word (m-gram) which occurred in the sample r times is r* PT = where r We call a procedure of replacing a count r with a modified count r ’ “discounting ” and a ratio rt/r a discount coefficient dr. When r ’ = r*, we have Turing’s discounting. Let us denote the m-gram wl, *.., w, as wy and the number

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A deterministic signal s in zero mean Gauss an se N isoberve through a zero memory nonlinearity f(x). The reconstruction of the sig-nal is considered when the nonlinearity, the noise covariance and the first or second order moments of the output process f[s+N] are known. Arbitrary signals can be reconstructed for monotonic and certain odd, not necessarily monotonic, nonlinearities; included here are hard limiters, quantiiers and infinite interval windows. Arbitrary signals can be re-constructed, up to a global sign, for two distinct classes of even non-linearities; included here are 2v-th law devices and symmetric interval

We are surrounded by electronic devices that take advantage of wireless technologies, from our computer mice, which require little amounts of information, to our cellphones, which demand increasingly higher data rates. Until today, the coexistence of such a variety of services has been guaranteed by a fixed assignment of spectrum resources by regulatory agencies. This has resulted into a blind alley, as current wireless spectrum has become an expensive and a scarce resource. However, recent measurements in dense areas paint a very different picture: there is an actual underutilization of the spectrum by legacy sys-tems. Cognitive radio exhibits a tremendous promise for increasing the spectral efficiency for future wireless systems. Ideally, new secondary users would have a perfect panorama of the spectrum usage, and would opportunistically communicate over the available re-sources without degrading the primary systems. Yet in practice, monitoring the spectrum resources, detecting available resources for opportunistic communication, and transmit-ting over the resources are hard tasks. This thesis addresses the tasks of monitoring, de-

Caractérisation des problèmes conjoints de détection et d'estimation

Abstract not found