Optimisation of multi-channel cooperative sensing in ... - IEEE Xplore

www.ietdl.org Published in IET Communications Received on 22nd June 2012 Revised on 11th March 2013 Accepted on 24th May 2013 doi: 10.1049/iet-com.2012.0748

ISSN 1751-8628

Optimisation of multi-channel cooperative sensing in cognitive radio networks Nan Zhao1, Fangling Pu1, Xin Xu1, Nengcheng Chen2 1

School of Electronic Information, Wuhan University, Wuhan Luojiashan 430072, People’s Republic of China State Key Lab for Information Engineering in Surveying, Mapping and Remote Sensing (LIESMARS), Wuhan University, 129 Luoyu Road, Wuhan 430079, People’s Republic of China E-mail: fl[email protected]

2

Abstract: Cooperative spectrum sensing (CSS) is a promising technique in cognitive radio networks (CRNs) that utilises multiuser diversity to mitigate channel instability and noise uncertainty. In this study, the relationship between ‘cooperation mechanisms’ and ‘spatial-spectral diversity’ over multiple channels jointly sensing is investigated in the presence of an imperfect reporting channel. The multiple channels are sensed at the receiver built on the filter bank-based multi-carrier system. The multi-channel CSS strategies are modelled by the introduced ‘cooperative ratio’ to balance the requirements on ‘sensing accuracy’, ‘efficiency’ and ‘overhead’, which is quantitatively characterised by the energy consumption. The target of CSS is to maximise the aggregate opportunistic throughput of secondary users (SUs) by jointly considering constraints on sensing overhead and the aggregate interference to primary users (PUs). The optimisation is divided into two sequential suboptimisation processes, ‘multi-user diversity optimisation’ and ‘multi-channel diversity optimisation’. An approach is developed from generic algorithms to solve the two sub-problems. Numerical results show that the optimal CSS scheme is effective in improving channel utilisation for SUs with low interference to PUs. This study establishes a valuable cooperative model for the design of multi-channel spectrum sensing algorithms in CRNs.

1

Introduction

The demand for radio spectrum has recently increased dramatically given the steadily increasing number of wireless applications. However, a large number of licensed bands, such as those for television broadcasting, are underutilised, resulting in spectrum wastage [1, 2]. Hence, the Federal Communications Commission was prompted to open licensed bands to unlicensed users through the use of cognitive radio (CR) technology [3]. In a cognitive radio network (CRN), the unlicensed secondary users (SUs) are allowed to access opportunistically the vacant portions of the spectrum that are assigned to the licensed primary users (PUs). Designing CRNs is considerably challenging. The secondary system should be capable of discovering as many spectrum opportunities as possible whereas strictly preventing interference to the primary transmissions. Thus, spectrum sensing is one of the essential components of CRNs to detect PUs efficiently and accurately. The performance of spectrum sensing is generally characterised by both ‘sensing accuracy’ and ‘sensing efficiency’. ‘Sensing accuracy’ refers to the precision in detecting PU signals, which is represented by the false alarm and detection probabilities. ‘Sensing efficiency’ refers to the number of spectrum opportunities discovered in terms of sensing throughput. ‘Sensing accuracy’ and ‘efficiency’ are two opposite aspects that reflect the performance of IET Commun., 2013, Vol. 7, Iss. 12, pp. 1177–1190 doi: 10.1049/iet-com.2012.0748

spectrum sensing. Given that the overall system performance of CRNs potentially depends on both ‘sensing accuracy’ and ‘efficiency’, the trade-off between them should be optimally addressed. Owing to numerous unpredictable problems, such as noise uncertainty, multi-path fading and shadowing, the performance of spectrum sensing may be significantly degraded [4]. By allowing multiple SUs to cooperate in spectrum sensing, cooperative spectrum sensing (CSS) can improve the sensing performance. The basic idea behind CSS rests on the ‘cooperation mechanisms’ that, the cooperative SUs should be selected for sensing cooperation and the local sensing results should be combined at the fusion centre (FC). In addition, most existing CSS strategies are centred at the detection performance and system throughput, that is ‘sensing gain’. Only a few ‘sensing overhead’ issues have been discussed in proposed schemes, which reveal realistic achievable ‘sensing gain’. Moreover, the PU–SU sensing channels and the SU–FC reporting channels are normally subject to fading or heavy shadowing, which bring out much more challenging problems to CSS [5, 6]. In this paper, we focus on one robust CSS technique to address these challenging issues. Previous studies on spectrum sensing have focused primarily on cooperation among multiple SUs, which are limited to the detection of signals over a single frequency band synchronously. In [7], the optimal linear cooperation

1177 This is an open access article published by the IET under the Creative Commons Attribution-NoDerivs License (http://creativecommons.org/licenses/by-nd/3.0/)

www.ietdl.org strategy was obtained by exploiting the hidden convexity in the seemingly non-convex problem under practical conditions, which may lose generality for opportunistic throughput optimisation. The work in [8] studied how to assign SUs to sense channels and to maximise the expected transmission time without any fusion rule. The work in [9] discussed how to solve the collaborative multi-band sensing problems with genetic algorithms (GAs) in the perfect reporting channels. In [10], the authors investigated how to assign SUs to cooperatively sense channels with hard decision fusion (HDF) schemes. The work in [11] investigated the sensing setting for multi-channel CSS under the data fusion rule without investigating the presence of the imperfect reporting channel. In [12], ‘cooperation mechanisms’ and the ‘sensing accuracy-efficiency’ trade-off were elaborated, but the mathematical model was not given to describe the cooperation mechanisms. Further, the problem of the interference to the primary systems was not investigated. In this paper, we attempt to exploit the relationship between ‘cooperation mechanisms’ and ‘spatial-spectral diversity’ over multiple channels jointly and develop an efficient multi-user cooperation framework for multi-channel spectrum sensing in the presence of an imperfect reporting channel. The main contributions of this paper are as follows: † By exploiting the cooperation strategies and design challenges in CSS, a common matrix model is derived by means of ‘cooperative ratio’ to describe the ‘cooperation mechanisms’ in CRNs. Considering the energy consumption of multi-channel CSS, the modelling of ‘sensing overhead’ is quantitatively characterised. ‘Cooperative ratio’ illustrates multi-user sensing assignment in multi-channel CSS to characterise the trade-off among ‘sensing accuracy’, ‘efficiency’ and ‘overhead’. The trade-off of various CSS mechanisms is analysed theoretically and simulatively. † Considering ‘spatial-spectral diversity’ over multiple channels, a multi-channel detection framework for multi-user CSS is proposed. In this framework, filter bank is used by each SU receiver to extract multi-channel signals with the aim of energy detector. Multi-user spatial diversity is exploited based on SUs sensing assignment and the linear combination of local sensing statistics from individual SUs. Considering the imperfect reporting channels, the detection and false alarm probabilities of the ‘spatial-spectral’ joint detection are investigated by theoretical analysis and numerical simulation. † To effectively assign SUs sensing multiple channels, an optimisation problem is formulated, which maximises the aggregate opportunistic throughput (AOT) of secondary

systems whereas limiting the energy consumption and aggregate interference (AI) to the primary system. An optimisation technique based on GAs is proposed to solve the problem and obtain the optimal ‘spatial-spectral’ joint detection. ‘Multi-channel diversity optimisation’ improves spectral efficiency by utilising spectral diversity. ‘Multi-user diversity optimisation’ enhances channel detection accuracy by exploiting spatial diversity. The performance of optimal CSS mechanisms is demonstrated through theory and simulations. The rest of the paper is organised as follows. The system model for multi-channel CSS is introduced in Section 2. Section 3 illustrates the CSS problem and GA-assisted optimisation algorithms. Numerical simulation results are given and discussed in Section 4, and Section 5 concludes the paper.

2

System model of multi-channel CSS

Consider the CRN deployment where each geographically nearby M SUs, which are scheduled to sense a single channel or several channels at the same time. For a given number of cooperative SUs, one channel with more sensing SUs will facilitate higher ‘sensing accuracy’ but less ‘sensing efficiency’. To exploit the relationship between ‘cooperation mechanisms’ and ‘spatial-spectral diversity’ over multiple channels jointly sensing, a multi-channel CSS model based on the filter banks is proposed in Fig. 1. Within this framework, filter bank-based receiver is presented for multi-channel extraction and local signal sensing. SUs forward their local statistics using energy detection (ED) to the FC, where the linear weighted soft decision fusion (SDF) is performed. 2.1

Characterisation of a PU–SU channel

Consider a primary communication system (e.g. multi-carrier modulation-based [13]) operating over K non-overlapping narrowband channels. Assume that the spectrum occupancy of PU is the same for all the SUs [The homogeneous assumption in this work is made mainly for the ease of exposition. It also partly covers the practical scenario when SUs stay relatively close compared to the PUs coverage area.] and is independent across channels [The assumption is frequently used in the literature (e.g. [6, 14]), and is reasonable when PUs traffic changes fast over channels. We may need to study the correlation between spectrum occupancies when PUs traffic changes slowly over channels, which is considered as a future direction.].

Fig. 1 Detailed system model of the proposed filter bank-based SDF CSS 1178 This is an open access article published by the IET under the Creative Commons Attribution-NoDerivs License (http://creativecommons.org/licenses/by-nd/3.0/)

IET Commun., 2013, Vol. 7, Iss. 12, pp. 1177–1190 doi: 10.1049/iet-com.2012.0748

www.ietdl.org At the nth time instant, let s(n) be the PU signal, which is assumed to be an independent and identically distributed Gaussian random process with zero mean; cm be the sensing channel gain between the PU and the mth SU; vm(n) be the sensing channel noise, which is assumed to be additive white Gaussian with zero mean and variance s2v , and xm(n) be the PU signal received at the mth SU receiver. Then, the sensing task at any arbitrary SU is formulated as the binary hypothesis test H0 :xm (n) = vm (n)

(1)

H1 :xm (n) = cm s(n) + vm (n)

(2)

where m = 1, 2, …, M, and n = 1, 2, …, N. N denotes the number of samples collected during the signal observation interval (i.e. the sensing period), emphasizing that the decision is made based on a limited number of signal samples. For simplicity, we assume that the transmitted signal in each channel has unit power and the transmitted signal s(n), channel gain cm, and additive noise vm(n) are independent of one another. The channel gains of the PU–SU and SU– FC channels are assumed to be constant over each operation period of interest, which can be justified by the slow-fading nature over these links, where the delay requirement is shorter than the channel coherence time [15]. Our sensing algorithm has to know only the noise power s2v and the squared values of the channel gain |cm|2. In practice, s2v can be calibrated in a given band that is known for sure to be idle (e.g. TV channel 37 is currently always empty). Accordingly, |cm|2 can be learned a priori during a period when the PU was known for sure to be working. This priori information can be obtained because most current TV stations transmit pilot signals periodically at a fixed power level [16].

2.2 Filter bank-based multi-carrier system for multi-channel sensing In this section, a signal-processing solution for multi-channel spectrum sensing is presented, where ED is performed at the receiver built on the filter bank-based multi-carrier system. The work [17] suggests that using filter banks for spectrum sensing would offer new opportunities of communicating at no extra cost. This means the reuse of sensing filter banks for transmission purpose also. More importantly, filter bank can extract multiple channels simultaneously with the aid of flexibly designed prototype filter. The output of the kth channel can be written as

ykm (n) =

L h −1

hk (i)xm (n − i)

(3)

i=0

where Es =

N −1

|s(n)|2 ,

d0 = s2v

L h −1

h2k (i) and

i=0

n=0

d1 = |cm |2 Es + s2v

L h −1

h2k (i).

i=0

From the filter bank point of view, conventional ED is based on a rectangular prototype filter and IDFT/DFT blocks. The resulting sub-channel filters are not very frequency selective because the first sidelobe is only 13 dB below the mainlobe [18]. Owing to the low spectral-leakage characteristics, cosine-modulated filter bank (CMFB)-based transmission scheme [19] is much more favourable for multi-channel spectrum estimations compared to the DFT-based one. The distinctive feature of CMFB scheme is the ability to provide improved frequency selectivity through the use of longer and spectrally well-shaped prototype filters. Moreover, CMFB can be implemented in a computationally efficient manner using polyphase representation of the filter band and fast DCT. Here, we mostly consider the CMFB model, but the ideas are readily applicable to all filter bank-models which are based on uniform highly selective filter banks. 2.3 Multi-user cooperative model for multi-channel jointly detection In this section, to describe the ‘cooperative mechanism’ in CRNs, a common matrix model is derived by means of ‘cooperative ratio’ ρ, which is represented as r = r1 r2 . . . rK ⎡ 1 ⎤ r1 r21 · · · rK1 ⎢ r1 r2 · · · rK ⎥ ⎢ 2 2 2 ⎥ ⎥ =⎢ .. .. .. ⎥ ⎢ .. ⎣ . . . . ⎦ r1M r2M · · · rKM

(5)

where rkm = 1 represents the assignment of mth SU for sensing the kth channel and rkm = 0 otherwise. In CSS, SUs involve in local sensing which consumes energy. The energy consumption overhead may be significant if the number of both cooperating SUs and sensed channels is large. Thus, energy overhead should be considered in CSS schemes. Let ukm be the amount of energy consumption for the mth SU sensing the kth channel. Since each SU performs channel sensing with the same sensing approach, we assume that ukm = u for each sensing assignment. The ‘sensing overhead’ Θ for all the M SUs cooperative sensing can be written as Q=

M K

rkm u

(6)

m=1 k=1

where k = 1, 2, …, K, hk(n) is the response of the kth filter with the length Lh. Then, the statistical properties of received signal can be expressed as ykm n|Hi N 0, di ,

i = 0, 1


(4)

Note that the ‘cooperative ratio’ effectively describes the common sensing schemes, including the three strategies discussed in [12]. Instead of grouping strategies used in [12] with each SU assigned at most one channel, this model illustrates the flexible assignment of SUs to channels, which means ‘cooperation mechanisms’.


www.ietdl.org and variances

According to the number of sensing SUs and sensed channels in one sensing period, multi-channel spectrum sensing could be broadly categorised into ‘one-to-one’, ‘one-to-many’, ‘many-to-one’, and ‘many-to-many’ sensing. The ‘cooperative ratio’ ρ facilitates a unified treatment of description of all four schemes. Table 1 shows the comparison among the aforementioned four classes of multi-channel sensing schemes. In some sense, during one sensing period, ‘sensing accuracy’ is related to the number of sensing SUs and the number of sensed channels is likely to influence the level of ‘sensing efficiency’. More SUs sense the same channel synchronously, resulting in higher ‘sensing accuracy’, and more sensing periods needed to sense all the channels, thus lowering ‘sensing efficiency’; with multiple channels detected in one sensing period, ‘sensing efficiency’ is significantly enhanced, and more SUs are needed for sensing to increase ‘sensing accuracy’. Furthermore, ‘sensing overhead’ is proportional to the number of sensing SUs and sensed channels in one sensing period. Thus, by assigning the sensing SUs and sensed channels with various ρ, the trade-off among ‘sensing accuracy’, ‘efficiency’ and ‘overhead’ could be adjusted to a different extent. Each channel sequence ykm (n) will then be individually averaged and squared using a separate energy detector. Thus, the estimated energy collected by the mth SU is

zkm = rkm

N /K−1

k 2

y (n) m

Var

2.4

2 2N d2i rkm = , K

i = 0, 1

(9)

Characterisation of an SU–FC channel

Lg −1

qkm (n) =

zkm (n − l)gm (l) + um (n)

(10)

l=0

where lth is the arbitrary sampling instant, the reporting channel noise um(n) is assumed to be zero mean and spatially uncorrelated additive white Gaussian with variances s2u , and gm(l ) is the finite multi-path channel impulse response with length Lg. The use of the additive white Gaussian noise model in this work is justified by the slow-changing nature of the channels between the M SUs and their corresponding FC links. Assume that the transmissions of the different SUs are orthogonal to one another, and that the transmitted statistics zkm are independent of the additive noise k um(n) [7]. Since k zm are normal random variables because of CLT, qm are Gaussian random variables. By considering the two hypotheses in (1) and (2), the received signal at the FC can be approximately normally distributed

(7)

According to the central limit theorem (CLT) [20], for large N, the statistics zkm are approximately normally distributed with means

i = 0, 1

zkm |Hi

The reliability of the reporting channel has the great impact on sensing performance. Like sensing channels, the reporting channel may be susceptible to multi-path fading. Moreover, the change of the PUs activities may affect the established reporting channel, especially when PU is located geographically nearby [21]. In this paper, we focus on the cooperative sensing performance with the consideration of the imperfect reporting free of PU activity. channel Here, the statistics zkm are transmitted by SUs to the FC through multi-path fading reporting channels. The base-band signal at the RF front-end of the FC received from the mth SU can be written as

n=0

N di rkm E zkm |Hi = , K

(8)

Table 1 Comparison among multi-channel sensing schemes modelled by ρ Sensing scheme

one-to-one

Sensing accuracy

Sensing efficiency

Sensing overhead

low

low

low

Typical ρ setting ⎡ ⎤ 1 0 ... 0 ⎢0 1 ... 0⎥ ⎢ ⎥ ⎢ ⎥ .. ⎣ ⎦ . 0 0 ... 1 ⎡

one-to-many

low

high

moderate

1 1 ⎢0 0 ⎢ ⎢ ⎣ 0 0 ⎡

many-to-one

many-to-many

high

high

low

high


moderate

high

1 ⎢1 ⎢ ⎢ ⎣ 1 ⎡ 1 ⎢1 ⎢ ⎢ ⎢ ⎢ ⎣0 0

0 0 0 0 1 0 1

⎤ ... 1 ... 0⎥ ⎥ ⎥ .. ⎦ . ... 0 ⎤ ... 0 ... 0⎥ ⎥ ⎥ .. ⎦ . ... 0 ⎤ ... 0 ... 1⎥ ⎥ ⎥ .. ⎥ . ⎥ ... 1⎦ ... 1


www.ietdl.org approximately expressed as

with means

E

qkm |Hi

Lg −1 N di rkm g (l), = K l=0 m

i = 0, 1

Pf(k) rk , vk , gk = Pr T k . gk |Hk0 ⎛ ⎞ k k ⎜gk − E T |H0 ⎟ = Q⎝ ⎠ Var T k |Hk0

(11)

and variances

Var

qkm |Hi

2 Lg −1 2N rkm d2i gm2 (l) + s2u , = K l=0

Pd(k) (rk , vk , gk ) = Pr (T k . gk |Hk1 ) ⎛ ⎞

i = 0, 1 (12)

k k ⎜gk − E(T |H1 )⎟ ⎠ = Q⎝ Var(T k |Hk1 )

qkm can be compactly represented in matrix form as follows Q = Q1 ⎡ 1 q1 ⎢ q1 ⎢ 2 =⎢ ⎢ .. ⎣. q1M

2.5

Q2

. . . QK

⎤ q21 . . . qK1 q22 . . . qK1 ⎥ ⎥ ⎥ .. ⎥ .. .. .⎦ . . q2M · · · qKM

3 (13)

H0

vkm qkm = vTk Qk +

gk

H1

m=1

(14)

where γk is the decision threshold of the kth channel, and the weighting coefficient vkm is the combining coefficient for the kth channel, which can be compactly written as v = v1 ⎡ 1 v1 ⎢ v1 ⎢ 2 =⎢ ⎢ .. ⎣. v1M

v2

. . . vK

E T k |Hi = mi,k =

K

L −1 g l=0

Opportunistic multi-channel detection

The design objective is to find the optimal vector of ρ, ω and γ = [γ1, γ2, …, γK]T, such that the spectrum resource is efficiently exploited, and an acceptably low level of interference is produced. The probabilities of false alarm and detection can be written as T P f (r, v, g) = Pf(1) r1 , v1 , g1 , . . . , Pf(K) rK , vK , gK

P d (r, v, g) = Pd(1) r1 , v1 , g1 , . . . , Pd(K) rK , vK , gK

gm (l)

(20) T (21)

⎤ v21 · · · vK1 v22 · · · vK2 ⎥ ⎥ ⎥ (15) .. .. .. ⎥ . . .⎦ v2M · · · vKM 2 Notably, vkm ≥ 0 satisfies the condition vk = 1, which is used to optimise the detection performance. Given that {Tk} are all normal random variables, then the normally distributed signals with mean and variance are given by N di rkm

Optimal cooperative multi-channel sensing

In this section, to maximise the throughput of CR networks, the problems of SU assignment and spectrum sensing parameter setting on multi-channel CSS are jointly considered. The optimisation problem is formulated under the SDF rule. 3.1

All the individual test statistics qkm are used to formulate the resultant detection statistics {Tk} linearly, which can be expressed as M

(19)

SDF scheme in FC

Tk =

(18)

M

vkm

(16)

m=1

Var T k |Hi = s2i,k Lg −1 M 2 2N rkm d2i 2 2 = gm (l) + su vkm K m=1 l=0

(17)

where i = 0,1. Using the decision rule in (14), the probabilities of false alarm and detection in the kth channel can be IET Commun., 2013, Vol. 7, Iss. 12, pp. 1177–1190 doi: 10.1049/iet-com.2012.0748

Consider M SUs sensing the K channels to take use of the unused ones for opportunistic transmission. Let rk denote the achievable throughput over the kth channel if used by SUs and r = [r1, r2, …, rK]T. If the transmit power and the channel gains between SUs are known, r can be estimated using the Shannon capacity formula [22]. Given that 1 − Pf(ρ, ω, γ) represents the probabilities of detecting the free channels. Since 1 − Pf(k) measures the opportunistic spectral utilisation of the kth channel, the AOT over the K channels is R(r, v, g) = rT 1 − P f (r, v, g)

(22)

Equivalently, 1 − Pd(ρ, ω, γ) is the vector of probabilities of missed detection (interference) in each channel. For a multi-channel primary communication system, the effect of interference induced by SUs can be characterised by a relative priority factor for PU transmitting over the corresponding channels, that is c = [c1, c2, …, cK]T, where ck indicates the cost incurred if PU in the kth channel is interfered with. The AI over the K channels can be expressed as I(r, v, g) = cT 1 − P d (r, v, g)

(23)


www.ietdl.org Given that the per-channel interference (1 − Pd(k) ≤ ak ), as well as the AI (23), is limited, a minimum utilisation (1 − Pf(k) ≥ bk ) is required. Suppose the total ‘sensing overhead’ Θ is bounded by ξ, this problem formulation is then described as follows max g

R(r, v, g)

s.t. I(r, v, g) ≤ 1 1 − P d (r, v, g) ≤ a 1 − P f (r, v, g) ≥ b M K rkm u ≤ j

(24)

m=1 k=1

where α = [α1, α2, …, αK]T, and β = [β1, β2, …, βK]T. Based on the per-channel utilisation and interference, CR systems can be classified into four groups [7]: † Conservative systems: In this system, an utilisation βk is less than or equal to 50% (βk ≤ 0.5) and a probability of interference αk is smaller than 50% (αk < 0.5). † Aggressive systems: In this system, an utilisation βk is higher than 50% (βk > 0.5) and an interference αk is less than 50% (αk < 0.5). † Hostile systems: In this system, more than 50% of spectrum utilisation is achieved (βk > 0.5), causing a maximum interference of at least 50% (αk ≥ 0.5). † Insolent systems: In this system, a transmission threshold is lower than or equal to 50% (βk ≤ 0.5) with the interference at 50% or more (αk ≥ 0.5). The objective and constraint functions in (24) are generally non-convex, making it difficult to efficiently solve for the global optimum by jointly optimising ρ, ω and γ. Although convex maximisation methods can solve the problem by approximating, limiting the solution domain or splitting into convex sub-problems, these reformulations of the problem reveal themselves to be counterproductive and compromise the performance [9]. In the next section, the GAs are introduced to solve the optimisation problems for the cooperative ratio ρ, the weight coefficients ω, and the thresholds γ without convexity limitations. 3.2

GA-assisted optimisation algorithms

The GA is known as a powerful and broadly applicable stochastic search and optimisation technique [23] that can solve complex multi-dimensional problems without in-depth function study, constraints, or reformulations, making it suitable for solving (24) with any value of α and β.

3.2.1 GA-assisted joint optimisation (GJO): Generally, the optimum can be found by GJO approach, which provides a direct solution to multi-parameter optimisation problem at a time. GJO approach first initialises their individuls stochastically and generates homogeneous individuals. Then, it can find the global optimal thresholds, cooperative ratio and weights, which maximise the throughput with limited interference and overhead. A generation is a set of potential solutions (the ‘cooperative ratio’ ρ, weighting coefficient vectors ω and thresholds γ) at

the lth iteration (l) (l) (l) (l) (l) Gl = r(l) , . . . , r , v , . . . , v , g , . . . , g pops pops pops 1 1 1 (25) A fitness score is calculated for each element using the objective of maximisation (24) ! ! (l) (l) (l) (l) (l) sl = R r(l) , v , g r , v , g , . . . , R (26) pops pops pops 1 1 1 Instead of exploitation of hidden convexity, GJO is used to avoid heavy approximations and performance compromise at a time. However, since the optimisation variables (ρ, ω and γ) are not homogeneous, the genetic evolution is computationally complex in a global sense, and then, the speed of convergence is slowed down to a certain extent. Hence, GA-assisted sequential optimisation (GSO) algorithm is proposed to solve the multi-channel CSS problem in Section 3.2.2. 3.2.2 GSO: GA-assisted sequential optimisation approach divides the optimisation of the original problem into two stages. In the first stage, referred to as ‘multi-user diversity optimisation’, the ‘cooperative ratio’ ρ and weight coefficients ω are chosen to maximise a performance measure for signal detection. In the second stage, called ‘multi-channel diversity optimisation’, the values of ρ and ω obtained from ‘multi-user diversity optimisation’ are fixed to optimise the thresholds γ across all the channels. Stage 1: Multi-user diversity optimisation. In this optimisation, the ‘cooperative ratio’ ρ and weight coefficients ω are chosen to achieve the maximum ‘modified detection coefficient’ for each channel, which can be described as follows k k 2 E T |H1 − E T k |Hk0 max rk , vk = r k ,v k var T k |Hk1 2 s.t. vk = 1 dk2

(27)

rkm = 0, 1 The ‘modified detection coefficient’ dk2 rk , vk can be interpreted as a signal-to-noise ratio (SNR) [7]. For any given probability of false alarm, a larger value dk2 rk , vk will result in a larger probability of detection if Tk is normally distributed under both Hk0 and Hk1 . A generation is a set of potential solutions (the ‘cooperative ratio’ ρ and weighting coefficient vectors ω) at the lth iteration (l) (l) (l) Gl = r(l) (28) 1 , . . . , rpops , v1 , . . . , vpops A fitness score is calculated for each element using the objective of maximisation (27) ! ! (l) 2 (l) (l) sl = d12 r(l) (29) 1 , v1 , . . . , dpops rpops , vpops Stage 2: Multi-channel diversity optimisation. Substituting the weight vectors ρ and ω obtained in the first stage into (18) and (19), the probabilities of false alarm and detection become functions of only the threshold γ. The bound



www.ietdl.org thresholds of γ are then calculated using

objective of maximisation (32)

gmin ,k = m0,k + s0,k Q−1 1 − bk

(30)

gmax ,k = m1,k + s1,k Q−1 1 − ak

(31)

Consequently, the original problem (24) has the following equivalent form max g

R(g)

s.t. I(g) ≤ 1

(32)

gmin ,k ≤ gk ≤ gmax ,k The ‘multi-channel diversity optimisation’ can also be used to solve the non-collaborative formulation (32) with given ρ and ω. A generation is a set of potential solutions (the threshold vectors γ) at the lth iteration (l) , . . . , g Gl = g(l) pops 1

(33)

A fitness score is calculated for each element using the

! ! (l) sl = R g(l) g , . . . , R pops 1

(34)

Consecutive generations of solutions and their scores are examined iteratively to determine the individuals that can survive up to the next generation. The highest values of sl are meant to be the closest to the maximum and are selected for survival. The next generation is created by the ‘selection’, ‘crossover’ and ‘mutation’ operator [23]. The evaluation and generation steps are performed iteratively to increase the percentage of ‘good members’. Computation is stopped when the population has converged to the same genotype (i.e. to the same fitness value), which is supposed to be the fittest and thus, the optimal solution. The size of the computational problem is controlled by setting the dimension of the population (pops). With a larger number of individuals, the algorithm evaluates a wider range of genotypes and generates a larger number of fit elements. However, computational load increases because more individuals require a higher number of fitness evaluations. Here, the optimisation is satisfactory when it approaches an error of tens of kilobits (out of some megabits) on the aggregate throughput [9]. The mean

Fig. 2 Optimisation of CSS with GA IET Commun., 2013, Vol. 7, Iss. 12, pp. 1177–1190 doi: 10.1049/iet-com.2012.0748


www.ietdl.org absolute percentage error is used for the aggregate throughput distance

Rˆ − R(i)

1 NUM MAPE(R) =

NUM i=1 Rˆ

(35)

where Rˆ comes from the true solution of the linear optimisation problem and is derived using (24) or (32). R (i) is the value calculated by the GA during the ith experiment, and NUM denotes the number of experiments. If the convergence criterion in (35) is satisfied, the optimisation algorithm is terminated. The proposed algorithm for ‘multi-user diversity optimisation’ is depicted in Fig. 2. The algorithms for GJO and ‘multi-channel diversity optimisation’ with GA are similar to Fig. 2.

4

Simulation results and discussion

In this section, numerical results are presented to evaluate the sensing performance of the proposed multi-channel CSS method. We consider a set of SUs sensing the spectrum over N = 800 sampling intervals with equal noise variance s2v = 1, s2u = 1. For simplicity, we assume that each SU consume unit power for sensing one channel, that is, θ = 1. Notably, gm and cm are assumed to be constant over all sensing time periods. In addition, CMFB-based multi-carrier system [19] was used as filter bank-based receiver, and the parameters of CMFB scheme were set as follows: the overlap ratio α = 0.9 and stopband attenuation As = 80 dB.

4.1

Multi-channel sensing by individual SU

The first evaluation method is to analyse the performance of multi-channel joint detection with eight channels and a single SU. The cooperative ratio ρ was set to be [1]1*K with ξ = K. Fig. 3 shows an example for each of the four CR classes in terms of per-band utilisation and interference [7]. Through αk and βk, we can limit transmission and interference in a single band. On one hand, βk is the minimum utilisation bound. The curves in Fig. 3 have an equal start from the operative point but subsequently diverge. This point corresponds to the lowest thresholds that ensure the channel utilisation equal to βk. The thresholds cannot be decreased below this point. Thus, a smaller disturbance is unfeasible. ‘Aggressive’ and ‘hostile’ systems set this point to a relatively high and unmotivated value, given that imposing a 50% of utilisation on each channel may be unnecessary. Thus, such systems cannot transmit at low interference. ‘Conservative’ and ‘insolent’ systems allow low-bitrate transmission with a higher AOT at low AI. On the other hand, the value of αk limits the interference. All curves with equal αk converge to the same asymptote, which corresponds to the maximum interference in all channels. ‘Hostile’ and ‘insolent’ systems allow more interference in a single band with a gain in AOT by increasing αk. Although an interference beyond 50% is not a practical condition, we can see how systems with a deliberate malicious behaviour achieve higher throughput for high interferences, by breaking the convexity.

4.2

Multi-channel CSS with various decision rules

Next, two SUs cooperatively sensing the eight channels by exchanging the summary statistics of their sensed data is

Fig. 3 AOT against the constraint on the AI to the primary communication system for multi-channel sensing Channel gains cm equal to (0.61, 0.49, 0.35, 0.45, 0.33, 0.35, 0.52, 0.59). Secondary rates rk = (612, 524, 623, 139, 451, 409, 909, 401) kbps, and interference costs ck = (1.91, 8.17, 4.23, 3.86, 7.16, 6.05, 0.82, 1.30). The length of prototype filter in the CMFB receiver Lh is 89 1184 This is an open access article published by the IET under the Creative Commons Attribution-NoDerivs License (http://creativecommons.org/licenses/by-nd/3.0/)


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Fig. 4 AOT against the constraint on the AI to the primary communication system for the cooperative SDF and HDF schemes Channel gains cm equal to: SU1: (0.61, 0.49, 0.35, 0.45, 0.33, 0.35, 0.52, 0.59), SU2: (0.38, 0.29, 0.26, 0.35, 0.39, 0.33, 0.23, 0.27). Channel gains gm equal to: SU1: (0.51, 0.42, 0.31, 0.18, 0.24, 0.27, 0.43, 0.36), SU2: (0.22, 0.16, 0.23, 0.24, 0.16, 0.34, 0.17, 0.35). Secondary rates rk = (612, 524, 623, 139, 451, 409, 909, 401) kbps, interference costs ck = (1.91, 8.17, 4.23, 3.86, 7.16, 6.05, 0.82, 1.30). The length of prototype filter in the CMFB receiver Lh is 89

considered. The cooperative ratio ρ was set to be [1]M*K with ξ = K*M. We compare the fusion decision schemes with both soft (the maximal-ratio combining (MRC) and equal gain combination (EGC)) [24] and hard decision (HD-OR) [16] rules. The MRC-based scheme assigns fractional coefficient weights relative to the corresponding SNR values at the |c |2 E SUs receivers with vk = SNRm = m 2 s . In EGC scheme, sv

the individual weights assigned to the M SUs at the FC are √ all equal to 1/M . In Fig. 4, we plot the maximum AOT, which is obtained using the optimal values of the threshold γ for different values of AI with αk = 0.1 and βk = 0.5, which is presented in literature for demonstration purposes [25]. The figure shows that the cooperation gain in the soft decision case is more than that in the hard decision rule. The maximum

Fig. 5 Optimised thresholds and the associated probabilities of missed detection and false alarm on individual channels with ε = 1.05 in Fig. 4 IET Commun., 2013, Vol. 7, Iss. 12, pp. 1177–1190 doi: 10.1049/iet-com.2012.0748


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Fig. 6 Performance of cooperative sensing schemes with different ρ The length of prototype filter in the CMFB receiver Lh is 34

achievable AOT increases as the limit on the AI tolerated by the PU ε in (24) increases. Compared with the other two SDF schemes, low bit rate transmission with a higher AOT at low AI can be achieved with the optimal SDF rule. In Fig. 5, the probabilities of false alarm Pf and missed detection Pmd are plotted in each channel for the soft and hard decision cooperative schemes, respectively. The cases where the bars tend to 0 indicate the perfect ‘sensing accuracy’ of the corresponding fusion rules. As shown in Fig. 5, better channel utilisation (1 − Pf ) is obtained when the soft decision scheme is used instead of HDF. The probability Pmd for each channel is bounded by αk = 0.1 for all the considered schemes, which represents one of the important constraints that guarantees the desired protection for PU whereas maximising the AOT of SUs.

4.3 Multi-channel CSS with various cooperative strategies We then study the performance of CSS schemes shown in Section 2.3 with four SUs cooperatively sensing the three channels (ξ = K*M ). Case 1 ⎡

⎤T ⎞ 1111 ⎝r = ⎣ 0000 ⎦ ⎠, 0000 ⎛

case 2 ⎛

⎡

1 0 ⎝r = ⎣ 0 1 0 0

0 0 0

and case 3 ⎛

⎡

1 1 ⎝r = ⎣ 0 0 0 0

0 1 0

⎤T ⎞ 0 0⎦ ⎠ 1

correspond to the cooperation mechanisms of ‘many-to-one’, ‘one-to-one’ and ‘many-to-many’ CSS, respectively. The channel parameters, which are the achievable opportunistic throughput rk, the cost of interfering with PU ck, and the channel gains, cm and gm, are generated randomly for each channel and each SU. Fig. 6 plots the sensing performances of the three cases and the optimal ρ. The corresponding ‘sensing overhead’ and probability of false alarm with ε = 0.2 on individual channels are also presented. The cases where the bars tend to 0 in the third sub-figures indicate the perfect ‘sensing accuracy’ of the corresponding ρ settings. Fig. 6 also indicates the trade-off between ‘sensing overhead’ and ‘sensing gain’. With the four SUs sensing the one channel synchronously (the maximum ‘sensing overhead’ in the first channel), case 1 achieves the highest ‘sensing accuracy’ in the 1st channel and the lowest ‘sensing accuracy’ in the other two channels, and thus the lowest AOT of all the three channels (with only one channel for transmission). Compared with the ‘one-to-one’ CSS (case 2 with the minimum ‘sensing overhead’), the ‘many-to-many’ scheme (case 3) achieves higher ‘sensing accuracy’ with more SUs in one sensed channel. Moreover, by effectively setting the four SUs cooperative sensing scheme, the optimal case

⎤T ⎞ 0 0⎦ ⎠ 1


⎡

1 0 r = ⎣1 0 0 1

1 1 0

⎤T 1 1⎦ , 1


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Fig. 7 AOT against the constraint on sensing overhead with ε = 0.2 Channel parameters as in Fig. 6

with the relatively high ‘sensing overhead’ achieves a highest AOT at low interference (‘sensing efficiency’). 4.4 Multi-channel CSS with various overhead constraints In Fig. 7, we present the maximum AOT, which is obtained using the optimal values of the cooperative ratio ρ for

different values of the constraint on ‘sensing overhead’ ξ. Increasing ξ will increase the number of sensing SUs and sensed channels, and therefore higher AOT are expected. When the ‘sensing overhead’ arrives at a certain constraint (e.g. ξ0), the AOT is close to the upper limit. However, when ξ is higher than ξ0, the AOT will saturate with the higher ‘sensing overhead’ and computational complexity.

Fig. 8 AOT against the constraint on the AI to the primary communication system for the performance of different optimisation schemes Channel parameters as in Fig. 4 IET Commun., 2013, Vol. 7, Iss. 12, pp. 1177–1190 doi: 10.1049/iet-com.2012.0748


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Fig. 9 AOT against the constraint on the AI to the primary communication system for the performance of different ED schemes Channel parameters as in Fig. 3

Fig. 10 Evaluation of convergence performance for ε = 1 Channel parameters as in Fig. 3

4.5 Multi-channel CSS with various optimisation approaches We then compare the GJO and GSO approaches in a scene where two SUs cooperatively sense the eight channels. The

numerical results of solving (24), which maximises the AOT subject to the constraints on the AI and ‘sensing overhead’, are illustrated in Fig. 8. It is observed that the spectrum sensing algorithms with cooperation result in higher opportunistic rates than the sensing algorithms



www.ietdl.org without cooperation. In addition, the GSO outperforms GJO approach with relatively lower computation complexity. By setting some initial points as the starting population of the GA, GSO obtains a faster convergence. 4.6

Multi-channel CSS with various ED schemes

Fig. 9 illustrates the performance of multi-channel detection with different ED techniques in a single CR. It can be seen that the multi-channel sensing algorithm with CMFB scheme can achieve a much higher opportunistic throughput than that achieved with the traditional ED. That is with lower spectral-leakage characteristics and higher frequency selectivity, the proposed CMFB-based multi-carrier scheme makes better use of the wide frequency band by balancing the conflict between improving spectrum utilisation and reducing the interference. 4.7

Convergence analysis of GA

To select an appropriate form of the algorithm to address the nature of the given problem, as well as to achieve more efficient evolutionary processes, the effect of various GA parameter settings was analysed using a set-and-test approach. The number of generations, ‘ngens’, was set as 100 with the population size pops = 30. In general, the number of computations is at least pops × ngens and grows in a measure that depends on the crossover criteria and the mutation scheme. The GA parameters and operators were set as follows: elite = 0.1, nbits = 6, Pc = 0.9, and Pm = 0.01 as in [26] for online applications, where Pc is two-point crossover rate, and Pm is bit-flip mutation rate. Roulette wheel selection was used. For the same channel condition, the maximum R fitness of the best chromosome and the mean fitness of all chromosomes in every generation are shown in Fig. 10. Noticeably, the proposed GA-based scheme converges within the first 15 generations, which shows that the computation complexity of the proposed scheme can meet real-time requirements. In this work, the CSS strategy model with the ‘cooperative ratio’ ρ is proposed to describe the relationship between ‘cooperation mechanisms’ and ‘spatial-spectral diversity’ over multiple channels jointly sensing. Simulation results verify the efficiency of this model and the optimisation setting of ρ to assign SUs to sense multiple channels synchronously. Moreover, results also show that multi-channel joint detection can improve spectral efficiency considerably by better utilising spectral diversity. Moreover, the CSS strategies of multi-user can further enhance system performance by exploiting spatial diversity.

5

Conclusion

In this paper, a multi-channel jointly CSS approach based on filter bank is proposed. The CSS strategy model with the ‘cooperative ratio’ ρ is presented to describe the relationship between ‘cooperation mechanisms’ and ‘spatial-spectral diversity’ over multiple channels jointly sensing. The modelling of ‘sensing overhead’ is quantitatively characterised with respect to energy consumption. The multi-channel joint ED problem with an imperfect reporting channel is formulated as an optimisation problem that the AOT is maximised subject to the constraints on AI, ‘sensing overhead’, per-channel interference and utilisation. The optimisation is divided into two stages. The first stage IET Commun., 2013, Vol. 7, Iss. 12, pp. 1177–1190 doi: 10.1049/iet-com.2012.0748

explores the ‘multi-user diversity optimisation’. The cooperative ratio and weight coefficients are achieved to maximise the probability of detection. The second stage explores ‘multi-channel diversity optimisation’. The thresholds for different channels detection are gained by maximising the AOT subject to AI and the computed bounds on thresholds. Both two stage problems are solved by a presented GA. The proposed ‘cooperative mechanism model’ and the sensing ‘accuracy-efficiency’ trade-off are analysed and evaluated with various simulations. Simulation results show that the proposed CSS schemes can improve the system performance of PUs detection.

6

Acknowledgments

The authors would like to acknowledge National Basic Research Program of China (no. 2011CB707102) for financial support and acknowledge the anonymous reviewers whose constructive criticism, comments, and suggestions led to a greatly improved manuscript.

7

References

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