Abstract
In this paper, a cognitive radio system in which the secondary user (SU) is powered by energy harvested exclusively from environment is considered. The SU operates in a timeslotted mode and uses a timeslot in turn for energy harvesting, spectrum sensing and data transmission. In order to optimize the SU’s expected achievable throughput, strategy for energy harvesting and spectrum sensing should be carefully designed to tackle the tradeoff among the three. Such a problem leads to a parametrized optimal stopping problem, i.e., a mash-up of static and dynamic optimization problems in which save-ratio for energy harvesting is fixed (as a static variable parameter) while spectrum sensing runs in a channel-by-channel manner based on sensing results (as an optimal stopping problem). We propose an efficient algorithm to derive the optimal save-ratio and spectrum sensing rule, which is significantly faster than conventional simulated annealing algorithm. To further reduce the computational complexity, we also propose a suboptimal solution with an alternative optimization problem, where save-ratio and number of channels to be sensed are both static variables to be optimized. The alternative problem is formulated as a mixed-integer non-linear programming (MINLP) problem and closed-form solution is derived with in-depth analysis. We show that the proposed suboptimal solution is close in performance to the optimal one and outperforms a baseline strategy, which decouples optimization for energy harvesting and spectrum sensing by combining two existing techniques.
Notes
Energy harvesting rate amount of energy harvested within a unit time (e.g., one second). P = p(1 − P f ) because it happens only when a channel is actually unoccupied and no false alarm happens
Strictly speaking, we focus greedy strategy since transition of channel gain from one timeslot to another is difficult to be characterized (e.g., Markov model with a precise transition matrix). Even transition of channel gain can be precisely characterized, discretization for state and action space inevitably leads to suboptimality as well.
The false alarm probability and detection probability are not separately discussed (the two have deterministic relationship for spectrum sensing with energy detection [33]) because the optimal spectrum sensing rule as well as the optimal save-ratio is directly related to the probability of capturing an available channel rather than either of the two.
A higher N c captures more intervals and only increase complexity of the first iteration. We set N c = 20 in the experiments.
We select average running time as the performance metric instead of average number of iterations due to the inherent difference between the two algorithms.
The experiment result shows that for the SA algorithm, even rigorous parameters (e.g., cooling rate up to 0.99) cannot 100% guarantee convergence to the global optimum. On the contrary, the proposed PLOC algorithm unexceptionally converges to the global optimum with less rigorous parameters.
Here the probability of false alarm P f is implicitly considered constant for each channel because the it depends solely on T s according to [33], which is a constant system parameter.
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Acknowledgements
The research was supported in part by grants from the National Natural Science Foundation of China (NO. 61471057, 61771064).
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Zhao, Z., Yin, S., Li, L. et al. Optimal-Stopping Spectrum Sensing in Energy Harvesting Cognitive Radio Systems. J Sign Process Syst 90, 807–825 (2018). https://doi.org/10.1007/s11265-018-1342-2
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DOI: https://doi.org/10.1007/s11265-018-1342-2