ECE 442 COMMUNICATION SYSTEM DESIGNLECTURE 3. OFDMHusheng Li

Dept. of EECS

The University of Tennessee

PEAK-TO-AVERAGE POWER RATIO

Peak-to-average power ratio (PAR) is an important attribute of a communication system:

A low PAR allows the transmit power amplifier to operate efficiently.

A high PAR forces the transmit power amplifier to have a large backoff in order to ensure linear amplification of the signal.

PAR is defined as

]|)([|

|)(|max2

2

txE

txPAR

TYPICAL POWER AMPLIFIER RESPONSE

DISTRIBUTION AND MAX OF PAR

When N (the number of subcarriers) is large, the PAR satisfies

The maximum PAR for N subcarriers is N.

There are many approaches to reduce PAR, such as signal clipping, peak cancellation and special coding techniques.

NxexPARp 11)(

FREQUENCY AND TIMING OFFSET

The signal of OFDM is orthogonal when the subcarrier frequency separation is 1/T (T is the duration of a symbol). But what if it is not exactly 1/T?

INTER CARRIER INFERENCE (ICI)

The total ICI power on subcarrier i is given by

where δ/T is the frequency deviation. Properties: The ICI increases with T ICI increases (quadratically) with δ The ICI is not explicitly affected by N.

20

2 )(|| TCIICIim

mi

CASE STUDY IN IEEE 802.11A

IEEE 802.11a is a wireless LAN standard, which occupies 300MHz n the 5GHz unlicensed band.

In 802.11a, N=64. The prefix occupies 16 samples.

There are three coding rates (1/2, 2/3, 3/4) and four modulations (BPSK, QPSK, 16-QAM and 64-QAM).

The 300MHz is divided into 15 channels, each occupying 20MHz.

WHY WANT HOPPING IN OFDM?

Hopping means the same user transmitting over different subcarriers in different times.

In the uplink multi-cell systems, the transmission of a user may experience the inference from other users in neighbors cells.

If hopping is used, the interference will be averaged, thus achieving interference diversity.

In the downlink, the interference diversity comes from the different powers for different users.

HOPPING PATTERN Virtual channel: each virtual channel contains N

subcarriers and N OFDM symbols. It can be assigned to one user

time

frequency

LATIN SQUARE

Each base station has its own hopping pattern which can be represented by a Latin square.

The virtual channels in the previous slide corresponds to the following Latin square:

subcarrier

OFDM symbols

A virtual channel

ORTHOGONAL LATIN SQUARES

For neighboring base stations, the virtual channels should have minimal overlaps.

If two Latin squares have exactly one collisions for every pair of virtual channels, we call them orthogonal.

When N is prime, for a =1,…,N-1, we can define an N by N matrix R(a) with

),mod()( NjaiaRij

FLASH-OFDM

HOMEWORK

Problem1. Write down the justification of the cyclic prefix in OFDM systems.

Problem 2. Find the data rate of an 802.11a system assuming QPSK modulation and rate ¾ coding.

Problem 3. Find the PAR of a raised cosine pulse with β=0., 0.5, and 1. Which pulse shape has the lowest PAR?