Question

The carrier frequency fc is equal to n/Ts for some fixed integer n.

Where 0≤ t ≤Ts and ES is the symbol energy. The carrier frequency fc is equal to n/Ts for some fixed integer n.

a) Sketch the output possible signals on the signal space.

b) What is the type of the modulation scheme used.

c) Draw DBs and DRs and find the distance between the signals.

d) Calculate the average transmitted energy.

e) Suggest a coherent Rx for this modulation technique.

f) Calculate the average probability of error if the noise is assumed to be AWGN with zero mean and PSD N0/2 Watt/Hz.

g) Compare the probability of error obtained in (f) with the BPSK.

h) Calculate the PSD of this system and compare it with the BPSK.


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Answer #1

Your question appears to be related to a digital modulation scheme, but it lacks specific details about the modulation technique, signal space, and other parameters. To provide a meaningful answer, I'll make some general assumptions about the scenario and provide a guideline on how to approach the various parts of your question:

a) Sketch the output possible signals on the signal space:

  • To sketch the output signals, we need to know the modulation scheme being used (e.g., QPSK, 16-QAM, etc.), the number of symbols, and the constellation points.

b) What is the type of modulation scheme used:

  • Determine the specific modulation scheme. For example, if it's QPSK (Quadrature Phase Shift Keying), 16-QAM (Quadrature Amplitude Modulation), etc.

c) Draw DBs and DRs and find the distance between the signals:

  • In digital modulation schemes, you have signal points in a signal constellation. You can calculate the distance between these points using the Euclidean distance formula. The distance between signals impacts the error probability.

d) Calculate the average transmitted energy:

  • The average transmitted energy depends on the modulation scheme and the symbol energy (ES). For example, for QPSK, it's 2*ES.

e) Suggest a coherent Rx for this modulation technique:

  • Coherent receivers are specific to the modulation scheme. Explain what type of receiver you're looking for based on the modulation scheme.

f) Calculate the average probability of error:

  • The average probability of error (bit error rate or symbol error rate) depends on the modulation scheme, noise characteristics, and the signal-to-noise ratio (SNR). For AWGN channels, this can often be calculated using Q-function or symbol error rate equations specific to the modulation scheme.

g) Compare the probability of error obtained in (f) with BPSK:

  • To compare the error rates, you need to have both the error rate for the modulation scheme in question and BPSK under the same conditions (SNR, noise, etc.).

h) Calculate the PSD of this system and compare it with BPSK:

  • The power spectral density (PSD) depends on the modulation scheme and the bandwidth. You can calculate the PSD based on the given parameters.

To provide a more detailed and accurate response, please specify the modulation scheme, constellation, and other parameters relevant to the scenario you are describing. Different modulation schemes have different characteristics and calculations associated with them.


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