Calculate: (a) (i) The overall noise temperature of the receiver (ii) The overall noise factor (iii) The overall noise figure in dB (iv) The system noise temperature 40 marks (b) If the receiver equivalent noise bandwidth is 65 MHz, and the signal to strength at the antenna connection to the RF band pass filter is 7pW (710−12W), calculate the signal to noise ratio in dB at the receiver output to the demodulator. 10 marks Tasks i. Write a computer simulation to calculate the waveforms at points A, B, C, D, E, F, G, H, I on the modulator/demodulator block diagrams (Figure 1) and print or plot these one beneath the other in their correct time relationship. Ensure that they are labelled unambiguously with the appropriate letter. In the case of the integrator outputs (H and I) the instantaneous waveforms are required. These will resemble figure 2.8 in Study Book 1. NB: You may not use a commercial simulation package, or a MATLAB toolbox. ii. Use a Fast Fourier Transform (FFT) algorithm to calculate the print or plot the frequency spectrum of the repeated transmitted modulated carrier E. Use as many repetitions of the waveform as possible. Question 1 Random variable R is Rayleigh distributed if 2 2 R X Y = + , where 2 X N : (0, ) σ and 2 Y N : (0, ) σ are independent normal random variables. Derive theoretically the probability density function (PDF) and cumulative density function (CDF) of the Rayleigh distribution as well as its amplitude, and plot the figures in MATLAB. Question 2 If a channel is not changing with time, it does not fade and instead remains at some particular level. Separate instances of the channel in this case will be uncorrelated with one another, owing to the assumption that each of the scattered components fades independently. Once relative motion is introduced between any of the transmitter, receiver, and scatterers, the fading becomes correlated and varying in time. The normalised autocorrelation function of a Rayleigh faded channel with motion at a constant velocity is a zeroth-order Bessel function of the first kind: ( ) (2 ) R J f o d τ = π τ at delay τ when the maximum doppler shift is d f . The Jakes model is a well-known and popularly used channel model in simulating a Rayleigh fading channel. The Jakes model has the following characteristics: ● approximate the Rayleigh fading process by summing a set of complex sinusoids; ● the sinusoids are weighted so as to produce an accurate approximation of desired channel Doppler spectrum; © University of Southern Queensland Assessments 9 ● Jakes shows that the theoretical Doppler spectrum for the isotropic scattering mobile radio channel can be well approximated by a summation of relatively small number of sinusoids with frequencies and relative phases of the sinusoids set according to a specific formulation. Write a MATLAB program to simulate a wireless channel based upon the Jakes model with Doppler shifts of 10 Hz, 100 Hz, and 1000 Hz. You should plot the amplitude of the wireless fading and compare with the theoretical results in Question 1. Comment on the comparison.