Cross-Layer Scheduling of QoS-Aware Multiservice Users in OFDM-Based Wireless Networks

Amoakoh Gyasi-Agyei

Faculty of Sciences, Engineering & Health Central Queensland University QLD 4702, Australia, gyasi-agyei@ieee.org

Abstract—Constraint scheduling is a dynamic process of arbitrating between competing users sharing a finite resource.

Cross-layer scheduling allows vertical interactions between some protocol layers to optimize system performance. This article proposes a cross-layer scheduling for orthogonal frequency-division multiplexing (OFDM) based wireless networks. The scheduler combines opportunistic communications and link adaptation to serve users with multiple concurrent flows (applications) of different quality of service (QoS) requirements.

For each time slot and on each OFDM subcarrier, the scheduler computes a cost function for each flow that depends on a flow's instantaneous link quality and service history. The flow with the least cost on an OFDM subcarrier is assigned the subcarrier, provided no other flow's delay constraint is in violation. The scheme is scalable, optimizes wireless throughput, traffic delay-aware, guarantees minimum service to all active flows, and has low implementation complexity.

Index Terms—Adaptive modulation and coding, constrained optimization, cross-layer RRM, dc-BLOT, wireless scheduling.

I. INTRODUCTION

Quality of service (QoS) provisioning is a versatile feature in multiservice wireless networks, as the multiple applications (services) they support have varying characteristics. Some traffic types (e.g Email) are more sensitive to transmission errors and data loss than delay, while other traffic types (e.g.

packet voice) are more sensitive to delay than errors and data loss. This dictates that the network be designed to provide different types of services to support individual services.

Scheduling is one of the mainstream mechanisms for QoS provisioning in multi-user networks. It is a dynamic process of efficiently allocating a finite resource to multiple competing resource users to meet certain network constraints. Relevant network constraints here include maximizing wireless throughput, providing fair service to avoid service starvation to certain users or flows, and guaranteeing that traffic delay constraints are not violated. Cross-layer scheduling is a new paradigm in scheduling whereby vertical interactions between protocol layers are permitted to achieve an optimized system design.

Wireless networks rely on transmission media whose behavior depends on operating radio frequency, spatial position of a wireless user, and the instantaneous time of communications, i.e specto-spatio-temporally varying connectivity. This dynamic channel behavior is attributed to multipath signal propagation, user mobility, non-stationary clutter and the length of the wireless communications link.

Multipath signal propagation causes short-term fading (aka fast fading), while non-stationary environmental clutter causes long-term fading (aka slow fading, shadowing or local mean).

The length of the communications link, i.e. distance between a transmitter and a receiver, causes path loss (aka large-scale fading or path attenuation). Path loss increases with frequency, distance and environmental clutter. Furthermore, as user population and traffic patterns are randomly varying, so is the network topology, and more so for infrastructureless networks. Owing to the above factors, multiple users sharing a wireless resource experience asynchronous and independently varying channel qualities: some users experience poor channels while others experience good channels at a given time. This is referred to as multi-user diversity [1], [2], the basis of opportunistic communications. The origin of opportunistic communications is attributed to the works in [1], [3]. Opportunistic scheduling is a channel-aware scheduling which exploits multi-user diversity to maximize the total system throughput (sum network capacity) [4], [2], [6], [7].

Orthogonal Frequency-Division Multiplexing (OFDM) [8]

is a multicarrier transmission technique which divides a wideband channel into several equally spaced orthogonal narrowband subchannels in order to support a high data rate on otherwise a frequency-selective fading channel. An OFDM based network lends itself readily to OS as the frequency-selectivity and spatial-frequency-selectivity of its multiple channels increase the degrees of freedom in multi-user diversity compared to single-carrier networks. As its name suggests, a composite OFDM symbol is composed of several subsymbols multiplexed together, each of which is modulated onto an independent radio frequency carrier (precisely, an OFDM subcarrier). Each OFDM subsymbol (or set of subsymbols) can contain independent information and hence be used by different users or flows.

This article proposes a scheduling algorithm for OFDM based wireless networks. The algorithm considers the interplay between wireless channel dynamics due to multipath signal propagation (or fading) and user mobility and queuing dynamics arising from heterogeneous traffic of different QoS demands. The scheme is scalable, optimizes wireless throughput, respects traffic delay constraints, guarantees minimum service to all active flows, and has low implementation complexity. According to the classification of radio resource management (RRM) algorithms in [6],

T. Sobh et al. (eds.), Innovative Algorithms and Techniques in Automation, Industrial Electronics and Telecommunications, 31–36.

© 2007 Springer.

31

Fig. 1. Multi-user system serving users with multiple concurrent services of varying QoS requirements.

this article engages on Type IV resource allocation scheme.

The proposed scheme is a direct consequence of OCASD [2]

and BLOT [6]. While OCASD and BLOT serves single-carrier systems, this work considers multisingle-carrier systems. Also BLOT serves only non-real-time traffic, and its performance was not studied analytically, but by simulations.

II. NETWORK MODEL

We consider a time-slotted wireless networks using an orthogonal frequency-division multiplexing/multiple access (OFDM/OFDMA) air interface with a base station (BS) serving multiple mobile users concurrently (Fig. 1). We refer to the discrete-time interval

[

t,t+1

)

, t=0,1,2,L as time slot t. The star network topology adopted in this work can represent a cell of a cellular wireless network, or the interface between multiple stations and a relay station in infrastructureless wireless networks [9]. Each user can maintain multiple queues of different applications simultaneously. Packets in each queue have the same delay requirements and hence are managed by the first-in first-out (FIFO) principle. However, in times of buffer overflow, packets are discarded from a queue according to the random early discard [10] principle to prevent the occurrence of global synchronization [10], [11]. Each of the multiple queues active at a user has different QoS or delay requirements. Table I defines key parameters used in the algorithm described herein.

In each time slot the scheduler serves a user/queue pair (referred to as flow and denoted by Fi,m which minimizes a cost function f(Rm(t), Bim(t)) subject to traffic QoS constraints.

Hence, each OFDM subcarrier is assigned to only a single flow in a given time slot. A fundamental challenge in such a system is how the BS can serve the system to achieve both flow-level and user-level fairness on a time-varying and random wireless channel, while meeting an individual flow's quality-of-service requirements and still use the radio resource optimally. The architecture in Fig. 1 explores all these issues to serve multiple real-time flows with delay constraints and non-real-time flows without delay constraints. For example, each user can maintain concurrently one or more sessions comprising of a streaming video, streaming audio, wireless

TABLE I NOTATION

Parameter Meaning

t Time slot or instantaneous time

tc Scheduling time frame for short-term fairness m User index, m = 1,2, …, M

i Traffic class or queue index, I = 1,2, …, I Fim Flow index, i.e. traffic class i at user m W Wideband wireless channel bandwidth K Number of OFDM subcarriers in the system K_im(t) Number of OFDM tones assigned to flow F_im Lim(t) Size of the head-of-line (HOL) packet in queue Fim Kimmax Number of tones needed by HOL packet of flow Fim

Rmk(t) Maximum data rate on user m 's kth OFDM subchannel B_im(t) Average amount of traffic scheduled from queue F_im Dim(t) Queuing delay of HOL packet in flow Fim's queue Dmax,i Maximum queuing delay of packets of traffic class i Internet gaming, packet voice (VoIP), Email, file transfer, Web browsing and telneting, and still expects a guaranteed minimum service for each of these active flows.

A. Link Layer Model

We consider a wideband wireless channel disturbed by an additive white Gaussian noise (AWGN) and a frequency-selective Rayleigh fading. However, in accordance with the OFDM philosophy, we assume that the wideband channel is so partitioned into subchannels that each OFDM subchannel is approximately liable to flat fading. Let B be the coherence _c bandwidth of the wideband channel of width W Hz and K be the number of OFDM subcarriers in the system. If K is chosen such that f =W/K<Bc then each of the OFDM subchannels experiences approximately a flat fading. This is one of the key motivations behind OFDM transmission. If K _x^t is the set of OFDM subcarriers allocated to flow x at time t then

j l K

K_l^t∩ ^t_j=0,∀ ≠ and

∑

_nK_n^t≤K ⁽¹⁾ Assume that both flows l and j are active at a given user, say m, at the same time t, and K_l^t,K^t_j∉

{ }

0 . This requires user m to serve two independent flows between itself and two different receivers at the same time. Can a single antenna at user m be used to accomplish this? Or, multiple antennas are required? This is where MIMO technology becomes necessary. Precisely, a MIMO system which uses different elements of an antenna array to transmit different signals.

However, this article does not explore MIMO issues further.

Assume that the physical layer uses multi-level quadrature amplitude modulation (M-QAM) and two-dimensional Gray encoding with perfect carrier and clock recovery circuits.

Under such an environment the average BER, the average signal-to-interference plus noise ratio (γ^___m,k) of user m's kth OFDM subchannel and the M-QAM constellation size M relate approximately as 2

(

1

)

(0.2/ , 1)/3

_____

,

__mk≈ M− ⋅ BERmk−

γ Δ

GYASI-AGYEI 32

[12]. In the following we slightly abuse terminology and replace average values by their corresponding instantaneous values, and approximation by equality, i.e.

( ) (

2 1

) (

0.2 ,

( )

1

)

3

,k t = M− ⋅ BERmk t −

γm (2)

Hence, the maximum feasible transmission rate on the kth OFDM subchannel at user m at time t is given by the Shannon-Hartley channel capacity theorem as

( ) ( ( ) )

For a packet of length Lim with independent bit errors the bit-error rate BERm,k(t) relates to the corresponding instantaneous packet error rate as BERm_,k

( )

t =1−

[

1−PERm_,k

( )

t

]

^{1Lim( )t} .

Wireless channel estimation is an essential mechanism in all channel-aware protocols. Various methods have been proposed to estimate the instantaneous quality of channels of wireless users in the form of signal-to-interference plus noise ratios (SINR) or bit-error rates. The SINR or BER aids in the estimation of the feasible data transmission rate on the channel at a given time. Interested readers may find more information on this topic in e.g. [13], [14], [15], [16].

B. Cross-Layer Scheduling at Layer 2

We want to design a simple resource allocator that guarantees a minimum service to each active flow over a given length of time, maximizes wireless throughput and meets individual flow's delay bounds. Designing such a scheduler is difficult, except by heuristic methods. We define a time-varying cost function which depends on active flows' service history and instantaneous data transmission rate of their corresponding users. This cost function provides only fairness and throughput maximization. To guarantee delay bounds to timing-sensitive traffic we subject the cost function to traffic delay constraints. Fig. 2 shows the protocol layers that communicate vertically in the proposed cross-layer scheduling. The instantaneous wireless channel quality in form of the instantaneous bit-error-rate on each OFDM subcarrier is estimated at the physical layer and fed to the Medium Access Control (MAC) sublayer at Layer 2 (L2) which hosts the scheduler. A traffic delay constraint,D_max,i

( )

t , is precisely known only by the corresponding application that generates it. Hence, these delay bounds are fed to the MAC sublayer from the Application Layer. Just as the delay, the amount of service,Bim

( )

t , that each active flow has received so far is communicated from the Application Layer to the MAC layer. Using these three instantaneous parameters, the MAC layer computes a cost function

( )

t f

(

B

( )

t PER

( )

t

)

Ck im mk

im = , , for each active flow at the

beginning of each time slot. The flow that minimizes the cost function on the given OFDM subcarrier is allocated the corresponding carrier to meet its delay bound of D_max,i

( )

t .

Fig. 2. Protocol interations in the delay-aware cross-layer scheduling.

For m=1,2, …, M; i=1,2…, , I; k=1,2, …, K we define the cost function [6]

( ) ( )

allocation problem in each time slot t is then

Minimize Cim^k

( )

t Subject to Dim

( )

t ≤Dmax,i

(5) (6) Thus the scheduler allocates the kth OFDM subchannel to flow Fi,m that fulfils (5) and (6). We note from the delay constraint (6) that the more a flow is delay insensitive the higher its delay bound. Hence, for non-real-time traffic class i we have D_max,i→∞. In the following we define the where T denotes the transposition operator. Hence, c(x) replaces C^kim(t). Also, defineg(x)=Dim(t)-Dmax,i≤0. The scheduling algorithm is compiled in Table II. We refer to the scheduling algorithm described above as delay-constrained BLOT (dc-BLOT), as it originated from [6] and [2].

III. OPTIMIZATION USING NEURAL NETWORKS

Optimization neural networks are gradient type networks whose behavior can be modeled by analog electrical circuits [17]. The temporal evolution of these neural networks is a motion in the state space whose trajectory follows the direction of the negative gradient of the system's energy function, which can be made equivalent to the cost function to be minimized. The solution of the optimization problem is equivalent to the point of minimum system energy.

Application Layer

Physical Layer (L1) Data Link Layer (L2) Network Layer (L3)

Scheduling Decision Dmax, i Bi,m(t)

BERm,k(t)

CROSS-LAYER SCHEDULING OF QOS-AWARE MULTISERVICE USERS 33

Table II Pseudocode for the cross-layer scheduling algorithm

We use neural networks' techniques to compute the vector

( ) ( ) ( )

[

Bim t BERmk t Dimt

]

^T

x*= ^* , ^* , ^* in each time slot that exploits the limited radio resource in an optimal way. To do this we first need to convert the constrained optimization problem into equivalent system of differential equations. These differential equations constitute the basic neural network algorithms that must be solved to solve the optimization problem in real-time.

The Lagrange function L:ℜ^n+k→ℜfor the problem (5)-(6) is ^L

(

^x

^{, ν , λ} ) ( )

^{=cx +}

^λ (

^g

( )

^{x +}

^ν

²

)

⁽⁷⁾

where λ∈ℜ^k,k=1is the Langrangian multiplier. In accordance with their roles in searching for the optimum solution of (5)-(6), ν and x are referred to as variable neurons or primal variables while λ is the Langrangian neuron. As the neural network dynamically searches for the optimum solution the variable neurons decrease L(x,ν,λ) while the Langrange neuron leads the search trajectory into the feasible region

{ ( )

≤0

}

= xgx

S . The Kuhn-Tucker optimality conditions are

( )

We want to design an artificial neural network (ANN) with an equilibrium point that fulfills the K-T conditions in (8). By noting that

we can formulate the state equations governing the transient behavior of this ANN by the system of equations [18]

( )

physically stable neural network has the equilibrium point x*

satisfying ~ 0

~*

~_x=x =

k dt

x

d which are equivalent to the Kuhn-Tucker sufficient conditions for optimality, (8). Hence, the state equations of the neural network, (10)–(14), are referred to as Lagrange Programming Neural Network [18].

A. Convexity of the Objective Function c(x)

In order to apply artificial neural network to solve the optimization problem we need to ensure that c(x) is twice continuous differentiable in x. If c(x) is convex then it is twice continuous differentiable in x. A sufficient condition for c(x) to be convex is that its Hessian matrix is positive semi-definite. From (4) we obtain the Hessian matrix of c(x) as

( ) ( )

Theorem 1: We establish conditions under which Hc(x) is a positive semidefinite matrix. Proof. A sufficient condition for Hc(x) to be a positive semidefinite matrix is that the determinants of all its upper-left submatrices are positive.

Denote by det Hc(k) the determinant of the square upper-left submatrix of Hc(x) of size k. Noting that Hc(x) is a symmetric matrix we require that

( )

1 0

( )

The validity of (20) is obvious from (17). Equation (16) obviously yields detHc(3)=0. Condition (21) is fulfilled if

( )

Figure 3 shows that this condition is fulfilled if x2(t) >10^-7. The required BER range is realistic for practical wireless systems. Fig. 3 also shows a plot of detHc(1). We observe that detHc(1)>0 for all practical BER values. Hence, we have proved that Hc(x) is a positive definite matrix.

Theorem 2: Positive semidefiniteness of ∇²xxL

(

x,ν,λ

)

B. The Lyapunov Function & Stability Test

This section establishes the convergence and hence the stability of the set of differential equations (10)-(14) that represent our optimization problem via Lyapunov's method.

Lyapunov stability theory is based on the idea that if some measure of the energy associated with a dynamic system is decreasing, then the system converges to its equilibrium state.

To do this we first need to compute a Lyapunov function,

( )

x E

( ) ( )

x Ex* C¹

V = − ∈ , of the given system, where E

( )

x is the energy function of the system and x* is the optimum point in the feasible set being searched for. The system's energy function is a function defined on the state space

{ ( )

≤0

}

⊂ℜ³

= xg x

S which is non-increasing along the

trajectories and it is bounded from below. Let us define the energy function

The system is globally stable in the Lyapunov sense, i.e., the trajectories xk(t), k=1,2,3, λ(t) and ν(t) converge to stationary points as t→∞, if and only if

At the stationary point we have dE/dt|x=x*}=0. Proving the stability of the system requires us to establish that

(

x, ,

)

≥0 and dE

(

x, ,

)

dt≤0

E ν λ ν λ (26)

The subsections below prove (26).

Theorem 3: Positive semidefiniteness of E

(

x,ν,λ

)

. Proof. Proving that E

(

x,ν,λ

)

≥0 is an obvious consequence of its definition. Hence, the Lyapunov function

10⁻⁸ 10⁻⁷ 10⁻⁶

Bit Error Rate (x 2) decreasing function of time. Using the state conditions (10)-(14) in (25) yields

We analyze the performance of dc-BLOT with respect to delay violations, stability, system throughput and minimum service guarantees to individual flows active at multiflow users over flat Rayleigh fading channels in this section. We assume that each user can have up to a mixture of three real-time and non-real-time flows active at the same non-real-time. Each flow generates a single packet in each time slot and, for the simplicity of comparison all packets have the same size. We apply multivariate fourth-order Runge-Kutta numerical integration method to evaluate the transient behaviors of the state variables describing the neural network for the dynamic system as given in (10)-(14). The fourth-order Runge-Kutta method is reputed for its good accuracy and simplicity. The fourth-order Runge-Kutta method for our multivariate system of differential equations (10)-(14) can be adapted from ([19], p. 326) as

CROSS-LAYER SCHEDULING OF QOS-AWARE MULTISERVICE USERS 35

( )

Fig. 4 shows the effects of inappropriate initial conditions on the transient behaviors of the state variables.

0 5 10 15 20

This article discusses the problem of delay-constrained cross-layer scheduling in multicarrier multiuser wireless networks to guarantee a minimum service in both flow level and user level. The proposed algorithm is Lyapunov stable for bit error rates higher than 10^-7. Hence, it is attractive for multi-service wireless networks. Our future work will extend the proposed scheme to serve both real-time and non-real-time flows in a multiple-input, multiple-output wireless networks.

REFERENCES

[1] R. Knopp and P. A. Humblet, “Information capacity and power control in single-cell multiuser communications,” in Proc. IEEE Int.

Conf. on Commun., vol. 1, Seattle, 18-22 June 1995, pp. 331–335.

[2] A. Gyasi-Agyei, “Multiuser diversity based opportunistic scheduling for wireless data networks,” IEEE Commun. Lett., vol. 9, no. 7, July

2005.

[3] P. Viswanath, D. N. C. Tse, and R. Laroia, “Opportunistic beamforming using dumb antennas,” IEEE Trans. Inform. Theory, vol. 48, o. 6, pp. 1277–1294, Jun 2002.

[4] A. Gyasi-Agyei, “BL2xF–channel state-dependent scheduling algorithms for wireless IP networks,” in Proc. IEEE Int. Conf. on Networks (ICON’03), Sydney, September 2003, pp. 623–628.

[5] ——, “OCASD–channel-aware scheduling for multi-service wireless IP networks,” in Proc. Australian Telecommunications,

and Networks Applications Conference (ATNAC), Sydney, December 2004, pp. 582–589. [Online]. Available:

http://www.titr.uow.edu.au/atnac/Proceedings/abstract.pdf

[6] A. Gyasi-Agyei and S.-L. Kim, “Cross-layer multiservice opportunistic

scheduling for wireless networks,” IEEE Commun. Mag., vol. 44, no.

6, June 2006.

[7] ——, “Comparison of opportunistic scheduling policies in time-slotted AMC wireless networks,” in IEEE Int. Symp. on Wir.

Pervasive Computing, Phuket, Thailand, Jan. 2006.

[8] L. Hanzo, M. Munster, B. J. Choi, and T. Keller, OFDM and MC-CDMA for broadband multi-user communications, WLANs and broadcasting. John Wiley & Sons, 2003.

[9] Q. Liu, X. Wang, and G. B. Giannakis, “A cross-layer scheduling algorithm with QoS support in wireless networks,” IEEE Trans. Veh.

Techn., vol. 55, no. 3, pp. 839–847, May 2006.

[10] S. Floyd and V. Jacobson, “Random early detection gateways

[10] S. Floyd and V. Jacobson, “Random early detection gateways

Dans le document Innovative Algorithms and Techniques in Automation, Industrial Electronics and Telecommunications (Page 42-48)