ROC Analysis of BLM Detector in AF Relays Based Cooperative Wireless Networks Omar GATERA 1, Ahmet Hamdi KAYRAN 1 and Haci ILHAN 2

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1 6 International Conference on Sustainable Energy, Environment an Information Engineering (SEEIE 6) ISBN: ROC Analys of BLM Detector in AF Relays Base Cooperative Wireless Networks Omar GATERA, Ahmet Hami KAYRAN an Haci ILHAN Istanbul Technical Univerty, Istanbul, Turkey Yiliz Technical Univerty, Istanbul, Turkey Keywors: AF relay networks, BLM Detector, Receiver operating characteristics (ROC). Abstract. In this paper, receiver operating characteristics (ROC) of Bayean linear moel (BLM) etector in amplify an forwar (AF) relays network is investigate. Cooperative communication with relay strategy is conere in this paper for its role of mitigating channel impairments such as multipath faing effects, shaowing, etc. Even though, the problem of channel impairments can be aresse, gnal etection is still neee at the receiver for recovering the original transmitte gnal from noise an other interference gnals. Therefore, BLM etector is propose for the sake of improving the gnal etection performance at the receiver an to reuce the implementation complexity of the system. Performance analys of the conere system is analyze in terms of ROC (probability of etection against the probability of false alarm). Simulation results showe that the propose metho is effective an can improve the etection performance in AF base multiple relays networks. Introuction Due to the nature of wireless channels, gnals propagation are usually affecte by channel impairments such as multipath faing, shaowing, noise, etc. Therefore, avance algorithms an techniques are require in orer to egn robust wireless networks an to ensure sustainable higher performance [-3]. Therefore, cooperative communications emerge as a technology to exten the network coverage, low cost of eployment, increase of spectral efficiency an reliable transmison. Cooperation schemes use ifferent protocols, the most common are amplify an forwar (AF) an ecoe an forwar (DF) [3-6]. Even though, all these methos can hanle the problem of channel impairments, in most cases, the transmitte gnal is corrupte by noise an coul not be known by the receiver. Therefore etection methos are use to recover the original gnal from noise [7-]. The etection performance analys was investigate firstly for eterministic gnal of unknown structure in Gausan noise [9] an this was extene for ranom amplitue gnals with ifferent faing channels such as Rayleigh, Nakagami an Rician istribution []. Upper an lower boun expresons of average etection probability were erive for fixe gain cooperative relay networks in []. In this paper, Bayean linear moel (BLM) etector is propose for the sake of enhancing the gnal etection in multipath propagation network. BLM etector is base on computing the gnal energy for each link in a multipath network, combining all gnal energies an obtaining the test statistic which is compare with the preetermine threshol. BLM etector is a practical subject ifferent from the previous stuies whereby theoretical analyses were conucte [7-]. Our contribution is base on proving practical tool that uses Bayean linear moel (BLM) approach for its low implementation complexity an effective gnal etection results. The results for ROC of the propose system are presente. The rest of the work is organize as follows; section II presents the system moel, section III eals with performance analys, section IV iscusses about mulation an results analys, an finally section V conclues the paper. 77

2 System Moel The network moel conere in this paper comprises of ngle fixe source (S), multiple relays (R i ) an ngle estination (D), an all noes are equippe with ngle antenna as illustrate in Figure. R h s h R i h h S h SM h R M h M D Figure. Network moel. We coner a system operating over IID Rayleigh faing channels, where h, h an h are channels between source & estination, source & relays an relays & estination as represente in Figure. These channels are assume to be complex faing coefficients with Rayleigh envelope, zero mean an variance, an. The normalize istances between the source & estination, source & relay an relay & estination are represente by, an respectively. We coner that the transmison is one in two phases: In the first phase, the source broacasts the gnal to all relays an estination. The receive gnals from the source are escribe as follows: y Ps h s w. () y Ps h s w. () In the secon phase, the source is lent an relays amplify the receive gnal from the source only an forwar it to the estination. We assume that relays o not prove aitional traffic on the transmitte gnal an the transmison is one in half uplex moe. y PG i ih y w. (3) y Ph i w. (4) where, Gi y is the generate gnal on the i th relay an the amplification factor G i is equivalent to G /{ E( h ) P N } where E (.) gnifies the expectation operator, P s is the i s power of the source, P i is the transmit power on the i th relay, s ( k ) is generate by the source for a given number of symbols k an equivalent to s ( k ). Coefficients w ( k ), w an w ( k ) are assume to be complex aitive white Gausan noise with zero mean an variance N. This matrix form can be represente by the linear equation as follows: y = Hs + w. (5) where y inicates the column matrix of the receive gnal, H inicates the channel matrix, s inicates the column matrix of the transmitte gnal an w inicates the column matrix of the receive noise at the estination. 78

3 Performance Analys The etection performance analys of our moel is measure in terms of receiver operating characteristic (ROC). Detection Performance Analys in Non Faing Environment In non faing environment, the ecion problem on the presence an absence of the gnal is governe by the following two hypotheses []; w : H y Hs w : H. (6) The receive gnal may be the noise only or absence of the gnal which correspons to the hypothes H. Otherwise, the receive gnal may be a combination of the transmitte gnal an the noise which correspons to the hypothes H that inicates the presence of the gnal. In case of Bayean linear moel, the probabilities of enty function of (7) are given respectively as follows: N/ / N/ / s s T exp ( ) y y I ( ) et ( I) : H py ( ) T exp y y ( C I) ( ) et ( C I) : H. (7) where y is an N vector of observations, H is a known N p observation matrix with N p, s is an p ranom vector with s : N(, C s ), an w is an N noise vector with PDF N(, I) an is inepenent of s. The theoretical results of probability of false alarm an probability of etection in non faing environment are given in [7-] as follows: P ( u, ) ( u) an P Q (, ). (.,.) is fa the upper incomplete Gamma function [3], u is the time banwth prouct of the observe gnal which gnifies the number of observe samples u N/, is the etection threshol of the th energy etector, (.) is the complete Gamma function an Q u (.,.) is the u orer generalize Marcum Q-function [3]. BLM Detection Performance Analys in Faing Environment In this case, BLM etector is base on computing test statistic by ung the following expreson [4]: T T T T( y) y HChH ( HChH NI) y. (8) The test statistic T( y ) of equation () can be efine as the total gnal energy receive at the receiver ue to the combination of gnal energies from the links of the source & estination an relays & estination noes. In orer to ece about the presence or absence of the gnal, the test statistic is compare with the preetermine threshol. In equation (), the covariance matrix C h iag(,,..., i ) an the noise variance NI iag( N,..., Ni ). The test statistic in (3) can be given by the following expreson: M T( y) y y i. (9) where an are average SNR between the source & estination an relay & estination respectively. The receiver eces the presence of the gnal when the test statistic is greater than the threshol ( T( y) ) for the hypothes H, otherwise, the receiver eces the absence of the u 79

4 gnal accoring to the hypothes H. Therefore, the probability of etection is P P ( T( y) H) an non-etection is Pn P ( T( y) H) [7, 8]: When the receiver eces the presence of the gnal whereas there is not, in this case we have the probability of false alarm as: P P ( T( y) H ). Another case is when the receiver eces fa the absence of the gnal whereas there is; in this case we have the probability of misse etection as: P P ( T( y) H ). The relation between the probability of etection an the probability of m r misse etection is: Pm P. In this scheme, the gnal energy is etecte for each link, combine an then compare with the preetermine threshol. The receiver etector can be conere as an optimal non-coherent multipath combiner [4]. Simulation an Results Analys In this paper, mulation results are presente in orer to evaluate the etection performance of BLM metho in cooperative multiple relays network. Two scenarios are conere in this paper; the first scenario evaluates the effect of number of relays on ROCs, the secon scenario evaluates the effect of istance between noes on ROCs. At the source the transmitte gnal is generate by the source an moulate with quarature phase shift keying (QPSK). In Figure 3 the results show that the P in cooperation moe is greater than the one in non cooperation moe an it improves when the number of relay increases. In Figure 4, the results show that the P improves when the relay is closer to the estination noe P.6.5 R 3R NonRelay P fa Figure 3. ROC for one an three relays S-R-D[..9] S-R-D[.9.] S-R-D[.5.5].6 P P fa Figure 4. ROC for ifferent istances [ ; sr ; r ]. 8

5 Concluon In this work, we have conucte a stuy on ROCs of BLM etector in AF relays base cooperative wireless networks when multipath propagation environment is conere. The mulation an results analys showe that BLM etector is feable an can prove an improve etection performance in the system. The ifference mae in this work is that, our propose methos can be applie practically in wireless communication networks in case the receiver knows the channel state information (CSI) of the system, whereas the reference work in [] is a stuy one with the purpose to obtain the theoretical optimum achievable energy etection. BLM etector can be applie in the current or next generation wireless networks an particularly where cooperative multiple relays network is applicable. References [] O. Simeone, N. Levy, A. Sanerovich, O. Somekh, B. M. Zael, H. V. Poor, S.Shamai (Shitz), Cooperative wireless cellular systems, An information-theoretic view, Now Publishers Inc.,. [] A. Golsmith, Wireless Communications. Stanfor Univerty, 4. [3] I. F. Akyiliz, D. M. Gutierrez-Estevez an E. C. Reyes, The evolution to 4G cellular systems: LTE-Avance, Elsevier, Phycal Communication, vol. 3, pp. 7-44,. [4] A. Senonaris, E. Erkip, an B. Aazhang, User cooperation iverty-part I: system escription, IEEE Trans. Comm., vol. 5, no., pp , Nov. 3. [5] J. N. Laneman, D. N. C. Tse, an G. W. Wornell, Cooperative iverty in wireless networks: efficient protocols an outage behavior, IEEE Trans. Inf. Theory, vol. 5, no., pp , Dec. 4. [6] R. U. Nabar, H. Bölcskei an F. W. Kneubuhler, Faing relay channels: performance limits an space-time gnal egn, IEEE J. Sel. Areas Commun., vol., pp. 99-9, 4. [7] F. F. Digham, M. S. Alouini, an M. K. Simon, On the energy etection of unknown gnals over faing channels, in the Proceeings of the International Conference on Communications (ICC 3), vol.5, pp , May 3. [8] F. F. Digham, M. S. Alouini, an M. K. Simon, On the energy etection of unknown gnals over faing channels, IEEE Trans. Commun., vol.55, pp.-5, 7. [9] H. Urkowitz, Energy etection of unknown eterministic gnals, Proceeings of the IEEE, vol.3, pp , 967. [] V. Kostlev, Energy etection of a gnal with ranom amplitue, in Proceeings of the IEEE International conference on communications, vol.3, pp. 66-6,. [] M. O. Mughal, L. Marcenaro, C. S. Regazzoni, Asymptotic etection performance of energy etector in fixe gain cooperative relay networks, The 5th International conference on Information, Intelligence, Systems an Applications (IISA) 4, China. [] M. Barkat, Signal etection an estimation. Artech House Inc. Secon eition, 5. [3] A. H. Nuttall, Some integrals involving the Qm function, IEEE Trans. Inf. Theory, vol., pp , 975. [4] S. M. Kay, Funamental of statistical gnal procesng: Detection theory. Prentice Hall, vol. II,