Abstract-With an abundance of tools based on kernel methods and information theoretic learning, a void still exists in incorporating both the time structure and the statistical distribution of the time series in the same functional measure. In this paper, a new generalized correlation measure is developed that includes the information of both the distribution and that of the time structure of a stochastic process. It is shown how this measure can be interpreted from a kernel method as well as from an information theoretic learning points of view, demonstrating some relevant properties. To underscore the effectiveness of the new measure, a simple blind equalization problem is considered using a coded signal.Index Terms-Blind equalization, entropy, generalized correlation kernel, information theoretic learning, reproducing kernel Hilbert space (RKHS).
In this letter we study the potential benefits of improper signaling for a secondary user (SU) in underlay cognitive radio networks. We consider a basic yet illustrative scenario in which the primary user (PU) always transmit proper Gaussian signals and has a minimum rate constraint. After parameterizing the SU transmit signal in terms of its power and circularity coefficient (which measures the degree of impropriety), we prove that the SU improves its rate by transmitting improper signals only when the ratio of the squared modulus between the SU-PU interference link and the SU direct link exceeds a given threshold. As a by-product of this analysis, we obtain the optimal circularity coefficient that must be used by the SU depending on its power budget. Some simulation results show that the SU benefits from the transmission of improper signals especially when the PU is not highly loaded.Index Terms-Cognitive radio, interference channel, improper signaling, asymmetric complex signaling.
In this paper, we introduce a kernel recursive least-squares (KRLS) algorithm that is able to track nonlinear, time-varying relationships in data. To this purpose, we first derive the standard KRLS equations from a Bayesian perspective (including a sensible approach to pruning) and then take advantage of this framework to incorporate forgetting in a consistent way, thus enabling the algorithm to perform tracking in nonstationary scenarios. The resulting method is the first kernel adaptive filtering algorithm that includes a forgetting factor in a principled and numerically stable manner. In addition to its tracking ability, it has a number of appealing properties. It is online, requires a fixed amount of memory and computation per time step, incorporates regularization in a natural manner and provides confidence intervals along with each prediction. We include experimental results that support the theory as well as illustrate the efficiency of the proposed algorithm.
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