Spectrum Sharing with Multi-hop Relaying

Transcription

1 Spectrum Saring wit Multi-op Relaying Yong XIAO and Guoan Bi Scool of Electrical and Electronic Engineering Nanyang Tecnological University, Singapore xiao001 and Abstract Spectrum saring is a tecnique in wic some unlicensed users communicated wit eac oter in te same frequency band as te licensed users. Tis is one of te most important metods to improve te utilization efficiency of te pysically limited spectrum resources for te cognitive radio systems. However, ow to improve te performance of te unlicensed users and simultaneously maintain te interference temperature, due to te transmission of te unlicensed users, at te licensed users is still an callenging problem. In tis paper, we try to improve te performance of te spatial spectrum saring system by using multi-op relaying. Compared to te direct transmission, multi-op relaying could reduce te interference temperature and introduce more flexibility on te transmission by using proper routing sceme. To investigate te performance gain of te multi-op relaying, te acievable rate of te multiop relay cannel for te spatial spectrum saring system is studied and compared to te direct transmission. Te optimal power allocation metod is proposed and te conditions of wic te multi-op relaying improves te acievable rate of te direct transmission under te spatial spectrum saring constraints are discussed. Index Terms Spectrum saring, relay cannel, cognitive radio. I. INTRODUCTION A recent finding publised in te Spectrum Policy Task Force SPTF by FCC [1] sows tat te allocated spectrum is eiter unused or rarely used for most of te time. To increase te spectrum utilization, a new tecnology, known as spectrum saring SS, is introduced to allow te unlicensed users, called secondary users SU, to transmit information witin te same frequency band as te licensed users, called primary users PUs. For a practical SS system, te main callenge is to maximize te performance of SUs and simultaneously minimize te interference, known as te interference temperature, wic is caused by te transmission of te SUs at te PUs []. Following te same line as tat in [], te existing SS metods can be categorized into two types: temporal spectrum saring TSS and spatial spectrum saring SSS. In te TSS, te SUs detect te existence of te transmission of PUs in te licensed frequency band and only transmit information wen te licensed frequency band is not used by te PUs. In te SSS, bot te SUs and PUs simultaneously transmit information in te same frequency band and te SUs control teir transmitted powers to make sure te interference temperatures at te PUs are lower tan a desire level. In tis paper, we focus on te SSS system and study a new metod, called te multi-op relaying, to improve te performance of te SUs witout increasing te interference temperature of te PU networks. In our network model, te SUs not only take advantage of te licensed spectrum of te PUs but also exploit te intermediate SUs to forward information to te final secondary receiver. To study te effects of te multi-op relaying on te acievable rate of te SU network for te SSS system, we consider a simple network model in Figure 1. In our network model, we assume a secondary sender tries to transmit information to a secondary receiver in te primary user networks, and tere is an intermediate node between te pat connecting te secondary sender and receiver. If witout multi-op relaying, te intermediate secondary node sould keep silent during te entire transmission process. In tis paper, we study te case tat te secondary sender-receiver pair tries to exploit te intermediate node to serve as te secondary relay. Several advantages can be obtained by using te above setting: 1 Exploiting te intermediate nodes to relay information could reduce te transmitted power of te sender and ence decrease te interference temperature at te PUs, Te transmission route provides more flexibility for te sender-receiver pair to furter reduce te interference temperature at te PUs, for example, by allowing te SUs to coose a circular multi-op route to avoid te possible interference to te nearby PUs. Te disadvantage of te above setting is tat, by using te intermediate secondary nodes to relay signals, tere will be more secondary transmitters wic may potentially increase te interference temperature on te primary user network. Terefore, in tis paper, we try to answer te following two questions: 1 Wen te multi-op relaying could improve te performance of te acievable rate under SSS constraints? How muc performance improvement can be expected by exploiting te intermediate secondary node? To study te above issues, we derive te acievable rate of te multi-op relay cannel under SSS constraints. We also discuss te conditions tat te multi-op relaying is able to improve te acievable rates of te direct transmission system. Te optimal power allocation metod is proposed to furter improve te performance of te multi-op relay cannel witout increasing te interference temperature at PUs. Te rest of tis paper is organized as follows. Te network model and preliminary results are presented in section II. Te performance improvement brougt by using te multiop relaying under SSS system are discussed in sections III, and tis paper is concluded in section IV APSIPA. All rigts reserved.

2 II. NETWORK MODEL AND PRELIMINARY In our model of te spatial spectrum saring network sown in Figure 1, a secondary sender is to send information to te secondary receiver. To maintain a priority for te communications among te PUs, te interferences caused by te secondary transmitters on te primary receivers are limited by a tresold Q. In tis paper, we assume te maximum tolerable interference temperatures at eac primary users are te same wit eac oter. In order to simplify our description, in tis paper, we assume tat eac secondary transmitter always as te best conditioned cannel wit its closest primary receiver. Terefore, we neglect oter primary receivers tat are relatively far from te secondary transmitters and only consider te case tat two secondary transmitters sare te same frequency wit two primary receivers, as sown in Figure 1. We label te secondary sender, secondary relay, and secondary receiver as 1,,, respectively, and label te closest primary receivers of te secondary sender 1 and relay as 1 and, respectively. Denote te fading coefficients of te cannels connecting two nodes as ij, for i, j [1,,, 1, ]. Te cannel fading coefficients are defined as follows, ij = ij, 1 d δ ij were ij is a random variable, d ij is te distance between nodes i and j, and δ is te cannel attenuation exponent. A sequence of source messages w = {w 1,w,.., w b } is transmitted from te secondary sender to te secondary receiver. Assume tat eac message is encoded into n symbols, were w i [1, nr ], i [1,b] and R is te overall transmission rate. In tis paper, we assume te transmitted signals, denoted as x 1 and x, from te secondary sender and relay are zeromean Gaussian distributed random variables wit te variances denoted as P 1 and P, respectively. In tis paper, we study te potential improvement brougt by using te multi-op relay cannel in te SSS system as sown in Figure 1. To clearly describe te performance improvement, we briefly discuss te previously reported results for te direct transmission cannel under SSS constraints as follows. Note tat, for te direct transmission system, te average power constraint is given by E P 1 Q. were E is te expectation of a random variable. Tis is different from te traditional wireless model were te constraints are on te transmitted power of te sender. Under te above power constraints, it was proved in [], if te transmitted power P 1 is uncanged during te transmission, te acievable rate of direct transmitted cannel under SSS constraint in is given by R DT1 = E log 1+ 1Q N E. If te secondary sender can track te instantaneous values of 1 and, te following rate is acievable by using te 1 ' Secondary Sender 1 Primary Receiver 1' 1' 1' ' Secondary Receiver Secondary Relay... Primary Receiver ' Fig. 1. A secondary sender-receiver pair sares te spectrum wit te primary receivers. optimal power allocation metods [4], R DT = E log 1 λ N were λ is a constant. In tis paper, we mainly focus on te multi-op relay cannel sown in Figure 1. Different form te direct transmission cannel, in our network model, tere are two secondary transmitter and te average power constraints are defined as follows, E P 1+E 1 P Q, 5 E 1 P 1+E P Q. 6 Note tat in 5 and 6, bot te transmitted powers of secondary sender and relay are limited by te maximum tolerable interference at te primary receivers 1 and. In tis paper, we consider te full duplex multi-op relaying protocol in wic te secondary relay can simultaneously send and receive signals. We also assume te secondary relay decodes its received signal and forwards an re-encoded version of te signal to te secondary receiver. Te signals received by te relay and receiver are given by y = 1 x 1 +ˆz + z, 7 y = x +ˆz + z, 8 were ˆz and ˆz denote te interference noises caused by oter secondary and primary transmitters at te secondary relay and receiver, respectively, and z and z denote te additive wite Gaussian noise at te secondary relay and receiver, respectively. We assume ˆz, ˆz, z and z are zero-mean Gaussian random variables wit variance ˆN, ˆN, N and N, respectively. To simplify our description, we combine te noises at te relay and receiver and assume ˆN + N = N and ˆN + N = N. III. SPECTRUM SHARING WITH MULTI-HOP RELAYING In tis section, we consider te multi-op relay cannel as sown in Figure 1. We first consider te case tat bot te secondary sender and relay fix teir transmitted powers during

3 te transmission in subsection III-A. Tis corresponding to te case tat te cannel status information CSI, or cannel fading coefficients and teir statistics, is only available at te receiver. Ten te optimal power allocation metods are derived by assuming full CSI is known by te secondary sender and relay in subsection III-B. In tis section, we consider te following optimization problem, { max R FD =min E log P 1,P 1+ 1P 1 N, 9 } E log 1+ P, N s.t. E P P Q, 10 E 1 P 1 + P Q. A. Fixed P 1 and P Assume P 1 and P remain uncanged during te transmission process. Solving 10 and, we can re-write P 1 and P as follows, Q E E 1 E E, 1 E 1 E 1 Q E P = E 1 E E. 1 E 1 E 1 Te acievable rate of te multi-op relay cannel can be obtained by substituting 1 and 1 into R DF defined in 9. It is observed tat te transmitted powers of bot te secondary sender and relay are limited by te fading coefficients of cannels connecting te secondary transmitters and teir closest primary receivers. To clearly discuss te performance improvement of te multi-op relaying. In te rest of tis subsection, we focus on two special cases presented in Figure. In te first case sown in Figure a, eac secondary transmitter and its corresponding closest primary receiver are far from eac oter, i.e., d 1,d 1. In te second case in Figure b, bot te secondary sender and relay ave similar distance wit eac of te closest primary receiver 1 or, i.e., d 1 d and d d 1. Te main difference between cases 1 and is as follows. In case 1, te power of eac secondary transmitter 1 or is only limited by its closest primary receiver 1 or, and adding more secondary nodes 1 or will not increase te interference to tat primary receiver. In te case, owever, eac secondary node causes te same interference at eac primary receiver and ence te transmitted power of te sender sould be decreased to maintain te same interference temperature at bot primary receivers. Case 1: If we assume te distances between te primary receiver 1 and secondary relay and tat between te primary receiver and secondary sender 1 are relatively far and te transmitted power of eac secondary transmitter is only limited by te maximum tolerable interference temperature of te closest primary receiver, as sown in Figure a, i.e., 1' 1 a ' 1' 1 Fig.. Two special cases for te multi-op relay cannel under spatial spectrum saring constraints. E 1,E 1 0. In tis case, 10 and can be re-written as follows, P = b ' Q E, 14 Q E 15 By substituting te above results and network model defined in 1 into R DF, te acievable rate of te multi-op relay cannel can be re-written as { R FD1 = min E log 1 + 1Q d δ 1 N E, } E log 1 + Q d δ N E. 16 If we furter assume te secondary relay node is located in te middle of te cannel connecting te secondary sender and receiver, i.e., d 1 = d = d1, 1, and 1 ave similar conditions, and Q is large enoug, i.e., we can write te R FD1 as 1 Q N E 1, R FD1 C1 δ log + R DT1. 17 Note tat, if Q is small or te average power constraint on te primary user network are tigt, i.e., 1 Q N E 1, te improvement brougt by using te multi-op relaying will be relatively less tan tat sown in 17. Te above results suggest tat if te transmitted power for eac secondary transmitter is only limited by its closest primary receiver, or unrelated to te overall number of te secondary transmitters, te multi-op relaying can always improve te direct transmission rate for te SSS system. Case : Consider te second case in wic te primary receivers are far from bot of te secondary transmitters, and te cannels connecting bot secondary transmitters to eac primary receiver 1 or as similar condition, i.e., E E 1 and E 1 E. In tis case, P 1 and P can be re-written as { } Q Q P =min E, E. 18

4 Follows te same line as in Case 1. By assuming d 1 = d = d1, 1 1 and Q is large, we can re-write te acievable rate R FD1 as R FD1 C δ 1 log + R DT1. 19 Te above results suggest tat if te interference temperature at eac primary receiver can be affected by all te secondary transmitters, te multi-op relaying can only improve te direct transmission rate wen te cannel attenuation exponent δ is large enoug, i.e., δ 1 in tis case. Note tat te multi-op relay cannels wit fixed P 1 and P also correspond to te case tat te transmitted powers of te secondary sender and relay are under peak receivedpower constraints as studied in [4], in wic te maximum interference noises at te primary receiver sould be less tan a tresold. In tis case, te transmitted powers of te sender and relay sould be te maximum power allowed by te primary receiver at te worst cannel condition. B. Optimal Power Allocation Metods In tis section, we assume te secondary sender and relay can adjust te transmitted powers according to teir instantaneous CSI of te transmitted cannels. For example, te secondary sender can track 1, 1 and, and te secondary relay can track, 1 and. In tis case, te transmitted powers of te secondary sender and relay are functions of te transmitted cannel coefficients, i.e., P 1 1, 1, and P,, 1. Using te Lagrangian metods [14] to solve te optimization problem in 9, te optimal power allocation metods for P 1 and P can be obtained as follows, λ 1 λ + λ 4 N + 1, 0 1 λ P = λ 1 + λ 4 N +, 1 λ 1 λ +λ 4 1 λ λ 1 +λ 4 were and are called waterlevels for P 1 and P, respectively. Te detailed derivation can be found in Appendix A. Te results in 0 and 1 are similar to te power allocation results under te transmitted power constraints reported in [14]. In oter words, te secondary sender or relay sould not send any signals if te cannel conditions of 1 or are lower tan tese water-levels. Te difference between te above results and te optimal power allocation metods under transmitted power constraint is tat te water-levels of P 1 and P in 0 and 1 are not constants but te functions of, 1 and 1,, respectively. More specifically, if and 1 or 1 and become larger, P 1 or P sould be decreased to maintain te interference temperature at te primary receivers 1 and. As in subsection III-A, let us consider te two special cases in Figure as follows, Case : Consider te same network model as discussed in case 1 and assume P 1 and P follows te optimal power allocation metods defined in 0 and 1. By assuming 1, 1 0, we can re-write P 1 and P as follows, λ 1 N +, 1 λ P = N +, were λ 1 = λ1 λ and λ = λ λ 4 are constants. By substituting te above results and cannel model defined in 1 into R DF, te acievable rate of te multi-op relay cannel wit optimal power allocation is given by { R FD C1 = min E log 1λ 1 d δ 1 N E, } E log λ d δ N E. 4 In 4, λ 1 = λ1 λ and λ = λ λ 4 are constants. Note tat λ 1 and λ are used to make sure te transmitted powers of te secondary sender and relay are under te power constraints defined in 5 and 6. Substituting and into 5 and 6, we ave λ 1 = Q + N E, 5 1 λ = Q + N E. 6 Let us consider te following two subcases: If te power constraints are relatively relaxed, i.e., Q N E,N E,weaveλ 1 = λ Q. In tis 1 subcase, if we assume d 1 = d = d1, 1 1 and E E, we can re-write RFD as follows, R FD C1 δ log + R DT. 7 Note tat te improvement brougt by te multi-op relaying is better in te multi-op relay cannel wit optimal power allocation tan in te cannel wit fixed transmitted powers. If te power constraints are tigt, i.e., Q E and 1 E, we ave λ 1 E and λ E. 1 DF C1 In tis case, te acievable rate R is difficult to analysis. However, it was proved in [19] tat, if and are independent wit 1 and, respectively, we ave E = E, and E 1 E = E 1. It is observed E tat in tis special case, te multi-op relaying almost cannot provide any acievable rate improvement for te SSS systems. Case 4: Let us consider te same network model as Case for multi-op relay cannel wit optimal power allocation metods. Assume te two primary receivers are far from bot of te secondary transmitters and d,d 1,d 1 and d serve as te dominant role in te corresponding cannel fading coefficients. More specifically, we assume, 1, 1 and 1

5 R Direct Transmission Fixed P Full Duplex op Relay Fixed P Direct Transmission PA Full Duplex op Relay PA d 1 Fig.. Numerical results for te multi-op relay cannel under spatial spectrum saring constraints, were E 1 = E = E 1 =, E =E 1 =E 1 =E =, d 1 = d = d 1, d = d =5, d 1 = d 1 = d 1 + d, δ =, and Q =1. can be regarded as constants. In tis case, we furter assume = 1 and 1 =. Under te above network model, from 0 and 1, we can re-write P 1 and P as follows, λ 1 N +, 8 1 λ P = N +, 9 were λ 1 = λ1 λ +λ 4 and λ = λ λ +λ 4 are constants. It is observed tat if te secondary transmitters ave te interference to te primary receiver, te water-levels of te transmitted powers of bot secondary transmitters sould be decreased to maintain te same interference temperatures at eac primary receiver. Let us use te same metods as in Case to furter simplify te network model. If we assume d 1 = d = d1, 1 1 and, we ave te following results R FD C δ 1 log + R DT. 0 Similar to Case, we ave te following observation. If eac secondary transmitter as similar interference temperature at te primary receiver, te multi-op relaying could only improve te transmission rate for te direct transmission wen δ is large, i.e., δ 1 in tis case. C. Numerical Results Te numerical results of te multi-op relay cannel are given in Figure in wic we assume te fading coefficients of te cannels in te secondary user networks are Rayleig distribution random variables, and teir average fading coefficients of te different ops of cannels are fixed during te transmission, i.e., E 1 =E =E 1 =.We also assume E =E 1 =E 1 =E = and d 1 = d = d1. We fix te distance between eac secondary transmitter and its closest primary receiver as 5, i.e., d = d =5, and assume d 1 = d 1 = d 1 + d. Note tat in our simulation in Figure, we consider te effects of te distance on te acievable rate. More specifically, we fix d and d and assume te distance between te secondary sender and receiver could cange in a relatively large range. In tis case, te case 1 corresponding to te case tat d 1 is large, i.e., d 1 d =5and te case corresponding to te case tat d 1 is small, i.e., d 1 d =5. It is observed tat te multi-op relaying is able to greatly improve te acievable rate for te secondary sourcedestination pair under SSS constraints. Furtermore, te optimal power allocation metod makes a furter increase in te acievable rate. As observed in [14], owever, te optimal power allocation demands te secondary source and relay to adjust teir transmitted power according to te instantaneous CSIs of te cannels, wic may not be applicable for some practical systems. As sown in Figure, under te setting discussed at te beginning of tis subsection, te acievable rate of te multi-op relay cannel wit fixed P 1 and P can outperform te direct transmission rate wit optimal power allocation metod. In oter words, te multi-op relaying could serve as a more practical and effective metods tan te optimal power allocation metods to improve te performance of te SSS system. IV. CONCLUSION Tis paper studies te performance of te multi-op relay cannel under spatial spectrum saring SSS constraints. Te acievable rates of te multi-op relay cannel are studied under different conditions and te optimal power allocation metods are proposed. Our results sow tat te acievable rate of te direct transmission under SSS constraints can always be improved by using te multi-op relaying if te interference temperature caused by te secondary transmitters at eac primary receiver is unrelated to te number of te secondary transmitters. However, if all te secondary transmitters cause similar interferences at eac primary receiver, te multiop relaying can only improve te acievable rate of te direct transmission wen te cannel attenuation exponent is large enoug. APPENDIX A DERIVATION OF OPTIMAL POWER ALLOCATION METHODS FOR THE SPATIAL SPECTRUM SHARING SYSTEM WITH MULTI-HOP RELAY CHANNEL Following te same network model defined in section II, we need to find te solution of te following optimization

6 problem, max r 1 P 1,P s.t. r E log 1+ 1P 1, N r E log 1+ P, N E P P Q, E 1 P 1 + P Q. To find te optimal power allocation strategy, we ave te Lagrange multiplier as follows, L = r + λ 1 [E log +λ [E log 1+ 1P 1 N 1+ P N ] r ] r ] [ +λ Q E P P [ +λ 4 Q E 1 P 1 + P ]. We ave te KKT conditions of te above equation [14] as follows, L =0 λ 1 1 P 1 N + 1 P 1 = λ + λ 4 1, L =0 λ P N + P = λ + λ Solving te above results, te optimal power allocation strategy for P 1 and P can be obtained as, λ 1 λ + λ 4 N +, λ P = λ 1 + λ 4 N Tis concludes te proof [8] T. M. Cover and A. El Gamal, Capacity teorems for te relay cannel, IEEE Trans. Inform. Teory, vol. 5, no. 5, pp , [9] R. U. Nabar, H. Bolcskei, and F.W. Kneubuler, Fading relay cannels: performance limits and space-time signal design, IEEE J. Select. Areas Commun., vol., no. 6, pp , Aug 004. [10] C. T. K. Ng and A. Goldsmit, Te impact of CSI and power allocation on relay cannel capacity and cooperation strategies, IEEE Trans. Wireless Commun., Vol. 7, No. 1, pp , Dec [] K. Azarian, H.E. Gamal, and P. Scniter, On te acievable diversitymultiplexing tradeoff in alf-duplex cooperative cannels, IEEE Trans. Inform. Teory, vol. 51, no. 1, pp , 005. [1] D. Gunduz, A. Kojastepour, A. Goldsmit, H. Poor, Multi-op MIMO relay networks: Diversity-multiplexing trade-off analysis, Submitted to IEEE Trans. on Wireless Commun.. [1] P. Gupta and P. R. Kumar, Te capacity of wireless networks, IEEE Trans. Infor. Teory, vol. 46, pp , 000. [14] A. J. Goldsmit and P. P. Varaiya, Capacity of fading cannels wit cannel side information, IEEE Trans. Infor. Teory, vol. 4, pp , [15] G. Ganesan and L. Ye, Cooperative Spectrum Sensing in Cognitive Radio, Part I: Two User Networks, IEEE Trans. on Wireless Commun., vol. 6, pp. 04-1, 007. [16] A. El Gamal, J. Mammen, B. Prabakar, and D. Sa, Optimal trougput-delay scaling in wireless networks - part I: te fluid model, IEEE Trans. Infor. Teory, vol. 5, pp , 006. [17] K. Dong, L. Long, and E. Hossain, Joint rate and power allocation for cognitive radios in dynamic spectrum access environment, IEEE Trans. Wireless Commun., vol. 7, pp , 008. [18] L. Long Bao and E. Hossain, Resource allocation for spectrum underlay in cognitive radio networks, IEEE Trans. Wireless Commun., vol. 7, pp , 008. [19] R. Heijmans, Wen does te expectation of a ratio equal te ratio of expectations?, Statistical Papers, vol. 40, pp , [0] L. Zang, Y.-C. Liang and Y. Xin, Joint beamforming and power allocation for multiple access cannels in cognitive radio networks, IEEE J. Select. Areas Commun., vol. 6, No. 1, pp. 8-51, 008. [1] X. Kang, Y.-C. Liang, A. Nallanatan, H. Garg, and R. Zang, Optimal Power Allocation for Fading Cannels in Cognitive Radio Networks: Ergodic Capacity and Outage Capacity, IEEE Trans. on Wireless Commun., vol.8, No., pp , February 009. ACKNOWLEDGMENT Te autors would like to tank Professor Y.-C. Liang for is elpful discussion. REFERENCES [1] Federal Communications Commission, Spectrum policy task force report, ET Docket No. 0-15, Nov. 00. [] S. Haykin, Cognitive radio: brain-empowered wireless communications, IEEE J. Select. Areas Commun., Vol., No., pp. 01-0, 005. [] M. Gastpar, On Capacity Under Receive and Spatial Spectrum-Saring Constraints, IEEE Trans. Inf. Teory, Vol. 5, No., pp , 007. [4] G. Amir and S. S. Elvino, Fundamental limits of spectrum-saring in fading environments, IEEE Trans. Wireless Commun., 6: pp , 007. [5] Z. Wei and K. Ben Letaief, Cooperative Communications for Cognitive Radio Networks, Proceedings of te IEEE, Vol. 97, No. 5, pp , 009. [6] A. Sendonaris, E. Erkip and B. Aazang, User Cooperation Diversity Part I: System Description, IEEE Trans. Commun., vol. 51, no., pp , 00. [7] T. M. Cover and J. A. Tomas, Elements of Information Teory. New York: Wiley, 1991.