Wireless OFDM

ECE-S306: Introduction to Modulation & Coding

11/30/2010

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Outline

• Introduction

• The wireless channel

• What is OFDM?

• Cyclic prefix

• Coding

• Summary and example

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Wireless Technology

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What Drives Wireless?

Wireless

Cellular

Indoor WLAN

RadioTV

Satellite Comm.

We strive for ubiquitous connectivity:• Started with cell phones• Now, portable Internet access• 4G in the near future

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Enablers for Wireless

• New spectrum made available

• Standardization effort

• Advances in wireless technology OFDM well-suited for wireless channel

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OFDM: A Key Wireless Technology

*Source: IEEE 6

The Wireless Channel

• Introduction

• The wireless channel

• What is OFDM?

• Cyclic prefix

• Coding

• Summary and example

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Multipath Fading

• Constructive and destructive combination of electromagnetic waves at the receiver

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Multipath Fading

Phase Difference Equal to a Multiple of 3600

Waves Reinforce Each Other

Waves Arrive Out of Phase

Weak Signal

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Multipath Reflections

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Multipath Reflections

Delay spread is the difference in the propagation delays along the two paths

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What do Wireless Signals Experience?

• Large fluctuations in strength (fading) due to constructive and destructive interference of multipath echoes

• Delay spreads leading to intersymbol interference (ISI)

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Naive Approaches to These Impairments

• In a wireless network, fading can be overcome by increasing transmitted power:o Very inefficient

o Generates interferences to other users

• ISI can be overcome by slowing down the rate of transmissiono Again, inefficient

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Signal Fluctuations

• Multipath fading has the effect of large fluctuations in the signal strength over distance, time, and frequency.

• E.g. Distance: A displacement of ½ wavelength roughly corresponds to a peak-to-valley change in the signal strength. For 2 GHz, the displacement is 15 cm

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Frequency ResponseDelay spread: Extent of the signal spread in time due to multipath.

Frequency Selectivity: Frequency components of the signals separated by more than approximately 1/delay spread will experience the wireless channel differently. A change in frequency of ~ 1/delay spread will cause peaks to turn into valleys and vice versa.

Question: How can we exploit these variations in the channel frequency response to design techniques to mitigate against multipath fading?

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Diversity ConceptA communication link is severely degraded by fading:

• An exponential decrease in the probability of error with a given SNR over an unfadedchannel becomes 1/SNR relation in the faded channel

Diversity is the mechanism of transmitting the signals that are subject to independent fading, thereby increasing link reliability

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How do Various Signaling Methods Address These Issues?

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Signal for Wireless Networks

• Two fundamental approaches Narrow band signals: bandwidth < 1/delay spreadWide band signals: bandwidth > 1/delay spread

• Able to harness the inherent frequency diversity of the channel

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Wideband Signals

• CDMA and OFDM use different mechanisms to transmit effectively over a wireless channel

• OFDM, in conjunction with coding, takes advantage of the inherent frequency selectivity of the wireless channel to overcome fading and ISI

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What is OFDM?

• Introduction

• The wireless channel

• What is OFDM?

• Cyclic prefix

• Coding

• Summary and example

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Sinusoids are a Natural Choice for Signaling

• They pass undistorted through a multipath fading channel modeled as a linear filter:o Amplitude and phase may vary with fading

o Frequency remains unchanged

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OFDM Concepts

• Orthogonal Frequency Division Multiplexing (OFDM)

• Modulate and transmit multiple carrierso Referred to as OFDM subcarriers

• To avoid generating multiple subcarriers, exploit Discrete Fourier Transform (DFT)

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Multiple Carriers

• Split a high-rate data stream into parallel streams• Transmit each digital symbol on a different carrier

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Some Mathematics

• The transmitted signal as a sum of N carriers modulated by the symbols x(k) (digital symbols such as PSK or QAM)

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• Choose the subcarrier frequencies fk and the signal duration T such that each carrier completes an integer number of cycles:

• When subcarriers are sampled N times in each interval T, the samples represent the Inverse Discrete Fourier Transform (IDFT) of the modulator carriers.

FFT and OFDM

• High-rate data stream can be de-multiplexed into parallel streams that are processed through an IDFT, and hence efficiently implemented as an IFFT

• OFDM symbol is the block of samples resulting from the IFFT operation

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Assembling OFDM Data

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• Input data PSK/QAM symbols at rate N/T• OFDM symbols transmitted at rate 1/T• OFDM samples transmitted at rate N/T• Compare single carrier vs. OFDM:

Single carrier: N symbols transmitted serially, duration of each T/N OFDM: N symbols transmitted in parallel, duration of each T

OFDM Receiver

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• Signal is coherently demodulated• Sampled at rate N/T• Passed to DFT to convert back to frequency domain• Complex numbers Dk represent PSK/QAM symbols

FFT as Sampling Device

• The FFT at OFDM receiver acts as a sample device in the frequency domain.

• The spacing of 1/T between carriers ensures that by sampling at the peak of each subcarrier, the other cross zero and do not interfere.

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OFDM vs. FDM

• FDM: o Carriers frequencies are separated such that signal

spectra do not overlap

o ‘Guard’ intervals between spectra

o Low spectral efficiency

• OFDM:o Signal separation at receiver is achieved through

signal processing rather than filtering

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What is OFDM?

• Introduction

• The wireless channel

• What is OFDM?

• Cyclic prefix

• Coding

• Summary and example

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Handle ISI: Guard Time

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• For the same throughput, OFDM symbols have N times longer duration than single carrier symbols.• Guard time is introduced to eliminate ISI

Inter-Carrier Interference

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• Subcarrier 2 does not exist during the full integration time• Orthogonality is lost , Inter-carrier interference degrades performance• Duration of cyclic prefix has to be longer than the expected delay spread

Cyclic Prefix

• To maintain orthogonalitybetween subcarriers

• Cyclic prefix: the data symbol is extended in the front such that the new transmitted symbol is as shown.

• By designing the OFDM symbol such that the cyclic prefix is approx. 20% of its duration, the loss in SNR is only -1dB.

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What is OFDM?

• Introduction

• The wireless channel

• What is OFDM?

• Cyclic prefix

• Coding

• Summary and example

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Coded OFDM - Overview

• Channel coding is the operation of introducing controlled redundancy in the data in order to increase the reliability of transmission.

• Codes are classified according to:o Rate = number of coded bits /

number of information bits

o Type = convolutional codes are widely applied in OFDM systems

• A convolutional code is obtained by passing the information sequence through a near finite-state shift register.

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Example: Rate ½ for 802.11

Why Use Channel Codes?

Two mechanisms:

• Coding gain

• Diversity gain

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Coding gain: for the same SNR, the probability of confusing between sequences (coded) is smaller than between single symbols (uncoded)

Diversity Gain in OFDM

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• Fading events in adjacent carriers are likely to be correlated. • Interleaving is an operation in which consecutive symbols are transmitted over non-adjacent frequency subcarriers.

What is OFDM?

• Introduction

• The wireless channel

• What is OFDM?

• Cyclic prefix

• Coding

• Summary and example

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Summary

Wireless OFDM:

• Signals transmitted over the wireless channel experience multipathleading to: fading and intersymbol interference.

• The OFDM signal consists of multiple symbols transmitted in parallel and implemented by FFT processing.

• The guard time is designed to protect OFDM symbols from the effects of ISI.

• To maintain orthogonality between carriers and avoid intercarrierinterference, the guard time is filled with the cyclic prefix.

• The cyclic prefix is obtained by taking a number of the last samples of the OFDM symbol and inserting them in the front.

• Coding and interleaving are used to extract channel diversity to mitigate the fading problem.

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OFDM Transceiver

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Example: 802.11 a,g

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Design a system with the following requirements:• Bit rate: 54 Mb/s• Bandwidth: 20 MHz• Tolerable delay spread: 200 ns

Example: 802.11 a,g (Part 1)

• Choose the OFDM symbol duration 5 times the guard time. Then the overhead loss due to guard time is:

10log10(4/5) ~ -1 dB.

• We have symbol time:

Ts = 5 * 800 ns = 4 us

• FFT integration time:

T = Ts – Tguard = 3.2 us

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802.11 a,g (Part 2)

• FFT integration time:

T = Ts – Tguard = 3.2 us

• Carrier spacing = 1/T = 0.3125 MHz

• For 54 Mb/s, each OFDM symbol needs to carry:

54 Mb/s * 4 us = 216 bits

• Take into account coding rate ¾:

216 * 4/3 = 288 bits

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802.11 a,g (Part 3)

• Target BW is 20 MHz, the number of subcarriers is:

20 MHz / 0.3125 MHz = 64 Subcarriers

• The number of subcarriers carrying signals: 48 (the rest are pilots or carry no symbols). The number of bits per subcarrier:

288 bits / 48 subcarriers = 6 bits / subcarrier

Use 64 QAM

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References

• Haimovich, A. “Wireless OFDM.” IEEE E-Learning.

(http://ieee-elearning.org/)

• Pandharipande, A. “Principle of OFDM.” IEEExplore. (http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=00997971)

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