Location-aware Cognitive Sensing for Maximizing Network Capacity

Transcription

1 Loction-wre Cognitive Sensing for Mximizing Network Ccity Peng Ji, Mi Vu, Tho Le-Ngoc Dertment of Electricl nd Comuter Engineering, McGill University, Montrel QC H3A A7 Emil: {mi.h.vu, Abstrct We develo closed-form otiml sectrum sensing threshold to mximize cognitive network weighted sum ccity. In n one rimry user nd one cognitive user network, stil loction side informtion is used by the cognitive trnsmitter to djust its sensing threshold ccordingly. Numericl results show tht, comred to nother threshold bsed on minimizing Byesin risk function, the roosed threshold imroves the network sum ccity significntly. The benefit of stil loction side informtion is lso reveled in the sum ccity. I. INTRODUCTION The incresing demnd on the bndwidth of recent communiction systems exerts extr lods on the lredy crowded sectrum lloction. However, it is found tht the sectrum scrcity is mostly becuse of inflexible sectrum mngement rther thn true nturl resource shortge 3], 4]. Some licensed sectrum is under-utilized most of the time. Cognitive Rdio, which hs the bility to sense the sectrum 8] in order to utilize idle times of the licensed, rimry link, is romising cndidte to solving the sectrum scrcity roblem. Another sect of cognition is the use of side informtion. Side informtion cn hel the rdios to djust their trnsmission nd coding schemes. For exmle, two trnsmitter nd two receiver cognitive chnnel model is considered in 5] with side informtion bout rimry user s signls. Without considering how to obtin the side informtion nd the chnnel coefficients, chievble rte regions re deduced theoreticlly nd simulted ccording to the different strtegies of the cognitive rdio bsed on the side informtion. In sectrum sensing, detecting the rimry user s trnsmission energy is clssicl sensing method. Its erformnce cn be imroved by the use of side informtion on loctions of the vrious trnsmitters nd receivers. Intuited by this ide, the uthors in ] ly model which chrcterizes interference nd trnsmission ower with distnces. Further, they utilize stil informtion to design otiml sensing thresholds bsed on Byesin criterion tht minimizes cognitive user s sensing cost. They rech the conclusion tht stil side informtion rovides substntil dvntge in reducing the sensing costs. However, they do not investigte the imct of stil informtion on the network ccity. Tking one ste further, we reformulte the sensing cost in the threshold design nd nlyze the rimry nd cognitive link ccities in 7]. It is shown tht the sensing cost must be crefully chosen for the side informtion to lso be beneficil to the ccity of the cognitive user, while bringing little or no hrm to the rimry user s ccity. In this er, we formulte new sensing threshold design roblem to directly mximize the weighted sum ccities of the rimry nd cognitive users. The otiml thresholds re derived for different sets of loction side informtion. The sme sets of loction informtion s in 7] re chosen for erformnce comrison. Numericl results show tht the roosed threshold cn drmticlly imrove the network ccity. The increse in the network sum ccity owes to imrovement in the cognitive user s ccity, but comes t drwbck on the rimry user ccity. Loction side informtion is gin found beneficil to the cognitive trnsmitter in setting its otiml sensing threshold to increse the network sum ccity. The imct of loction informtion on the individul user s ccity deends on the weight in the network sum ccity objective. Interestingly, with equl weights, it is found tht more loction informtion to the cognitive users ctully hels increse the rimry user s ccity t some exense to the cognitive user s ccity. Reminder of the er is orgnized s follows. In Section II, we introduce the two-user network model nd the chnnel model. In Section III, we introduce the network ccity formultion nd the sensing objective. In Section IV, the otiml threshold imed t mximizing the network weighted sum ccity with different sets of loction informtion re derived. We discuss the numericl results in Section V. Finlly, we rovide our concluding remrks in Section VI. II. NETWORK AND CHANNEL MODELS We consider the sme network nd chnnel models s in 7] s shown in Fig.. The network consists of one cognitive user nd one rimry user, ech hs ir of rndomly locted trnsmitter nd receiver. The loction rndomness cn rise from mobility or from the rndom network ccess. Let the cognitive trnsmitter C tx be the center of the network t the olr coordintes,. The cognitive receiver C rx is uniformly distributed within the disc centered t the origin with rdius R c. Let the imct rdius of the cognitive trnsmitter be R i such tht ny rimry receiver flling within this rdius will be noticebly interfered by the cognitive trnsmitter. The considered rimry receiver P rx lies uniformly within this rdius R i. Centered t P rx, the rimry trnsmitter P tx is uniformly distributed within the disc with rdius R. The rdii R c, R i nd R re known network rmeters. Furthermore, rotection regions of rdius ɛ centered t receiving nodes re ssumed s shown in Fig.. Any ctive trnsmitter cnnot be inside this region to exclude the ossibility tht the receive signl nd interference ower rises to infinity. Let S t nd resectively secify the loctions of P tx, P rx nd C rx within the olr coordintes. Consider

2 formulte the ccity equtions nd then set u the ccity objective for designing the sensing threshold. Fig.. Network model. for exmle, nd let r denotes its rdius nd θ denote its ngle. For uniformly distributed C rx, r hs the density f r r = r/rc ɛ with ɛ r R c, nd θ is uniform between nd π. The distributions for the rdius nd ngles in nd S t cn be similrly derived. The chnnel between ny trnsmitter nd receiver is modeled s h = h PL h FD, where free-sce th loss h PL = A d α/ with α s the thloss exonent models the verged ower chnging with distnce nd Ryleigh fding comonent h FD models the smll-scle vrition. A is constnt deendent on the frequency nd trnsmitter/receiver ntenn gin, nd h FD CN, is comlex circulr Gussin rndom vrible with indeendent rel nd imginry rts with equl vrince. To sense the rimry trnsmission, the cognitive trnsmitter needs to erform hyothesis testing to decide between the following two hyotheses: H : y = z H : y = x + z where y is the received smles t C tx, x is the signl received t the cognitive trnsmitter from the P tx fter exeriencing th loss nd fding, nd z is the therml noise. Bsed on the studied chnnel model, the distributions of x nd z re x CN, x, z CN, z, where = Ph PL with P s the rimry trnsmit ower, nd the noise ower is constnt. III. NETWORK CAPACITY FORMULATION AND SENSING OBJECTIVE In the considered network, the cognitive trnsmitter erforms the detection of the rimry signl. Only when the cognitive trnsmitter detects tht there is no rimry trnsmission, it will begin its own trnsmission. In this er, we consider the design of n otiml ower sensing threshold to directly mximize the network weighted sum ccity. We will first A. Ccity Formultion Consider the ccity of the rimry nd the cognitive links, verged over ll rdio loctions. For the rimry user, the ccity deends on its robbility of trnsmission nd the mount of interference, if ny, from the cognitive user nd thus, is function of the miss-detection robbility. For the cognitive user, the ccity deends on the oortunity to trnsmit nd whether there is ny interference from the rimry user. Thus, the ccity of the cognitive user is function of both the flse-lrm nd miss-detection robbilities. Secificlly, these two ccities cn be written s ] C = E Sr,Scr {PrH H, λ E log + L ]} + PrH H, λ E log + L + I c C c = E Sr,Scr {PrH H, λ E log ]} + PrH H, λ E log + + I c where + Lc z is the sensing threshold. λ is the trnsmission robbility of the rimry user. PrH H, is the miss-detection robbility, when the secondry trnsmitter mkes decision to trnsmit while the rimry trnsmitter is lso ctive. Denote ] = PrH H, = PrH H,. 3 PrH H, is the flse-lrm robbility, when the secondry trnsmitter mkes decision not to trnsmit while the rimry link is idle. Denote q = PrH H, = PrH H,. 4 L nd re the rndom received signl ower of the rimry nd cognitive receiver, I c nd I c re rndom interference ower from the cognitive trnsmitter to the rimry receiver, nd from the rimry trnsmitter to the cognitive receiver, resectively. Since the loctions of the rdios re rndom, we re interested in the ccity verged over ll the rndom loctions. Deending on the knowledge bout ny of the rdio loctions, the design of n otiml sensing threshold nd the evlution of the ccities will vry s subsequently nlyzed. B. Sensing Objective Our objective here is to design sensing threshold to directly mximize the weighted sum of rimry nd cognitive users ccity s follows C = µc + µc c = E St, + bq + c] 5 where < µ < is the weight to emhsize either the rimry or the cognitive link ccity imortnce, nd nd q re given in 3 nd 4. Here ctures the ccity terms ssocited with rimry user trnsmitting, b with rimry user

3 not trnsmitting, nd c ctures the common ccity terms given s =µλ E log + L ] µλ E log + L ] + I c ] µλ E log + + I 6 c b = µ λ E log + L ] c 7 c =µλ E log + L ] + I c ] + µλ E log + + I 8 c where E{.} denotes the execttion with resect to chnnel fding. Our gol is to design the cognitive sensing threshold to mximize this network weighted sum ccity C. The otiml threshold design is ided with the informtion bout loction of other rdios known to the cognitive trnsmitter. Bsed on the loction informtion, the cognitive trnsmitter cn djust its sensing threshold to chieve higher network ccity. In deriving the otiml threshold, we investigte four different cses of loction informtion to be resented in Section IV. These cses hve lso been considered in 7] in designing sensing threshold to minimize Byesin risk function, which is different from the ccity objective 5. As in 7], in ll the four cses, we ssume tht nd z re known, but S ct does not use to infer the distnce to the rimry trnsmitter s it cn lter the distribution of. IV. OPTIMAL THRESHOLD In this section, we derive in closed-form the otiml thresholds to mximize the weighted sum ccity 5. We rovide detiled nlysis for Cse with full loction informtion, nd then the extension for the other 3 cses. A. Cse : When, nd S t re vilble For Cse, since the cognitive Tx knows the loction of every rdio,, b, c re known for ech network reliztion nd cn be regrded s constnts. Mximizing the objective 5 is equivlent to mximizing + bq + c for ech reliztion of {S t,, }. Furthermore, the signl ower received t the cognitive Tx from the rimry Tx follows the two degree chisqure distribution in both cses of rimry trnsmitting nd non-trnsmitting with different vrinces. Thus, for ech set of {S t,, }, we cn exress the objective function s f = + bq + c = x d + b x e z e z d + c = e z + x be x + b + c 9 Our gol is to find to mximize f. From 6 nd 7 we observe tht coefficient b is lwys ositive, but cn be smller or equl to zero in some loctions under certin rimry trnsmission robbilities. When, to mximize 9, the threshold should be set to infinity, which mens the cognitive rdio lwys trnsmit. On the other hnd, when >, the first nd the second derivtives of f cn be found s f = + + x + b x e f = + e z + x b e e z The second derivtive is negtive, f <, when < + x z ln z + b z Let the first derivtive be equl to zero, f =, we obtin n otiml threshold s = + x z ln z + b The otiml vlue lwys stisfies condition, hence f is mximized t this vlue. So the otiml threshold cn be obtined s {, if, = + x z ln x z + x b if >. The network weighted sum ccity cn be comuted using this otiml threshold for ech reliztion of {,, S t }, then verged over ll loction reliztions. B. Cse : When nd re known Since C tx hs no knowledge of S t, it should design the threshold bsed on the objective function verged over S t for ech ir of {, }. Mximizing 5 is equivlent to mximizing f =E St ] +E St b] + + e d + E St c]. e z + x d Similr to cse, the otiml threshold for ech ir of {, } cn be derived s {, if ESt], = + z ln x z + E x St b] E St ] if E St ] >. 3 In this new threshold, the ccity terms nd b re verged over the unknown loction S t. The resective ccities re clculted s follows. C = E Sr + λ E St λ E St log + L z log + L ]} + I c log + Lc C c = E St,Sr q λ E + E Sr,Scr λ E St log + ]}] ]] z + I c ]}]

4 The difference from Cse is tht, for ech ir of {, }, there is only one otiml threshold for ll ossible S t, nd corresonding terms in the ccity exressions need to be verged over S t while using this threshold. C. Cse 3: When only is known Similr to Cse, since C tx does not know S t nd, it should design the threshold by mximizing the objective function verged over ll {S t, } for ech given. The otiml threshold for ech in this cse is If E St, ], 3 = If E St, ] >, 3 = + x z ln z + x z E Stx,x b] E Stx,x ] 4 The resective ccities should be clculted s follows. ]} C = E Scr λ E St,Sr log + L ]}] + λ E St,Sr log + L + I c ]} C c = E St,Sr {q λ E log + Lc ]}] + E Scr λ E St,Sr log + + I c D. Cse 4: When no loction informtion is vilble As C tx hs no loction informtion, the objective function should be verged cross ll loctions, resulting in only single otiml threshold for ll loction reliztions. This otiml threshold for ll the loction sets is given s follows. If E St, ], 4 =, If E St, ] >, 4 = + z ln z + x z E St, b] E St, ] 5 The resective ccities cn be clculted ccording to nd using single threshold for ll network reliztions. E. Generliztion to multile cognitive users The roosed design cn be generlized to network with multile cognitive users. Ech cognitive trnsmitter needs to know only its resective loction informtion, such s the loctions of its own receiver nd of the rimry trnsmitter nd receiver. Ech cognitive user then indeendently senses the sectrum using the roosed threshold, which is designed to mximize the weighted sum of its own ccity nd the rimry user s ccity s in 5. In comuting these ccities, the interference from other cognitive users cn be treted s noise ssuming certin vrince, so the effective imct of hving multile cognitive users is incresing the noise floor. The cognitive users cn then choose to collborte to fuse the sensing decisions. Since the sensing erformnce of ech individul cognitive user is imroved with this threshold design, s illustrted next, network erformnce should be imroved s the whole. A. Simultion Settings V. NUMERICAL RESULTS We use the model in Fig. nd set the network rdii R c = R = R i =, the rotection region ɛ = nd the th loss rmeter α =.. The rimry nd secondry trnsmit ower nd the therml noise re set such tht t the edge of disc, the signl-to-noise rtio SNR is db. For Cse, we first generte 3 sets of loctions S t, nd. For ech set, Ryleigh fding chnnels re generted er link. We then comute the otiml threshold for ech set of loctions, erform detection nd comute the ccities. The ccities re then verged over fding nd the different loctions. For Cse, since S t is unknown, the sme 3 sets of nd s in Cse re used. Then for ech ir of {, }, nother 3, S t re generted to comute the threshold 3 by verging nd b over S t nd fding. After obtining the threshold for ech set of loctions, the sme number of Ryleigh fding chnnels s in Cse re generted to erform the detection. Then the rogrm comutes the rimry nd cognitive ccities verged over S t nd fding, given the secific ir {, }. In the lst ste, these ccities re verged over ll {, } irs. For Cse 3, we use the sme methodology nd rmeters s in Cse. For Cse 4, since the cognitive trnsmitter hs no loction informtion, the sme loctions of S t, nd s Cse re used. And the threshold 5 is comuted by verging nd b over ll three loctions. B. Results nd Discussion In Fig., the weighted sum ccities 5 with different sets of loction informtion re shown for µ =.5. Furthermore, to comre with the erformnce of the revious threshold roosed in 7], the weighted sum ccity of 7] with full loction informtion is lso lotted. As the rimry link trnsmission robbility goes u, the network becomes more sensitive to miss detection, nd the loction informtion merit is better reveled. While more loction informtion results in better ccity gin s exected, the comrtively modest gin with more loction informtion is due to network rmeters the rdii R c, R, R i. Secificlly, close insection of the four log-terms in the ccity exressions, b nd c 6, 7, 8 revels tht, by setting the network rmeters such tht the verge difference between the two terms without interference nd the two with interference is lrger, more ccity enlty will incur becuse of miss detection nd flse lrm. On the other hnd, comred to the threshold in 7], which is designed to minimize Byesin sensing risk function, the ccity-otiml threshold increses the network throughut significntly, with gin rnging from 5% to 36% deending on λ. To investigte where this gin comes from, we decomose the objective function into serte rimry link ccities nd cognitive link ccities in Fig.3 nd Fig.4. The corresonding ccities from 7] with full loction informtion re lso shown for comrison.

5 .5.8 Objective Function Ccity λ λ Fig.. Objective functions with different loction informtion. The dotted line is lotted using threshold in 7] Fig. 4. Primry link ccity with different loction informtion. The dotted line is lotted using threshold in 7] Ccity λ Fig. 3. Cognitive link ccity with different loction informtion. The dotted line is lotted using threshold in 7] From Fig.3, the cognitive link ccities re incresed significntly comred to 7]. The gin is more ronounced s the rimry user trnsmits more frequently i.e., s λ increses. In 7], when λ roches, the cognitive user s ccity dros to ner zero, while with the new threshold, the cognitive user cn still mintin significnt ccity. However, in Fig.4, we discover tht the network reches its mximum weighted sum ccity by scrificing the rimry link s rte. As λ increses, the rimry user s ccity is decresed from its mximl vlue in 7] by u to 5%. If we djust the weight µ in 5 to be greter thn.5, the gs between the ccities using threshold nd the threshold in 7] in both Fig.3 nd Fig.4 will be nrrower. Thus when designing sensing threshold, the objective is imortnt. The Byesin risk objective in 7] does not result in mximum network ccity, but it ffects the rimry user s ccity little. The ccity objective 5 results in higher network sum ccity nd higher cognitive user s ccity but t enlty to the rimry user s ccity. Using which design should deend on the reference of the network oertor. VI. CONCLUSION In this work, we nlyticlly derive n otiml sensing threshold which mximizes the weighted sum network ccity. Furthermore, we nlyze the ccity with different sets of loction side informtion. Simultion results show tht, comred to nother threshold designed to minimize Byesin sensing risk function 7], the roosed threshold cn significntly imrove the network sum ccity. The gin comes from higher cognitive user s ccity, but it is lso t n, lbeit smller, enlty on the rimry user s ccity. Moreover, loction informtion is lso helful, for stil side informtion is beneficil to the cognitive rdio in mking otiml sensing decision. However, unlike in 7], the ccity is not s sensitive to the loction informtion s the Byesin risk function. These results suggest tht choosing the right objective is crucil in designing sensing threshold. REFERENCES ] H. L. Vn Trees, Detection, Estimtion, nd Modultion Theory, Prt I. New York: Wiley, 968. ] Seung-Chul Hong; Vu, M.H.; Trokh, V., Cognitive Sensing Bsed on Side Informtion, IEEE Srnoff Symosium, 8, vol., no.,.-6, Aril ] FCC, Sectrum olicy tsk force reort, ET Docket, Tech. Re. - 55, Nov.. 4] S. Hykin, Cognitive Rdio: Brin-Emowered Wireless Communictions, IEEE Journl on Selected Ares in Communictions, vol. 3, no.,., Februry 5. 5] Devroye, N.; Mitrn, P.; Trokh, V., Achievble rtes in cognitive rdio chnnels, IEEE Trnsctions on Informtion Theory, vol.5, no.5, , My 6 6] Jfr, S.A.; Srinivs, S.; Mric, I.; Goldsmith, A., Breking Sectrum Gridlock With Cognitive Rdios: An Informtion Theoretic Persective, Proceedings of the IEEE, vol.97, no.5, , My 9 7] P. Ji, M.H Vu, T. Le-Ngoc, Ccity Imct of Loction-wre Cognitive Sensing, IEEE Globecom9, Honolulu, Hwii, Nov.3-Dec.4, 9 8] Gndetto, M.; Regzzoni, C., Sectrum sensing: A distributed roch for cognitive terminls, IEEE Journl on Selected Ares in Communictions, vol.5, no.3, , Aril 7