# Multi Carrier Modulation and OFDM

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Multi Carrier Modulation and OFDM

Transmission of Data Through Frequency Selective Time Varying Channels
We have seen a wireless channel is characterized by time spread and frequency spread. Time Spread Frequency Spread

Single Carrier Modulation in Flat Fading Channels
if symbol duration >> time spread then there is almost no Inter Symbol Interference (ISI). channel time 1 1 phase still recognizable Problem with this: Low Data Rate!!!

… in the Frequency Domain
this corresponds to Flat Fading channel Frequency Frequency Flat Freq. Response Frequency

Single Carrier Modulation in Frequency Selective Channels
if symbol duration ~ time spread then there is considerable Inter Symbol Interference (ISI). channel time ? ? 1 phase not recognizable

One Solution: we need equalization
channel equalizer time time 1 1 Channel and Equalizer Problems with equalization: it might require training data (thus loss of bandwidth) if blind, it can be expensive in terms computational effort always a problem when the channel is time varying

The Multi Carrier Approach
let symbol duration >> time spread so there is almost no Inter Symbol Interference (ISI); send a block of data using a number of carriers (Multi Carrier) 1 time channel “symbol”

Compare Single Carrier and Multi Carrier Modulation
Frequency channel Block of symbols subcarriers Each subcarrier sees a Flat Fading Channel: Easy Demod MC 1 One symbol Flat Fading Channel: Easy Demod SC

Structure of Multi Carrier Modulation
In MC modulation each “MC symbol” is defined on a time interval and it contains a block of data OFDM Symbol data data data data data guard interval data interval with MAX channel time spread

NO Inter Block Interference!
Guard Time We leave a “guard time” between blocks to allow multipath TX RX Guard Time the “guard time” is long enough, so the multipath in one block does not affect the next block Data Block Data Block data+guard RX TX NO Inter Block Interference!

MC Signal Transmitted Signal: Baseband Complex Signal:

“Orthogonal” Subcarriers and OFDM
guard interval data interval Choose: Orthogonality:

Orthogonality at the Receiver
transient response Transmitted subcarrier Channel (LTI) Received subcarrier steady state response still orthogonal at the receiver!!!

OFDM symbols in discrete time
Let be the sampling frequency; be the number of data samples in each symbol; the subcarriers spacing Then: with the guard time.

Summary OFDM Symbol TIME: FREQUENCY: # samples # subcarriers
Sampling Interval guard data TIME: Freq spacing FREQUENCY: # samples # subcarriers

OFDM Symbol and FFT Where: positive subcarriers negative subcarriers
unused subcarriers

Guard Time with Cyclic Prefix (CP)
CP from the periodicity IFFT{ X } CP

OFDM Demodulator See each block: No Inter Block Interference with

Overall Structure of OFDM Comms System
IFFT +CP P/S FFT -CP S/P

Simple One Gain Equalization
To recover the transmitted signal you need a very simple one gain equalization: transm. noise received channel Use simple Wiener Filter:

OFDM as Parallel Flat Fading Channels
Significance: a Freq. Selective Channel becomes N Flat Fading Channels OFDM Mod OFDM Demod Frequency Selective channel N Flat Fading Channels

Summarize basic OFDM Parameters: sampling rate in Hz
N length of Data Field in number of samples L length of Cyclic Prefix in number of samples total number of Data Subcarriers data time frequency guard

IEEE a: Frequency Bands: GHz and GHz (12 channels) Modulation OFDM Range: 100m IEEE g Frequency Bands: GHz Modulation: OFDM Range: 300m

Channel Parameters: FCC
Example: the Unlicensed Band 5GHz U-NII (Unlicensed National Information Infrastructure) 8 channels in the range GHz 4 channels in the range GHz

Channel Parameters: Example IEEE802.11
In terms of a Transmitter Spectrum Mask (Sec in IEEE Std a-1999) Typical Signal Spectrum Typical BW~16 MHz

In either case: Sampling frequency FFT size Cyclic Prefix DATA CP

Sub-carriers: (48 data + 4 pilots) + (12 nulls) = 64
Frequency Time IFFT Pilots at: -21, -7, 7, 21

Frequencies: Subcarriers index DATA

Time Block:

Overall Implementation (IEEE 802.11a with 16QAM).
1. Map encoded data into blocks of 192 bits and 48 symbols: data Encode Interleave Buffer (192 bits) Map to 16QAM … … 1101 +1+j3 -1+j +3-j3 +1-j 4x48=192 bits

Overall Implementation (IEEE 802.11a with 16QAM).
2. Map each block of 48 symbols into 64 samples time domain frequency domain null +1+j3 -3-j +3-j3 +1-j 24 data 2 pilots null 24 data 2 pilots IFFT

Channel Parameters: Physical
Frequency Spread Time Spread Constraints on OFDM Symbol Duration: roughly!!! to minimize CP overhead for channel Time Invariant

Summary of OFDM and Channel Parameters
Max Time Spread sec Doppler Spread Hz Bandwidth Hz Channel Spacing Hz OFDM (design parameters): Sampling Frequency Cyclic Prefix FFT size (power of 2) Number of Carriers

Example: IEEE802.11a Channel: Max Time Spread Doppler Spread Bandwidth Channel Spacing OFDM (design parameters): Sampling Frequency Cyclic Prefix FFT size (power of 2) Number of Carriers

Applications: various Area Networks
According to the applications, we define three “Area Networks”: Personal Area Network (PAN), for communications within a few meters. This is the typical Bluetooth or Zigbee application between between personal devices such as your cell phone, desktop, earpiece and so on; Local Area Network (LAN), for communications up 300 meters. Access points at the airport, coffee shops, wireless networking at home. Typical standard is IEEE (WiFi) or HyperLan in Europe. It is implemented by access points, but it does not support mobility; Wide Area Network (WAN), for cellular communications, implemented by towers. Mobility is fully supported, so you can move from one cell to the next without interruption. Currently it is implemented by Spread Spectrum Technology via CDMA, CDMA-2000, TD-SCDMA, EDGE and so on. The current technology, 3G, supports voice and data on separate networks. For (not so) future developments, 4G technology will be supporting both data and voice on the same network and the standard IEEE (WiMax) seems to be very likely

More Applications 1. WLAN (Wireless Local Area Network) standards and WiFi. In particular: IEEE a in Europe and North America HiperLAN /2 (High Performance LAN type 2) in Europe and North America MMAC (Mobile Multimedia Access Communication) in Japan 2. WMAN (Wireless Metropolitan Network) and WiMax IEEE 3. Digital Broadcasting Digital Audio and Video Broadcasting (DAB, DVB) in Europe 4. Ultra Wide Band (UWB) Modulation a very large bandwidth for a very short time. 5. Proposed for IEEE (to come) for high mobility communications (cars, trains …)

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