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日期：2021-12-26 10:43

ELEC6217 Wireless Transceiver Design and Implementation

Assignment 2 - Introduction to OFDM and

filtered OFDM

Multicarrier Modulations - Motivation

In broadband wireless communications, signals transmitted over channels experience

frequency-selective fading, which results in strong inter-symbol interference;

When single-carrier based transmission schemes are employed, receiver needs to

implement a powerful equalizer for attaining desirable performance;

However, this kind of equalizer usually has a high-complexity of implementation;

Multicarrier based transmission is capable of efficiently mitigating this problem, and

provides the flexibilities for attaining other benefits;

Multicarrier Modulations - Motivation

In multicarrier (MC) modulation, a transmitted bitstream is divided into many

different substreams, which are sent in parallel over many subchannels;

The parallel subchannels are typically orthogonal under ideal propagation conditions;

The data rate on each of the subcarriers is much lower than the total data rate;

The bandwidth of subchannels is usually much less than the coherence bandwidth

of the wireless channel, so that the subchannels experience flat fading. Thus, the

ISI on each subchannel is small;

MC modulation can be efficiently implemented digitally using the FFT (Fast

Fourier Transform) techniques, yielding the so-called orthogonal frequency division

multiplexing (OFDM);

Multicarrier Modulations - Useful Concepts

Delay spread, Tm: The difference between the time of arrival of the earliest

significant multipath component and the time of arrival of the last multipath

components.

Channel’s coherence bandwidth, Bc: Bc = 1Tm.

Frequency-selective fading: Assume that the bandwidth of transmit signals is

W. Then, if W ≥ Bc, then the transmitted signals experience frequency-selective

fading. However, if W < Bc (usually W << Bc), the transmitted signals experience

frequency non-selective fading.

In the time-domain, if Tm << 1/W , then the transmitted signals experience

frequency non-selective fading. While, if Tm ≥ 1/W , then the transmitted signals

experience frequency-selective fading.

Time-Frequency Properties of Wireless Channels

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Wireless Transceiver Design and Implementation M. El-Hajjar, meh@ecs.soton.ac.uk

OFDM

Orthogonal frequency division multiplexing (OFDM) applies multicarrier modulation

principle, dividing the data stream into several bit streams, each of which has much

lower bit rate, and using these substreams to modulate several carriers.

Consider a linearly modulated system with data rate R and bandwidth B;

The coherence bandwidth of the channel is assumed to be Bc < B, so signals

transmitted over this channel experience frequency-selective fading.

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Wireless Transceiver Design and Implementation M. El-Hajjar, meh@ecs.soton.ac.uk

OFDM

When employing the Multicarrier modulations:

The bandwidth B is broken into N subbands, each of which has a bandwidth

BN = B/N for conveying a data rate RN = R/N ;

Usually, it is designed to make BN << Bc, so that the subchannels experience

(frequency non-selective) flat fading.

What is OFDM good for?

1- Combating fading: in a “parallel” transmission, each symbol in a subcarrier has

a much larger symbol duration, equal to N times of the symbol duration in “serial”

transmission.

In a deep fade, several symbols in the single carrier system can be affected seriously

and lost completely. However, in parallel transmission, each of the N symbols is only

slightly affected and can still be recovered correctly.

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Wireless Transceiver Design and Implementation M. El-Hajjar, meh@ecs.soton.ac.uk

OFDM

2- Combating frequency selective: Channel can be severely frequency selective, but

for each sub-carrier, the sub-channel is flat or at least only slightly frequency selective

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Wireless Transceiver Design and Implementation M. El-Hajjar, meh@ecs.soton.ac.uk

OFDM Transceiver

OFDM transmitter/receiver: Let transmitted frequency frame be [S1, S1, · · · , SN?1]

using N subcarriers and the transmitted time frame be [s1, s1, · · · , sN?1]

From discrete Fourier theory: {sm}N?1m=0 ? {Sn}N?1n=0 .

Cyclic Prefix

If the channel is ideal, at receiver, from N time samples, N frequency samples can

be recovered via FFT.

If the channel is dispersive, say, the CIR length is NhTs, then the transmitted

length of N time symbols will spread to a length of Nh + N , and N frequency

samples is insufficient.

A solution is to add some dummy symbols to make it N +Nh frequency samples

or cyclic extension.

An equivalent and more efficient alternative is to add cyclic extension in a

transmitted time frame as follows: The last Nh time samples is copied back

to the beginning of the frame, and transmitted samples are N +Nh.

Coursework Instructions

In this part of Assignment 2, you are required to understand the concept of OFDM

and explain it briefly in your report.

Also, you are expected to read about filtered OFDM (f-OFDM) used in 5G and write

a summary of your understanding. The following papers are good references for

you to understand the concept of f-OFDM: https://arxiv.org/pdf/1508.07387.pdf

and https://arxiv.org/pdf/1807.10371.pdf.

In your description of f-OFDM, you are expected to explain the basic idea of

f-OFDM and the motivation to use f-OFDM and compare f-OFDM with OFDM.

Finally, you should simulate an OFDM system using BPSK modulation, 64

subcarriers and 4-tap channel impulse response. Here, you are expected to

plot the BER versus SNR for a variable cyclic prefix length and analyse your results.