-QAM). QAM & hop 4 QAM & hop QAM & 3 hop 4 QAM & 3 hop L p Fig. 5. BER veru L p (I T /N =,ρ = db). power than in the -hop cae for reducing the interference level to the primary uer, leading to higher performance degradation. Thee reult recommend that the relay election in underlay DF multi-hop cognitive network i crucial in enhancing the network performance. A good relay not only provide reliable communication to the detination but alo caue le interference to the primary uer. The problem of the relay election will be conidered in a future work. V. CONCLUSION Thi paper invetigated analytically the BER performance of underlay DF multi-hop cognitive network over Rayleigh fading channel in conideration of imperfect CSI. The derived expreion wa hown to have a convenient algebraic form which allow traightforward to timely evaluation of the correponding performance. The propoed analytical reult were upported and validated with reult from computer imulation while variou reult demontrated that the imperfect CSI affect ignificantly the BER of underlay DF multi-hop cognitive network. In addition, it wa hown that the BER performance i dependent upon both the number of hop and the network topology. REFERENCES [] FCC. Spectrum policy tak force report. ET Docket -35,. [] J. Mitola III, Cognitive radio an integrated agent architecture for oftware defined radio, Ph.D. diertation, Dept. Teleinformatic, KTH Royal Intitute of Technology, Stockholm, Sweden,. [3] K. Ho-Van, P. C. Sofotaio, Bit Error Rate of Underlay Multi-hop Cognitive Network in the Preence of Multipath Fading, in IEEE International Conference on Ubiquitou and Future Network (ICUFN 3), pp. 6-64, Da Nang, Vietnam, July 3. [4] K. Ho-Van, P. C. Sofotaio, Outage Behaviour of Cooperative Underlay Cognitive Network with Inaccurate Channel Etimation, in IEEE International Conference on Ubiquitou and Future Network (ICUFN 3), pp. 5-55, Da Nang, Vietnam, July 3. [5] K. Ho-Van, P. C. Sofotaio, Exact BER Analyi of Underlay Decodeand-Forward Multi-hop Cognitive Network with Etimation Error, IET Communication, To appear. [6] F. R. V Guimarae, D. B. da Cota, T. A. Tifti, C. C. Cavalcante, and G. K. Karagiannidi, Multi-Uer and Multi-Relay Cognitive Radio Network Under Spectrum Sharing Contraint, IEEE Tranaction on Vehicular Technology, accepted for publication. [7] K. Ho-Van, P. C. Sofotaio, S. V. Que, T. D. Anh, T. P. Quang, L. P. Hong, Analytic Performance Evaluation of Underlay Relay Cognitive Network with Channel Etimation Error, Accepted for publication in IEEE International Conference on Advanced Technologie for Communication (ATC 3), HoChiMinh City, Vietnam, Oct. 3. [8] K. Ho-Van, P. C. Sofotaio, S. Freear, Underlay Cooperative Cognitive Network with Imperfect Nakagami-m Fading Channel Information and Strict Tranmit Power Contraint: Interference Statitic and Outage Probability Analyi, IEEE/KICS Journal of Communication and Network, To appear. [9] J. Lee, H. Wang, J.G. Andrew, and D. Hong, Outage probability of cognitive relay network with interference contraint, IEEE Tran. Wirel. Commun., vol., pp , Feb.. [] A. Goldmith, S.A. Jafar, I. Maric, and S. Srinivaa, Breaking pectrum gridlock with cognitive radio: An information theoretic perpective, Proceeding of the IEEE, vol. 97, pp , May 9. [] J.N. Laneman, D.N.C. Te, and G.W. Wornell, Cooperative diverity in wirele network: Efficient protocol and outage behavior, IEEE Tran. Infor. Theory, vol. 5, pp , Dec. 4. [] J. P. Hong, B. Hong, T. W. Ban, W. Choi, On the cooperative diverity gain in underlay cognitive radio ytem, IEEE Tran. Commun., vol. 6, no., pp. 9 9, Jan..

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