SPECTRUM sensing is a core concept of cognitive radio

Transcription

1 World Acadey of Science, Engineering and Technology International Journal of Electronics and Counication Engineering Vol:6, o:2, 202 Efficient Detection Using Sequential Probability Ratio Test in Mobile Cognitive Radio Systes Yeon-Jea Cho, Sang-Uk Park, Won-Chul Choi and Dong-Jo Park International Science Index, Electronics and Counication Engineering Vol:6, o:2, 202 wasetorg/publication/697 Abstract This paper proposes a sart design strategy for a sequential detector to reliably detect the priary user s signal, especially in fast fading environents We study the coputation of the log-likelihood ratio for coping with a fast changing received signal and noise saple variances, which are considered rando variables First, we analyze the detectability of the conventional generalized log-likelihood ratio GLLR schee when considering fast changing statistics of unknown paraeters caused by fast fading effects Secondly, we propose an efficient sensing algorith for perforing the sequential probability ratio test in a robust and efficient anner when the channel statistics are unknown Finally, the proposed schee is copared to the conventional ethod with siulation results with respect to the average nuber of saples required to reach a detection decision Keywords Cognitive radio, fast fading, sequential detection, spectru sensing I ITRODUCTIO SPECTRUM sensing is a core concept of cognitive radio networks [3], [4] for ensuring that cognitive radios do not cause harful interference to priary user networks Much of the related research on sensing and detection ethods [5], [6] has already been conducted including sequential ethod devised by Wald [2] In this paper, we consider the sequential ethod to reduce the average nuber of saples required to reach a detection decision by using the sequential probability ratio test SPRT and a practical energy detector Spectru sensing for cognitive radio systes considering fast fading is of interest in obile counication research The cooperative sequential detection schee for reducing the average sensing tie in cognitive radio networks has been well studied by Qiyue Zou []; coposite hypotheses using the generalized log-likelihood ratio GLLR are well handled in [] in ters of independent and identically distributed iid saples acquired by the detector In this paper, we use an energy detector for SPRT; the sensing is based on the difference between the received signal and noise variances Therefore, the statistics of the acquired signal and noise saples depend on the received signal and noise power level, respectively Here, we design the sequential detector for spectru sensing when the saples acquired by cognitive radios are independent but not identically distributed inid This is called fast fading and is caused by the effect of fast changing channel characteristics in obile cognitive radio systes More generally, we allow not only the received The authors are with the Departent of Electrical Engineering, Korea Advanced Institute of Science and Technology KAIST, Daejeon , Korea e-ail: yeonjeacho@kaistackr; sangukpark@kaistackr; wcchoi@kaistackr; djpark@kaistackr signal statistics but also the noise statistics to be fast changing due to noise power uncertainty and characteristics of the obile radio syste Throughout this paper, we adopt a syste odel siilar to that in [] that consists of M cognitive radios and assue that the nth acquired saple by the th =,2,,M cognitive radio is a zero ean Gaussian rando variable with received signal and noise variances v, n and v 0, n v, n >v 0, n, ie, H i : x [n] 2πvi, n exp x [n] 2, i =0,, 2v i, n where the two hypotheses are defined as H 0 : target signal is absent H : target signal is present The nth instantaneous saple variances under H 0 and H are v 0, n and v, n, respectively In this fast fading environent, unknown instantaneous variances v 0, n V 0, and v, n V, are considered to be rando variables for,2,, and =,2,,M whose statistics are deterined fro the channel characteristics, and p v 0, and p v, are the probability density functions of v 0, n and v, n, respectively We assue that the paraeter spaces V 0, and V, are disjoint, where and V 0, = x L 0, x U 0, } 2 V, = y L, y U, } 3 The distributions of v i, n,2,, by the sae cognitive radio are the sae over the long ter But, the distributions of v i, n =,2,,M between the other cognitive radios can be different fro each other Under H 0 and H, the distributions of the acquired signal at the th radio are characterized by the probability density functions p 0, x [n];v 0, n and p, x [n];v, n, respectively II SEQUETIAL DETECTIO I FAST FADIG EVIROMETS A Sequential Detection using GLLR As explained in Section I, the received signal and noise variances change continuously during sensing In this fast fading environent, an ideal sequential probability ratio test International Scholarly and Scientific Research & Innovation scholarwasetorg/ /697

2 World Acadey of Science, Engineering and Technology International Journal of Electronics and Counication Engineering Vol:6, o:2, 202 SPRT ust perfor the following test: The th=,2,,m cognitive radio acquires saple x [] and coputes ln p,x [];v 0, p 0,x [];v 0, 2 The base station updates the sequential log-likelihood ratio LLR ideal according to LLR ideal = LLR ideal + M ln = p, x [];v 0, p 0, x [];v 0, 4 International Science Index, Electronics and Counication Engineering Vol:6, o:2, 202 wasetorg/publication/697 3 If LLR ideal δ 0, H 0 is accepted; if LLR ideal δ, H is accepted, where δ 0 and δ are conceptual thresholds 4 Otherwise, take one ore saple and repeat to 4 However, v i, n i=0,, =,2,,M,,2,, is not a deterinistic value but a rando variable, so an exact coputation of LLR ideal is ipossible Thus, we try to perfor the SPRT using the GLLR by replacing v i, n with their axiu likelihood estiates and we analyze how this schee works with respect to the robustness of this sensing ethod We have GLLR = = where ˆx and ŷ of x and y, ie, ˆx ŷ = arg ax M ln p, x [n];ŷ, 5 p 0, x [n];ˆx are the axiu likelihood estiates x V 0, = arg ax y V, ln p 0, x [n];x ln p, x [n];y Although the acquired saples are not identically distributed received signal and noise variances are not fixed in fast fading environents, the axiu likelihood estiates converge to the following values: under H 0, ˆx converges to E v 0, n} and ŷ converges to L, 2 under H, ˆx converges to U 0, and ŷ converges to E v, n} For exaple, under H 0, Fig shows the convergence of the axiu likelihood estiate of x The first figure shows that the instantaneous noise variance v 0, n for,2,, is fast changing according to the each saple tie n The second figure shows that, in this environent, the axiu likelihood estiate ˆx converges to E v 0, } The corre- Fig The convergence of the axiu likelihood estiate of x The first figure shows that the instantaneous noise variance v 0, n for,2,, is fast changing and the second figure shows that the axiu likelihood estiate ˆx converges to E v 0, n} v 0, n has a unifor distribution and the above grey horizontal line indicates E v 0, n} = 085 V 0, = x 08 x 09} sponding proof of the above concepts is following: ˆx = arg ax x V 0, = arg ax x V 0, E v0, ln p 0, x [n];x } ln p 0, x [n];x ln p 0, x [n];v 0, n 6 The distributions of x [n],2,, depend on the nth instantaneous signal variance v 0, n, respectively By the law of large nubers, as, } p0, x [n];x E v0, ln p 0, x [n];v 0, n = E v0, p 0, x [n];v 0, n = 2 p, x [n];x p 0, x [n];v 0, n E ln v 0, n} E v 0, n} ln x + x } dx [n] Then, we differentiate the above result with respect to x to find ˆx d } p0, x [n];x E v0, ln dx p 0, x [n];v 0, n = E v 0, n} 2x 2 2x =0, Fro the above equation, the solution is E v 0, n} Therefore, under H 0, ˆx converges to E v 0, n}, ŷ converges to L, by the pre-known bound fro 7 8 International Scholarly and Scientific Research & Innovation scholarwasetorg/ /697

3 World Acadey of Science, Engineering and Technology International Journal of Electronics and Counication Engineering Vol:6, o:2, 202 International Science Index, Electronics and Counication Engineering Vol:6, o:2, 202 wasetorg/publication/697 the paraeter spaces, and the corresponding GLLR, is expressed by ln p,x [n];l, p 0,x [n];ev 0,} Siilarly, under H, ˆx converges to U 0,, ŷ converges to E v, n}, and the corresponding GLLR, is expressed by ln p,x [n];ev,} p 0,x [n];u 0, Thus, we can copute the expectation of the related log-likelihood ratio to verify the distinguishability of two hypotheses as in the following: } p, x [n];l, E H0 ln p 0, x [n];ev 0, } = p v 0, p 0, x [n];v 0, n p, x [n];l, dx [n] dv 0, p 0, x [n];ev 0, } = ln E v 0,} E v 0,} + < 0, 2 L, L, 9 where E v 0, } <L, Siilarly, } p, x [n];ev, } E H ln p 0, x [n];u 0, = p v, p, x [n];v, n p, x [n];ev, } dx [n] dv 0, p 0, x [n];u 0, = ln E v,} + E v,} > 0, 2 U 0, U 0, 0 where E v, } >U 0, The conditions 9 and 0 guarantee that the two hypotheses are also distinguishable by using the conventional GLLR schee in fast fading environents and also ensure the detectability by [, Lea 2] B Efficient detection with unknown p v 0, and p v, It is known that we do no use the conventional GLLR schee, to select the proper received signal and noise variances, which are used to copute LLR, for the SPRT to also ensure conditions 9 and 0 Here, we define LLR, p, x [n];y = ln p 0, x [n];x, where the representative values x and y are set by force If p v 0, and p v, are known, it ay be possible to choose optial x and y values with respect to the average nuber of saples required to reach a detection decision In real obile systes, it can be very difficult to find the exact probability density functions of v 0, and v, Therefore, we propose a practical sensing algorith to efficiently cope with unknown p v 0, and p v, The proposed sequential sensing algorith is efficiently applicable to fast fading environent and is suarized in Algorith We verified that the conventional SPRT Algorith The Proposed Cooperative Sequential Sensing Algorith in Fast Fading Environent 0: Modeinitial state : Set η 0 and η are pre-defined values 2: The th =,2,,M cognitive radio perfors the SPRT by using the GLLR 3: When H 0 is accepted, store the saples acquired by the th =,2,,M cognitive radio and accuulate these saples in tp 0 4: When H is accepted, store the saples acquired by the th =,2,,M cognitive radio and accuulate these saples in tp 5: If the total nuber of saples in tp 0 is larger than η 0 and the total nuber of saples in tp is larger than η, go to Mode2 6: Otherwise, repeat steps 2 to 6 7: Mode2The use of LLR, 8: Copute ˆx η0 η0 = arg ax lnp 0, x V 0, by using the saples in tp 0 9: Copute ŷ η η = arg ax lnp, y V, x tp 0 [n];x x tp [n];y by using the saples in tp 0: Use the values x and y to copute LLR, = ln p,x [n];y p 0,x [n];x, where x = ˆx η0 and y = ŷ η : The th =,2,,M cognitive radio perfors the SPRT by using the LLR, 2: When H 0 is accepted, update the saples in tp 0 3: When H is accepted, update the saples in tp 4: If initialization coand is executed, go to Mode 5: Otherwise, repeat steps 8 to 5 using the GLLR is a detectable schee especially in fast fading environents in Section II A, fro that fact, it is possible to perfor the SPRT in the initial state by using the GLLR In Mode, tp 0 and tp play an iportant role of accuulating saples needed to obtain the axiu likelihood estiates ˆx η0 and ŷ η, where both η 0 and η are the nuber of saples needed to obtain highly accurate estiates In Mode2, ˆx η0 saples in tp 0 and tp ˆx η0 ŷ η = ax in = ax in η 0 and ŷ η, respectively, where η 0 η η are obtained fro the } } 2,U0, x tp 0 [n],l 0,, 2 } } 2,U, x tp [n],l, 3 If η 0 and η are large enough, ˆx η0 and ŷ η converge to E v 0, n} and E v 0, n}, respectively This fact is also International Scholarly and Scientific Research & Innovation scholarwasetorg/ /697

4 World Acadey of Science, Engineering and Technology International Journal of Electronics and Counication Engineering Vol:6, o:2, 202 International Science Index, Electronics and Counication Engineering Vol:6, o:2, 202 wasetorg/publication/697 Fig 2 Sequential detection in fast fading environents under H 0 The siulation paraeters are listed in Table I and the detection thresholds δ 0 and δ in the sequential ethod are deterined through coputer experients proved in Section II A That is, LLR, ln p, x [n];e v, } p 0, x [n];e v 0, } 4 Basically, the obile radio signal consists of a fast fading signal superiposed on a local ean value which reains constant over a sall area However, when the local ean value varies slowly, the saples in tp 0 and tp are continuously updated as in steps 2 and 3 in Algorith In this proposed algorith, we assue that false alar and iss detection probabilities are sufficiently sall such that the effect of unreliable saples induced by a false alar and iss detection is negligible on calculating ˆx η0 and ŷ η III SIMULATIO RESULTS To illustrate the efficiency of the proposed algorith, siulations are conducted with respect to the average nuber of saples required to reach a detection decision In this siulation, cooperative sensing using a sequential ethod is perfored with four cognitive radios M =4 The siulation paraeters needed to describe the fast fading environents and used to deterine η 0 and η values are listed in Table I, and the received signal and noise variances v, n and TABLE I THE SIMULATIO PARAMETERS = =2 =3 =4 L 0, U 0, L, U, η η Fig 3 Sequential detection in fast fading environents under H The siulation paraeters are listed in Table I and the detection thresholds δ 0 and δ in the sequential ethod are deterined through coputer experients v 0, n have a unifor distribution Monte Carlo siulations are perfored in both Mode and Mode2 for various values of δ 0 and δ to find the thresholds that guarantee the pre-defined false alar and iss detection constraints α and β We use different values of δ 0 and δ for different α = β because δ 0 and δ depend on α and β [] The siulation results are shown in Fig 2 and Fig 3 under H 0 and H, respectively Figure 2 and Figure 3 show that Mode2 using LLR, is ore efficient than Mode using GLLR [] in fast fading environents with respect to average nuber of saples required to reach a detection decision In addition, Mode2 in Algorith has less coputational coplexity naely, O M than Mode, which has coputational coplexity O M 2 IV COCLUSIO We have proposed an efficient sensing algorith to cope with fast fading by the ode change ethod In Section II, we analyzed how the SPRT using the GLLR works with respect to the robustness of a sensing ethod, and then we proposed a ore efficient sensing algorith applicable to cognitive radio networks considering fast fading effect Our siulation results show that Mode2 using LLR, is ore efficient than Mode using GLLR in fast fading environents with respect to average nuber of saples required to reach a detection decision This paper can also give soe intuition when studying a siilar syste odel ACKOWLEDGMET This work was partially supported by Defense Acquisition Progra Adinistration and Agency for Defense Developent under the contract UD0006MD REFERECES [] Q Zou, S Zheng, and A H Sayed, Cooperative Sensing via Sequential Detection, Proc IEEE Trans Signal Process, vol 58, no 2, Dec 200 [2] A Wald, Sequential Analysis ew York: Wiley, 947 International Scholarly and Scientific Research & Innovation scholarwasetorg/ /697

5 World Acadey of Science, Engineering and Technology International Journal of Electronics and Counication Engineering Vol:6, o:2, 202 [3] J Mitola, III and G Q Maguire, Cognitive radio: Making software radios ore personal, IEEE Personal Coun, vol 6, no 4, pp 3-8, 999 [4] S Haykin, Cognitive radio: Brain-epowered wireless counications, IEEE J Select Areas Coun, vol 23, no 2, pp , Feb 2005 [5] D Cabric, A Tkachenko, and R W Brodersen, Spectru sensing easureents of pilot, energy, and collaborative detection, in Proc MILCOM, Oct 2006, pp -7 [6] I F Akyildiz, B F Lo, R Balakrishnan, Cooperative spectru sensing in cognitive radio networks: A survey, Physical Counication Journal Elsevier, vol 4, no, pp 40-62, March 20 International Science Index, Electronics and Counication Engineering Vol:6, o:2, 202 wasetorg/publication/697 International Scholarly and Scientific Research & Innovation scholarwasetorg/ /697