Holiday assignment

**Performance of the OFDM technique in a multipath channel. **

Currently, OFDM orthogonal frequency division multiplexing technique is widely used in communication systems. As WiFi is based on the standard LEEE 802.11 standard, WiMax (Worldwide Interoperability for Microwave Access) based on the standard IEEE 802.10, 4G-LTE (Long Term Evolution) and the SG. This success is the consequence of the number of preliminaries offered by the OFDM,

an efficient implementation using Fast Fourier Transform (FFT)

robustness to the effects of multiple paths by using a cyclic prefex (CP)

a spectral efficiency loop allowing the recovery between the spectra of the different sub-carriers.

The objective of this project is to study the OFDM modulation, the impact of the channel selectivity on the performances of this technique.

A conventional transmission system having a carrier frequency F characterized by an emitting stage, a propagation channel block and a receiving stage 1 is considered.

**OFDM transmitter:.**

Answer the questions:

- Identify the necessary blocks for the synthesis of an OFDM signal from a binary whose bit rate and fixed to Db consider that the binary equivalence first undergoes a transcoding in M-QAM ??

- Give the link between the useful life OFDM symbol (Tu) the bit rate (Db) Of the number of bits per symbol of the elementary in Modulation n = log, M and number of subcarriers N??

- Express the width of a sub carrier del f in Function of (Tu)- justify why this relation In sampling period Te,??

- Simulate by Matlab the transmitter OFDM ??

- By switching on all the sub-carriers, enter the speed of the signal and its histogram. Comment on this risky manipulation (visualizations) comment results???

- Draw the signal spectrum in both cases

**OFDM receiver**:

Answer the questions

1) Identify the OFDM demodulation operations to detect the transmitted bit sequence.

2) Simulate by Matlab the OFDM receiver

**Multipath target channel and cyclic prefix**:

Answer the questions:

- With an ideal channel (unit gain and without delay), draw the constellations of the different subcarriers. Comment on result
- Now consider a multipath channel. Plot its frequency response (module and phase).
- Draw the constellation of a given subcarrier before equalization. Comment on the result.
- Add a cyclic prefix. What is its minimum duration? justify
- Explain the impact of this addition on the bit rate.
- What is the effect of cyclic prefix addition? Draw the constellation of the Subcarrier considered in 3 Comment on the result.
- Add an equalization block to recover the constellation emitted
- Generate random multipath channel and plot the bit error rate.

**Deliverables:**

Final report

Matlab program

Final presentation

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