A review on spectrum sensing for cognitive radio: challenges and solutions <s> Robust Spectrum Sensing <s> With application to radar and data transmission, a game situation is studied where one player selects a suitable receiving filter, and the other a function describing the noise power density under restriction of a fixed total amount of power. The payoff function is a signal to noise ratio. The information the players have about each others' choice defines two extreme situations of practical interest. The fundamental relation of game theory holds for pure strategies. <s> BIB001 </s> A review on spectrum sensing for cognitive radio: challenges and solutions <s> Robust Spectrum Sensing <s> This paper contains a new approach toward a theory of robust estimation; it treats in detail the asymptotic theory of estimating a location parameter for contaminated normal distributions, and exhibits estimators—intermediaries between sample mean and sample median—that are asymptotically most robust (in a sense to be specified) among all translation invariant estimators. For the general background, see Tukey (1960) (p. 448 ff.) <s> BIB002 </s> A review on spectrum sensing for cognitive radio: challenges and solutions <s> Robust Spectrum Sensing <s> The problem of designing robust matched filters for situations in which there is uncertainty in the signal structure or noise statistics is considered. Two general aspects of this problem are treated. First, maximin robust designs are characterized for a general Hilbert-space formulation of the matched filtering problem and explicit solutions are given for two intuitively appealing models for uncertainty. These results are seen to generalize earlier results for specific matched filtering problems. The second general aspect treated is the application of the theoretical maximin results to the particular problem of designing filters to combat uncertain nonlinear channel distortion. Channel distortion is modeled by considering an unknown received signal which may differ in L_{2} -norm from the transmitted or nominal signal by no more than a fixed amount. The effect of the channel distortion is seen to be equivalent to that of adding a white noise to the channel whose spectral height depends on the degree of distortion. General expressions are developed for the determination of the robust filter and its performance, and numerical results are presented for the case of baseband detection in Gauss-Markov noise. <s> BIB003 </s> A review on spectrum sensing for cognitive radio: challenges and solutions <s> Robust Spectrum Sensing <s> In recent years there has been much interest in robustness issues in general and in robust signal processing schemes in particular. Robust schemes are useful in situations where imprecise a priori knowledge of input characteristics makes the sensitivity of performance to deviations from assumed conditions an important factor in the design of good signal processing schemes. In this survey we discuss the minimax approach for the design of robust methods for signal processing. This has proven to be a very useful approach because it leads to constructive procedures for designing robust schemes. Our emphasis is on the contributions which have been made in robust signal processing, although key results of other robust statistical procedures are also considered. Most of the results we survey have been obtained in the past fifteen years, although some interesting earlier ideas for minimax signal processing are also mentioned. This survey is organized into five main parts, which deal separately with robust linear filters for signal estimation, robust linear filters for signal detection and related applications, nonlinear methods for robust signal detection, nonlinear methods for robust estimation, and robust data quantization. The interrelationships among many of these results are also discussed in the survey. <s> BIB004
In many detection applications, the knowledge of signal and/or noise is limited, incomplete, or imprecise. This is especially true in cognitive radio systems, where the primary users usually do not cooperate with the secondary users and as a result the wireless propagation channels between the primary and secondary users are hard to be predicted or estimated. Moreover, intentional or unintentional interference is very common in wireless communications such that the resulting noise distribution becomes unpredictable. Suppose that a detector is designed for specific signal and noise distributions. A pertinent question is then as follows: how sensitive is the performance of the detector to the errors in signal and/or noise distributions? In many situations, the designed detector based on the nominal assumptions may suffer a drastic degradation in performance even with small deviations from the assumptions. Consequently, the searching for robust detection methods has been of great interest in the field of signal processing and many others BIB002  BIB001 BIB003 . A very useful paradigm to design robust detectors is the maxmin approach, which maximizes the worst case detection performance. Among others, two techniques are very useful for robust cognitive radio spectrum sensing: the robust hypothesis testing  and the robust matched filtering BIB001 BIB003 . In the following, we will give a brief overview on them, while for other robust detection techniques, the interested readers may refer to the excellent survey paper BIB004 and references therein.