Question

2. Orthogonal frequency division multiplexing (OFDM), where the signal is built in the frequency do- main and then a fast Fourier transform (FFT is taken to get samples of the time domain signal for transmission, is used in a large range of wireless communication standards such as 4G cellular. One drawback of OFDM is that the time domain samples can exhibit large peaks, hence making efficient amplification difficult. Motivated by the Central Limit Theorem (which we will learn later), the time domain samples can be modeled as Gaussian random variables, hence motivating this problem. Power amplifiers saturate at high input voltages. Suppose I have a 20 dB amplifier that has output Y for input X defined by the input-output characteristic: 100, Y-10X, 100, X <-10 -10 3X <10 X210 Suppose that the input X is a Gaussian random variable with mean 0 and variance 36. Find the probability density function fy (y) of the output. (Leibnitz's rule see Wikipedia - might be useful for differentiating the CDF)

Answer 1

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