Simulink Tutorial on Digital Modulation Methods - Cengage Learning
Simulink Tutorial on Digital Modulation Methods - Cengage Learning Simulink Tutorial on Digital Modulation Methods - Cengage Learning
632 CHAPTER 13. SIMULINK TUTORIAL ON DIGITAL MODULATION Problems 13.1 Show that additive white Gaussian noise remains white after sampling if a squareroot raised-cosine receive filter is used. 13.2 BPSK requires estimation of the carrier phase at the receiver. Show analytically what is the effect of a carrier-phase offset ϕ, i.e., demodulation with 2cos(2πfct + ϕ). 13.3 In Section 1.3.2 differential phase-shift keying was introduced as a method to enable detection without carrier-phase estimation. Build a
PROBLEMS 633 filter are limited in time to a duration of 12T. Determine the overall delay of the transmission system. Verify your solution in the respective
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632 CHAPTER 13. SIMULINK TUTORIAL ON DIGITAL MODULATION<br />
Problems<br />
13.1 Show that additive white Gaussian noise remains white after sampling if a squareroot<br />
raised-cosine receive filter is used.<br />
13.2 BPSK requires estimati<strong>on</strong> of the carrier phase at the receiver. Show analytically<br />
what is the effect of a carrier-phase offset ϕ, i.e., demodulati<strong>on</strong> with 2cos(2πfct +<br />
ϕ).<br />
13.3 In Secti<strong>on</strong> 1.3.2 differential phase-shift keying was introduced as a method to<br />
enable detecti<strong>on</strong> without carrier-phase estimati<strong>on</strong>. Build a <str<strong>on</strong>g>Simulink</str<strong>on</strong>g> model for binary<br />
differential phase-shift keying with NRZ rectangular pulses based <strong>on</strong> the BPSK model<br />
in Figure 13.2. Observe if error-free detecti<strong>on</strong> is possible in the case of carrier-phase<br />
offset.<br />
13.4 Derive the effect of a carrier-phase-offset ϕ analytically in a QPSK system.<br />
13.5 Derive the effect of a carrier-frequency-offset ∆f analytically in a QPSK system.<br />
13.6 Another method to avoid diag<strong>on</strong>al transiti<strong>on</strong>s of the trajectory through the origin<br />
is differential π/4-QPSK. The informati<strong>on</strong> is coded in the phase difference of successive<br />
symbols according to<br />
ϕk = ϕk+1 + ∆ϕm<br />
where k is the time index and<br />
∆ϕm = π π<br />
m +<br />
2 4<br />
where m = 0, 1, 2, 3 is the index of the transmit symbol. Show by an example that<br />
every other symbol is taken from a QPSK c<strong>on</strong>stellati<strong>on</strong> that is phase-shifted by π/4<br />
relative to the QPSK c<strong>on</strong>stellati<strong>on</strong> of the previous symbol and therefore, transiti<strong>on</strong>s<br />
through the origin are avoided.<br />
13.7 According to Figure 1.28 we obtain orthog<strong>on</strong>al signal waveforms for FSK if the<br />
frequency separati<strong>on</strong> between the two signal waveforms is a multiple of 1/(2T). What<br />
is the advantage of choosing a frequency separati<strong>on</strong> of 1/(2T)?<br />
13.8 Show that Offset-QPSK with cosine pulses according to (13.8.2) has a c<strong>on</strong>stant<br />
envelope. Assume a delay of T between in-phase and quadrature comp<strong>on</strong>ent as in the<br />
Offset-QPSK representati<strong>on</strong> of MSK.<br />
13.9 Show that for NRZ rectangular pulses, an integrate and dump receiver yields the<br />
same output samples as a rectangular NRZ receive filter, i.e. the matched filter can be<br />
implemented as integrate and dump.<br />
13.10 What is the design criteri<strong>on</strong> for the receive filter which yields the matched filter<br />
soluti<strong>on</strong>?<br />
13.11 Assume a transmissi<strong>on</strong> system with causal square-root raised-cosine pulse shaping<br />
and a matched filter receiver. Both the impulse resp<strong>on</strong>ses of transmit and the receive<br />
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