1. Chance Constrained Robust Energy Efficiency in Cognitive Radio Networks with Channel Uncertainty Yongjun Xu and Xiaohui Zhao College of Communication Engineering, Jilin University In this poster, we propose a novel method for chance constrained robust power control problem in cognitive radio networks. Considering channel uncertainties, the proposed method aims to minimize total transmit power of secondary users under chance constraints on interference temperature and signal to interference plus noise ratio. Without making distributional assumption, based on optimal probability theory, we convert the chance constraints into the deterministic forms under given mean and covariance matrix of distribution, and reformulate the problem into a second order cone programming, which is solved by interior point methods. In addition, a robust approach is proposed to estimate the mean and covariance matrix. Simulation results verify the performance improvement of the proposed method as compared to robust method based on the worst case constraints and the known probabilistic distribution, respectively. We introduce a new approach for robust power control problem in underlay cognitive radio network under probabilistic interference temperature and SINR constraints. The problem can be efficiently solved by the proposed approach based on optimal probability theory and second order cone constraints under the unknown distribution information. The presented approach can minimize total transmission power of secondary users and the interference power at PU-Receiver is strictly below the predefined threshold. Simulation results demonstrate the effectiveness of the proposed approach. The Lagrangian function is With the partial derivative and we have Substituting (6), (7) into (3), together with we have The probability SINR constraint (1b) can be also obtained by this transformation. Thus, problem (1) can be converted into the second order cone programming form as Since the exact statistical information about mean and covariance may be difficult to obtain, we need to consider the estimation error in those parameters. We assume that and are unknown but bounded variables. They follows the set where and denote the estimation values. Similarly, real mean is obtained by Lagrange dual method, namely, According to Cauchy-Schwarz inequality, we have Therefore, the upper bound of covariance estimation error is Combing with (12) and (14), the robust interference temperature constraint with parametric estimation is Similarly, the robust SINR constraint can be expressed as Therefore, we get the equivalent optimization problem as If the convex optimization problem (16) is feasible, the robust power control solution can be obtained by the interior point method. The optimization objective is to minimize total power consumption of SUs in CR network subject to interference temperature constraint and SINR constraint. Considering channel uncertainty between SUs and PUs together with channel uncertainty among SUs, robust optimization problem under probability constraints is Let denote channel gain between SUs and PUs. It has the mean and covariance matrix. Let us define the outage set as. From (1a), the outage probability of interference temperature is Based on optimal probability theory, the upper bound of the outage probability is where denotes the minimum distance decided by the size of uncertainty. The exact is obtained by the following optimization problem With explosive growth in wireless application, there has been increasing demand for radio spectrum. Since traditional fixed spectrum allocation policy leads to spectrum underutilization, cognitive radio (CR) as an opportunistic spectrum access technology has emerged to exploit unused frequency bands by adaptively adjusting transmission parameters (e.g., transmit power, modulation types). There are many sources of uncertainty in communication system such as channel estimation errors, delays in feedback channel, and mobility, etc. Since acquiring accurate channel information is challenging in practice, the design of robust power control algorithm for CR system is an essential problem for reliable communication. Most of the existing robust resource allocation with probability constraints focus on throughput maximization and robust beamformer, few works consider energy efficiency. Moreover, the schemes are proposed on the basis of the assumption of well known distribution information of uncertain parameter. However, it is unavailable in practice due to random nature of wireless channel. Background Abstract Methods Conclusions We illustrate the performance of the proposed algorithm and the performance of comparison with the non-robust method, the worst case method, and the probability method based on Gaussian distribution. We assume there are three secondary users and two primary users in the CR network. The estimated channel gain among secondary users is randomly chosen from (0,1). The maximum transmission power of each SU-transmitter is 1 W. Each point in the following figures is an average of 5000 independent channel realizations. The main results is from Fig.1 to Fig. 4. Results Fig. 1. Total power consumption versus estimation error Fig. 2. The actual satisfaction probability versus SINR target Fig. 3. Total transmission power versus SINR target under different methods Fig. 4. Total transmission power versus estimation error under different methods