Liten-and-Talk: Full-duplex Cognitive Radio Network Yun Liao, Tianyu Wang, Lingyang Song, and Zhu Han State Key Laboratory of Advanced Optical Communication Sytem and Network, School of Electrical Engineering and Computer Science, Peking Univerity, Beijing, China, Electrical and Computer Engineering Department, Univerity of Houton, Houton, TX, USA. arxiv:7.335v [c.ni] 3 Jul Abtract In traditional cognitive radio network, econdary uer SU typically acce the pectrum of primary uer PU by a two-tage liten-before-talk LBT protocol, i.e., SU ene the pectrum hole in the firt tage before tranmit in the econd tage. In thi paper, we propoe a novel litenand-talk LAT protocol with the help of the full-duplex FD technique that allow SU to imultaneouly ene and acce the vacant pectrum. Analyi of ening performance and SU throughput are given for the propoed LAT protocol. And we find that due to elf-interference caued by FD, increaing tranmitting power of SU doe not alway benefit to SU throughput, which implie the exitence of a power-throughput tradeoff. Beide, though the LAT protocol uffer from elf-interference, it allow longer tranmiion time, while the performance of the traditional LBT protocol i limited by channel patial correction and relatively horter tranmiion period. To thi end, we alo preent an adaptive cheme to improve SU throughput by witching between the LAT and LBT protocol. Numerical reult are provided to verify the propoed method and the theoretical reult. I. INTRODUCTION With the fat development of wirele communication, pectrum reource ha become increaingly carce. Cognitive radio, a a promiing olution to pectrum hortage, ha caued wide attention for more than a decade [] []. In cognitive radio network CRN, unlicened or econdary uer SU are allowed to opportunitically utilize the vacant lot in the pectrum allocated to primary uer PU. SU therefore need to earch for pectrum hole reliably and efficiently to protect the PU network a well a maximize their own throughput [3]. Traditionally, the o-called liten-before-talk LBT trategy in which SU ene the target channel before tranmiion ha been extenively tudied []. Optimization of ening and tranmiion duration ha been dicued in [5] and [6]. Thi LBT trategy require little infratructure upport and it prove to be effective. However, it till ha everal problem uch a acrifice of tranmitting time and dicontinuity of tranmiion even if the white pace of pectrum i continuou. The major reaon i that mot current deployed radio for wirele communication are half duplex uch that to diipate the preciou reource by either employing time-diviion or frequency-diviion. A full-duplex ytem, where a node can end and receive at the ame time and frequency reource, offer the potential to double the pectral efficiency. However, due to the cloe proximity of a given modem tranmit antenna to it receive antenna, trong elf-interference introduced by it own tranmiion make decoding proce nearly impoible, which i the reaon why realization of FD technique ha not be deemed poible until recently. The lat everal year witne the advent of interference reduction technique [7] that provide the poibility of introducing FD to wirele communication. A number of work have been done to meaure the performance of FD technique which how that under certain circumtance, uing FD can achieve better pectral efficiency than traditional half-duplex ytem [8]. Motivated by the FD technique, in thi paper, we propoe a liten-and-talk LAT protocol imultaneouly ening the pectrum and tranmitting data for CRN. At each moment, one of the antenna at each SU ene the target pectrum band, and judge if the PU i buy or idle; the other antenna tranmit data imultaneouly or keep ilent on the bai of the ening reult. Energy detection under imperfect elfinterference uppreion SIS i ued a the pectrum ening trategy. We cloely look into two cae when the SU i tranmitting or remaining ilent. Alo, adaptive threhold of detection are given. To compare the LAT protocol with the conventional LBT protocol, we derive the probability of fale alarm and mi detection, and the ytem throughput for thee two protocol. We alo analyze the power-throughput tradeoff for the LAT protocol. While overcoming dicontinuity of tranmiion in conventional LBT protocol, the propoed LAT protocol till uffer the throughput lo by evere elf-interference when tranmit power increae. To thi end, we propoe an adaptive witching cheme between conventional and LAT approache in puruit of maximum throughput with the contraint of detection probability. Simulation reult are provided to verify the propoed method in term of the ignal-to-noie ratio SNR, average SU tranmit power, SIS factor in the LAT protocol, patial correlation coefficient and ening duration in the conventional LBT protocol. The ret of the paper i organized a follow. Section II decribe the ytem model of the conventional LBT and the propoed LAT protocol. In Section III, we derive the analytical performance of the LAT protocol. In Section IV, we propoe a witching cheme between the LBT and LAT protocol. Simulation reult are preented to verify our analyi and viually how the throughput gain of the adaptive cheme, in comparion with both LBT and LAT protocol in Section V. We conclude the paper in Section VI.
PU dynamic SU lot SU -Ant.& SU -Ant. SU -Ant. Fig.. inactive τ T active change threhold inactive Sytem model: LBT and LAT protocol a Liten before Talk b Liten and Talk II. SYSTEM MODEL Conventional ening FD ening with SI FD ening without SI Data tranmiion Silent In thi paper, we conider a CRN coniting of one PU and one SU pair, where SU tranmit data to SU. Each SU i equipped with two antenna Ant and Ant. The pectrum band occupancy by the PU can be modeled a an alternating ON/OFF random proce. The ening and tranmiion proce i time-lotted. For implicity and without lo of generality, energy detection i adopted a the ening cheme, and the tet tatitic can be given a M = N yn, N n= where N denote the number of ample, and yn i the received ignal of the n th ample. Let f repreent the ampling frequency in ening proce, and for ening duration t, we have N f t. We refer to the ituation when PU i inactive a hypothei H, and the ituation when PU i active i hypotheih. The probability of fale alarm and mi detection can be written a P f ǫ = PrM > ǫ H and P m ǫ = PrM < ǫ H, 3 repectively, where ǫ denote the detection threhold. A. Traditional Liten-before-Talk Protocol In thi protocol, each lot T i divided into two ublot a hown in Fig. a: ening ublot with duration τ, and data tranmiion ublot with duration T τ. Note that for comparion fairne with the FD baed cheme, a MIMO i ued for both pectrum ening and data tranmiion. And the ignal received at SU in the ening tage can be repreented by h p +u, H, y = u, H, where y, h, and u are vector repreenting the received ignal, channel from PU to SU, and noie term, repectively, and P i the PU ignal which i aumed to be PSK modulated with variance σp. The noie i independent and identically ditributed i.i.d. random Gauian with zero mean and variance. With the eparable correlation model [7], h can be expreed a h = Φ / h where h CN,σ h, and Φ tand for the normalized correlation matrix at SU. The data are tranmitted in a patial multiplexing way, and at SU, we can have r = H t +u, 5 where H = Φ / r H t Φ / t i a channel matrix from SU to SU, H t i i.i.d. complex-valued Gauian with zero mean and variance σ h, and t i the tranmit ignal vector with variance σ. For implicity, the exponential correlation model [9] i ued for both ening and tranmiion, and the correlation matrix can be repreented by Φ = β β, β [,, 6 where the correlation coefficient β i the patial correlation factor. B. Liten-and-Talk Protocol A hown in Fig. b, SU perform ening and tranmiion imultaneouly uing the FD technique: one of the two antenna at SU, ay Ant, ene the pectrum while the other Ant tranmit when a pectrum hole i detected. The challenge in thi mode i that the tranmit ignal at Ant of SU i received by Ant, which caue elf-interference at Ant. Thu, for ening, the received ignal i largely decided by the tate of the other antenna: if Ant of SU i not tranmitting, there i no difference to the conventional ening method in, while if SU i tranmitting, elf-interference will be introduced to the ytem. Given the difference above, we conider the circumtance when SU i tranmitting or not eparately. Sening without tranmiion: In thi cae, the SU perform ening by one antenna only, and we have h P +u, H, y = 7 u, H, where H and H repreent the hypotheie when SU i ilent, and the PU i buy or idle, repectively, and h i the Rayleigh channel from PU to Ant of SU, u CN, denote the noie. Sening and tranmiion: With elf-interference, the received ignal can be written a h P +h i t +u, H, y = 8 h i t +u, H, where H and H are the hypotheie under which SU i tranmitting and the PU i either buy or idle, repectively. t in 8 denote the tranmit ignal at Ant of SU and h i repreent the elf-interference channel from Ant to Ant. According to [8], h i t can be modeled a a Rayleigh ditribution with zero mean and variance χ σ, where χ repreent the SIS factor. In the LAT protocol, only one link i ued to data tranmiion and the received ignal at Ant of SU i r = h t +u, 9
TABLE I PROPERTIES OF PDFS OF LAT PU activity SU activity Hypothei PU SU E[M LAT ] var[m LAT ] H idle ilent σ u buy ilent S active S H buy ilent +γ σ u +γ H idle active +γ i σ u H buy active +γ +γ i σ u +γ i +γ +γ i idle ilent S active S where h CN,σ h i the tranmit channel from SU to SU, and u CN, repreent the AWGN noie. III. LISTEN-AND-TALK PROTOCOL ANALYSIS In thi ection, we mainly tudy the analytical performance of the LAT protocol, derive throughput under the contraint of a given mi detection probability, and tudy the powerthroughput tradeoff. A. Probability of Mi Detection and Fale Alarm Note that the tet tatitic M LAT i not only determined by PU activity, but alo by the SU tranmitter behavior. We conider four condition when PU i active or not, and SU i tranmitting or not, eparately. According to, for each condition, the tet tatitic can be written a M LAT = N,LAT N,LAT n= yn, where N,LAT = f T i the ample number in the LAT protocol and y take different form in different condition. Note that y in each ample i i.i.d. and we aume N,LAT i large enough. According to central limit theorem CLT, the PDF of M LAT can be approximated by a Gauian ditribution. The tatitical propertie and the decription under each condition are given in Table. I, where γ = σ h σ P σ in Table. I u denote the SNR in ening, andγ i = χ σ σ i the interferenceto-noie ratio INR. Detailed derivation of the ditribution u propertie are provided in Appendix A. Let ǫ be the detection threhold when SU i ilent H, H. Recalling the received ignal in 7, and uing, the probability of fale alarm Pf,LAT can be written a Pf,LAT ǫ ǫ f = Q T, where Q i the complementary ditribution function of the tandard Gauian ditribution. Furthermore, the probability of mi detection can be obtained from 3 a Pm,LAT ǫ f ǫ = Q +γ T. For a given probability of mi detection Pm, the ening threhold ǫ i given by Q Pm ǫ = f T σ u + +γ σ u. 3 Fig.. P f,lat SU tate tranition graph of the LAT protocol Subtitute 3 to, we have the analytical fale alarm probability written a P m = Q Q Pm +γ +γ f T. Similarly, when SU i tranmitting H, H, and the detection threhold i ǫ, the mi detection probability Pm,LAT and the fale alarm probability P f,lat are Pm,LAT ǫ ǫ f = Q +γ +γ i T, and Pf,LAT ǫ ǫ = Q +γ i f T, 5 repectively. And for a fixed probability of mi detection Pm, the fale alarm probability can be derived a P m P f,lat = Q Q Pm + γ + γ f T. +γ i +γ i The change among the four tate are modeled a two dicrete-time Markov chain DTMC illutrated in Fig., in which we aume that the PU activity change lowly compared to the duration of each time lot T, and a ingle lot when the PU change it tate can be neglected. Given that the probability for the ytem taying in each tate p ij i,j =, can be calculated conidering the teady-tate ditribution of the Markov chain: p P m,lat = p P m,lat, p Pf,LAT = p Pf,LAT, 6 p +p =, p +p =. Then, the mi detection probability of the ytem i P m,lat P m,lat = p = +Pm,LAT, 7 P m,lat and the probability of the overall fale alarm i P f,lat P f,lat = p = Pf,LAT. 8 +P f,lat Within the limit of overall mi detection probability P m,lat = P m, we obtain the contraint of P m,lat and P m,lat from 7. For implicity, we et P m,lat = P m,lat,
and thu, Pm,LAT = P m,lat = P m. From and, the tet threhold can be obtained according to SU activity a follow: When SU i ilent, uing, we have Q P m ǫ P m = + +γ σ f T u. 9 When SU i active, uing, the threhold ǫ i Q P m ǫ P m = + +γ +γ i f T. In how in 9 and that when SU tranmit, the detection threhold increae due to reidual elf-interference. Conequently, the probability of fale alarm Pf,LAT and P f,lat are different: P f,lat P m = Q Q P m +γ +γ f T, Pf,LAT P m = Q Q P m + γ + γ f T. +γ i +γ i Subtituting to 8, we can obtain the fale alarm probability of the whole ytem. B. SU Throughput During tranmiion, with tranmit power σ, channel gain h t CN,σ h, and noie variance, the um-rate can be written a R LAT = log + σ σ h σ u = log +γ t, whereγ t repreent the SNR in tranmiion. And the throughput can be expreed a C LAT = R LAT P f,lat. 3 It i hown in the expreion of R LAT and P f,lat that the throughput increae with SNR in ening γ, and decreae with SIS factor χ. C. Power-Throughput Tradeoff Analyi In the LAT protocol, σ i poitively proportional to γ t, and thereby poitively related to the um rate. On the other hand, the power ha trong influence on ening performance, ince it i alo proportional to elf-interference. Theoretically, with fixed SIS factor χ, the ening reult deteriorate with the tranmit power. With regard to the throughput, when tranmit power i mall, elf-interference become negligible. The ening reult are reliable, and yet the throughput i limited. When the power i large, however, tranmit power i no longer the limitation for the achievable um rate R LAT, but elf-interference may caue an unbearable high probability of fale alarm. Thi may lead to evere wate of pectrum hole, which i alo likely to decreae the throughput. Hence, there exit an optimal tranmit power to achieve the bet throughput. Note that due to pace limitation, the mathematical proof will be given in our future work. TABLE II PROPERTIES OF PDFS OF THE TEST STATISTICS BY LBT H H Mean E[M LBT ] Variance var[m LBT ] σ u γ +σ u f τ [β γ +γ + ] f τ IV. SWITCHING BETWEEN LAT AND LBT There exit limitation for both LBT and LAT protocol. In the LBT, the data tranmiion time i reduced becaue of pectrum ening, and the overall throughput i alo affected by patial correlation. In the LAT, reidual elf-interference i the main problem that decreae the performance. In thi ection, we firt briefly derive the ening performance and throughput in the LBT protocol, and then propoe an adaptive witching cheme to maximize SU throughput by electing the right protocol between the LAT and LBT protocol for CRN. A. Performance Analyi of LBT The tet tatic M LBT can be generally written a M LBT = N,LBT N,LBT n= y n + y n, wheren,lbt = f τ i the number of ample in each ening ublot, and y i pecified in. Again, the ditribution of M LBT can be approximated by a Gauian ditribution according to CLT, given that each ample y + y i i.i.d. and N,LBT i ufficiently large. The propertie of the PDF under both hypotheie are preented in Table. II, in which β denote the patial correlation coefficient in ening. Detailed derivation of the ditribution propertie are provided in Appendix A. The probabilitie of fale alarm and mi detection can be written, repectively, a ǫ f P f,lbt ǫ;τ = Q τ, ǫ γ +σ u P m,lbt ǫ;τ = Q f τ ξσ u, 5 where ξ := βγ +γ +. And for a given probability of mi detection P m, the analytical fale alarm probability can be derived from 5 a P f,lbt P m ;τ = Q Q P m ξ +γ f τ. 6 In tranmiion, with the contraint of average total power σ, the tranmit power at each antenna i P each = σ T T τ, 7 and the average um rate i given by [ R LBT = E log det I+ P ] each H H H. 8
At high SNR, R LBT in 8 can be reduced a [ Tσ ] R con E log det T τ H H H T = log +log T τ γ t +log β t +log β r, 9 where β t and β r repreent the patial correlation at SU tranmitter SU and receiver SU, repectively. The throughput can be expreed a C LBT = R LBT P f,lbt, 3 which indicate that the throughput increae with tranmit power σ and SNR in ening γ, and it decreae with the patial correlation coefficient β, β r, and β t. B. Switching Algorithm Combining the throughput of conventional LBT and the propoed LAT protocol in 3 and 3, repectively, the theoretical optimal witching criterion can be derived. Let C be the difference of throughput between the two mode, we have C = C LBT C LAT, 3 and thu, the witching criterion i decided by the value of C: Liten-before-talk, C, operation mode = 3 Liten-and-talk, C <. With C =, the optimal witching point can be eaily calculated. Note that from 3, it implie that the witching point i related to the following tatitical factor: SNR γ, γ t and tranmit power σ during ening and data tranmiion, patial correlation coefficient β, β r, β t and the proportion of ening time in a whole time lot τ T in the LBT protocol, and SIS factor χ in the LAT protocol. V. SIMULATION RESULTS In thi ection, imulation reult are preented to evaluate the performance of the propoed LAT protocol. Table. III lit ome important parameter in the imulation. For implification, we et the patial correlation coefficient β = β r = β t = β. In Fig. 3, we conider the optimal witching point baed on the patial correlation coefficient, in which the probability of mi detection P m i fixed by.3, the ening SNR i db, and the relative tranmit power i 3dB. We invetigate the cae when the SIS factor χ i. and., and when the ening duration in the LBT protocol change between and. Fig. 3 include both analytical reult the real line and dotted line and numerical reult variou type of dot, which match perfectly. It can be hown that in the conventional LBT protocol, the achievable throughput decreae with the increment of patial correlation, and to a certain point, the LAT protocol outperform the conventional LBT protocol. Alo, when reidual elf-interference increae, e.g., from. to., the performance of the LAT protocol become wore, and the witching point move to a higher β. Throughput Fig. 3. Parameter TABLE III SIMULATION PARAMETERS The duration of each time lot T Value. m The duration of ening time in LBT τ.5t,.t The ampling frequency f MHz The number of ample in LAT N,LAT The relative noie variance σ u The relative tranmit power over noie P t SNR in ening proce γ 3dB db SIS factor in LAT χ.,. The patial correlation coefficient β.7,.8.9 Probability of mi detection P m.3 5 3 LAT: χ =. LAT: χ =. LBT: τ/t = / LBT: τ/t = /...6.8 Spatial correlation coefficient β SU achievable throughput veru patial correlation coefficient β In Fig., we ue the receiver operating characteritic curve ROC curve to preent the ening performance under different ituation. With SIS factor χ =.,. in the LAT protocol, patial correlation coefficient β fixed on.7, and the ening time take up, in each time lot in the conventional protocol, we have the relationhip between the fale alarm probability and mi detection probability. From Fig., it i hown that the ening performance become wore, i.e., P f increae and P m decreae with the increment of reidual elf-interference and the decrement of ening time. Fig. 5 evaluate the achievable throughput of SU when tranmit power change within a certain range. We can oberve that the power-throughput tradeoff in the LAT protocol, i.e., there exit an optimal tranmit power in the low power range to achieve maximum throughput, and the optimal power decreae with the increment of SIS factor χ. When the tranmit power i low, due to longer tranmit time and mall reidual elf-interference, the LAT protocol can achieve better throughput. When tranmit power become high, the LAT protocol uffer from evere elf-interference while the conventional mode profit from the multiplexing gain, and thu, the conventional LBT protocol gradually become a better option.
Probability of detection P d Fig.. Throughput Fig. 5..8.6. FD: χ=.. FD: χ=. Conventional: τ / T = / Conventional: τ / T = /...6.8 Probability of fale alarm P f ROC curve of both protocol 9 8 7 6 5 3 LAT: χ =. LAT: χ =. LBT: β =.7 LBT :β =.9 Power σ Throughput of both protocol veru tranmit power VI. CONCLUSIONS In thi paper, we preent a LAT protocol that allow SU to imultaneouly ene and acce the pectrum hole. Beide, a witching cheme between the LAT and LBT protocol i provided to improve the throughput of SU. Moreover, a tradeoff in LAT protocol between tranmit power and the throughput i invetigated by both analytical and numerical reult. We find out that, the increment of tranmit power doe not alway yield the improvement of SU throughput, and a mediate value i required to achieve the bet performance. APPENDIX A PROOF OF TABLE. I AND TABLE. II We firt provide the general propertie of the tet tatitic. Given that each yn in i i.i.d., the mean and the variance of M can be calculated a [ E[M] = E y ] ; var[m] = [ var y ]. N Further, if the received ignal y i complex-valued Gauian with mean zero and variance σy, we have and E[M] = σ y, var[m] = [ E y ] σy = σ y. 33 N N Then we conider the concrete form of the received ignal under each hypothei. In the LAT protocol, given the PU ignal, reidual elf-interference, and i.i.d. noie, the received ignal y i complex-valued Gauian with zero mean. The variance of y under the four hypotheie are H, +γ H, +γ i H, and +γ +γ i H, repectively. By ubtituting them into 33, we can obtain the reult in Table. I. Ditribution propertie in the LBT protocol can be obtained by imilar method, and under hypothei H, we have σy =. Under hypothei H, recalling, we have [ ] y + y E = E[ y H y ] = [ ] E h H Φ / H Φ / h + = γ +, and the variance var[m] = N E [ y H y ] = N E [ y H y ] +γ, in which h E[ H h + u H u +h H h u H u = N 3+β σ h +6σ u +6σ h σ u, and thu, var[m] = N [ β γ +γ + ] σ u REFERENCES [] J. Mitola and G. Q. Maguire, Cognitive Radio: Making Software Radio more Peronal, IEEE Peronal Comm., vol. 6, no., pp.3-8, Aug. 999 [] J. Mitola, Cognitive Radio An Integrated Agent Architecture for Software Defined Radio, Ph.D. Thei, Royal Intitute of Technology, Sweden, May.. [3] I. F. Akyildiz, W. Y. Lee, M. C. Vuran, and S.Mohanty, Next Generation/Dynamic Spectrum Acce/Cognitive Radio Wirele Network: A Survey, Computer Network, vol. 5, no. 3, pp. 7-59, Sep. 6. [] T. Yucek and H. Arlan, A Survey of Spectrum Sening Algorithm for Cognitive Radio Application, IEEE Comm. Survey & Tutorial, vol., no., pp. 6-3, Mar. 9. [5] Y. C. Liang, Y. Zeng, E. C. Y. Peh, and A. T. Hoang, Sening- Throughput Tradeoff for Cognitive Nadio Network, IEEE Tran. Wirele Comm., vol. 7, no., pp. 36-337, Apr. 8. [6] S. Huang, X. Liu, and Z. Ding, Short Paper: On Optimal Sening and Tranmiion Strategie for Dynamic Spectrum Acce, in Proc. IEEE DySPAN, Chicago, IL, Oct. 8 [7] M. Kieling and J. Speidel, Mutual Information of MIMO Channel in Correlated Rayleigh Fading Environment - a General Solution, in IEEE Int. Conf. Comm., vol., pp. 8-88, Pari, France, Jun.. [8] M. Jain, J. I. Choi, T. Kim, D. Bharadia, S. Seth, K. Srinivaan, P. Levi, S. Katti, and P. Sinha. Practical, Real-time, Full Duplex Wirele, in Proc. ACM MobiCom, New York, NY, Sep.. [9] S. L. Loyka, Channel Capacity of MIMO Architecture Uing the Exponential Correlation Matrix, IEEE Comm. Lett., vol. 5, no. 9, pp. 369-37, Sep.. [] S. Huang, X. Liu, and Z. Ding, Opportunitic Spectrum Acce in Cognitive Radio Network, in Proc. IEEE INFOCOM 9, Rio de Janeiro, Brazil, Apr. 9. ]