understanding ofdm by iitg

EC635 Advanced Topics in Communication Systems R. S. Kshetrimayum

A.1 An Introduction to OFDM Topics:

A.1.1 Introduction

A.1.2 Principle of OFDM

A.1.3 Implementation of transreceivers

A.1.1 Introduction One of the main reason to use OFDM is to increase robustness against

frequency-selective fading or narrowband interference In a single-carrier system, a single fade or interferer can cause the entire link

to fail, but in a multi-carrier (MC) system, only a small percentage of the sub-carriers (SCs) will be affected

The difference between the conventional non-overlapping MC technique and overlapping MC technique is: we save almost 50% of the BW in the latter case

To realize this, however, we need to reduce cross-talk between SCs, which

means that we want orthogonality between the different modulated carriers OFDM is a modulation scheme that is especially suited for high-data-rate

transmission in delay-dispersive environments It converts a high data stream into a number of low-rate streams that are

transmitted over parallel, narrowband channels that can be easily equalized OFDM dates back some 40 years; a patent was applied in mid 1960s by Chang

[1966] Climini [1985] was the first to suggest OFDM for wireless communications But it was only in the early 1990s that advances in hardware for DSP made

OFDM a realistic option for wireless systems Currently OFDM is used for DAB, DVB, WLANs (IEEE 802.11a, IEEE

802.11g)

A.1.2 Principle of OFDM OFDM splits the information into N parallel streams which are then

transmitted by modulating N distinct carriers (henceforth called SCs or tones) Symbol duration on each SCs thus becomes larger by a factor of N In order for the receiver to be able to separate signals carried by different SCs,

they have to be orthogonal


The SCs constitute an orthogonal (orthonormal, to be more precise) set Given that the frequencies of the SCs satify fn=nW/N, i=1,2,,N and W is the

total available bandwidth

In most simple case, W=N/T We further assume that modulation SCs is PAM with rectangular basis pulses It follows that the SCs themselves satisfy the conditions of orthonormality

over the symbol period T, as the following series of manipulations of the cross

correlation of the exponential SCs shows

( 2 )1 1( 2 ) ( 2 ( ) )e e e

0 0

1cos( 2 ( ) ) sin( 2 ( ) )

0 0

sin( 2 ( )) 12 ( ) 0

T Tj f tnj f t j f f tk k ndt dtT T

T Tjf f t dt f f t dtk n k nT T

f fk n for all k nf fk n for all k n

pipi pi

pi pi

pi

pi

=

= +

=

= =

Guard interval

Fig. A.1.1 FDMA (Guard interval)


Fig. A.1.2 OFDM (Carrier spacing W/N) In order for the receiver to be able to separate signals carried by different SCs,

FDMA have large freq. spacing between carriers This however wastes precious spectrum

A narrower spacing of SCs can be achieved in OFDM as shown in Fig. A.1.2 Let us assume modulation on each SCs is PAM with rectangular pulse shape

in time domain, the spectrum of each modulated carrier has sinc shape The spectra of different modulated carriers overlap, but each carrier is in the

spectral nulls of all other carriers

Therefore, as long as the receiver does the appropriate demodulation (multiplying by exp (-j2frt) and integrating over symbol duration), the data streams of any SCs will not interfere

A.1.3 Implementation of transreceivers OFDM can be implemented in two ways: one in analog interpretation, as

depicted in Fig. A.1.3 We first split our original data stream into N parallel sub-streams, each of

which has a lower data rate

We furthermore have a number of local oscillators available, each which oscillates at a frequency fn=nW/N, where n=0,1,,N-1

Each of the parallel data streams then modulates one of the carriers


,0kC

,1kC

, 1k NC

0je

2 Wj tNe

pi

( )2 1 Wj N tNe

pi

( )s t

Fig. A.1.3. OFDM transmitter (analog) This picture allows an easy understanding of the principle, but is ill-suited for

actual implementation the hardware effort of multiple local oscillators is too high

OFDM transmitter OFDM receiverH

Channel

s(t) Hs(t)

Fig. A.1.4 Analog OFDM transreceiver

,0kC

,1kC

, 1k NC

0je

2 Wj tNe

pi

( )2 1 Wj N tNe

pi

( )Hs t

Fig. A.1.5 OFDM receiver (analog) An alternative implementation divides the transmit data into blocks of N symbols

This block is subjected to an IFFT and then transmitted This approach is much easier to implement using digital technology In the following, we will show that the two techniques are equivalent

Let us first consider the analog interpretation


Let the complex transmit symbol at time instant i on the nth

carrier be Cn,i The transmit signal is then

1( ) ( ) ( )

,

0

Ns t s t C g t iTi n i ni i n

= =

= ==

where the basis pulse gn

(t) is a normalized frequency shifted rectangular pulse

21 0( )0

tj nTe for t Tg t

n Totherwise

pi

<


The success of OFDM is based on fast digital implementation that allows an implementation of the transreceivers that is much simpler and cheaper

In particular, highly efficient structures exist for the implementation of FFT ( so called butterfly structures, and computational effort (per bit) of performing an FFT increases with log (N)

,0kC

,1kC

, 1k NC

( )s t

(a)

(b) Fig. A.1.5 OFDM (a) transmitter and (b) receiver using IFFT

References: Ahmad R. S. Bahai, B. R. Saltzberg and M. Ergen, Multicarrier Digital

Communications Theory and Applications of OFDM, Springer 2004 R. Prasad, OFDM for Wireless Communication Systems, Artech House, 2004 A. F. Molisch, Wireless Communications, John Wiley & Sons, 2005 A. Goldsmith, Wireless Communications, Cambridge University Press, 2005 http://www.s3.kth.se/signal/grad/OFDM/URSIOFDM9808.htm

data

sink

P/S

,0kC

,1kC

, 1k NC

( )Hs tS/P FFT


Incomplete

understanding ofdm by iitg

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