Power Allocation for Cognitive Radios Based on Primary User Activity in an OFDM System

1. Power Allocation for Cognitive Radios Based on Primary User Activity in an OFDM System Ziaul Hasan *, Ekram Hossain †, Charles Despins, and Vijay K. Bhargava * * University of British Columbia, Vancouver, Canada †University of Manitoba, Winnipeg, Canada GLOBECOM 2008 1 1

2. Outline • Introduction • System Model • Optimal Power Allocation for Cognitive Radios based on Sub-channel Availability • Suboptimal Schemes for Power Allocation based on Sub-channel Availability • Performance Evaluation • Conclusions 2 2

3. Introduction (1) • Traditional water-filling power allocation [1] approaches for OFDM-based cognitive radio (CR) systems have been found to be inefficient • due to interaction with licensed or primary users (PU) • [2] considers the limit on the interference caused by the unlicensed or secondary user (SU) sub-carriers to the nearby PU band • Since both SU and PU may exist in side by side band and their access technologies may be different, the mutual interference is the limiting factor for performance of both networks [1] D. Tse and P. Vishwanath, Fundamentals of Wireless Communications, Cambridge University Press, 2005 [2] G. Bansal, J. Hossain, and V. K. Bhargava, “Adaptive power loading for OFDM-based cognitive radio systems,” IEEE ICC’07

4. Introduction (2) • [3] considers the limit on the interference caused to the PU present in the same sub-carrier band but physically apart from the SU • PU defines a protection area and requires the interference power at the margin of the area be lower than a certain value [3] P. Wang, M. Zhao, L. Xiao, S. Zhou, and J. Wang, “Power allocation in OFDM-based cognitive radio systems,” Globecom’07

5. In This Paper • We consider reliability/availability of sub-carriers or primary user activity for power allocation • define a cost function which gives the rate loss whenever PU reoccupies the sub-channel • propose optimal and suboptimal algorithms to allocate power under a fixed power budget for such a system with linear rate loss

6. System Model (1) • A wireless system consisting of M sub-channels licensed to different primary users • All the sub-channels are divided into N sub-carriers and they are opportunistically available to some SU • We assume a centralized system where the CR controller gathers all the information • ex. channel gains, etc.

7. System Model (2) • Let αj be the probability that the channel gets reoccupied by the jth PU sometime uniformly during the current time frame • given that the channel was available for SU in the previous time frame • Let us define a mapping φ • We assume that • background additive Gaussian noise is of power spectral density N0 • each sub-carrier has a bandwidth of B Hz • The estimated channel gain at the transmitter of the SU for sub-carrier i is denoted by hi • power allocated to the sub-carrier i is denoted by Pi

8. Rate Loss (1) • The achievable rate ri as per the Shannon capacity limit is given by • η would depend on decoder pairs deployed by these users but for simplicity we normalize it to unity • In the cognitive environment, there is always a rate loss whenever a PU comes back to reuse the channel • Suppose the SU was able to use the channel for time Ti in a time frame T, rate loss would be given by • True rate Ri achieved is therefore ri −Δri

9. Rate Loss (2) • This rate loss that we discussed above is a simple representation of loss due to time factor • in general there are other costs involved while allocating power • such as interference caused to primary users and time-delays • we model those costs also as rate loss dependent on power invested in the band • We define a real-valued increasing, concave and normalized average rate loss function L(p) • for a power p invested in a sub-carrier whenever a PU reoccupies a sub-channel during the current time frame • The expected rate loss is given by • Given the probability αφ(i) that the primary user will be active and the power invested Pi in the ith sub-carrier

10. Properties of Rate Loss Function (1) • The expected capacity of the ith sub-carrier is as follows • If E{Ri} is a concave increasing function of power Pi, we could find an optimum power allocation • using standard convex optimization techniques • with a constraint on total power budget • For E{Ri} to be concave

11. Properties of Rate Loss Function (2) • Therefore, • Since E{Ri} is positive, increasing function of power , it gives • We also assume that zero power invested gives no loss, i.e L(0) = 0 • Choosing a common loss function for all sub-carriers which satisfies all desired properties is not easy • We will now consider a special case when this rate loss function L is approximated with a linear expression • Clearly, this would satisfy (7) as in this case for all sub-carriers

12. Linear Rate Loss • A linear rate loss function could be represented as follows • The quantity C could be visualized as average rate loss per unit power for the SU to allocate resources • The expected rate/capacity in the ith sub-carrier for the SU is therefore given by

13. Optimal Power Allocation for Linear Rate Loss • A power allocation vector P = [P1P2..PN] gives the amount of power allocated to each sub-carrier • Our goal is to find the power allocation vector that maximizes the expected rate

14. Optimal Solution • Proposition 1: Solution to the optimization problem defined by (12), (13) and (14) is given by • where [x]+ ≡ max {0, x} and λ is threshold constant to be determined by the total transmit power constraint as follows • The optimal power allocation approach for this model is still a water filling but with different water levels for each sub-channel • The water level of a sub-carrier licensed to primary user j is now • The threshold constant λ in (16) is part of a non-linear equation and we must rely on numerical methods to determine the threshold constant

15. Suboptimal Schemes for Power Allocation based on Sub-channel Availability • It is both intuitively and mathematically clear that we would achieve better expected capacity by allocating more power to the bands with higher probability of their availability • Scheme 1: Relative Water Levels • Scheme 2: Proportional Water Levels

16. Relative Water Levels • We modify the water level for jth primary user’s band from to • Here κ is a predetermined design parameter • Constraint equation is given as follows • Power allocated for sub-carrier i is hence given by

17. Proportional Water Levels • The water level is given by • ν being a design parameter • The quantity C carries a negative power in denominator to ensure that higher the value of C, more is the difference in water levels • Constraint equation is given as follows • Allocated power to sub-carrier i is therefore given by

18. Simulation Parameters and Assumptions • We consider a system consisting of • Take a rayleigh fading channel with average channel power gain i.e. E{|h|2} equal to 1 • for heavily built-up urban environments • 3 primary users: PU1, PU2 and PU3 • 16 subcarriers • 1 to 8 belong to PU1 with an activity probability: α1 =0.10 • 9 to 12 belong to PU2 with α2 =0.89 • 13 to 16 belong to PU3 with α3 = 0.50 • Total power budget Ptotal =10−5 W • Noise power N0 =10−11W/Hz • A linear rate loss function with normalized cost per unit power C = 3 × 103 bits/s/mW • For scheme 1, κ =4×10−12 • For scheme 2, ν =1.05×106

19. Simulation Results • Average expected • normalized capacities • 4.6216, • 7.2216, • 8.8776, • 9.5848 bits/s

20. Allocated Power and Expected Capacity vs. PU Activity • Capacities become negative. This is because we used a constant value of C to simulate this graph

21. Discussions of the Loss Function • Linear loss function is an approximation for a general loss function though there are several advantages choosing a linear loss function • it reduces the computational burden and simplifies the allocation problem • it also preserves the linearity to the overall expected loss/risk as weighted additive sum of powers • But the effectiveness of the algorithm depends on the optimum choice of C

22. Guidelines to Choose C Value • According to equation (8), optimal solution is valid when C satisfies • Taking the minimum over the left hand side of equation (22), we obtain the following upper bound for C

23. Conclusions • Take into account reliability of available channels which depends on primary user activity • Introduced a risk-return model to incorporate the sub-channel availability by defining an average rate loss function in presence of a primary user • Owing to complex nature of the optimal solution, we suggested two suboptimal schemes and compared their performance with respect to water-filling and optimal schemes