2410

IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 8, NO. 5, MAY 2009

Joint Cross-Layer Scheduling and Spectrum Sensing for OFDMA Cognitive Radio Systems Rui Wang, Vincent K. N. Lau, Linjun Lv, and Bin Chen

Abstract—In most of the existing works on cognitive radio (CR) systems, the spectrum sensing and the cross-layer scheduling are designed separately. Specifically, the sensing module first determines whether or not a channel resource is available for the CR system based on the sensing information. The scheduling module then schedules the data transmission of different users on the available channels based on the hard-decision sensing information (HSI). In this paper, we shall propose a joint crosslayer and sensing design and study its performance advantages over the aforementioned traditional decoupled approaches. We shall consider the downlink transmission of an OFDMA-based secondary system sharing the spectrum with primary users using cognitive radio technology. We shall rely on the joint design framework to optimize a system utility, which adapts the power allocation and the subcarrier assignment across the secondary users (under a average interference constraint to the primary users) based on both the channel state information (CSI) and the raw sensing information (RSI). In addition, we shall also propose a distributed implementation for the cross-layer sensing and scheduling design using primal-dual decomposition approach. Simulation results reveals the substantial performance gain of the proposed joint design over the conventional CR systems. Index Terms—Cognitive radio, cross-layer, distributed algorithm.

I. I NTRODUCTION

C

OGNITIVE radio is an intelligent wireless communication technology that is aware of its surrounding environment by performing spectrum sensing and is able to adapt its transmission on the unlicensed frequency band such that the interference to the primary users (which is the licensed user of the frequency band) is avoided or limited to an acceptable level. Recently, there have been a lot research interests focusing on the CR systems. For example, in [1], [2], the authors studied the information theoretical capacity of the point-to-point CR channel under various scenarios. Although these are very fundamental works on the analysis of CR channel capacity, they all assumed the secondary user is capable of detecting the information transmitted by the primary transmitter and should relay this information from the primary transmitter to primary receiver while transmitting its own information simultaneously by dirty paper coding Manuscript received October 16, 2007; revised February 13, 2008; accepted May 2, 2008. The associate editor coordinating the review of this paper and approving it for publication was H.-H. Chen. R. Wang and V. K. N. Lau are with the Department of Electronic and Computer Engineering, Hong Kong University of Science and Technologies, Clear Water Bay, Hong Kong, China (e-mail: {wray, eeknlau}@ust.hk). L. Lv and B. Chen are with the Huawei Technologies Co., Ltd., Shen Zhen, China (e-mail: {lvlinjun, binchen}@huawei.com). This work was supported by the Research Grants Council of the Hong Kong Government through the grant RGC 615606. Digital Object Identifier 10.1109/TWC.2009.071147

(DPC) and hence, they are still practically infeasible due to the complexity of DPC and the fact that secondary users may not even know about the codebook of primary users. There are also some other works focusing on the system and spectrum access aspects of CR systems. For example, the first commercial CR system, namely the Wireless Regional Area Network (WRAN), is currently being standardized by IEEE802.22[3]. In the WRAN systems, the spectrum sensing and the cross-layer OFDMA scheduling are performed in a decoupled manner. Specifically, each user in the WRAN systems determines whether a particular channel is vacant or not and reports the sensing information to the base station. The base station makes a centralized hard-decision to determine whether this particular channel is available or not using simple schemes such as majority voting. This hard-decision sensing information (HSI) is then passed to the cross-layer OFDMA scheduler where the power and subcarrier scheduling are performed on the available channels only. This isolated approach of spectrum sensing and cross-layer scheduling also appears in [4], [5]. In [6]–[8], the authors discuss the power control problem on a shared channel, where multiple secondary transmitters are transmitting simultaneously in the presence of primary users. However, these works assumes the secondary transmitters have perfect knowledge of the instantaneous channel state information (CSI) between the secondary transmitters and the primary users. Yet, in practice, such information is very difficult to obtain and to track. Furthermore, the secondary users are allowed to transmit simultaneously on the shared channel, which is also very difficult to be realized in practice due to the severe mutual inference. In general, there are still several technical questions not yet addressed by the literatures: • How to jointly utilize the CSI and the raw sensing information (RSI) in the cross-layer scheduling? • How much additional benefit on system performance will the joint sensing and cross-layer scheduling approach provide? • What is the minimum feedback overhead needed to convey the RSI and CSI without performance loss? In this paper1 , we shall attempt to shed some lights on the above problems. We shall propose a combined spectrum sensing and cross-layer power and subcarrier adaptation design for downlink OFDMA-based CR systems. We assume each secondary user in the CR systems performs spectrum sensing and reports the RSI to the base station. By utilizing the CSI and RSI jointly, the secondary users in the CR systems 1 Due to the page limits, we have condensed some descriptions and proofs in this paper. The reader may refer to [9] for more details.

c 2009 IEEE 1536-1276/09$25.00 

WANG et al.: JOINT CROSS-LAYER SCHEDULING AND SPECTRUM SENSING FOR OFDMA COGNITIVE RADIO SYSTEMS

could exploit the spectrum holes of the primary users more effectively, and therefore, achieve a significantly higher system throughput. In addition, we shall also propose a distributive implementation where the power control is distributed to individual mobiles to reduce the computational overhead at the base station. We shall show that we can still achieve the optimal performance asymptotically with a feedback cost of ln K for sufficiently large K, where K is the number of secondary users. As a result, the overall average feedback cost per user is asymptotically zero as the number of secondary users increases. This paper is organized as follows. In Section II, we introduce the system model. In Section III, we formulate the joint optimization problem and propose a centralized solution. In Section IV, we elaborate the distributed algorithms. In Section V, we show the performance of our joint design by simulations. Finally, we make conclusions in Section VI. II. S YSTEM M ODEL A. System Model of OFDMA-based CR System In this paper, we consider the downlink of a CR system with one base station (BS) and K mobile users (MS) over frequency selective fading channels. In the following discussions, we shall refer this system as the secondary system and the corresponding BS and MS as the secondary BS and secondary MS respectively. We consider OFDMA by which the whole spectrum is divided into M subcarriers. The spectrum used by the secondary system is licensed to some primary users. The secondary system could transmit only when the primary users are inactive. Thus, the mobiles of the secondary system should sense the spectrum at the beginning of frames, feed back the sensing results (maybe through another licensed control channel) to the base station and operate according to the scheduling of base station. Let Hk,m be the channel gain of the mobile k on the m-th subcarrier and Xk,m be the symbol to be transmit to the k-th mobile on the m-th subcarrier, then the received symbol Yk,m (when there is no primary user activity on this subcarrier) can be expressed as: Yk,m = Hk,m Xk,m + Zk,m where Zk,m ∼ CN (0, 1) is the noise. Moreover, we consider the block fading channel where Hk,m is quasi-static within each frame. B. Spectrum Sensing Model and Interference Temperature Let S = [S1 , ..., SM ] denotes the instantaneous primary user activities over the M subcarriers in a frame where Sm = 0 if there is active primary user on the m-th subcarrier and Sm = 1 otherwise. For simplicity, we assume S for sequent frames is an ergodic random process which is quasi-static within one frame, and the probability that there is primary user activity on one subcarrier of a frame is qp . In the CR system, each secondary user is equipped with a spectrum sensor which performs a binary hypothesis testing for each subcarrier. The sensing (hypothesis testing) results of the k-th mobile on the m-th subcarrier is denoted by sˆk,m , wherein sˆk,m = 0 means that the subcarrier is occupied and sˆk,m = 1 means otherwise.

2411

In this paper, we assume the sensing is imperfect and the false alarm probability and the detection probability of a sensing node is qf and qd respectively. In this paper, we consider a joint design approach in which the cross-layer scheduler dynamically adapts the power and subcarrier allocation based on CSI H = {Hk,m |k ∈ {1, K}, m ∈ {1, M }} and the raw sensing information (RSI)  = {ˆ S sk,m |k ∈ {1, K}, m ∈ {1, M }} directly without the intervention of the sensing module. Furthermore, we consider the average interference constraint on the closest primary receiver to the secondary BS. Specifically, the average interference constraint for the m-th subcarrier is given by: Im

=

(p) 2 ESm ,H (p) |S m [pm |Hm | (1 − Sm )]

=

2 pm σm (1

m

 m ]) ≤ T0 − E[Sm |S

(1)

(p) Hm

is the channel gain from the secondary BS to the where (p) 2 primary receiver on the m-th subcarrier, σm = E(|Hm |2 ) is the path loss from the secondary BS to the primary receiver on the m-th subcarrier, pm is the transmit power of the secondary  m = {ˆ BS on the m-th subcarrier and S sk,m |k ∈ {1, K}}. C. System Utility for the Secondary System In this paper, we shall maximize the average weighted system throughput. Firstly, Define the set of power allocation for all K users in all M subcarriers as follows P=

{pk,m ≥ 0|k ∈ {1, K}, m ∈ {1, M },

 k

m

pk,m ≤ P0 } (2)

where P0 is the total transmit power constraint. Define A = {(A1 , ...AM )|Am ∈ {1, K}} to be the set of user assignment to the M subcarriers where Am denotes the user index assigned to the m-th subcarrier. Since the secondary BS is assumed to have perfect CSI knowledge, the largest possible achievable data rate rk,m of the k-th user on the mth subcarrier is given by: rk,m = log2 (1 + pk,m βk,m ) where βk,m = |Hk,m |2 . As a result, the total instantaneous weighted throughput is given by:

U (A, P, S, H) =

M 

Sm μAm log2 (1 + pAm ,m βAm ,m ) (3)

m=1

where μk is the weight of the k-th secondary mobile, H = {Hk,m |k ∈ {1, K}, m ∈ {1, M }} and Sm indicates whether the subcarrier is available or not. Since the secondary BS has knowledge on the CSI H and  only, the power control and subcarrier allocation can the RSI S  only as well. therefore be adaptive with respect to H and S As a result, we shall formally define the following policies: Definition 1 (Power Allocation Policy): The power alloca ∈ {0, 1}K×M }  : H ∈ C K×M , S tion policy P = {P(H, S) defines the power control actions P for any feasible realization  such that the power constraint in (2) is of CSI H and RSI S satisfied. Definition 2 (Subcarrier Allocation Policy): The  : H ∈ subcarrier allocation policy A = {A(H, S)

2412

IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 8, NO. 5, MAY 2009

 ∈ {0, 1}K×M } defines the subcarrier allocation C K×M , S  actions A for any feasible realization of CSI H and RSI S. Given the power allocation policy P and subcarrier allocation policy A, the average system throughput U (P, A) is given by:

A. Scheduling Solution We define a dual problem of Problem 1 as follows: Problem 2 (Dual Problem): d∗ =min g(λ, ν) λ,ν

 U (P, A) = ES,S,H 

M 



=min λ,ν

Sm μAm log2 (1 + pAm ,m βAm ,m )

m=1

 M

m=1

+νm T0

(4)

max[ max lAm ,m (pAm ,m , βAm ,m λ, νm )] Am pAm ,m



+ λP0

s.t. λ ≥ 0 νm ≥ 0 ∀m ∈ {1, M }

III. J OINT C ROSS -L AYER S CHEDULING FOR OFDMA- BASED CR S YSTEMS

where

 to be the conditional system utility From (4), we define U as follows:  (P, A, H, S)=E  U S[

M 

=

αm μAm log2 (1 + pAm ,m βAm ,m )

(5)

m=1

where  m |] = αm = E[Sm ||S

 m ||Vm ] (1 − qp ) Pr[|S  m ||Vm ] + qp Pr[|S  m ||V¯m ] (1 − qp ) Pr[|S (6)

and Vm is defined to be the event that the m-th subcarrier  m | denotes the number of  1 in the is actually available, |S  m . In fact, αm represents the confidence level that the set S BS believes the m-th subcarrier is available. Since a policy is defined to be the set of actions for each realization of CSI  and the objective function U(.) can be deH and RSI S  (.)], maximizing the average weighted composed into EH,S [U system throughput U with respect to the policies P and A is equivalent to maximizing the conditional average weighted  (.) (5) for each realization of CSI and system throughput U RSI. Hence, we have the following optimization problem: Problem 1: Given a CSI realization H and a RSI realization  find the optimal user selection action A and the optimal S, power allocation action P such that the conditional average  is maximized, while satisfying  system utility U(P, A, H, S) that the total transmit power is less than P0 and the average interference of the primary receiver on each subcarriers is less than T0 . That is: p∗ =max P,A

=max P

s.t.

M 

M  m=1 M  m=1

lAm ,m (pAm ,m , βAm ,m , λ, νm ) =αm μAm log2 (1 + pAm ,m βAm ,m ) − λpAm ,m 2 −νm pAm ,m σm (1 − αm )

 H] Sm μAm log2 (1 + pAm ,m βAm ,m ) |S,

m=1 M 

  max αm μAm log2 (1 + pAm ,m βAm ,m ) (7) Am

(8)

m=1

2 (1 − αm ) ≤ T0 pAm ,m σm

∀m ∈ {1, M }

(11)

and λ as well as ν is the Lagrange multiplier. The dual problem can be decomposed into three subproblems: Subproblem 1 (Power Scheduling): Given the multipliers (λ, ν), for any Am ∈ {1, K} and any m ∈ {1, M } optimize the transmit power pAm ,m such that lAm ,m (11) is maximized. ∗ Denote p∗Am ,m and lA be the optimized variable, that is: m ,m p∗Am ,m (βAm ,m , λ, νm )=arg max lAm ,m (pAm ,m , βAm ,m , λ, νm ) =

pAm ,m

αm μAm 1 − 2 (1 − α )] ln 2 [λ + νm σm βAm ,m m

+

and ∗ lA (βAm ,m , λ, νm ) = lAm ,m (p∗Am ,m , βAm ,m , λ, νm ) m ,m ⎧ ∗ 0 ⎪ ⎪  pAm ,m = 0 ⎪ ⎨ αm μAm βAm ,m 2 (1−α )] ln 2 = αm μAm log2 [λ+νm σm m ⎪ ⎪ 2 ⎪ α μ λ+ν σ (1−α m m m) ⎩− m Am + otherwise ln 2 βA ,m m

where [x]+ = max{0, x}. Subproblem 2 (User Selection): Given the optimized ∗ Am ,m (.) where m ∈ {1, M } and Am ∈ {1, K}, find the optimal user of each subcarrier, thus, ∗ (βAm ,m , λ, νm ) A∗m (λ, νm ) = arg max lA m ,m

(12)

∗∗ ∗ lm (λ, νm ) = max lA (βAm ,m , λ, νm ) m ,m

(13)

Am

and

αm μAm log2 (1 + pAm ,m βAm ,m )

pAm ,m ≤ P0

(10)

(9)

Am

Subproblem 3 (Multiplier Update): Find the optimal multipliers (λ, ν) which minimize the dual function g(.), thus, {λ∗ , ν ∗ } = arg min

M 

∗∗ [lm (λ, νm ) + νm T0 ] + λP0

λ≥0 ν0 m=1

(14)

We shall adopt the subgradient algorithm to solve for the optimal multipliers (λ∗ , ν ∗ ). Specifically, the subgradient of

WANG et al.: JOINT CROSS-LAYER SCHEDULING AND SPECTRUM SENSING FOR OFDMA COGNITIVE RADIO SYSTEMS

the dual function g(λ, ν) in (10) is given by the vector: ⎛ ⎞ M P0 − m=1 p∗A∗m ,m (λ, νm ) ⎜ T − σ 2 (1 − α )p∗ (λ, ν ) ⎟ ⎜ ⎟ 0 1 A∗ 1 1 1 ,1 ⎟ Δ(λ, ν) = ⎜ (15) . ⎜ ⎟ . ⎝ ⎠ . 2 (1 − αM )p∗A∗ T0 − σM

M ,M

(λ, νM )

As a result, the iterative subgradient search is given by η (n+1) = [η (n) − sn Δ(λ(n) , ν (n) )]+ (n)

(16)

(n)

where η (n) = [λ(n) , ν1 , ..., νM ]T is the vector of Lagrange multipliers during the n-th iteration and {sn } is a sequence of scalar step size. The iterative algorithm terminates when |g(η (n+1) ) − g(η (n) )| ≤  where  is a terminating threshold. The subgradient update is guaranteed to converge to the optimal multipliers (λ∗ , ν ∗ ) as long as sn is chosen correctly[10]2. One important issue is whether solving the dual problem is equivalent to solving the original primal problem(or whether the duality gap is zero[11]). Notice that the optimization problem in (7) includes both the real and combinatorial variables, and hence, the duality gap p∗ − d∗ may not be always zero for general weights {μ1 , .., μK } in the system utility3 . In Lemma 1, we shall summarize that under a similar condition as in [12], the duality gap p∗ − d∗ = 0 for general weights {μ1 , .., μK }. Lemma 1: (Duality Gap for the Mixed Real and Combinatorial Problem) Suppose each primary user will span 1/Q of the total spectrum and the number of resolvable multipathes is L. For sufficiently large M such that min(M/Q, M/L) → ∞, we have the duality gap between (7) and (10) p∗ − d∗ → 0. Proof: This result is an extension of [12] and can be proved using similar techniques. We shall omit it here due to the page limit. The condition in Lemma 1 is quite mild and can be satisfied in most practical systems. For example, we have M = 2048, Q ≈ 30 (FCC Part 74 device) and L ≈ 6 in WRAN (IEEE 802.22) systems with B = 6MHz bandwidth. In the following, we shall refer every adjacent min(M/Q, M/L) subcarriers to one independent subband. All the subcarriers within one independent subband have the highly correlated channel fading and primary activities. B. Asymptotic Throughput Performance In this part, we shall discuss the asymptotic performance of the joint sensing and cross-layer scheduling design. We consider sum-rate utility (μk = 1 ∀k ∈ {1, K}) as an example for illustration. Problem 1 can be reduced to max P

s.t.

M 

m=1 M 

Am

notations. (A) Analysis for Large P0 : Intuitively, the average system  is an increasing function of the total power throughput U  will saturate at high SNR P0 constraint P0 . However, U due to the interference constraint (19). We shall derive the closed-form of the saturated throughput in this part. First, we introduce the following lemma: Lemma 2 (Asymptotic System Throughput for High SNR): When the P0 is sufficiently large, i.e. Mtotal SNR T0 P0 ≥ , the optimal power for each 2 (1−α ) m=1 σm m subcarrier is given by: pm =

T0 − αm )

2 (1 σm

∀m

(20)

and the average system throughput approaches:   M  K−1 K   K −1  m | = n) Kαm U= Pr(|S (−1)k−1 k ln 2 m=1 n=0 k=0

e

2 (k+1)(1−αm )σm T0

k+1

2 (k + 1)(1 − αm )σm Ei[− ] T0

(21)

m| where Ei(.) is the exponential integral, αm depends on |S and  m | = n) Pr(|S     K K (1 − qd )n qdK−n qp = (1 − qf )n qfK−n (1 − qp ) + n n (22) Proof: Please refer to [9]. Figure 2 illustrates the average system throughput U versus qp for different mobile sensing accuracy. We observe that the average system througput is a monotonic decreasing function of qp and better mobile sensing accuracy leads to better throughput performance. (B) Analysis for Large K: In this part, we shall analyze the asymptotic performance of our joint design when the number of mobiles K tends to infinity. We first introduce the following Proposition: Proposition 1: When the number of mobiles K tends to infinity, the spectrum sensing become perfect: (1) when there is no primary transmission on one subcarrier (say the m-th subcarrier), (23) αm → 1 when K → +∞ (2) when there exists primary transmission on one subcarrier (say the m-th subcarrier),

(17)

αm → 0 when K → +∞

pm ≤ P0

(18)

Proof: Please refer to [9]. As a result, the BS has perfect sensing on each subcarrier for sufficiently large K and we have the following lemma on the asymptotic throughput analysis for large K. Lemma 3 (Asymptotic System Throughput for Large K): For sufficiently large K, the average system throughput per channel use (b/s/Hz) has the order of growth O[(1 − qp ) log2 ln K].

2 (1 − αm ) ≤ T0 pm σm

∀m ∈ {1, M }

(19)

φ this paper sn is chosen as n where φ is a constant. we solve the optimization problem in (7) by solving for A and then solve the optimization with respect to power p (which is a real variable), the power optimization problem may not be a convex problem for any utility weights {μ1 , μ2 , ..., μK } 3 If

∗ where βm = max βAm ,m and pm = pA∗m ,m to simplify the

∗ αm log2 (1 + pm βm )

m=1

2 In

2413

(24)

2414

IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 8, NO. 5, MAY 2009

Proof: Please refer to [9]. From this lemma, we observe that despite the false alarm and mis-detection probabilities, the system throughput enjoys a multi-user diversity gain of log log K and is proportional to the percentage of idle period (1 − qp ) in the primary system. IV. D ISTRIBUTIVE C ROSS -L AYER I MPLEMENTATION The distributive implementation of the algorithm presented in the previous section can follow the standard approach of primal-dual decomposition in [13]. However, this implementation requires huge feedback overhead especially when K is large. In this section, we shall propose a generalized threshold-based mechanism to reduce the feedback overhead. Threshold-based feedback has been proposed in [14] for crosslayer scheduling to reduce the feedback overheads. In this paper, we shall extend the idea to consider a generalized feedback threshold where the threshold is compared with a generalized objective function at a user (rather than CSI in [14]). We assume there are N QoS classes with weights [μ1 , μ2 , ..., μN ] and percentage of users in the N QoS classes are [R1 , R2 , ..., RN ]. Without loss of generality, we assume μ1 ≤ μ2 ≤ ... ≤ μN . The proposed algorithm is summarized below. Algorithm 1: Distributed Algorithm with Generalized Threshold: 1) In the sensing slot, each user performs spectrum sensing on each subcarrier, and then, determine whether each subcarrier is occupied by the primary transmitter. 2) In the first iteration, the base station broadcasts the initial {αm } where α1 = α2 = ... = αM = α, (1) (1) initial multiplier η (1) = [λ(1) , ν1 , ..., νM ]T where (1) (1) ν1 = ... = νM as well as a system feedback threshold τ to the K mobiles. 3) In the first iteration, each user (say the user k) performs the optimization described in the subproblem 1. Each user attempts to feedback the local objective value ∗ ∗ |m ∈ {1, M }} only for those subcarriers lk,m ≥ τ. {lk,m In the first iteration, the user will also feed back the ∗ ≥ τ } and optimized power {p∗k,m |m ∈ {1, M }, lk,m ∗ the sensing report {ˆ sk,m |m ∈ {1, M }, lk,m ≥ τ } to the base station. 4) For m = 1 : M , the base station picks up one best user for each of the N QoS classes (user with the largest ∗ among the QoS class) and notify the selected users. lk,m Furthermore, the base station updates the multiplier η (1) to η (2) according to (15) and (16). 5) In the n-th iteration (n > 1), for each subcarrier only the mobiles notified in the step (4) (say the user k) performs the optimization described in the subproblem 1, and ∗ and the corresponding feeds back objective values lk,m ∗ optimized power pk,m to the base station. 6) The base station selects the user for each subcarrier according to (12), and update the multiplier η (n) to η (n+1) according to (15) and (16). 7) If the difference |g(η (n+1) ) − g(η (n) )| is less than a threshold  then terminate the algorithm; otherwise, jump to step (5).

In general, this algorithm is suboptimal in throughput performance because (1) not all the mobiles will give the sensing feedback; (2) it’s possible that some subcarriers are abandoned as there may be no feedback on these subcarriers due to the overlarge τ . We refer the case where no user gives feedback on certain subcarrier/subcarriers as feedback outage. Obviously, there is a tradeoff between feedback outage probability and feedback overhead. However, when K is sufficiently large, we can achieve both infinitely small feedback outage and infinitely small feedback overhead per user. Lemma 4 (Asymptotic Feedback Overhead): Given any sensing accuracy at the mobiles (qd > 0, qf < 1) and for sufficiently large K, the proposed algorithm 1 for N -classes of users achieves optimal average throughput performance, wherein the system threshold τ is given by   K τ = αμ ln ln ln K for some constant μ ∈ [μ1 , μN ], and the corresponding average feedback overhead (total number of feedback attempts) per independent subband is O(ln(K)), where the independent subband means the aggregation of adjacent subcarriers having highly correlated channel fading and primary user activities. Proof: Please refer to [9]. As a result, for any non-degenerating sensing sensitivity at the mobiles (qf , qd ), the proposed algorithm is asymptotically optimal for large K with average feedback cost (number of feedback attempts per user per independent subband) given by O(ln(K)/K) which tends to 0 for large K. V. S IMULATION R ESULTS AND D ISCUSSIONS In this section, we shall compare our joint sensing and cross-layer scheduling design with several baseline references. Baseline 1 refers to the isolated design where the HSI per subband is generated from the RSI and the cross-layer scheduler obtains the optimal power and subcarrier allocation based on the CSI and the HSI. In baseline 2, we consider a reference system with round robin scheduling only. In our simulation, we consider two QoS classes (N = 2) with the weights μ1 = 1 and μ2 = 0.5 respectively. The number of subcarrier is M = 2048 and the number of independent subband is 4. The average interference constraint T is 0dB. Each point in the figures is obtained by averaging over 2000 independent fading realization. A. Joint Design versus Isolated Design In Figure 1, we compares the average system throughput versus SNR of our proposed joint design and baseline 1 and 2 at moderate and high primary user activities qp = [0.5, 0.8]. The simulations are done at qd = 0.5, qf = 0.2 and K1 = K2 = 10, where K1 and K2 are the number of users belong to the first and second QoS classes respectively. In the figure, we can see that the average weighted throughput of the isolated design becomes saturated much earlier than the joint design. For example, the isolated design saturates at P0 /N0 = 4dB and 2dB at qp = 0.3 and 0.8 due to the average interference constraint. However, the joint design continue to increase with SNR (and shall saturate at a higher SNR). This

WANG et al.: JOINT CROSS-LAYER SCHEDULING AND SPECTRUM SENSING FOR OFDMA COGNITIVE RADIO SYSTEMS

2415

4.5

4

Closed−form, qf=0.4

Joint design; q = 0.5 p

Joint Design; qp = 0.8

Average System Throughput (b/s/Hz)

Average Weighted Throughput (b/s/Hz)

4

Isolated design; qp = 0.5

3.5

Isolated design; qp = 0.8

3

round robin scheduling, qp=0.5 2.5

round robin scheduling, qp=0.8

2 1.5 1

2

3

4

5 6 SNR P0/N0 (dB)

7

8

9

3.5

Fig. 1. Average weighted throughput U versus transmit SNR P0 /N0 at K1 = K2 = 10, qf = 0.2, qd = 0.5, M = 4 and T = 0dB. Isolated design refers to the design where the base station determines the availability of each subcarrier by majority voting and performs power and subcarrier scheduling on the available subcarriers. round robin scheduling refers to the design where the user for each subband is selected with equal probabilities (round robin algorithm)

significant performance gain demonstrates that the joint design could exploit the gaps in the primary user activity profile much more effectively. B. Asymptotic Performance for Large P0 or K Figure 2 illustrates the average throughput performance versus the primary user activities at qf = [0.2, 0.3, 0.4], qd = 0.5, K1 = K2 = 5 at sufficiently large SNR P0 4 . The simulation results match the closed-form expression derived in Lemma 2 closely at high SNR. Furthermore, we can also observe that the average throughput is a monotonically decreasing function of the primary user activity qp and false alarm qf . Figure 3 illustrates the the spectral efficiency versus the total number of users K at P0 = 10dB, qf = 0.2, qd = 0.5 for low, moderate and high primary activity qp = [0.3, 0.5, 0.8] respectively. It can be observed that the simulation results matches the closed-form expression closely, which justifies the ln ln(K) growing order of the average system throughput at sufficiently large K at various qp . C. Tradeoff of Performance and Feedback Overhead in the Threshold-Based Algorithm Figure 4 illustrates the average weighted throughput versus the average feedback overhead by implementing algorithm 1 at different primary user activity qp = [0.3, 0, 5, 0.8]. For each qp , we use different feedback thresholds to generate different average throughput performance with different feedback overhead. The optimal average throughput (obtained from the distributive algorithm [13] with full feedbacks) for qp = [0.3, 0, 5, 0.8] is also marked in the figure as a reference. It is observed 4 Note that under large P , the system is interference limited, meaning that 0 the base station is not able to utilize all the available power and the system performance is limited by the interference requirement.

f

Simulation, qf=0.2 Simulation, q =0.3

3

f

Simulation, qf=0.4

2.5 2 1.5 1

0 0.3

10

qf=0.3 qf=0.4

0.4

0.5 0.6 0.7 Probability of Primary Transmisson qp

0.8

0.9

Fig. 2. Average system throughput U versus primary user activity qp at qd = 0.5, K = 10, M = 4, T = 0dB and sufficiently large P0 .

5 Average System Throughput per Channel Use (b/s/Hz)

1

Closed−form, q =0.2

f

0.5

0.5 0

Closed−form, qf=0.3 q =0.2

4.5 qp=0.3

4 3.5 3

q =0.5

2.5

p

qp=0.8

2 1.5 1 100

150

200

250 300 350 Total Number of Users K

400

450

500

Fig. 3. Average system throughput U versus the number of users K at P0 = 10dB, qf = 0.2, qd = 0.5, M = 4 and T = 0dB.

that for all qp , the throughput performance of algorithm 1 is very close to the optimal performance at an reduced average feedback overhead of 15. Compared to the optimal solution with full feedbacks where the average feedback overhead is 80, the proposed threshold-based algorithm saves up to 80% feedback overhead with negligible performance loss. On the other hand, when average feedback overhead too small, the throughput performance of algorithm 1 will degrade accordingly, illustrating a natural tradeoff. VI. S UMMARY In this paper, we proposed a combined spectrum sensing and cross-layer scheduling design for downlink OFDMA-based CR systems, where we utilize both the RSI and CSI jointly in the cross-layer OFDMA power and subcarrier adaptations to maximize the weighted system throughput for the secondary system under an average interference constraint at the primary receivers. Compared to the conventional isolated design, the secondary systems with the joint design could exploit the spectrum holes of the primary users more effectively and therefore,

2416

IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 8, NO. 5, MAY 2009

[9] R. Wang and V. K. N. Lau, “Joint cross-layer scheduling and spectrum sensing for ofdma cognitive radio systems." [Online] Available: http://www.ee.ust.hk/∼wray/doc/CR.pdf. [10] D. Bertsekas, Nonlinear Programming. Belmont, MA: Athena Scientific, 1999. [11] S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge University Press, 2004. [12] Y. Wei and R. Lui, “Dual methods for nonconvex spectrum optimization of multicarrier systems," IEEE Trans. Commun., vol. 54, pp. 1310-1322, July 2006.

4

Average Weighted Throughput (b/s/Hz)

qp=0.8 q =0.5

Optimal Throughput =3.5b/s/Hz at qp=0.3

p

3.5

qp=0.3

3

2.5 Optimal Throughput=2.5b/s/Hz at q =0.5 p

2

[13] D. P. Palomar and M. Chiang, “Alternative decompositions and distributed algorithms for network utility maximization," in Proc. IEEE GLOBECOM, vol. 5, Nov. 2005. [14] V. Hassel, M.-S. Alouini, G. E. Oien, and D. Gesbert, “Rate-optimal multiuser scheduling with reduced feedback load and analysis of delay effects," in Proc. EUSIPCO-2005, Sept. 2005.

1.5 Optimal Throughput=1b/s/Hz at qp=0.8 1

0.5

0

5

10 15 20 25 Average Feedback Overhead

30

35

Fig. 4. Average weighted throughput U versus average feedback overhead at P0 = 10dB, K1 = K2 = 10, qf = 0.2, qd = 0.5, M = 4 and T = 0dB.

achieving a significantly higher system throughput as shown by the simulations. Furthermore, we have also proposed a distributive implementation where the power control is distributed to individual mobiles to reduce the computational loading at the base station. In addition, for any non-degenerating sensing sensitivity at the mobiles (qf , qd ), this algorithm can achieve both asymptotically zero feedback overhead per user and optimal system throughput for sufficiently large K. R EFERENCES [1] N. Devroye, P. Mitran, and V. Tarokh, “Achievable rates in cognitive radio channels," IEEE Trans. Inform. Theory, vol. 52, pp. 1813-1827, May 2006. [2] P. Mitran, N. Devroye, and V. Tarokh, “On compound channels with side information at the transmitter," IEEE Trans. Inform. Theory, vol. 52, pp. 1745-1755, Apr. 2006. [3] Draft Standard for Wireless Regional Area Networks Part 22: Cognitive Wireless RAN Medium Access Control (MAC) and Physical Layer (PHY) specifications: Policies and procedures for operation in the TV Bands, IEEE Std. 802.22, P802.22/D0.2, Nov. 2006. [4] Q. Zhao, L. Tong, A. Swami, and Y. Chen, “Decentralized cognitive MAC for opportunistic spectrum access in ad hoc networks: a POMDP framework," IEEE J. Select. Areas Commun., vol. 25, pp. 589-600, Apr. 2007. [5] Q. Zhao, S. Geirhofer, L. Tong, and B. M. Sadler, “Opportunistic spectrum access via periodic channel sensing," to appear in IEEE Trans. Signal Processing. [6] J. Huang, R. Berry, and M. L. Honig, “Auction-based Spectrum Sharing," ACM Mobile Networks Applications J. (MONET), vol. 11, pp. 405-418, June 2006. [7] S. Sharma and D. Teneketzis, “An externality-based decentralized optimal power allocation scheme for wireless mesh networks," in Proc. 4th Annual IEEE Commun. Society Conf. Sensor, Mesh Ad Hoc Commun. Networks 2007 (SECON ’07). [8] Y. Xing, C. N. Mathur, M. A. Haleem, R. Chandramouli, and K. P. Subbalakshmi, “Dynamic spectrum access with QoS and interference temperature constraints," IEEE Trans. Mobile Computing, vol. 6, pp. 423-433, Apr. 2007.

Rui Wang obtained B.Eng in computer science from the University of Science & Technology of China (USTC, 2000-2004) and Ph.D. in electronic and computer engineering from the Hong Kong University of Science & Technology (HKUST, 20042008). He is currently a post-doctoral researcher in HKUST. His current research interests include cross-layer optimization, wireless ad-hoc network, and cognitive radio. He is also interested in the standardization of wireless systems, i.e. IEEE 802.22, IEEE 802.16m and IMT-Advanced. Vincent K. N. Lau obtained B.Eng (Distinction 1st Hons) from the University of Hong Kong (19891992) and Ph.D. from the Cambridge University (1995-1997). He joined the Bell Labs - Lucent Technologies as member of technical staff from 1997-2003 and the Department of ECE, Hong Kong University of Science and Technology (HKUST) as Associate Professor afterwards. His current research focus includes robust cross layer scheduling for MIMO/OFDM wireless systems with imperfect channel state information, communication theory with limited feedback as well as delay-sensitive cross layer optimizations. He is currently an associate editor of IEEE T RANSACTIONS ON W IRELESS C OMMUNICATIONS, {IEEE JSAC, EUARSIP W IRELESS C OMMUNICA TIONS AND N ETWORKING . Linjun Lv obtained B.Eng from the University of Science & Technology of China in 1998. He has been working on the development of GSM systems, CDMA systems and optical communication systems. He also has research experiences on cognitive radio systems. His current research interests focus on the signal detection and coding of LTE-A systems.

Bin Chen graduated from Harbin Institute of Technology and achieved Master degree of Computer Science in 1998. From then on, he has been working at R&D of communication products and standard, especially 3GPP serious standards. He has more than 20 patents and several of them have been drafted in 3GPP WCDMA/HSPA standard. Now his research interests are 4G wireless communication, cognitive radio and spectrum aggregation.

Joint Cross-Layer Scheduling and Spectrum Sensing for ... - IEEE Xplore

secondary system sharing the spectrum with primary users using cognitive radio technology. We shall rely on the joint design framework to optimize a system ...

343KB Sizes 2 Downloads 285 Views

Recommend Documents

Joint Link Adaptation and User Scheduling With HARQ ... - IEEE Xplore
S. M. Kim was with the KTH Royal Institute of Technology, 114 28. Stockholm ... vanced Institute of Science and Technology, Daejeon 305-701, Korea (e-mail:.

Throughput Maximization for Opportunistic Spectrum ... - IEEE Xplore
Abstract—In this paper, we propose a novel transmission probability scheduling scheme for opportunistic spectrum access in cognitive radio networks. With the ...

Joint Adaptive Modulation and Switching Schemes for ... - IEEE Xplore
Email: [email protected]. Tran Thien Thanh ... Email: thienthanh [email protected] ... the relaying link even it can provide better spectral efficiency.

Joint DOA Estimation and Multi-User Detection for ... - IEEE Xplore
the transmitted data, uniquely identifies a desired user. The task of recognizing a ..... position is more important in the spatial spectrum than the peak value itself.

Mel-cepstrum modulation spectrum (MCMS) - IEEE Xplore
and discriminative range of features. In this work, the cep- strum reconstructed from the lower cepstral modulation fre- quency components is used as the static ...

Compressive Sensing With Chaotic Sequence - IEEE Xplore
Index Terms—Chaos, compressive sensing, logistic map. I. INTRODUCTION ... attributes of a signal using very few measurements: for any. -dimensional signal ...

Spectrum Requirements for the Future Development of ... - IEEE Xplore
bile telecommunication (IMT)-2000 and systems beyond IMT-2000. The calculated spectrum ... network environments as well, supporting attributes like seam-.

Reciprocal Spectrum Sharing Game and Mechanism in ... - IEEE Xplore
resources for CR users' networking services by granting them ... International Workshop on Recent Advances in Cognitive Communications and Networking.

Optimal Multiuser Spectrum Balancing for Digital ... - IEEE Xplore
a factor-of-four increase in data rate over the distributed DSM algorithm iterative waterfilling. Index Terms—Digital subscriber line (DSL), dual decom- position ...

Joint Random Field Model for All-Weather Moving ... - IEEE Xplore
Abstract—This paper proposes a joint random field (JRF) model for moving vehicle detection in video sequences. The JRF model extends the conditional random field (CRF) by intro- ducing auxiliary latent variables to characterize the structure and ev

Batch scheduling algorithm for SUCCESS WDM-PON - IEEE Xplore
frames arrived at OLT during a batch period are stored in Virtual. Output Queues (VOQs) and scheduled at the end of the batch period. Through simulation with ...

Distributed Spectrum Estimation for Small Cell Networks ... - IEEE Xplore
distributed approach to cooperative sensing for wireless small cell networks. The method uses .... the advantages of using the sparse diffusion algorithm (6), with.

Pricing-based distributed spectrum access for cognitive ... - IEEE Xplore
Abstract: A pricing-based distributed spectrum access technique for cognitive radio (CR) networks which adopt the geolocation database (GD) is proposed.

Joint NDT Image Restoration and Segmentation Using ... - IEEE Xplore
Abstract—In this paper, we propose a method to simultaneously restore and to segment piecewise homogeneous images degraded by a known point spread ...

A Joint Relay Selection and Buffer Management ... - IEEE Xplore
Dept. of Computer Science, UCLA. Los Angeles, USA. {tuanle, kalantarian, gerla}@cs.ucla.edu. Abstract—Due to the unstable network topology of Delay.

Designing Router Scheduling Policies: A Privacy ... - IEEE Xplore
scheduling policy of the shared resource, we develop a dynamic program to compute the optimal privacy preserving policy that minimizes the correlation ...

Scheduling Jobs With Unknown Duration in Clouds - IEEE Xplore
Here, we present a load balancing and scheduling algo- rithm that is throughput-optimal, without assuming that job sizes are known or are upper-bounded. Index Terms—Cloud computing, performance evaluation, queueing theory, resource allocation, sche

Delay-Privacy Tradeoff in the Design of Scheduling ... - IEEE Xplore
much information about the usage pattern of one user of the system can be learned by ... include, a computer where the CPU needs to be shared between the ...

IEEE Photonics Technology - IEEE Xplore
Abstract—Due to the high beam divergence of standard laser diodes (LDs), these are not suitable for wavelength-selective feed- back without extra optical ...

Cooperative Spectrum Sensing and Cognitive ...
Broadband and Wireless Group .... distances are smaller than their distances to the PU, so that ..... New York, NY: Springer Science Business Media, LLC,. 2007.

wright layout - IEEE Xplore
tive specifications for voice over asynchronous transfer mode (VoATM) [2], voice over IP. (VoIP), and voice over frame relay (VoFR) [3]. Much has been written ...

Device Ensembles - IEEE Xplore
Dec 2, 2004 - time, the computer and consumer electronics indus- tries are defining ... tered on data synchronization between desktops and personal digital ...

wright layout - IEEE Xplore
ACCEPTED FROM OPEN CALL. INTRODUCTION. Two trends motivate this article: first, the growth of telecommunications industry interest in the implementation ...