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2 Theory work
2.1 White sequence，Gaussian random variable and vectors
Definition: A real random variable X is said to be Gaussian, or normal, if all its valuesbelong to R and its characteristic fiinction has the expression: Where m is a real parameter and cr is a positive parameter. If cr ：？^： 0，it can be shown that theprobability distribution has a probability density ftmction with the egression: The above equation is the PSD expression for the process X(t).In general the PSD of the continuous-time random process X(t) can be obtained fromthe PSD of the random process sampled at (n) and vice-versa after some manipulations.
2.2 Sampling a WSS process
A signal is a function of independent variables such as time, distance, position andtemperature that is used to convey some important information. Examples of signals arespeech，music, picture and video signals. Signals can be generated naturally or syntheticallyby computer simulations, from a single source (scalar) or multiple sources (vector). It can beeither a real or complex-valued function characterized by the number of independentvariables. For example a one dimensional signal (1-D) that is a function of a singleindependent variable, 2-D, 3-D or Multi-Dimensional (M-D) signals. An analog signal is acontinuous-time signal with continuous amplitude while a digital signal is a discrete-timesignal with discrete-valued amplitudes represented by a finite number of digits. A signal canalso be classified by the certainty by which it can be uniquely described for example adeterministic signal or random signal.A deterministic signal is one that can be uniquely determined by a well-definedprocess (for example mathematical) while a random signal is one that cannot be predicted ahead of time. Signal processing is therefore involved with the mathematical representation ofthe signal and the algorithmic operation carried out on it in order to extract the vitalinformation being conveyed. The functional dependence of a signal in its mathematicalrepresentation is in most cases shown, for example for a continuous 1-D signal; thecontinuous independent variable is usually denoted by t and that of a discrete independentvariable by n, X(t) and X(n) respectively. Each member X(n) is called a sample. Figure2.1 shows the block diagram representation of digital signal processing.
3 Btind sensing energy detection ........19
3.1 EDI energy detector.......... 19
3.2 ED2 energy detector ...........20
4 Simulations and anatysls ............24
4.1 Introduction ...........24
4.2 EDI and ED2 simulation parameter settings .............25
4.2.1 Scenario one ..............25
5 Conclusion and prospects............ 48
5.1 Conclusion ............ 48
5.2 Prospects.............. 49
4 Simulations and analysis
4.1 Introduction
This chapter deals with the simulation of the energy detectors in two differentfrequency (IkHz) and (lOGHz). The two energy detect
