#### Communications

1. The available bandwidth for FM radio is 88 - 108 MHz. When each channel is allocated a bandwidth of 200 kHz, what is the maximum number of channels that are available assuming the bands are adjacent with no guard bands?

9. Consider an 1800 MHz mobile radio system for cellular communication. The base station is at a height of 3 m above the ground and the mobile at 1 m. The gain of the base station antenna is 6 dBi and for the mobile antenna, the gain is 2 dBi. It is required to determine the minimum transmitted power in order for the BS to serve a mobile at a distance of 1000 m in a Line-of-sight communication link. The received power is -104 dBm.

10. The channel bandwidth allocated for a communication link is 300 MHz. If the signalto-noise ratio is 10, what will be the channel capacity?

To do this project: • Download and open the maatlab file e4123f20p05angleModd.mlx (e4123f20p05angleModd.mlx)

Problem 1. (12 points) A random variable X takes on the value +1 exactly 3/8 of the time, -1, exactly 1/8 of the time and can take on any values in the interval [-3 to 3] uniformly the rest of the time. a) Sketch the probability density function (PDF) of X. fx(x) b) Sketch the CDF (cumulative distribution function) of X, Fx (x) c) Calculate the mean value of X, that is E(x) d) Calculate the probability X> +1.

Problem 2 (24 points). The information signal m(t) = 0.5cos(2000xt) is to be AM L-C modulated. Specifically, AM(t)= [1+3m(t)] cos(et), where the carrier frequency is 3 MHz. Hint, think about what you did in your computer simulation of AM LC. a. Determine the modulation index. b. Determine the total power of the modulated signal, z(t) c. Sketch the spectrum of z(t) including amplitudes. d. If you demodulated z(t) with an envelope detector, carefully sketch the output of the detector. e. What is the percentage of the total power in the information-carrying portion of the signal AM(1)? f. If you demodulated the signal AM(t) coherently, carefully sketch the output of the demodulator.

This contains total of 10 questions. 1. A modulating signal m(t)-Scos(2x10 t) is amplitude modulated with a carrier signal c(t)=20cos(2mx10° t). Find the frequency of the modulating signal, frequency of carrier signal and the modulation index.

Problem 1. (12 points) A random variable X takes on the value +1 exactly 3/8 time, -1, exactly 1/8 of the time and can take on any values in the interval [-3 to 3] uniformly the rest of the time. a) Sketch the probability density function (PDF) of X. f(x) d) Calculate the probability X> +1.

3. The amplitude modulated signal is, s(t)=15[1+0.65 cos(4x10²t)] cos(8mx10't). Find the frequency of modulating signal, carrier frequency, amplitude of carrier signal, modulation index and amplitude of modulating signal.

2. If the resistance is 50, modulation index is 0.35 and a carrier signal c(t)=70 cos(2x10⁰ t). Find the carrier power, and the power required for transmitting the amplitude modulated wave.