Abstract
Standard condition number (SCN) detector is a promising detector that can work efficiently in uncertain environments. In this paper, we consider a Cognitive Radio (CR) system with large number of antennas (eg. Massive MIMO) and we provide an accurate and simple closed form approximation for the SCN distribution using the generalized extreme value (GEV) distribution. The approximation framework is based on the moment-matching method where the expressions of the moments are approximated using bi-variate Taylor expansion and results from random matrix theory. In addition, the performance probabilities and the decision threshold are considered. Since the number of antennas and/or the number of samples used in the sensing process may frequently change, this paper provides simple form decision threshold and performance probabilities offering dynamic and real-time computations. Simulation results show that the provided approximations are tightly matched to relative empirical ones.
Highlights
Cognitive Radio (CR), firstly proposed by Mitola [1], is the technology that provides solution for the scarcity and inefficiency in using the spectrum resource [2]
Several SS techniques were proposed in the last decade [3], Eigenvalue Based Detector (EBD) has been shown to overcome noise uncertainty challenges and performs adequately even in low SNR conditions as it does not need any prior knowledge about the noise power or signal to noise ratio
In [10], the authors have provided an approximated relation between the threshold and the False-Alarm Probability (Pf a) by exploiting the TracyWidom distribution (TW) for the largest eigenvalue while maintaining the Marchenco-Pastur law (MP) law for the smallest one
Summary
Cognitive Radio (CR), firstly proposed by Mitola [1], is the technology that provides solution for the scarcity and inefficiency in using the spectrum resource [2]. We are interested in finding a simple approximation for the SCN detector’s performance probabilities and decision threshold. This allows the system, equipped with tens to hundreds of antennas, to dynamically compute its threshold online according to the instantaneous scenario. For this purpose, we propose to asymptotically approximate the SCN distribution with the Generalized Extreme Value (GEV) distribution by matching the first three central moments. Derivation of an asymptotic approximated form of the central moments of the SCN from that of the extreme eigenvalues. Symbols ∼ stands for "distributed as", E[.] for the expected value and . 2 for the norm
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