A review on spectrum sensing for cognitive radio: challenges and solutions <s> Robust Matched Filtering. <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 Matched Filtering. <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> BIB002 </s> A review on spectrum sensing for cognitive radio: challenges and solutions <s> Robust Matched Filtering. <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> BIB003
We turn the model (4) into a vector form as where s is the signal vector and η is the noise vector. Suppose that s is known. In general, a matched-filtering detection is T MF = g T x. Let the covariance matrix of the noise be R η = E(ηη T ). If R η = σ 2 η I, it is known that choosing g = s is optimal. In general, it is easy to verify that the optimal g to maximize the SNR is In practice, the signal vector s may not be known exactly. For example, s may be only known to be around s 0 with some errors modeled by where Δ is an upper bound on the Euclidean-norm of the error. In this case, we are interested in finding a proper value for g such that the worst-case SNR is maximized, that is, It was proved in BIB001 BIB002 that the optimal solution for the above maxmin problem is where δ is a nonnegative number such that δ 2 g 2 = Δ. It is noted that there are also researches on the robust matched filtering detection when the signal has other types of uncertainty BIB003 . Moreover, if the noise has uncertainties, that is, R η is not known exactly, or both noise and signal have uncertainties, the optimal robust matched-filtering detector was also found for some specific uncertainty models in BIB003 .