In this study, a new spectrum sensing method for cognitive radio (CR) is proposed for primary user (PU) signals which are modelled as random with unknown power. It is also assumed that, being dynamic, the PU might exhibit multiple status changes in the channel within the sensing period. As a novel approach for detecting dynamic and randomly modelled PUs, we propose a cumulative sum based weighted energy detector (CuS-WED) that only utilizes the samples between the last status change point (LSCP) of the PU and the end of the sensing period contrary to using all the observed data samples in the sensing period. It is shown that the proposed sensing strategy provides noticeable performance improvement in detecting dynamic and randomly modelled PUs. Probability of detection performance of the proposed sensing scheme is investigated for strictly one, at most two, and at most three status changes of the PU. Based on simulation results, it is concluded that the proposed method performs better than the other existing techniques, especially for low probability of false alarm values.

In this paper, a boundary analysis is carried out for the derivative of driving point impedance functions, which is mainly used for synthesis of networks containing RL, RC and RLC circuits. It is known that driving point impedance function, Z(s), is an analytic function defined on the right half of the s-plane. In this study, we derive inequalities for the modulus of derivative of driving point impedance function, |Z'(0)|, by assuming the Z(s) function is also analytic at the boundary point s = 0 on the imaginary axis and the sharpness of these inequalities is proved. Furthermore, an equation for the driving point impedance function, Z(s), is obtained as a natural result of the proved theorem in this study.

In this paper, the relation between Schwarz-Pick lemma and driving point impedance function is investigated. Schwarz-Pick lemma is given as the generalized version of Schwarz lemma. Here, a generic driving point impedance function is obtained by applying Schwarz-Pick lemma to positive real functions. At first, a novel inequality is obtained for the modulus of the derivative of the driving point impedance function and in the next step, an extremal function is found by applying sharpness analysis to this inequality. At the end, obtained extremal function is considered as a generic driving point impedance function and corresponding circuit schematics are presented with their spectral analyses. Obtained driving point impedance function is not an arbitrary function but it is the intuitive result of the considered problem in this study. Accordingly, it is guaranteed to obtain a practically realizable driving point impedance function. Also, novel upper bounds are determined for the magnitude of driving point impedance function and for its derivative.