s 100 kHz and the modulating message is a cosine wave at 1 kHz. (c) Draw the spectrum when the modulation method is SCDSB. (d) Draw the corresponding spectrum of SSB modulation. Problem 4.4 (a) Draw the constellation diagram (or signal space diagram) for an 8-PSK signal SO that the in-phase carrier waveform represents bit combination 000. Write in the diagram which bit combination each signal could represent. Take care that you minimize the bit error rate. (b) Draw the constellation diagram of a 16-QAM signal where a carrier with a 45° phase shift and a high amplitude corresponds to a bit combination of 1100. Write bit combina- tions for each signal SO that the bit error rate is minimized. [Hint: Use Gray code for two bits for columns (I component) and two bits for rows (Q com- ponent) and combine them for each signal in the constellation.] Problem 4.5 Explain how the radio wave propagation modes differ at (a) low-frequency, (b) medium frequency, and (c) and ultra high frequency bands. Introduction to Telecommunications Network Engineering Problem 4.6 Estimate the transmission capacity of an optical fiber that operates over the 0.9- to 1.6-m wavelength range if coherent optical transmission is used. Assume that the speed of light is the same as in space (300,000 km/sec) and the following modulation methods are in use: (a) Voice signal bandwidth is 4 kHz and it is SSB modulated into the fiber. (b) Voice signal is PCM coded and transmitted in a binary form through the cable. Assume that the modu- lation scheme in use is capable of transmitting 1 bps/Hz. Problem 4.7 Derive on your own the formula, L = =[4rfllc]2, step by step for the free-space loss (see Section 4.2.6). Use the formula for the effective aperture area of iso- tropic antenna, Aci = and a spherical surface area A = 4rt over which transmitted power is distributed. Problem 4.8 Show that the equation for radio wave attenuation in decibels, Ldb = 92.4 + 20log10f/GHz +20 log101/km dB,follows from the equation of attenuation L = [4frllc]2. Note that, for exa