Cooperative Spectrum Sensing with Secondary. User Selection for Cognitive Radio Networks

Transcription

1 Cooperative Spectrum Sensing with Secondary 1 User Selection or Cognitive Radio Networks over Nakagami-m Fading Channels Quoc-Tuan Vien, Huan X. Nguyen, and Arumugam Nallanathan Abstract This paper investigates cooperative spectrum sensing (CSS) in cognitive wireless radio networks (CWRNs). A practical system is considered where all channels experience Nakagami-m ading and suer rom background noise. The realisation o the CSS can ollow two approaches where the inal spectrum decision is based on either only the global decision at usion centre (FC) or both decisions rom the FC and secondary user (SU). By deriving closed-orm expressions and bounds o missed detection probability (MDP) and alse alarm probability (FAP), we are able to not only demonstrate the impacts o the m-parameter on the sensing perormance but also evaluate and compare the eectiveness o the two CSS schemes with respect to various ading parameters and the number o SUs. It is interestingly noticed that a smaller number o SUs could be selected to achieve the lower bound o the MDP rather using all the available SUs while still maintaining a low FAP. As a second contribution, we propose a secondary user selection algorithm or the CSS to ind the optimised number o SUs or lower complexity and reduced power consumption. Finally, numerical results are provided to demonstrate the indings. Q.-T. Vien and H. X. Nguyen are with the Middlesex University, United Kingdom. {q.vien; h.nguyen}@mdx.ac.uk. A. Nallanathan is with the King s College London, United Kingdom. arumugam.nallanathan@kcl.ac.uk.

2 2 Index Terms Cognitive radio, cooperative spectrum sensing, user selection, Nakagami-m ading. I. INTRODUCTION Cognitive radio (CR) has recently emerged as a novel technology to eiciently exploit spectrum resource by implementing dynamic spectrum access [1], [2]. The secondary users (SUs) can opportunistically utilise the licenced requency bands o the primary users (PUs) when they are not occupied. Thus, spectrum sensing is a basic element required at the SUs to detect the occupation and reappearance o the PUs [3]. Incorporating relaying techniques in cognitive wireless radio networks (CWRNs), cooperative spectrum sensing (CSS) has been proposed not only to help the shadowed SUs detect the licenced requency bands but also to improve sensing reliability o the SUs [4] [9]. Basically, a CSS scheme consists o sensing (SS) phase, reporting (RP) phase and backward (BW) phase. Every SU perorms local spectrum sensing (LSS) to determine the availability o the licenced spectrum in the SS phase and then orwards its local decisions to a usion centre (FC) in the RP phase. Collecting all LSS decisions, global spectrum sensing (GSS) is then carried out at the FC to make a global decision on the spectrum availability, which is then broadcast back to all the SUs in the BW phase. In order to save the energy consumption o CSS in CWRNs, user selection approaches have been investigated in various works, such as [10] [15]. Speciically, an energy-based user selection algorithm was proposed in [10] given battery lie constraints o SUs. To deal with the dynamic changes o the network topology and channel conditions, a correlation-aware distributed user selection algorithm was developed in [11] to adaptively select the uncorrelated SUs or the CSS.

3 3 The overhead energy caused by the CSS was also dealt with in [12] where an energy-eicient node selection was proposed to select the best node based on the binary knapsack problem. In [13], the selection o sensing nodes can also be realised by linearly weighting the sensing data at all sensing nodes. Considering the scenario when only partial inormation o SUs and PUs is available in the wireless sensor networks, an energy-eicient sensor selection algorithm has been proposed in [14] to minimise the energy consumption while still satisying the average detection probability. An optimisation ramework has also been developed in [15] to solve the problem o joint sensing node selection, decision node selection and energy detection threshold aiming at saving energy consumption in cognitive sensor networks. In this paper, we irst analyse the probabilities o missed detection and alse alarm o two CSS schemes over Nakagami-m ading channels, including i) Global decision based CSS (GCSS): The GSS decision is the inal spectrum sensing (FSS) decision at the SUs (e.g. [5]) and ii) Mixture o local and global decisions based CSS (MCSS): Both the LSS and GSS decisions are taken into account to make the FSS decision at the SUs (e.g. [9]). In particular, we consider a practical scenario where all SS, RP and BW links suer rom ading and noises. Our work neither assumes the RP/BW channels are error-ree [4], [5], [7], [12]. nor impractically requires instantaneous signal-to-noise ratio (SNR) inormation and excessive overhead [16], [17]. Our scheme requires a minimal 1-bit overhead or the report and eedback o sensing decisions. While a general criteria or decision-approach selection has been analytically derived in the presence o realistic channel propagation eects in [18], our work speciically aims at analysing and understanding behaviour o sensing perormance over Nakagami-m channel with minimal overhead. By deriving closed-orm expressions o missed detection probability (MDP) and alse alarm

4 4 probability (FAP), we irst compare the sensing perormance achieved with the above CSS schemes and evaluate the eects o the number o SUs and the ading channel parameters on the perormance. It is observed that GCSS scheme achieves a lower FAP while MCSS schemes improves the MDP. The ading parameters o the RP and BW channels are shown to have eects on both the MDP and FAP, while those o the SS channels only aect the MDP. Furthermore, the bounds o the MDP and FAP are then derived or a large number o SUs, which allows us to develop a secondary user selection algorithm or reducing the complexity and power consumption in the CSS. The rest o the paper is organised as ollows. In Section II, we introduce the system model o CWRNs and the process o GCSS and MCSS schemes. Section III derives the expressions and bounds o FAP and MDP or both CSS schemes over Nakagami-m ading channels. The secondary user selection algorithm or the CSS is presented in Section IV. Numerical results are presented and discussed in Section V. Finally, Section VI concludes the paper. A. System Model II. SYSTEM MODEL & COOPERATIVE SPECTRUM SENSING The system model o a CWRN under investigation is illustrated in Fig. 1 consisting o PU, {SU 1, SU 2,..., SU N } and FC. We assume there are K non-overlapping licenced requency bands 1, 2,..., K. Two hypothesis that the k-th requency band is occupied and unoccupied by PU are denoted by H 1,k and H 0,k, respectively. For convenience, let us deine a spectrum indicator vector (SIV) s (M) A, M {L, G, F j}, A {, F C}, i = 1, 2,..., N, j = 1, 2, o length K (in bits) to report the availability o the licenced spectrum in the LSS at, the GSS at FC and the FSS at using scheme j. The unavailable and available requency bands

5 5 SU 1 SU 2 FC PU... SU N SS phase RP phase BW phase Fig. 1: System model o cognitive wireless relay network. are represented in s (M) A by bits 0 and 1, respectively. The channel or a link A 1 A 2 is denoted by h A1 A 2, {A 1, A 2 } {P, S i, F }, A 1 A 2, and assumed to suer rom quasi-static slow Nakagami-m ading. Complex Gaussian noise vector n (T ), T {SS, RP, BW }, is assumed at A receiver node A in phase T, in which each entry has zero mean and variance o σ 2 0. B. Cooperative Spectrum Sensing (CSS) Three phases o CSS can be briely described as ollows: 1) Sensing (SS) Phase - Local Spectrum Sensing (LSS): The signal sensed at, i = 1, 2,..., N, at k, k = 1, 2,..., K, can be expressed as h P Si x[k] + n (SS) r (SS) [k], H 1,k, [k] = n (SS) [k], H 0,k, (1)

6 6 where x[k] is the transmitted signal rom PU. Then, detects the availability o k by comparing the energy o the received signal in (1) with an energy threshold ε i [k] via an energy measurement ξ[ ] as ollows: s (L) [k] = 0, i ξ[r (SS) [k]] ε i [k], 1, otherwise. 2) Reporting (RP) Phase - Global Spectrum Sensing (GSS): The received signal at FC rom, i = 1, 2,..., N, at k, k = 1, 2,..., K, can be written by (2) r (RP ) i [k] = Λ i h Si F x (L) [k] + n (RP ) F C [k], (3) where Λ i is the transmission power o and x (L) [k] is the binary phase shit keying (BPSK) modulated version o s (L) [k] (see (2)). Then, FC decodes and combines all the decoded SIVs (denoted by {s (RP ) i [k]}) rom all { } using the OR rule to make a global decision as 0, i N s (G) F C [k] = i=1 s(rp ) i [k] < N, 1, otherwise. 3) Backward (BW) Phase - Final Spectrum Sensing (FSS): The received signal at, i = 1, 2,..., N, rom FC with respect to k, k = 1, 2,..., K, is given by (4) r (BW ) [k] = Λ F C h F Si x (G) F C [k] + n(bw ) [k], (5) where Λ F C is the transmission power o FC and x (G) F C [k] is the BPSK modulated version o s (G) F C [k] (see (4)). Then, decodes the received signal as s (BW ) [k]. GCSS scheme: The GSS decision received rom FC is also the FSS at. Thus, we have s (F 1) [k] = s (BW ) [k]. (6)

7 7 MCSS scheme: combines its local SIV with the global SIV received rom FC as [9]: 0, i (s (L) s (F [k] + s (BW ) [k]) < 2, 2) [k] = (7) 1, otherwise. III. PERFORMANCE ANALYSIS In this section, we analyse the FAP and MDP o two CSS schemes. Without loss o generality, a speciic requency band is considered and thus the index o the requency band (i.e. k) is omitted in the rest o the letter. The Nakagami ading parameters o the SS, RP and BW channels are denoted by m ss, m rp and m bw, respectively. We assume that the RP and BW channels o the same link have the same Nakagami ading parameters (i.e. m rp = m bw ) and all the SUs have the same energy threshold (i.e. ε i [k] = ε[k] i = 1, 2,..., N). Deine α ε/(2σ 2 0) and β i m ss σ 2 0/(m ss σ γ P Si ), i = 1, 2,..., N, where γ P Si is the average SNR at over h P Si. The FAP and MDP o the LSS are given by [19] P () P () m = Pr{s (L) = 0 H 0 } = Γ u(ρ, α), (8) Γ(ρ) = Pr{s (L) = 1 H 1 } = 1 ϑ i,1 ϑ i,2, (9) where ϑ i,1 = e ( αβ i ) m ss 2 mss [β mss 1 i L mss 1( α(1 β i )) + (1 β i ) β j i L j( α(1 β i ))], (10) ϑ i,2 = β mss i ρ 1 e α j=1 j=0 α j j! 1 F 1 (m ss ; j + 1; α(1 β i )), (11) ρ denotes the time-bandwidth product o the energy detector, Γ( ) is the gamma unction [20, eq. ( )], Γ u (, ) is the upper incomplete gamma unction [20, eq. ( )], 1 F 1 ( ; ; ) is the conluent hypergeometric unction [20, eq. ( )] and L i ( ) is the Laguerre polynomial o degree i [20, eq. ( )].

8 8 Over a Nakagami-m ading channel h AB, the average bit error rate (BER) or BPSK modulation with respect to the average SNR o γ AB is obtained as in [21] and given below ( P b (E AB ) = 1 + γ ) mab AB Γ(m AB + 1/2) m AB 2 πγ(m AB + 1) 2 F 1 (m AB, 1/2; m AB + 1; 1/(1 + γ AB /m AB )) ψ AB, where 2 F 1 (, ; ; ) is the Gauss hypergeometric unction [20, eq. (9.100)]. Considering the GSS at FC, we obtain the ollowing: (12) Lemma 1. The FAP and MDP o the GSS are determined by 1 P = 1 [Γ(ρ)] N P m = N [Γ l (ρ, α)(1 ψ Si F ) + Γ u (ρ, α)ψ Si F ], (13) i=1 N [(1 ϑ i,1 ϑ i,2 )(1 ψ Si F ) + (ϑ i,1 + ϑ i,2 )ψ Si F ], (14) i=1 where ψ Si F is given by (12) and Γ l (, ) is the lower incomplete gamma unction [20, eq. ( )]. Proo: From (4), the FAP and MDP at FC are given by P = Pr{s (G) F C = 0 H 0} = 1 P m = Pr{s (G) F C = 1 H 1} = Thus, over the Nakagami-m ading RP channels, we have P = 1 P m = N i=1 N i=1 Pr{s (RP ) i = 1 x = 0}, (15) Pr{s (RP ) i = 1 x 0}. (16) N [(1 P () )(1 ψ Si F ) + P () ψ Si F ], (17) i=1 N [P () m (1 ψ Si F ) + (1 P () m )ψ Si F ]. (18) i=1

9 9 Substituting (8) and (9) into (17) and (18) with the act Γ u (ρ, α) + Γ l (ρ, α) = Γ(ρ) [20, eq. ( )], the lemma is proved. In the BW phase, we have the ollowing indings: Lemma 2. The FAP and MDP o the FSS at, i = 1, 2,..., N, using GCSS scheme are determined by P (),1 = 1 [(1 P )(1 ψ F Si ) + P ψ F Si ], (19) P () m,1 = P m (1 ψ F Si ) + (1 P m )ψ F Si. (20) Proo: From (6), the proo can be straightorwardly obtained as in Lemma 1. Lemma 3. The FAP and MDP o the FSS at, i = 1, 2,..., N, using MCSS scheme are determined by P (),2 = 1 1 Γ(ρ) [Γ l(ρ, α)(1 ψ F Si )+Γ u (ρ, α)ψ F Si ][(1 P )(1 ψ F Si )+P ψ F Si ], (21) P () m,2 = [(1 ϑ i,1 ϑ i,2 )(1 ψ F Si )+(ϑ i,1 +ϑ i,2 )ψ F Si ][P m (1 ψ F Si )+(1 P m )ψ F Si ]. (22) Proo: From (7), P (),2 and P () m,2 can be given by P (),2 = Pr{s (F 2) = 0 H 0 } = 1 Pr{s (L) = 1 x = 0}Pr{s (BW ) = 1 x = 0}, (23) P () m,2 = Pr{s (F 2) = 1 H 1 } = Pr{s (L) = 1 x 0}Pr{s (BW ) = 1 x 0}. (24) Thus, over the Nakagami-m BW channels h F Si, P (),2 and P () m,2 can be obtained by (21) and (22), respectively. Remark 1 (Lower FAP with GCSS scheme and Lower MDP with MCSS scheme). From (19), (20), (21) and (22) in Lemmas 2 and 3, it can be easily shown that P (),1 < P (),2 and

10 10 P () m,1 > P () m,2, i = 1, 2,..., N. Remark 2 (Lower MDP but Higher FAP with Increased Number o SUs). From (13) and (14) in Lemma 1, it can be seen that P and P m monotonically increase and decrease, respectively, over N. Thus, rom (19), (20), (21) and (22), the increased number o SUs helps both CSS schemes improve the MDP, however, causing a higher FAP. Remark 3 (Impact o Nakagami-m Fading Parameters on MDP and FAP). Both the MDP and FAP decrease when the ading parameters o RP and BW channels increase, while only MDP is improved with increased ading parameters o SS channels. In act, it is known that the BER o a Nakagami-m ading channel h AB monotonically decreases as m AB increases (see (12)). Thus, rom (19), (20), (21) and (22), it can be proved that P (),j and P () m,j, i = 1, 2,..., N, j = 1, 2, monotonically decrease as either m rp or m bw increases. Additionally, as shown in (8) and (9), P (), i = 1, 2,..., N, o the LSS is independent o m ss, while a lower P () m m ss increases. is achieved as Bounds o FAPs and MDPs: According to Remark 2, there is a signiicant impact o the number o SUs on FAPs and MDPs. For the sake o providing insightul meanings o the above derived expressions or the FAPs and MDPs o the two CSS schemes, let us investigate a speciic scenario o identical channels, i.e. γ P Si γ ss, γ Si F γ rp, γ F Si γ bw, i = 1, 2,..., N. Thus, rom (10) and (11), we can rewrite ϑ i,1 = ϑ 1 and ϑ i,2 = ϑ 2. Lemma 4. When the number o SUs is very large, i.e. N, FAP and MDP o GCSS scheme

11 11 approach P (SU),1 N and P (SU) m,1 N, respectively, where P (SU),1 N = 1 ψ bw, (25) P (SU) m,1 N = ψ bw. (26) Proo: As N, rom Lemma 1, it can be seen that P 1 and P m 0. Substituting into (19) and (20), we obtain P (SU),1 N and P (SU) m,1 N as shown in (25) and (26). Lemma 5. When the number o SUs is very large, i.e. N, FAP and MDP o MCSS scheme approach P (SU),2 N and P (SU) m,2 N, respectively, where P (SU),2 N = 1 Γ l(ρ, α) ψ bw Γ u(ρ, α) Γ l (ρ, α) ψ 2 Γ(ρ) Γ(ρ) bw, (27) P (SU) m,2 N = (1 ϑ 1 ϑ 2 )ψ bw (1 2ϑ 1 2ϑ 2 )ψ 2 bw. (28) Proo: The proo is similarly obtained as in Lemma 4. Remark 4 (Lower MDP with MCSS scheme and Approximately Similar FAPs). In act, rom (26) and (28), it can be easily shown that P (SU) m,2 N < P (SU) m,1 N, which means that a lower MDP bound is achieved with MCSS scheme. Considering the FAP bound, it is noted that Γ l (ρ, α) Γ(ρ) as α = ε/(2σ 2 0). Also, we have ψ 2 bw ψ bw < 1. Thus, rom (27), we have P (SU),2 N 1 ψ bw = P (SU),1 N. IV. SECONDARY USER SELECTION FOR THE CSS From Lemmas 4 and 5, it is noted that, given a large number o available SUs or CSS, we can select a smaller number o SUs to achieve the lower bound o the MDP instead o using all the SUs while still guaranteeing an achievable lower FAP.

12 12 Let N opt denote the optimised number o SUs or the CSS. We achieve the ollowing: Lemma 6. The optimised number o SUs or the CSS is determined by n n N opt = n ( 1)k [ψ rp + (ϑ 1 + ϑ 2 )(1 2ψ rp )] k = τ, (29) k=0 k where τ 0 + is an extremely small positive number. Proo: In Lemmas 4 and 5, the lower bound o the MDP o Scheme j, j = 1, 2, i.e. P (SU) m,j N, is achieved as P m 0. From (14) with identical ading channels, the MDP o the GSS can be rewritten as P m = [ψ rp + (1 ϑ 1 ϑ 2 )(1 2ψ rp )] N = [1 ψ rp (ϑ 1 + ϑ 2 )(1 2ψ rp )] N. (30) Applying Taylor expansion o power series [20, eq. (1.111)], we obtain n n P m = ( 1)k [ψ rp + (ϑ 1 + ϑ 2 )(1 2ψ rp )] k. (31) k=0 k Denote τ as an extremely small positive number, i.e. τ 0 +. Since P m 0, the optimised number o SUs can be ound by solving P m = τ. The lemma is proved. It is noted in Lemma 6 that N opt can be determined using numerical method. A secondary user selection algorithm can thus be proposed as summarised in Table. I 1. 1 Note that the determination o the optimised number o SUs and the user selection or the CSS can be carried out with the assistance o a coordinator, e.g. FC.

13 13 TABLE I: Secondary user selection algorithm or the CSS Given m ss, m rp, σ 0, γ ss, γ rp, ε, ρ, τ: Step 1: Find ϑ 1, ϑ 2 and ψ rp using (10), (11) and (12), respectively. Step 2: Find N opt in Lemma 6: n = 1 while n N do compute S = n k=0 n ( 1)k [ψ rp + (ϑ 1 + ϑ 2)(1 2ψ rp)] k k i S τ then break end i n = n + 1 end while N opt = n Step 3: Select N opt among N available SUs based on their local sensing data (e.g. [7]). V. NUMERICAL RESULTS Fig. 2 shows the MDP against the FAP o two CSS schemes (i.e. FCSS and MCSS) with respect to various ading parameters and various values o the energy threshold. We assume there are 10 SUs (i.e. N = 10) and the time-bandwidth product o the energy detector is ρ = 5. The SNRs o the channels are set as ollows: {γ P Si } = {10, 8, 9, 12, 5, 7, 8, 4, 2, 6} db, {γ Si F } = {8, 7, 10, 4, 6, 8, 9, 11, 8, 10} db and {γ F Si } = {10, 11, 13, 9, 8, 14, 11, 10, 12, 7} db. Two Nakagami-m ading scenarios are considered: i) m ss = 3, m rp = m bw = 1 and ii) m ss = 1, m rp = m bw = 2. It can be observed that, at a given energy threshold, the MCSS scheme achieves a lower MDP than the FCSS scheme, while a lower FAP is achieved with the FCSS compared to the MCSS. This observation conirms the statement in Remark 1. Additionally, the

14 m ss =3,m rp = P m m ss =1,m rp = FCSS (simulation) FCSS (analysis) MCSS (simulation) MCSS (analysis) m ss =1,m rp = P Fig. 2: Perormance comparison o two CSS schemes. analytical results o the FAP and MDP or both CSS schemes derived in Lemmas 2 and 3 are shown to be consistent with the simulation results. Investigating the impact o Nakagami-m ading parameters on the sensing perormance o the CSS, Fig. 3 plots the MDP versus FAP o MCSS scheme with respect to various ading scenarios 2. A total o 10 SUs is considered and the SNRs o the SS, RP and BW channels are similarly set as in Fig. 2. As shown in Fig. 3, given ixed m ss, both the MDP and FAP are improved as m rp (or m bw ) increases. Considering the scenario o ixed m rp and m bw, a lower MDP is achieved as m ss increases, while the FAP is unchanged or all values o the energy threshold. These above comparisons veriy the statement in Remark 3. The impact o the number o SUs on the sensing perormance o various CSS schemes is 2 The impact o the ading parameters on the sensing perormance o GCSS scheme can be similarly observed, and thus is omitted or brevity.

15 Increased m ss Increased m rp (or m bw ) 10 2 P m m ss =1,m rp =1 m =1,m =m =2 ss rp bw m ss =2,m rp =1 m =2,m =m =4 ss rp bw m ss =4,m rp = P Fig. 3: Perormance o MCSS scheme Upper bound P 0.3 GCSS with m =1,m =m =2 0.2 ss rp bw MCSS with m =1,m =m = 2 ss rp bw GCSS with m =2,m =m =1 ss rp bw MCSS with m =2,m =m =1 ss rp bw N Fig. 4: FAP o CSS schemes over the number o SUs.

16 GCSS with m ss =1,m rp = Lower bounds MCSS with m ss =1,m rp =2 GCSS with m ss =2,m rp =1 MCSS with m ss =2,m rp =1 P m N Fig. 5: MDP o CSS schemes over the number o SUs. shown in Figs. 4 and 5 where the FAP and MDP o the two aorementioned CSS schemes are plotted as unctions o N. The SNRs o the SS, RP and BW links are set as 8 db, 10 db and 12 db, respectively. We consider two ading scenarios: i) m ss = 1, m rp = m bw = 2, ii) m ss = 2, m rp = m bw = 1 and iii) m ss = 1, m rp = m bw = 10. It can be observed that both schemes approach the similar FAP upper bound as N is large, while the MDP o the MCSS scheme approaches a lower MDP bound. This accordingly veriies the statements in Remarks 2 and 4. Also, the FAP and MDP o the two CSS schemes are shown to approach the bounds given by (25), (26), (27) and (28) in Lemmas 4 and 5. Fig. 6 plots the optimised number o SUs as a unction o the SNR o SS links. Various ading scenarios are considered and the SNR o the RP and BW links are set as 6 and 4 db, respectively. As shown in Lemma 6, N opt is determined using numerical method with τ = 10 5 and 100 available SUs (i.e. n max = 100). It can be seen that a lower number o SUs can be

17 m ss =1,m rp =1 m =1,m =m =2 ss rp bw m =2,m =m =1 ss rp bw m ss =2,m rp =4 m =4,m =m =2 ss rp bw N opt SNR ss [db] Fig. 6: Optimised Number o SUs over SNR o SS links. selected to achieve the lower bound o the MDP rather than using all 100 SUs, which accordingly means a lower complexity and reduced power consumption are achieved with the proposed user selection or the CSS in CWRNs. Moreover, a lower N opt is required as either the SS perormance improves or the ading parameters increase. VI. CONCLUSIONS In this paper, we have analysed the MDP and FAP or two CSS schemes in CWRNs considering the practical scenario where all SS, RP and BW channels suer rom Nakagami-m ading. The derived expressions have shown the MCSS scheme achieves an improved MDP while causing a higher FAP when compared to the GCSS scheme. Both the MDP and FAP are improved as the ading parameters o the RP and BW channels increase, while the increased ading parameters o SS channels only results in a lower MDP. Furthermore, the bounds o the

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