www.ietdl.org Published in IET Communications Received on 14th October 2012 Revised on 27th February 2013 Accepted on 2nd March 2013 doi: 10.1049/iet-com.2012.0627
ISSN 1751-8628
Secondary user access based on stochastic link estimation in cognitive radio with fibre-connected distributed antennas Wendong Ge1,4, Hong Ji2, Xi Li2, Victor C.M. Leung3 1
Beijing University of Posts and Telecommunications, Beijing 100876, People’s Republic of China School of Information and Communication Engineering, Beijing University of Posts and Telecommunications, Beijing 100876, People’s Republic of China 3 Department of Electrical and Computer Engineering, the University of British Columbia, Vancouver, Canada, BC V6T 1Z4 4 Institute of Automation, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China E-mail:
[email protected] 2
Abstract: In this study, the authors consider the application of a system architecture called cognitive radio (CR) with fibreconnected distributed antennas in IEEE 802.22 wireless regional area networks (WRANs) as it could bring the benefits of much shorter wireless transmission distances, lower transmission power and the possibility of utilising multi-antenna transmission techniques. In this architecture, the authors study the secondary user (SU) access problem in uplink, where the SU to primary user (PU) link estimation is subject to random errors because PU could not assist link estimation of SU. This SU access problem is divided into two parts: antenna selection and access control. Thus, first antenna selection problem is modelled as a restless bandit problem, which is solved by the primal-dual index heuristic algorithm based on first order relaxation. In addition, the access control problem is modelled as a stochastic knapsack (SASK) problem with random weight, and then relaxed to be a deterministic second order cone programming problem. With the deduced upper bound, the access control problem is solved by the branch and bound algorithm, which yields the SU access based on SASK scheme. Simulation results illustrate the significant performance improvement of SASK scheme, compared with existing SU access methods.
1
Introduction
IEEE 802.22 wireless regional area networks (WRANs) offer a promising approach for covering vast areas with sparse populations using the white spaces in the television band [1]. Cognitive radio (CR) technology is adopted to enable the secondary system, which consists of secondary users (SUs) accessing a secondary base station (SBS), to share the spectrum with the licensed television users, namely primary users (PUs). Owing to the large coverage area with significant path loss, the SUs and SBS of a WRAN may need to transmit with a high power, potentially causing substantial interference to the PUs. Enabling efficient SU access without infringing on PUs’ transmissions is an important research problem that has attracted much interest. In an 802.22 WRAN, a secondary system may access the spectrum licensed to PUs using the overlay or underlay methods. Overlay access involves sensing the spectrum for idle bands using algorithms such as energy detection algorithm or waveform-based sensing algorithm [2] and then utilising them for communications within the secondary system. In [3], the authors propose a joint design of spectrum sensing and channel access in CR networks. In the underlay method, the secondary system could access the IET Commun., 2013, Vol. 7, Iss. 8, pp. 731–737 doi: 10.1049/iet-com.2012.0627
whole spectrum as long as its total interference to each PU is kept under certain threshold, called the ‘interference temperature’. This can be achieved by properly controlling the transmit power of the SUs and SBS. Optimal and suboptimal power loading algorithms are presented in [4] that maximise the downlink transmission data rate of a secondary system while keeping the interference to the PU within a given limit. Joint power and rate control for SUs in a CR network is investigated in [5] using non-cooperative game theory. Existing research in this area mostly considers a cellular network structure in which one SBS covers the whole cell using antenna(s) installed at the centralised cell site, and one secondary system shares the spectrum with one PU, which does not help to utilise the spectrum holes efficiently in different locations. Therefore we introduce an architecture called CR-fiber-connected distributed antennas (FCDA), that is, CR with fibre-connected distributed antennas (DAs) [6], into WRAN, and show that this design could provide a greatly improved solution to the SU access problem of WRANs. In CR-FCDA, the SBS can deploy a large number of DAs at various locations in the cell, which are interconnected to the SBS using radio over fibre (RoF) for centralised signal processing at the SBS. This brings the 731
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www.ietdl.org benefits of much shorter wireless transmission distances, lower transmission power and the possibility of utilising multi-antenna transmission techniques [7]. Thus, the secondary system could sense the spectrum holes at different locations and utilise them efficiently. As much reduced transmit power and use of space diversity in this architecture, the interference from each SU to PU has a low level and multiple SUs at different locations could share the spectrum of one PU. Then the problems we need to consider are how to select DAs for SU and how to select the appropriate SUs from the candidate set to access the spectrum band licensed to the PU. In addition, we find that most previous work assumes that the channel gain from SU to PU is known, which may not be realised in practice since the PU has no knowledge about the existence of SUs and could not provide information to SU [8]. Our work relaxes this assumption to make it more applicable to a real system. In this paper, we study the SU access problem in WRANs employing the CR-FCDA architecture. The channel gain from SU to PU receiver (PU-RX) is represented by a stochastic variable, which is more practical. The SU access problem in the CR-FCDA architecture is divided into antenna selection and access control. Firstly, antenna selection problem is modelled as a restless bandit problem, which is solved by the primal-dual index heuristic algorithm based on first order relaxation. Additionally, the access control problem is elaborated as selecting an appropriate group of SUs to access the spectrum band licensed to PU with the goal of maximising the total SUs throughput and controlling the interference from SUs to PUs under certain threshold. It is formulated as a stochastic knapsack problem (SKP) with random weight and then relaxed to be a deterministic second order cone programming problem (SOCP). With the deduced upper bound, the access control problem is solved by the branch and bound algorithm, which yields the SU access based on stochastic knapsack (SASK) scheme. The rest of this paper is organised as follows. The system model is introduced in Section 2. Section 3 discusses the antenna selection, Section 4 proposes the SASK scheme. Simulation results are provided in Section 5 to illustrate the performance comparison and Section 6 concludes this paper.
2
System model
In this section, we first describe the system scenario, and then stochastic link estimation is discussed. 2.1
System description
We consider a WRAN employing CRs, in which a secondary system opportunistically accesses the spectrum licenced to the primary link, as illustrated in Fig. 1. A PU link consists of a PU transmitter transmitting data to a PU-RX over the spectrum band that is licensed to the PU. The secondary network consists of a SBS equipped with M DAs connected to the SBS via RoF and N SUs, where the DAs and SUs are denoted as M = {1, 2, . . . , M } and N = {1, 2, . . . N }, respectively. Every SU could share this licensed spectrum band to transmit data to the SBS via multiple DAs, under the constraint that SUs are not to cause excessive interference to PU; that is, we consider an underlay system. Obviously, the SUs and the DAs form a single-input multiple-output macro-diversity system over the uplink. Since each SU may communicate via its own set of DAs nearby, multiple SUs can share the spectrum band 732 & The Institution of Engineering and Technology 2013
Fig. 1 Scenario
simultaneously using space diversity. If the duration is divided into T equal-length epochs, which are denoted as T = {1, 2, . . . , T }, in each access period, the access process can be divided into two parts: antenna selection and access control, which will be discussed in the following sections. 2.2
Stochastic link estimation
To maintain the normal operation of PU, it is necessity to estimate the interference from SUs to PU-RX. If the nth SU is allowed to share the spectrum band, this interference can be shown as gnsp Pns , where gnsp is the channel gain from the nth SU to PU-RX, Pns is the transmit power of this SU and n [ N . Most previous work assumes that gnsp is either known or can be estimated without error. However, from a practical viewpoint, as primary and secondary systems usually belong to different operators, it may not be feasible for them to cooperate. Thus, the channel gain from SU to PU is hardly known with high accuracy. Accordingly in this paper, we consider gnsp to be a stochastic variable, which is denoted as ξn. (ξn stands for channel gain in some given epoch. If in the tth epoch, it ought to be rewritten as ξn(t)). Since the factors related to this channel gain are numerous and independent mostly, for simplicity we assume that it follows the normal distribution according to the Lindeberg–Levy central limit theorem, and is denoted as ξn ∼ N (μn, σn), where the parameters could be estimated from the forward link if the forward and reverse links are symmetrical. We denote Ith as the interference threshold from SU to PU, and also define excessive interference as the phenomenon that the total interference from SUs to PU exceeds the acceptable interference threshold. We consider that the probability of excessive interference cannot exceed pth, where Ith and pth are determined by PU. Additionally, ss we denote gnm as the channel gain from the nth SU to the mth DAs. As transmitters and receivers of SUs can cooperate to estimate the channel gain between them, we ss assume that gnm is determined perfectly.
3
Antenna selection
In this section, the antenna selection problem is modelled as the restless bandit problem, which is solved by the primal-dual index heuristic algorithm based on first order relaxation. 3.1
Restless bandit
The restless bandit problem was first investigated by Whittle [9] in 1988, which provides a powerful modelling framework IET Commun., 2013, Vol. 7, Iss. 8, pp. 731–737 doi: 10.1049/iet-com.2012.0627
www.ietdl.org in clinical trials, aircraft surveillance, worker scheduling and so on. In this problem, there are N parallel projects, each of which can be in one of a finite number of states. In each discrete epoch, M projects are selected and set active, where M < N. The active projects can contribute active reward and change its state in a Markovian fashion, according to an active transition probability matrix, while non-active projects can achieve passive reward and evolve with a passive transition probability matrix. The rewards are time discounted by a discount factor. According to the states and transition probability and reward of each project, M projects are selected from N projects in every epoch under some policy. The problem is to find the optimal policy in order to maximise the total discounted rewards.
3.2
reward function can be defined as ⎧ ⎨ R1 (t) = Tn (t) n mn (t)Pns ⎩ 0 Rn (t) = 0
The set of admissible policies is denote as Z. The scheduling policy z [ Z is an (t) T ×N , where the element an(t) represents the action taken to select the nth SU in the tth epoch. The time discount factor for the rewards is set to be β in order to compare the sum of infinite rewards [9], where 0 < β < 1. Accordingly, the antenna selection problem is to find an optimal scheduling policy that maximises the total expected discount reward over an infinite horizon, which can be represented as
Problem formulation
In each access period, each SU needs to select several appropriate antennas, which is equivalent to assigning DAs to SUs. We assume that each DA endeavors to select one SU with higher throughput and lower interference to PU. Thus, for the mth DA, the action of the nth SU is defined as an (t) [ A = {0, 1} in the tth epoch, where an(t) = 1 means that the nth SU is active (or selected) in the tth epoch, while an(t) = 0 means that it is passive (or not selected). Thus the actions of SUs need to satisfy the following equation N
an (t) = 1
(1)
(4)
max Ez
T N
z[Z
t=1
a (t) Rinn (t)
bt
n=1
s.t. N
(5) an (t) = 1
n=1
pain jn (t) = Pr sn (t + 1) = jn sn (t) = in , an (t) = a where in, jn ∈ Dn. This problem is a typical restless bandit problem, which will be solved in next subsection.
n=1
3.3 The states of SUs are the channel gains from SU to DAs. We assume the channel gain from the nth SU to the mth DA as ξn(t), which can be modelled as a Markov chain by dividing the continuous interference state into discrete levels for simplification [10]. Thus, this gain evolves according to a finite-state Markov chain, which is characterised by a set of states Dn = d1 , d2 , . . . , dD , where D is the quantity of available state levels. The number of discrete levels is not specified. A less-discrete level number may reduce the complexity, whereas a larger quantity may enhance the accuracy. In addition, the transition probability matrix of the state with action a can be represented as Pan (t) = paxn yn (t) , where
Primal-dual index Heuristic algorithm
We first introduce the first-order relaxation of this restless bandit problem. The total expected discounted time that the nth SU is in state in and active under the scheduling policy z [ Z can be represented as
x1in (z) = Ez
u1in (t)bt
(6)
where
u1in (t) = (2)
t=1
D×D
paxn yn (t) = Pr jn (t + 1) = yn jn (t) = xn , an (t) = a
T
⎧ ⎪ ⎨ ⎪ ⎩
1, 0,
if the nth SU is in state in and active at the tth time slot otherwise (7)
and xn, yn ∈ Dn, a ∈ A. The values in the state transition probability matrix can be obtained by the history information of training. The reward function includes two parts: throughput of SU and interference to PU. If the nth SU is selected, the throughput can be represented as
Similarly, the total expected discounted time that the nth SU is in state in and passive under the scheduling policy z [ Z can be defined as x0in (z). We denote that X =
j (t)Pns Tn (t) = B log2 ps n In (t) + BN0
a xinn (z)
in [S,an
z [ Z [A,n[N
(8)
(3)
where B is the bandwidth of the spectrum, Inps (t) is the interference from PU to this SU and N0 is the power spectrum density of additive white Gaussian noise. Thus the IET Commun., 2013, Vol. 7, Iss. 8, pp. 731–737 doi: 10.1049/iet-com.2012.0627
Whittle introduced a relaxed version of the restless bandit problem which can be solved in polynomial time [11]. In this section we reformulate Whittle’s relaxation as a polynomial-size linear program. The projection of restless a bandit polytope over the space of the variable xinn for the 733
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www.ietdl.org nth SU is another polytope, which can be represented as
a
an [A
x jnn = P jn + b
a
in [S an [A
a
pinnjn xinn
, j [ S n[N n (9)
where P jn is the probability that the initial state of the nth SU is jn [ S. In addition, when T → ∞, we can also deduce the equation as follows in [S n[N
x1in (z)
= lim
T 1
= lim
T 1
= lim
T 1
in [S n[N T
⎡
Ez ⎣
t=1 T
Ez
T
in [S n[N
bt =
t=1
⎤
u1in (t)⎦bt
(10)
1 1−b
X
in [S an [A n[N
s.t. an [A
a
in [S n[N
x1in (z)
a
a
in [S an [A
a
pinnjn xinn
, i [ S n[N n
l j n ,l
jn [S n[N
s.t.
lin − b lin − b
jn [S
jn [S
P jn l jn +
Problem formulation
(11)
1 l 1−b
p0in jn l jn ≥ R0in
, i [ S n[N n
p1in jn l jn + l ≥ R1in
(12)
, i [ S n[N n
The dual problem is also a linear programming problem. Thus the problem given by (11) and (12) can be solved by the classical algorithm for the linear programming problem a such as simplex search method. We denote { xinn } and {lin , l} as the optimal solutions of primal problem (11) and dual problem (12). Therefore the corresponding optimal reduced cost coefficients can be represented as i − b 0in = l g n
j − R0i p0in jn l n n
(13)
− R1i j + l p1in jn l n n
(14)
jn [V
jn [V
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Rn = B log2 ⎝1 +
⎞
ss s gnm Pn ⎠ ps I + BN0 n m[An
(16)
In this paper, we address the SU access problem over the uplink. Over the downlink, each SU will be served by the nearest or the best DA, and spectrum management over the downlink is outside of the scope of this work. We define T the SU access function as X = x1 , x2 , . . . , xN , where
l≥0
i − b 1in = l g n
In this section, based on the antenna selection, access control problem is modelled as a SKP problem and then an upper bound of the SKP is calculated. With this bound, the SKP is solved by the branch and bound algorithm, which yields the SASK scheme.
⎛
1 = 1−b
This is a linear programming problem. The dual problem of this primal problem can be shown as min
Access control
With the antenna selection mentioned above, the set of DAs allocated to the nth SU is denoted as An , where An , M and Ai > Aj = ∅ i = j . Owing to the high quality of links from SU to DA and macro-diversity, the transmit power of SU is so low [12] that the interferences among these SUs are trivial enough to be ignored, compared with the interference from PU and background noise. Thus, if the maximal ratio combining is adopted in SBS, the throughput of the nth SU can be represented as
Rinn xinn
x jnn = P jn + b
a
(15)
Accordingly, in each epoch, every DA calculates the indices of all the SUs according to their states. The SU that have the smallest index is selected.
4.1
Thus the first-order relaxation can be represented as max
1in − g 0in din = g
4
u1in (t)bt
t=1
0in , g 1in ≥ 0. g 0in and g 1in represent the rates of decrease where g in the objective value of the primal problem per unit increase in the values of the variables x0in and x1in , respectively. Here we define din as the index for the nth SU when it is in state in [ S, which is shown as
xn =
1 the nth SU is allowed access 0 the nth SU is not allowed access
(17)
The SBS updates the SU access function periodically. In each access period, SBS first collects the sensing information and determines X. Then, it broadcasts X to all the SUs and the selected SUs are allowed to access the spectrum of PU. Accordingly, the SU access problem is to find an appropriate X in order to maximise the total throughput subject to the constraint of total interference from SUs to PU not exceeding the acceptable limit, which can be represented as max X
s.t. Pr
N
N
xn Rn
n=1
xn jn Pns
. Ith
, pth
(18)
n=1
This problem is a typical SKP [13], which is a hot issue in optimisation theory. In SKP, there are a set of items. Each item has different weight and value, and the weight of each IET Commun., 2013, Vol. 7, Iss. 8, pp. 731–737 doi: 10.1049/iet-com.2012.0627
www.ietdl.org item is a stochastic variable. The problem is how to select a subset of items in order to maximise the total value of selected items, with the constraint that the weight overflow probability is below some given threshold. The solution of SKP is given in the following section. 4.2
Upper bound solution
We first rewrite the constraint of the problem (18) as follows Pr
N
xn jn Pns
≤ Ith
≥ 1 − pth
(19)
n=1
We denote Q = j1 P1s , j2 P2s , . . . , jN PNs and the covariance matrix of Q as H. As the secondary system endeavors to prevent excessive interference to the primary system, pth is usually close to zero; that is, 1 − pth > 0.5. Thus, according to [14], the inequality (19) is equivalent to N
1 xn mn Pns + F−1 1 − pth H 2 X ≤ Ith
(20)
i=1
√ where F−1 (x) = 2 erf −1 (2x − 1). Additionally, we relax xn to be 0 ≤ xn ≤ 1, which is equal to [14] ! ! ! ! xn !W n X ! ≤ xn , !W n X ! ≤ 1, W n [ R1×N
(21)
Denote U = m1 P1s , m2 P2s , . . . , mN PNs and V = R1 , R2 , . . . , RN ], and define Ej as [ei]1 × N, where ei =
1 i=j 0 i=j
(22)
Thus, the relaxation of the problem (18) can be represented as max VX
X[RN
s.t. 1
H 2 X ≤ −
1 I UX + −1 th F 1 − pth F 1 − pth −1
(23)
! ! !W X ! ≤ E X i i ! ! !W X ! ≤ 1 i
This problem is a deterministic SOCP, which can be solved by SOCP code [15]. Thus, we obtain an upper bound of the problem (18). 4.3
Step 2: Plunge the tree as follows: beginning at the root of the tree, add the current SU if and only if change constraint is still satisfied when adding the SU. Allocate the maximum value of the objective function found to the variable which stores the current lower bound of the objective function and is denoted as θinf. Add the found branch to the list of branches. Set the associated upper bound θsup to infinity. Step 3: If there is no branch left on our list of branches, go to step 7. Else take the branch of our list of branches having the maximum objective function value. Go to step 4. Step 4: If the associated upper bound θsup is greater than the current lower bound θinf, go to step 5. Else delete the branch from the list. Go to step 3. Step 5: If there is no accepted SU left in the selected branch that does not already have a plunged or rejected subtree, delete the branch from the list. Go to step 3. Else choose the first accepted SU that does not already have a plunged or rejected sub-tree with regard to our ranking. Calculate an upper bound θsup for the sub-tree defined by rejecting this item. Go to step 6. Step 6: If θsup ≤ θinf, reject this sub-tree, go to step 5. Else plunge the sub-tree as described in Step 2 and add the found branch together with the value θsup to the list of branches. If the value of the objective function of this branch is greater than θinf, update θinf. Step 7: The selection corresponding to the current value θinf is the optimal solution of problem (3).
5
In this section, simulation results compare the performances of the SASK scheme and the existing scheme, which considers gnsp as fixed values (mean values). As none of the previous studies considers the SU access problem mentioned above, we consider that random selection is adopted in the existing scheme until excessive interference occurs. The parameters in the simulations are chosen based on the parameters widely adopted [4, 14] as follows. In a 500 m by 500 m area, we design two DAs distribution schemes. In the low-density scheme there are 16 DAs to cover this area uniformly, and in the high-density scheme the quantity of DAs are up to 64.20 SUs are also placed in this area uniformly. We assume the wireless channels from SUs to DAs to be Rayleigh fading without distortions such as inter-symbol interference. The transmit power set is denoted as {0.01,0.02,0.04,0.08,0.16,0.32} (W ), and every SU selects its transmit power according to the closed loop power control. The background noise N0 is assumed to be −117 dBm. We also define the average variance of gnsp as o=
Branch and bound algorithm
With the upper bound, we utilise the branch and bound algorithm proposed by Cohn and Barnhart [16] to solve this SKP. Define
dn =
" # 1 Rn 2 sn jn Pns
n[N
(24)
Thus, the steps of the algorithm are as follows: Step 1: Rank the SUs in N according to δn. This ranking defines a binary tree with the highest rank SU at the root. IET Commun., 2013, Vol. 7, Iss. 8, pp. 731–737 doi: 10.1049/iet-com.2012.0627
Simulation results and analysis
5.1
N 1 s2 N n=1 n
(25)
Comparison of throughput
Fig. 2 compares the throughput performances of the SASK scheme and the existing scheme under different interference limitations. In these simulations, we set pth = 0.05 and vary Ith/N0 from 4 to 12. This figure indicates that the total throughput of SUs under the SASK scheme is higher than the existing scheme regardless of interference limitation and antenna density, which can be attributed to the fact that the SASK scheme selects an optimal set of SU to access the 735
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Fig. 2 Comparison of throughput with different interference limitation
spectrum fully utilising the excessive interference limit. Additionally, the total throughput in the high antenna density scenario is superior to the low-density scenario. A high antenna density is beneficial to enhance the channel gain between SU and DA, which decreases the transmit power of SUs and reduces the interference from SU to PU. Thus, more SUs might share the spectrum band with PU. In Fig. 3, the influence of excessive interference probability limitation over throughput is illustrated for different access schemes. Here we set Ith/N0 = 8 and vary pth from 0.01 to 0.1. With the increment of pth, the total throughput of SUs increases gradually in the SASK scheme, while it hardly changes in the existing scheme. The reasons are as follows. The SASK scheme considers the interference from SU to PU as a stochastic variable. Thus, when a higher excessive interference probability is allowed, more SUs will be granted access. However, the existing scheme dose not take into account the stochastic nature of interference from SU to PU. The variation of pth does not affect the throughput performance in this scheme. In addition, the SASK scheme is superior to the existing scheme under different pth, for the same reasons described above.
Fig. 4 Comparison of overflow probability
5.2 Comparison of probability of excessive interference Fig. 4 illustrates the probability of excessive interference in different access schemes. In these simulations, we set pth = 0.05 and Ith/N0 = 8. From this figure, we can observe that the SASK scheme keeps the probability of the excessive interference below 0.05, regardless of o, because the proposed scheme utilises the SKP model to control this probability exactly. However, the existing scheme cannot satisfy the demand of excessive interference probability limitation, as it only considers the expectation of interference. Besides, with the increment of o, the excessive interference probability in the existing scheme also increases. The high o means that the interference might exceed the expectation easily, which causes the phenomenon described above.
6
In this paper, we have addressed the SU access problem over the uplink of a WRAN employing the CR-FCDA architecture, where only stochastic link estimates from SU to PU are available. We have modelled this problem as a SKP and relaxed it to be a deterministic SOCP in order to deduce an upper bound. With this bound, this SKP can be solved by the branch and bound algorithm, which yields the SASK scheme. Finally, we have presented extensive simulation results which show that the proposed SASK scheme offers substantially better performance than the existing scheme.
7
Fig. 3 Comparison of throughput with different overflow probability 736 & The Institution of Engineering and Technology 2013
Conclusion
Acknowledgments
This paper is jointly sponsored by the National Natural Science Foundation under Grant no. 60832009, Beijing Municipal Natural Science Foundation under Grant no. 4102044, National Youth Science Foundation under Grant no. 61001115, and the Canadian Natural Sciences and Engineering Council under Grant no. STPGP 396756. Part of this work was published in the Proceedings of IEEE ICC’2011. IET Commun., 2013, Vol. 7, Iss. 8, pp. 731–737 doi: 10.1049/iet-com.2012.0627
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