In the non-homogeneous case, the real-time data terminals for the first-tier cells (cell 2 to cell 8) are: ND,h = 25 − 2 ∗ (i − 1) and ND,l = 40− ND,h, i=2, · · ·, 8, while for the central and second-tier cells, the real-time data terminals are: ND,h = ND,l = 20.
Figure 4 shows the packet error probabilities of the three tiers in the multi-cell WCDMA system. As the figure reveals, only FQ-SDAM, FQ-RCE/EXP, and LIDA with β=10% meet the QoS requirement because FQ-SDAM and FQ-RCE/EXP consider the received adjacent-cell interference power as an input parameter for resource estimation. The resource allocation in the adjacent-cells is perceived by observing the interference fluctuation. Consequently, the resource allocations between cells can be conceptually coordinated implicitly. Additionally, compared to Fig. 2 at ND,h = 20, the packet error probability in the non-homogeneous case is larger than that in the homogeneous case because the fluctuation of received adjacent-cell interference ,in the non-homogeneous case, differs from cell to cell when the cells compete for the residual capacity in the multi-cell environment. Without coordination, each cell allocates myopically, causing the system to over-loading.
Fig. 5 shows the aggregate throughputs of non-real-time data traffic in the three tiers of the multi-cell WCDMA system. Here, the aggregate throughputs of the LIDA withβ=0% and β=5% are not considered due to their QoS violation. The aggregate throughput in the non-homogeneous case is smaller than that in the non-homogeneous case due to the higher interference fluctuation. Also, the FQ-SDAM and FQ-RCE/EXP schemes still achieves higher aggregate throughput by an amount of 31.53% and 28.346% (35.5% and 33.63%) (34.2% and 32%) for the cells in the central (first-tier) (second-tier) than the LIDA with β = 10% scheme does.
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Fig. 1. Structure of FQ-RCE
Fig. 2. Packet error probabilities: homogeneous case
TABLE I
TRAFFICPARAMETERS INTHE MULTI-CELLWCDMA SYSTEM
Traffic Type Traffic Parameters
2-level real-time voice Mean talkspurt duration: 1.00 seconds Mean silence duration: 1.35 seconds Peak rate (Rp,h): 4-fold of basic rate High-bursty Mean rate: 1-fold of basic rate real-time data traffic ρh: 0.25
Peak rate (Rp,l): 2-fold of basic rate Low-bursty Mean rate: 1-fold of basic rate real-time data traffic ρl: 0.5
Mean data burst size: 200 packets Non-real-time data traffic rmin: 1-fold of basic rate
rmax: 8-fold of basic rate
Fig. 3. Aggregate throughput of non-real-time data traffic: homogeneous case
Fig. 4. Packet error probabilities: non-homogeneous case
Fig. 5. Aggregate throughput of non-real-time data traffic: non-homogeneous case
A Cellular Neural Network and Utility-based Scheduler for Multimedia CDMA Cellular
Networks
Scott Shen and Chung-Ju Chang Department of Communication Engineering
National Chiao Tung University Hsinchu 300, Taiwan ROC E-mail: [email protected]
Tel. No.: 886-3-5731923 Fax No.: 886-3-5710116
Abstract
In this paper, a cellular neural network and utility (CNNU)-based scheduler is proposed for multi-media CDMA cellular networks supporting differentiated quality-of-service (QoS). The cellular neural network is powerful for complicated optimization problems and has been proved that it can rapidly converge to a desired equilibrium; the utility-based scheduling algorithm can efficiently utilize the radio resource for system and provide QoS requirements and fairness for connections. A relevant utility function for each connection is here defined as its radio resource function further weighted by both a QoS requirement deviation function and a fairness compensation function. The CNNU-based scheduler determines a radio resource assignment vector for all connections so that the overall system utility is maximized and the system throughput can be achieved as high as possible. At the same time, the performance measures of all connections are kept closed to their QoS requirements in an efficient way.
I. INTRODUCTION
In future wireless networks, heterogeneous and customized services with diverse traffic charac-teristics and QoS requirements are expected to be provided via a number of air interfaces. Also, multimedia applications are commonly accepted as enabling services, which are categorized into several classes [1]. To meet various traffic characteristics and QoS requirements of these potential
Chapter 3
A Cellular Neural Network and
Utility-based Scheduler for Multimedia
CDMA Cellular Networks
applications, a sophisticated scheduling algorithm plays an essential role so that the system resource allocation is optimal, while retaining a pre-defined QoS requirements and fairness among them.
Many scheduling algorithms have been widely studied for wireline networks [2]-[3]. In the wireless communication networks, the radio channel have quite different characteristics from those in wireline networks. The transmission error probability is by several order greater than that in wireline links, and the available maximum transmission rate to each connection is location-dependent and time-varying due to link loss, shadowing, and multi-path fading. The QoS requirements and the weighted fairness among all connections should be modified.
The literature studied the resource scheduling and allocation among connections with consider-ation of physical layer processing, power control range, and link conditions [4]-[5]. Bhargharvan, Lu, and Nandagopal [6] proposed a framework to achieve long-term fairness in wireless network.
Varsou and Poor [7] proposed another class of scheduling algorithm from EDF concept in wireless environment. This class of scheme considers delay bound as its QoS requirement. In [8], a throughput-optimal scheduling algorithm for delay bounded system was proposed and proved. Shakkottai and Stolyar [10] considered both link quality and QoS requirements as the criteria and derived the exponential form of scheduling function via fluid Markovian techniques.
Many of these scheduling algorithms above, [4]-[5], [8]-[10], were formulated in utility-based approaches.
The utility-based scheduling algorithm over radio channels, is usually formulated as a com-plicated constrained optimization problem with real time requirement. To solve this optimization problem, the class of generalized HNN has been adopted for real-time tasks with several inherent defficiencies. A special type of Hopfield neural networks (HNN), named cellular neural network (CNN) proposed in [11], has been proved that it can rapidly converge to desired equilibrium on vertex along the prescribed trajectories by proper design [12]. The CNN was widely applied in image processing field and was suitable for VLSI implementation. However, to adopt the CNN technique for the scheduling optimization problem, modifications of its architecture are necessary.
In the paper, we propose a CNN and utility (CNNU)-based scheduler for downlink in mul-timedia CDMA cellular networks. The CNNU-based scheduler contains a utility function (UF) preprocessor, a radio-resource range (RR) decision maker, and a CNN processor. Noticeably, the
utility function for each connection, adopted in the UF preprocessor, jointly considers radio resource efficiency, diverse QoS requirements, and fairness. It is a radio resource function weighted by both its QoS requirement deviation function and its fairness compensation function.
The UF preprocessor generates a matrix of normalized utility functions of all connections.
On the other hand, the RR decision maker determines a matrix showing the upper limit of radio resource assignment for each connection. The CNN processor receives the two matrix as inputs and determines an optimal normalized radio resource assignment vector for connections in multimedia CDMA cellular systems, by minimizing the system cost function which is in terms of the overall system utility function under system constraints of maximum transmission power, minimum spreading factor, and remaining queue length. The architecture of the CNN is constructed via the energy-based approach [13]-[14]. by mapping the system cost function to a proper energy function. It is designed in a two-layered configuration, which consists of a decision layer and an output layer, to reduce the number of inter-connections in the CNN. It can be shown that the stable equilibriums locate in the desired state space and the stability exists.
The performance of the proposed CNNU-based scheduler is investigated by comparing with Exponential Rule [10] for systems using both dedicated and shared channel. Results show that the CNNU-based scheduler is efficient and effective for multimedia CDMA cellular networks.
The rest of the paper is organized as follows. Section II presents the features and the operations of the considered system. In section III, an relevant utility function is then proposed. In section IV, the architecture of CNNU-based scheduler and the structure of CNN are discussed. Finally, simulation results and concluding remarks are summarized in section ??.
II. SYSTEMMODEL
Assume that there are N real-time (RT) and non-real-time (NRT) connections (users) in the downlink transmissions of the multimedia CDMA cellular system with chip rate W . RT connections transmit on dedicated channels and NRT connections transmit on shared channels.
For every active connection using either dedicated or shared channels, a fixed number of code channels with their corresponding spreading factors are given in the connection setup phase.
A minimum spreading factor SFi is therefore associated with the assigned code channels for connection i. The system radio resource is here defined to be the transmission power. It is limited by a maximum power budget denoted by Pmax∗ and scheduled to all connections every frame
time period Tf.
For a downlink connection i, there are four QoS requirements defined in either the packet level, such as BER∗i, or the call level, such as delay bound Di∗, packet dropping ratio PD,i∗ , and minimum transmission rate Rm,i∗ . For RT connections, hard delay bound Di∗ exists and PD,i∗ can be larger than zero; while for NRT connections, no explicit delay bound is imposed, but R∗m,i > 0 should be satisfied for interactive connections and Rm,i∗ = 0 be set for best effort connections.
For a RT connection i, a transmission suspension in a soft fashion is carried out by allocating zero transmission power when its utility calculated by the scheduler is lower than those of NRT connections. At that moment, its link gain ζi(t) is lower than the averaged mean link gains of all NRT connections ζNRT by a relative margin, and this relative margin should be considered to restrict the probability of transmission suspension below PD,i∗ due to the delay-sensitive nature. Denote by ζi∗ the suspension threshold of connection i, which is obtained by P {ζi(t) ≤ ζi∗} ≤ PD,i∗ . Then the relative margin of ζi(t) is a function of ζNRT and ζi∗, and is dependent on the design of scheduling algorithm. For NRT connections, their transmissions are scheduled so that NRT connections will be allocated with proper radio resource to achieve high system utilization and keep the fairness and the QoS requirements fulfilled as much as possible.
Assume that the link-gain ζi(t) and the interference Ii(t) for connection i at time t can be measured at the user side and perfectly signaled to the base station. The ζi(t) consists of the mean path loss, long-term fading, and short-term fading, and is given by ζi(t) = d−4i · 10ζLi (t)10 · ζiS(t), where diis the distance between the user i and its base station, ζiL(t) is the log-normal shadowing component, and ζiS(t) is the Rayleigh-fading component. The adaptive QAM modulation is adopted and the modulation order Mκi with index κi for connection i is determined according to the link gain quality and interference. The traffic source of connection i generates packets and packets are queued in its individual buffer. The buffer size is infinite. The source models are assumed to be on-off for RT connections, Perato for NRT interactive (NRT-I) connections, and batch Poisson with truncated geometrical batch size for NRT best-effort (NRT-B) connections.
The proposed CNNU-based scheduler determines an optimal normalized radio resource as-signment vector c∗(t) = (c∗1(t), . . . , c∗N(t)) to N connections via maximizing an overall system utility function. The transmission rate for connection i at t-th frame , denoted by ri(t), is then allocated according to ci(t) of connection i.
III. FORMULATION OFTHE UTILITY FUNCTION
The utility function for connection i, Ui(t), is defined as the radio resource function of connection i, Ri(t), weighted by its QoS requirement deviation function Ai(t) and its fairness compensation function Fi(t). It can be expressed as
Ui(t) = Ri(t) · Ai(t) · Fi(t). (III.1)