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1 Chalers Publication Library HARQ Feedback in Spectru Sharing Networks This docuent has been downloaded fro Chalers Publication Library CPL. It is the author s version of a work that was accepted for publication in: IEEE Counications Letters ISSN: Citation for the published paper: Makki, B. ; Graell i Aat, A. ; Eriksson, T. 212 "HARQ Feedback in Spectru Sharing Networks". IEEE Counications Letters, vol. 169, pp Downloaded fro: Notice: Changes introduced as a result of publishing processes such as copy-editing and foratting ay not be reflected in this docuent. For a definitive version of this work, please refer to the published source. Please note that access to the published version ight require a subscription. Chalers Publication Library CPL offers the possibility of retrieving research publications produced at Chalers University of Technology. It covers all types of publications: articles, dissertations, licentiate theses, asters theses, conference papers, reports etc. Since 26 it is the official tool for Chalers official publication statistics. To ensure that Chalers research results are disseinated as widely as possible, an Open Access Policy has been adopted. The CPL service is adinistrated and aintained by Chalers Library. article starts on net page

2 1 HARQ Feedback in Spectru Sharing Networks Behrooz Makki, Aleandre Graell i Aat, Senior Meber, IEEE, and Thoas Eriksson Abstract This letter studies the throughput and the outage probability of spectru sharing networks utilizing hybrid autoatic repeat request HARQ feedback. We focus on the repetition tie diversity and the increental redundancy HARQ protocols where the results are obtained for both continuous and bursting counication odels. The channel data transission efficiency is investigated in the presence of both secondary user peak transission power and priary user received interference power constraints. Finally, we evaluate the effect of secondary-priary channel state inforation iperfection on the perforance of the secondary channel. Siulation results show that, while the throughput is not necessarily increased by HARQ, substantial outage probability reduction is achieved in all conditions. I. INTRODUCTION To tackle today s spectru shortage proble, several solutions have been proposed aong which spectru sharing is one of the ost proising ones [1] [6]. In a spectru sharing network, unlicensed secondary users SUs are peritted to work within the spectru resources of licensed priary users PUs as long as the PUs quality-of-service requireents are satisfied. Hybrid autoatic repeat request HARQ is an efficient approach for increasing the data transission efficiency of different counication setups. Utilizing HARQ in spectru sharing networks has recently attracted considerable attention, e.g., [3] [6]. In [3], [4], the SU works as a relay helping the PU, which uses increental redundancy INR HARQ. Also, in [5], [6] the INR HARQ is eploited by the PU for increasing its protection against the SU interferences. In this paper, as opposed to [3] [6] where the use of INR HARQ is liited to the PU, we consider both the repetition tie diversity RTD and the INR HARQ protocols in the secondary channel to study the data transission efficiency of spectru sharing networks. The goal is to analyze the SU-SU channel throughput and the SU outage probability under PU received interference power and SU peak transission power constraints. Considering block fading channels, the results are obtained for both continuous and bursting counication odels in the case where the SU transitter is provided with iperfect SU- PU channel state inforation CSI. The results indicate that ipleentation of HARQ does not necessarily increase the throughput. However, substantial outage probability reduction is achieved by HARQ in all conditions. II. SYSTEM MODEL Consider a block fading spectru sharing network where a PU shares the sae narrow-band frequency with an unlicensed SU. Let h pp, h ps, h sp and h ss be the fading rando variables in the PU-PU, PU-SU, SU-PU and SU-SU links, respectively. Correspondingly, we define the channel gains g pp. = hpp 2, g ps. = Aleandre Graell i Aat was supported by the Swedish Agency for Innovation Systes VINNOVA under the P MAGIC project. Behrooz Makki, Aleandre Graell i Aat and Thoas Eriksson are with the Departent of Signals and Systes, Chalers University of Technology, Gothenburg, Sweden, Eail: {behrooz.akki, aleandre.graell, thoase}@chalers.se h ps 2, g sp. = hsp 2 and g ss. = hss 2. The channel gains reain constant for a duration of L c channel uses, generally deterined by the channel coherence tie, and then change independently according to the fading probability density functions pdfs f gpp g, f gps g, f gsp g, f gss g, respectively. The siulations are focused on Rayleigh fading channels, f g = 1 µ e µ, where µ represents the fading paraeter deterined based on the path loss and shadowing between the terinals. Finally, the AWGN at the PU and the SU receivers is assued to have independent and identically distributed cople Gaussian distribution CN, N. Also, in harony with, e.g., [1] [6], the PU transission signal is supposed to have Gaussian pdf with power P p, which leads to AWGN interference at the SU receiver. We assue perfect CSI about the SU-SU and PU-SU channel gains at the SU receiver, which is an acceptable assuption in block fading channels [4], [6] [8]. Also, the SU transitter is provided with soe iperfect CSI of the SU-PU channel odeled by h sp = βh sp + 1 β 2 ε, ε CN,, β 1 1 where h sp is the SU-PU channel estiate provided at the SU transitter, β is a known correlation factor odeling the estiation quality, is the SU-PU fading paraeter and ε is a cople Gaussian variable independent of h sp. This is a well accepted odel for partial CSI [2], [9], [1]. A aiu of M retransission rounds are considered, i.e., the data is retransitted by the SU a aiu of M + 1 ties until it is successfully decoded by the SU receiver or the aiu nuber of rounds is reached. Both the RTD and the INR protocols are ipleented for the HARQ. Finally, the feedback bits are assued to be delivered at the SU transitter error- and delay-free. III. SYSTEM THROUGHPUT We call the transission of a codeword along with all its possible retransission rounds a packet. The long-ter throughput in nats-per-channel-use npcu is defined as [7] η =. D 2 l where D and l denote the epected value of the successfullydecoded inforation nats 1 and the total nuber of channel uses within a fading block, respectively. Both continuous and bursting counication schees [8] are considered. Under the continuous counication odel, it is assued that there is an infinite aount of inforation available at the SU transitter and it is always active. Thus, ultiple packets, each packet containing ultiple HARQ rounds, are transitted within one fading block of length L c. If the channel is good, any packets are sent within a fading block, while only few can be transitted within the sae period for bad 1 All results are presented in natural logarith basis.

3 2 channels. In this case, the long-ter throughput is calculated as follows. Let Rg ss, g ps be the SU instantaneous data rate of the HARQ approach for given gain realizations g ss and g ps. Then, the total nuber of inforation nats decoded in each state is obtained by Dg ss, g ps = L c Rg ss, g ps. Consequently, the longter throughput is given by η = E{L crg ss, g ps } = E{Rg ss, g ps } = L R, 3 c i.e., the channel average rate. Under the bursting counication odel, on the other hand, it is assued that there is a long idle period between the transission of two packets. Therefore, while the HARQ retransission rounds of each packet eperience the sae gains realizations, the channels change independently fro one packet to another. In this case, the denoinator of 2 is not constant and, as discussed in the sequel, should be calculated separately. More specifically, as opposed to the continuous counication odel, where all the L c channel uses of a fading block are utilized, in the bursting counication odel only one packet is sent within each block that, depending on the channels conditions, can be decoded by the SU receiver in different retransission rounds. Let A be the event that the data is successfully decoded at the -th, = 1,..., M + 1, retransission round of the HARQ protocol and not before. In this way, the syste throughput under the continuous counication assuption is obtained by η = R Pr{A } 4 where R represents the equivalent data rate after retransission rounds. Also, the data is lost and an outage happens if the data can not be decoded after M +1 retransission rounds. Therefore, the outage probability is found as Pr {outage} = 1 Pr{A }. 5 To find the syste throughput under the bursting counication odel, assue that D inforation nats are transitted in each packet transission. Provided that the data is decoded at any retransission round, all the D nats are received by the SU receiver. Therefore, the epected nuber of received inforation nats in each packet is D = D 1 Pr{outage}. 6 If the data retransission successfully stops at the -th retransission round the total nuber of channel uses is l n, where l n is the length of the codeword sent in the n- th retransission round. Also, there will be l n channel uses if an outage happens, as all possible retransission rounds are used. Hence, the epected nuber of channel uses within a packet is found as l = l n Pr{A } + l n Pr{outage} 7 and the throughput in the bursting counication odel is D1 Pr{outage} η = l n Pr{A } + l n Pr{outage}. 8 In the following, 4-8 are studied in ore detail for both the RTD and the INR HARQ protocols. A. RTD protocol Using RTD, D inforation nats are encoded in each codeword of length L, L L c, i.e., the initial transission rate is R = D L. The sae codeword is retransitted in the successive retransission rounds. Hence, the equivalent transission rate at the end of the -th retransission round is R = D L = R. Also, the receiver perfors aiu ratio cobining of the received signals. Thus, the SU received signal-to-interferenceand-noise ratio SINR in the -th retransission round is γ = Ω, Ω =. P s g ss 9 P p g ps + N where P s denotes the SU transission power. Therefore, the probability ter Pr{A } is obtained by 2 Pr {A } = Pr {log1 + 1Ω R < log1 + Ω} = F Ω er 1 1 F Ω er 1 1 and the outage probability is found as Pr{outage} = Pr {log1 + M + 1Ω < R} = F Ω er 1 M + 1. Here, F Ω is the cuulative distribution function cdf of the auiliary variable Ω obtained based on the PU and the SU quality-of-service requireents see Subsection III.C. Considering R = R and 1 the throughput in the continuous counication odel 4 is obtained easily. On the other hand, as we have R = D L and l = L, the throughput under the bursting counication assuption 8 is rephrased as R1 Pr{outage} η = Pr{A } + M + 1 Pr{outage}. 11 B. INR protocol In the INR schee, new variable-length codewords are sent in the successive retransission rounds of a packet. Then, in each retransission round the essage is decoded by the SU receiver using all previously received signals of the packet. Hence, denoting the equivalent transission rate at the end of the D -th retransission round by R =, the probability ln ter Pr{A }, the throughput in the continuous counication odel, and the outage probability are Pr {A } = Pr {R log1 + Ω < R 1 } 12 = F Ω e R 1 1 F Ω e R 1, η = R FΩ e R 1 1 F Ω e R 1, 13 Pr{outage} = Pr{log1 + Ω < R } = F Ω e R 1, respectively, and the throughput in the bursting counication odel is 1 Pr{outage} η = 1 R Pr{A } + 1 R Pr{outage}. 14 Here, 12 is based on the fact that the data is decoded at the end of the -th retransission round if 1 it has not been decoded before, i.e., log1 + Ω < R 1 <... < R 1, and 2 the equivalent transission rate at the end of the -th tie slot is supported by the channel gains realizations, that is, R log1 + Ω. 2 In 1, we have used the fact that with an equivalent SINR the aiu decodable transission rate is 1 log1 + if a codeword is repeated ties.

4 3 C. Transission power constraints We consider two siultaneous transission power constraints; 1 the SU peak transission power should be less than a threshold, i.e., P s, and 2 the PU received interference power should not eceed a given value. Therefore, the SU transission power is selected as P s = in, Ip g sp where g sp = h sp 2 is the SU-PU channel estiate available at the SU transitter. In this way, as illustrated in Appendi A, the cdf of the auiliary variable Ω, defined in 9, is found as F Ω = 1 1 e Ip µsppa e N µsspa 1+ Ppµps µsspa µssip N µ e Ppµps + µssip µspµpspp spµ psp p Γ 1, P pµ ps + µ ss N + µssip µ sp 15 where Γ, y is the incoplete Gaa function. As g sp g sp, the PU received interference power φ p = P s g sp ay eceed the threshold. However, using the PU received interference cdf F φp = 1 e +e µsppa Qβ µsppa 2 + t r Q u r 2, P, 2Ip aw P 1 aw t r w = 1 β 2, u = β2 w + Ipµsp w t = u 4Ip w, r = u 2 16β2 w 2 u+r 2 e u 2Pa I 2β w see Appendi A one can find a new threshold Îp such that the PU received interference threshold is satisfied with soe probability π, i.e., Pr{φ p < } π. The new threshold is found as the solution of F φp Îp = π. Also, since Q, = 1 and I = 1, the interference cdf F φp is rephrased as F φp = t 16 2 r as, i.e., under relaed SU peak power constraint. Finally, the PU SINR constraint is not considered here, although it can be apped to the interference constraint in soe cases. Also, the PU SINR constraint is norally studied under iperfect PU-PU CSI assuption, which is not considered in our odel. IV. SIMULATION RESULTS AND DISCUSSIONS For both protocols, the initial transission rate is set to R 1 =.5. Also, we consider equal-length coding for the INR which, as D R =, leads to R n= ln = R1, i.e., the sae rates as in the RTD schee. Setting = 2 and P p =.5, Figs. 1a and 1b show the throughput and the outage probability of the considered protocols in the bursting and continuous counication odels under perfect SU-PU CSI assuption β = 1. Here, the syste perforance with no HARQ feedback, i.e., M =, is considered in the figures as a coparison yardstick. Note that the outage probability is the sae in these counication odels. Also, with proper scaling, the results can be apped to the case with iperfect SU-PU CSI. Assuing iperfect SU-PU CSI β =.8, Figs. 2a and 2b study the syste throughput as a function of the PU received interference probability constraint π and the PU transission power P p, respectively. Here, the results are obtained for a aiu of M = 1 retransission round and under different SU peak transission power constraints. Finally, in all siulations the fading paraeters are set to µ ss = µ ps = = 1. The results ephasize a nuber of points listed as follows: INR outperfors the RTD schee in ters of both the throughput Fig. 1a and the outage probability Fig. 1b. Depending on the fading pdfs, HARQ does not necessarily increase the syste throughput. For Rayleigh fading channels in particular, the HARQ-based throughput with the continuous bursting counication odel is higher lower than the throughput when no HARQ is considered Fig. 1a. The intuition behind the better syste perforance in the continuous odel is that the good channel conditions are ore efficiently eploited in this odel. Particularly, using Jensen s inequality, conveity of f = 1, 7, 13 and 14 for, e.g., the INR protocol, we have η continuous > D1 Pr{outage}2 l D1 Pr{outage} 2 l n Pr{A } = 1 Pr{outage}η bursting which ephasizes the validity of the arguent as the outage probability vanishes, for instance when the nuber of retransission rounds increases. The sae inequality can be written for the RTD protocol. Finally, although not seen in the figures, the sae conclusion is valid when, using the closed for epressions of the cdfs, e.g., 15, the transission rates are optiized, in ters of throughput, via 4, 11, 13 and 14. In all conditions, substantial outage probability reduction is achieved with liited nuber of retransission rounds Fig. 1b. Thus, the ipleentation of HARQ is ore eaningful when the goal is to reduce the channel outage probability. With iperfect SU-PU CSI, the PU tolerance, odeled by the probability constraint π, plays a great role in the SU-SU channel throughput; with relaed PU received interference constraints sall π s the syste throughput increases. However, the ore secure the interference constraint should be satisfied, the less throughput is achieved at the secondary channel, converging to zero Fig. 2a. The throughput difference between the bursting and continuous odels diinishes under hard PU received interference power constraints, i.e., when decreases Fig. 2a. The throughput is ore affected by the SU peak transission power constraint as the PU transission power increases, i.e., when the SU received SINR decreases Fig.2b. V. CONCLUSION This letter studies the effect of HARQ on the perforance of spectru sharing networks. The results are obtained under bursting and continuous counication odels when the SU is provided with iperfect SU-PU CSI. Under SU peak transission power and PU received interference power constraints, the SU-SU channel throughput and the SU outage probability are deterined for the INR and the RTD HARQ protocols. The results show that, although ipleenting HARQ protocols does not necessarily increase the syste throughput in Rayleigh fading channels, considerable outage probability reduction is achieved in various conditions. Moreover, with iperfect interference inforation available at the SU transitter, the PU tolerance significantly affects the SU perforance. For different PU interference and SU peak transission power constraints, the INR protocol outperfors the RTD schee in ters of

5 4 Outage probability P =2, P =.5, β=1 INR a p RTD M=1, rates:.5, Received interference power constraint, 1 P =2, P =.5, β=1 a p 1 1 Continuous a Bursting M=1, rates:.5,.25, M=2, rates=.5,.25,.166 b RTD, M=1 M=1 INR, M=1 RTD, M=2 INR, M=2 M= Received interference power constraint, Figure 1. a and b outage probability vs PU received interference power constraint, perfect SU-PU CSI β = 1, = 2, P p = INR, continuous RTD, continuous INR, bursting RTD, bursting.1 I =.2 p Priary user received interference probability constraint, π.11.1 RTD Relaed peak power constraint, β=.8, M=1, rates=.5,.25,p p =1, INR = Priary user transission power, P p a Continuous odel, π=.8, β=.8, =.5 M=1, rates:.5,.25, b =1 =4 Figure 2. vs a PU received interference probability constraint π and b PU transission power P p, iperfect SU-PU CSI β =.8, a aiu of M = 1 retransission round. Figures 2a and 2b are obtained for relaed SU peak power constraint and continuous counication odel, respectively. both the throughput and the outage probability. Also, higher rates are obtained in the continuous counication odel when copared with the bursting counication odel. APPENDIX A CALCULATING THE CDFS F Ω AND F φp I P Define the auiliary rando variable Z =. P s g ss. Since P s = in, Ip g sp, the cdf { of Z is found as } F Z z = 1 Pr g ss > z & g ss > z gsp = 1 Pr{ g sp Ip } Pr{g ss > z } Ip f gsp y 1 F gss zy dy Pa a = 1 e z µsspa 1 e Ip µsppa e Ip µsppa + z µsspa 1+ µsp µssip z 17 where a is based on the fact that for Rayleigh fading channels and the considered CSI iperfection odel, 1, we have f gsp = 1 e µsp [2], [9], [1]. In this way, fro 17, F Ω = f gps zf Z P p z + N dz and the definition of the incoplete Gaa function Γ, y = y u 1 e u du, the cdf F Ω is found as stated in 15. Further, the interference cdf F φp can be written as F φp = Pr{P s g sp } = 1 Pr{g sp & g sp Ipgsp } = 1 18 Ipu f gsp, g sp u, vdudv. Pa Here, f gsp, g sp is the joint pdf of the variables g sp and g sp which, using 1 and siple variable transforations, is found as y+z f gsp, g sp y, z = e 1 β 2 µsp 2β yz 1 β 2 µ 2 I sp 1 β 2 19 where I is the zeroth-order odified Bessel function of the first kind [2], [9] [12]. Therefore, 18 is rephrased as 1 F φp = 1 1 β 2 µ e y 2 1 β 2 µsp dy sp b = 1 e µsppa + 1 Pa e y µsp Q c = 1 e µsppa + t +e µsppa Q β Pa Ipy e z 1 β 2 µsp I 2β yz 1 β 2 dz 2y 2Ipy 1 β 2 β, 1 β 2 2, u+r 2 r Q u r 2 P, 2Ip aw w w = 1 β 2, u = β2 w + Ipµsp w t = u 4Ip w, r = u 2 16β2 w. 2 dy t u r e 2Pa I 2β P aw Again, b is obtained by variable transfor θ = z and the definition of the Marcu Q-function Qa, b = b ye y 2 +a 2 2 I aydy. Finally, c follows fro variable transfor ξ = y and [11, eq. 55]. REFERENCES [1] V. Asghari and S. Aissa, Resource anageent in spectru-sharing cognitive radio broadcast channels: Adaptive tie and power allocation, IEEE Trans. on Coun., vol. 59, no. 5, pp , May 211. [2] H. A. Suraweera, P. J. Sith, and M. Shafi, Capacity liits and perforance analysis of cognitive radio with iperfect channel knowledge, IEEE Trans. on Veh. Tech., vol. 59, no. 4, pp , May 21. [3] W. C. Ao and K. C. Chen, End-to-end HARQ in cognitive radio networks, in WCNC, 21, pp [4] R. Narasihan, Hybrid-ARQ interference channels with receiver cooperation, ICC, pp. 1 5, May 21. [5] K. Eswaran, et. al, Bits through ARQs: Spectru sharing with a priary packet syste, in ISIT, June 27, pp [6] R. A. Tannious and A. Nosratinia, Cognitive radio protocols based on eploiting hybrid ARQ retransissions, IEEE Trans. on Wireless Coun., vol. 9, no. 9, pp , 21. [7] G. Caire and D. Tuninetti, The throughput of hybrid-arq protocols for the Gaussian collision channel, IEEE Trans. on Info. Theory, vol. 47, no. 5, pp , 21. [8] C. Shen, T. Liu, and M. P. Fitz, On the average rate perforance of hybrid-arq in quasi-static fading channels, IEEE Trans. on Coun., vol. 57, no. 11, pp , Nov. 29. [9] B. Makki, et. al, On the capacity of rayleigh-fading correlated spectru sharing networks, Eura. J. on Wireless Coun. and Net., no. 83, 211. [1] K. S. Ahn and R. W. Heath, Perforance analysis of aiu ratio cobining with iperfect channel estiation in the presence of cochannel interferences, IEEE Trans. on Wireless Coun., vol. 8, no. 3, pp , March 29. [11] A. H. Nuttall, Soe integrals involving the Q-function, Naval Underwater Syst. Cent., New London, CT, Tech. Rep. 4297, April [12] C. Tellabura and A. D. S. Jayalath, Generation of bivariate rayleigh and nakagai-m fading envelopes, IEEE Coun. Lett., vol. 4, no. 5, pp , May 2.