Congestion Control in Cognitive Radio networks ...

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Abhinav Sinha. TATA Consultancy Services Limited. Pune, Maharashtra, India. Prasanna Kumar Sahu. National Institute of Technology, Rourkela, Odisha, India.
Congestion Control in Cognitive Radio networks using Fractional Order Rate reaching law based Sliding Modes Rajiv Kumar Mishra, Tirtha Majumder, Sudhansu Sekhar Singh School of Electronics Engineering Kalinga Institute of Industrial Technology (KIIT University), Bhubaneswar, Odisha, India

Abhinav Sinha TATA Consultancy Services Limited Pune, Maharashtra, India

Prasanna Kumar Sahu National Institute of Technology, Rourkela, Odisha, India

ABSTRACT: Under the constraints of limited bandwidth and exponentially rising user demand, there is a dire need to maximize throughput. Maintaining Quality of Service (QoS) in a communication network demands congestion control with high accuracy. This paper focuses on this challenging task that incorporates design of effective congestion controller to reduce packet loss in cognitive radio networks. Limited buffer capacity and bandwidth impose restriction on the performance when number of requests increase. The controller is designed on the notions of sliding mode which is a variable structure control technique known for its robustness and disturbance rejection capabilities.Attempts are made to reduce efforts in design complexity by incorporating fractional order rate reaching law based first order sliding mode control. An optimal design strategy is used in development of the controller. The efficiency of the controllers is confirmed by numerical simulations.

1

INTRODUCTION

Significant developments in communication and networks have led to rapid increase in user demand, thereby increasing traffic. This sudden rise in traffic leads to congestion in networks and degrades Quality of Service (QoS). Cognitive Radio Network (CRN) is an intelligent system that promises effective utilization of wireless spectrum by dynamically altering the transmission parameters to improve bandwidth uses.Most wireless spectrums are underutilized in spite of their large capacity to handle user requests and traffic. CR uses technologies such as Adaptive Radio and Software Defined Radio to direct the traffic from occupied and congested channels to the vacant ones in order to provide smooth concurrent communication. This technique allows secondary (low priority) users to temporarily use the unused licensed band of primary (high priority) users, thereby significantly improving spectrum efficiency by opportunistic spectrum utilization. There are two types of traffic queue in CRN on which the QoS are categorized, viz., high priority or premium service and low priority or ordinary service.

Former provides bandwidth to the delay and loss sensitive user while latter regulates the input flow and delay is not given much concern here. The leftover capacity of former is used for the latter. Best effort traffic is given the least significance where consumed bandwidth is left over from both services. Varying needs and data communication rate of different users cause network congestion. Controlling this serious problem is a challenging task. Several control strategies have been proposed to tackle this problem. Most techniques involved linearizing the nonlinear model that simplifies the design problem but limits the region of operation. Other control techniques such as Adaptive and Fuzzy algorithms (A. Pitsillides and J. Lambert 1997), (Y. C. Liu and C. Douligeris 1997), (A. Pitsillides and A. Sekercioglu 1999) have also been used but they are unable to cope up with fast changing scenario as they are non-model based strategies. They provide well adaptation and good approximation to hard nonlinearities but have to be combined with other strategies to yield high performance. Random Early Detection (RED) (C. Chrysostomou, A. Pitsilliides, L.

Rossides, M. Polycarpou and A. Sekerciouglu 2003) and its variants are also proposed in literature but their parameters are very sensitive to network load (Ming Yan, Tatjana D. Kolemisevska- Gugolovska, Yuanwei Jing and Georgi Dimirovski 2007). Other methods such as Active Queue Management (Ming Yan, Tatjana D. Kolemisevska- Gugolovska, Yuanwei Jing and Georgi Dimirovski 2007) are also available. Sliding mode control is a model based strategy that is known to be very effective in controlling uncertain dynamical systems. It provides advantages over other controls by eliminating the need for exact modeling and providing very good disturbance rejection. Using this control, the dynamic behavior of the system can be tailored using a particular choice of sliding function (Abhinav Sinha, Pikesh Prasoon, Prashant Kumar Bharadwaj and Anuradha C. Ranasinghe 2015). Under uncertainties such as link failures and in both steady state and non-stationary conditions, this controller delivers a high performance. However, the hardware used in realizing the controller may introduce infinite switching, known as chattering and is undesirable. In this work, we present Fractional Order Rate reaching law based sliding mode control to tackle the congestion control problem in CR networks. 2

NETWORKS DYNAMICAL MODEL

The analytical modelling of the CR network is done using queuing model or Fluid Flow Model (J. Filipiak 1988), (Bouyoucef and Khorasani 2007). The model used here is simpler than probabilistic model and allows distributed control and reduces computational time in performance evaluations. Let us consider an arbitrary channel C¯ with maximum capacity of Cmax (David Tipper and Malur K.Sundareshan 1990), N (t) is the number of packets in the system, i. e., queue+server at time t and x(t) as the state variable that represents the average number of packets in the system at any given time t. x(t) is also the ensemble average of the number of packets in the system at time t, i. e., x(t) = E{N (t)}. If d(t) and a(t) represent the flow out and into the system respectively, then we can define fin and fout as ensemble average of the flow in and out of the queue respectively, i. e., fout (t) = E{d(t)} and fin (t) = E{a(t)}. Thus, by flow conservation law, we have x(t) ˙ = fin (t) − fout (t)

(1)

Assuming the storage capacity of the queue to be unlimited and the users arriving at the queue according to a nonstationary Poisson process with rate λ(t), the model for M/G/1 queue is x(t) ˙ = −C(t)

x(t) + λ(t) 1 + x(t)

(2)

Here, x(t) is the queue length of the buffer, C is the assigned to be link capacity and the nonlinear term

λ(t) denotes incoming traffic rate. Premium services require guaranteed delivery within given loss bound and delay but rate regulation is not allowed beyond the delay bound. The buffer state is controlled to be close to a reference value such that maximum allowable delay and packet loss bound is guaranteed in premium service (A. Pitsillides, P. Ioannou, M. Lestas and L. Rossides 2005). Maximum bandwidth Cmax is dynamically assigned to the premium service such that 0 ≤ Cp (t) ≤ Cmax . Ordinary services can tolerate queuing delay and allow the regulation of flow but packet losses are not allowed. The bandwidth for ordinary service can be given as Cs (t) = Cmax − Cp (t) where Cs (t) > 0. By suitable change of variable, the model can also be rewritten in the observable canonical form, which will further aid us in optimization and development of controller. Hence, we have x˙1 = x2 x2 (t) ˙ + λ(t) (1 + x1 (t))2 We can also write in general x˙1 = f1 (x)

x˙2 = −C(t)

(3)

x˙2 = f2 (x) + b(x)u + ϕ (4) with u and ϕ are control effort and matched uncertainties respectively. 3

PROBLEM FORMULATION

The control objective lies in maintaining desired queue length in the buffer, provided the buffer length of the router has been defined in priori. The error variable is required to be stabilized to the origin for accurate tracking, and is defined as ei = xi − xiref (5) 4

CONTROLLER DESIGN

The development of sliding mode controller has been carried out in two steps viz. development of a stable hyper surface that is the geometrical locus consisting of boundaries, and formulation of the control law that is the combination of equivalent and corrective control. Let us define the surface variable as n X σ(x) = ci x i = c1 x 1 + c2 x 2 = cT X (6) i=1

with ci that are weighting parameters affecting the system trajectory and states (Abhinav Sinha and Rajiv Kumar Mishra 2013) and in turn, its performance. Choice of ci has been done by minimizing the quadratic cost function based on optimal integral rule. This requires second order sufficiency, so the model from equation (3) has been taken and put into regular form.

      0 0 I 0 ˙ (7) Z + ¯ u+ Z= ϕ¯ 0 g b The surface variable can be rewritten as σ(Z) = p1 z1 + p2 z2 = pT Z (8) From equation (7), we have Z˙ = f ∗ + b∗ u + ϕ∗ (9) The design of control law requires σ(Z) ˙ = 0 . We propose a control law of the form −pT f ∗ pT ϕ∗ max + µ|σ|α u= T ∗ − (10) p b p T b∗ µ is a design parameter in the above law and α ∈ (0, 1). The formulated law is based on fractional power reaching law which is continuous, bounded and robust to perturbations. 5

STABILITY ANALYSIS

Stability is the most important factor to be considered in any design problem. Analysis of stability has been carried out by considering a Lyapunov candidiate of 12 σ 2 (x). Negative definiteness of this candidate ensures stability in Lyapunov sense. By simple mathematical calculations, it can be easily shown that V˙ (x) = σ σ˙ < 0 for all µ > 0. Hence, the control law is stable in Lyapunov sense and also ensures finite time reachability. The weighting parameters govern the dynamics of the system during sliding. The solution for the differential equation of equation (8) in z1 (t) yields the following solutions p1 z1 (t) = exp (− )z1 (0) (11) p2 p1 p1 and z2 (t) = − exp (− )z1 (0) (12) p2 p2 As long as p1 p2 > 0, the state Z will show exponential convergence to zero, whatever initial conditions Z(0) may be. Alternatively we may say that exponential convergence to zero will occur in finite time when all the roots of the polynomial γ(s) = p1 + p2 s are essentially present in the negative half plane. 6

Figure 1: Queue for primary user using higher order sliding mode

Figure 2: Queue for secondary user using higher order sliding mode

Utkin and Umit Ozguner 1999), (Levant 1993), the profile is smooth. However, increasing the order also increases the complexity of the design. We have used

SIMULATION RESULTS

The simulation has been performed using Mathworks MATLABTM and SimulinkTM and the disturbance is randomly generated. The network parameters that have been considered here are overall server capacity as 1000 packets/sec, disturbance input rate as 80 packets/sec and desired queue length as 50 packets (R. Barzamini and M. Shafiee 2013). Other design and surface parameters have been selectively tuned. The results of using higher order sliding mode control, as used in (R. Barzamini and M. Shafiee 2013) et al. are shown here. From figures 1 and 2, it is clear that desired queue length has been achieved in around 0.5 seconds. Since, higher order sliding modes have been used here (R. Barzamini and M. Shafiee 2013) to counteract chattering (K. David Young, Vadim I.

Figure 3: Queue for primary user using proposed law

first order sliding mode instead. From figures 3 & 4, it is clear that the proposed law can provide better results under same conditions without increasing design complexity, given selective tuning of the design parameters. The results are self explanatory. 7

CONCLUSION

A robust controller has been designed to control the congestion in cognitive radio networks. The simple

tional Intelligence and Networks(CINE ‘15), Bhubaneswar, India. Bouyoucef, K. and K. Khorasani (2007, July). A sliding mode-based congestion control for time delayed differentiated-services networks. In Proc. 15th Mediterranean Conference on Control and Automation, Athens, Greece.

Figure 4: Queue for secondary user using proposed law

and low order fluid flow model of the network dynamics allows for ease in controller design based on sliding mode technique. The control algorithm has been derived analytically considering the original nonlinear model of the network. This provided increased operating range. The proposed control law is easier to design and insensitive to network anomalies and asymptoical stability is guaranteed in Lyapunov sense. Significant improvements have been observed using the proposed law and there is no packet loss. The controller eliminated the need for higher order sliding mode controller as the problem of chattering has been tackled, provided all the design parameters must be carefully tuned. REFERENCES A. Pitsillides and A. Sekercioglu (1999, May). Fuzzy logic based effective congestion controller. TCD workshop on Applications of Computational Intelligence to Telecommunications. A. Pitsillides and J. Lambert (1997). Adaptive Congestion Control in ATM based networks. Journal of Computer Communication (20), 1239–1258. A. Pitsillides, P. Ioannou, M. Lestas and L. Rossides (2005, Feb). Adaptive nonlinear congestion controller for a differentiated-services framework. IEEE/ACM Transactions on Networking 13(1), 94–107. Abhinav Sinha and Rajiv Kumar Mishra (2013, December). Smooth sliding mode controller design for robotic arm. In Proc. IEEE International Conference on Control, Automation, Robotics and Embedded Systems(CARE ‘13), Jabalpur, India. Abhinav Sinha, Pikesh Prasoon, Prashant Kumar Bharadwaj and Anuradha C. Ranasinghe (2015, January). Nonlinear autonomous control of a two- wheeled inverted pendulum mobile robot based on sliding mode. In Proc. IEEE International Conference on Computa-

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