教育部網路通訊人才培育先導型計畫 Probability, Random Processes and Noise 1 Outline 5.1 Probability Theory 5.2 Random Variables 5.3 Random Processes 5.4 Transmission of a Random Process through a Linear Time-Invariant System 5.5 Noise 5.6 Summary References Problems 5.5

教育部網路通訊人才培育先導型計畫 Probability, Random Processes and Noise 2 Thermal Noise Thermal noise is the noise arising from the random motion of charge carriers in a conducting, or semiconducting, medium. Such random agitation at the atomic levels is a universal characteristic of matter at temperatures other than absolute zero. Although the noise is small, when the noise is amplified by a high-gain receiver (approximate dB before demodulation), it can become a problem. 5.5

教育部網路通訊人才培育先導型計畫 Probability, Random Processes and Noise 3 Thermal Noise A noisy resistor ( ) at a temperature ( T ) can be modeled by an ideal noiseless resistor ( ) at in conjunction with a noise voltage source ( ) as shown If we assume that the resister value is independent of temperature then the value of resistor. 5.5

教育部網路通訊人才培育先導型計畫 Probability, Random Processes and Noise 4 Thermal noise The available power spectral density (PSD) is the maximum actual PSD that can be obtained from a source. Under matched condition (load resister ) and from quantum mechanics, it can be shown that the available PSD is [4] where J-sec is Planck’s constant, J/K is Boltzmann’s constant, is the absolute temperature of the resistor. 5.5

教育部網路通訊人才培育先導型計畫 Probability, Random Processes and Noise 5 Thermal noise At room temperature for frequency bellow 1000 GHz,, so that is a good approximation. Then the above equation reduces to 5.5

教育部網路通訊人才培育先導型計畫 Probability, Random Processes and Noise 6 White noise Consider the noise after amplifiers and before detection, the available PSD without considering the bandpass filter is approximately a constant such as where is the total noise figure of the receiver system, so it can be written generally as Note that the power spectral density is independent of the operating frequency. From the sense that white light contains equal amounts of all frequencies within the visible band, we call the noise as white noise. 5.5

教育部網路通訊人才培育先導型計畫 Probability, Random Processes and Noise 7 White noise The corresponding autocorrelation for white noise is We note that is zero for and each such noise sample has zero mean, these imply that any two different samples of white noise are uncorrelated. 5.5