MC OFDM Principles 4up

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Southampton School of ECS, Univ. of Southampton, UK. http://www-mobile.ecs.soton.ac.uk 1/ 49 ⇒|

Principles of Multicarrier Modulation andOFDM a

Lie-Liang Yang

Communications Research GroupFaculty of Physical and Applied Sciences,University of Southampton, SO17 1BJ, UK.

Tel: +44 23 8059 3364, Fax: +44 23 8059 4508

Email: [email protected]

http://www-mobile.ecs.soton.ac.uk

aMain reference: A. Goldsmith, Wireless Communications, Cambridge University Press, 2005.

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MC Modulation and OFDM - Summary

❐ Principles of multicarrier (MC) modulation;

❐ Principles of orthogonal frequency-division multiplexing (OFDM);

❐ Inter-symbol interference (ISI) suppression;

❐ Implementation challenges.

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Multicarrier Modulations - Introduction

❐ In multicarrier (MC) modulation, a transmitted bitstream is divided into manydifferent substreams, which are sent in parallel over many subchannels;

❐ The parallel subchannels are typically orthogonal under ideal propagationconditions;

❐ 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 band-width 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 (FastFourier Transform) techniques, yielding the so-called orthogonal frequency-division multiplexing (OFDM);

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Multicarrier Modulations - ApplicationExamples

❐ Digital audio and video broadcasting in Europe;

❐ Wireless local area networks (WLAN) - IEEE802.11a, g;

❐ Fixed wireless broadband services;

❐ Mobile wireless broadband communications;

❐ Multiband OFDM for ultrawideband (UWB) communications;

❐ A candidate for the next-generation cellular mobilecommunications systems.





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Multicarrier Modulations - Transmitter

×SymbolMapper

R/N bps s0

g(t)

cos(2πf0t)

s0(t)

×

+Serial-to-ParallelConverter

R bps

..........

SymbolMapper

R/N bpsg(t)

×SymbolMapper

R/N bpsg(t)

s1 s1(t)

cos(2πf1t)

sN−1 sN−1(t)

cos(2πfN−1t)

s(t)

Figure 1: Transmitter schematic diagram in general multicarrier modulations.

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Multicarrier Modulations - Principles

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

❐ The coherence bandwidth of the channel is assumed to be Bc < B, sosignals transmitted over this channel experience frequency-selective fading.

When employing the MC modulations:

● the bandwidth B is broken into N subbands, each of which has a bandwidthBN = B/N for conveying a data rate RN = B/N ;

● Usually, it is designed to make BN << Bc, so that the subchannelsexperience (frequency non-selective) flat fading.

● In the time-domain, the symbol duration TN ≈ 1/BN of the modulated signalsis much larger than the delay-spread Tm ≈ 1/Bc of the channel, which henceyields small ISI.

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An example

Consider a MC system with a total passband bandwidth of 1 MHz.Suppose the channel delay-spread is Tm = 20 µs. How manysubchannels are needed to obtain approximately flat fading in eachsubchannel?

● The channel coherence bandwidth isBc = 1/Tm = 1/0.00002 = 50 KHz;

● To ensure flat fading on each subchannel, we takeBN = B/N = 0.1 × Bc << Bc;

● Hence, N = B/(0.1 × Bc) = 1000000/5000 = 200 subcarriers.

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Multicarrier Modulations - TransmittedSignals

s(t) =N−1∑

i=0

sig(t) cos (2πfit + φi) (1)

where

✔ si: complex data symbol (QAM, PSK, etc.) transmitted on the ithsubcarrier;

✔ φi: phase offset of the ith subcarrier;

✔ fi = f0 + i(BN): central frequency of the ith subcarrier;

✔ g(t): waveform-shaping pulse, such as raised cosine pulse.





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0 T

Amplitude

Time

Figure 2: Illustration of multicarrier modulated signals.

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Multicarrier Modulations - Receiver

to-SerialConverter

Parallel-

f0

s0(t) + n0(t)Demodulator

cos(2πf0t)

R/N bps

..........

DemodulatorR/N bps

DemodulatorR/N bps

f1

fN−1

s1(t) + n1(t)

cos(2πf1t)

cos(2πfN−1t)

sN−1(t) + nN−1(t)

R bps

s(t) + n(t)

Figure 3: Receiver schematic diagram in general multicarrier modulations.

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Overlapping MC

f4 f5 f6 f7f3f2f1f0

The set of orthogonal subcarrier frequencies, f0, f1, . . . , fN−1 satisfy:

1

TN

∫ TN

0

cos(2πfit + φi) cos(2πfjt + φj)dt =

0.5, if i = j

0, else(2)

The total system bandwidth required is:

B ≈ N/TN (3)

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Overlapping MC - Detection❐ Without considering the fading and noise, the received MC signal can be

expressed as

r(t) =

N−1∑

i=0

sig(t) cos (2πfit + φi) (4)

❐ Assuming that the detector knows {φi}, then, sj can be detected as

sj =

∫ TN

0

r(t)g(t) cos (2πfjt + φj) dt

=

∫ TN

0

(N−1∑

i=0

sig(t) cos (2πfit + φi))g(t) cos (2πfjt + φj) dt

=

N−1∑

i=0

si

∫ TN

0

g2(t) cos (2πfit + φi) cos (2πfjt + φj) dt

=N−1∑

i=0

siδ(i − j) = sj , j = 0, 1, . . . , N − 1 (5)





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Fading Mitigation Techniques in MCModulation

❐ Coding with interleaving over time and frequency to exploit thefrequency diversity provided by the subchannels experiencingdifferent fading;

❐ Frequency-domain equalization: When the received SNR isα2iPi, the receiver processes it as α2

iPi/α2i ≈ Pi to reduce the

fading;

❐ Precoding: If the transmitter knows that the channel fading gainis αi, it transmits the signals using power Pi/α

2i , so that the

received power is Pi;

❐ Adaptive loading: Mitigating the channel fading by adaptivelyvarying the data rate and power assigned to each subchannelaccording to its fading gain.

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Implementation of MC Modulation UsingDFT/IDFT

❐ Let x[n], 0 ≤ n ≤ N − 1, denote a discrete time sequence. TheN -point discrete Fourier transform (DFT) of {x[n]} is defined as

X[i] =DFT{x[n]}

,1√N

N−1∑

n=0

x[n] exp

(

−j2πni

N

)

, 0 ≤ i ≤ N − 1 (6)

❐ Correspondingly, given {X[i]}, the sequence {x[n]} can berecovered by the inverse DFT (IDFT) defined as

x[n] =IDFT{X[i]}

,1√N

N−1∑

i=0

X[i] exp

(j2πni

N

)

, 0 ≤ n ≤ N − 1 (7)

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Implementation of MC Modulation UsingDFT/IDFT

❐ When an input data stream {x[n]} is sent through a linear time-invariantdiscrete-time channel having the channel impulse response (CIR) {h[n]}, theoutput {y[n]} is given by the discrete-time convolution of the input and theCIR, expressed as

y[n] = h[n] ∗ x[n] = x[n] ∗ h[n] =∑

k

h(k)x[n − k] (8)

❐ Circular Convolution: when {x[n]} is a N -length periodic sequence, then theN -point circular convolution of {x[n]} and {h[n]} is defined as

y[n] = h[n] ~ x[n] = x[n] ~ h[n] =∑

k

h(k)x[n − k]N (9)

❐ which has the property

DFT{y[n] = h[n] ~ x[n]} = X[i]H[i], i = 0, 1, . . . , N − 1 (10)

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Implementation of MC Modulation: CyclicPrefix

Cyclic Prefix Original Length N Sequence

Append Last µ Symbols to Beginning

x[N − µ], x[N − µ + 1], ..., x[N − 1] x[0], x[1], ..., x[N − µ − 1] x[N − µ], x[N − µ + 1], ..., x[N − 1]

Figure 4: Cyclic prefix of length µ.

❐ The original N -length data block is x[n] : x[0], . . . , x[N − 1];

❐ The µ-length cyclic prefix block is x[N − µ], . . . , x[N − 1], whichis constituted by the last µ symbols of the data block {x[n]};

❐ The actually transmitted data block is length N + µ, which is

x[n] : x[N − µ], . . . , x[N − 1], x[0], x[1], . . . , x[N − 1]





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Implementation of MC Modulation: CyclicPrefix

❐ Then, when {x[n]} is input to a discrete-time channel having the CIRh[n] : h[0], . . . , h[µ], the channel outputs are

y[n] =x[n] ∗ h[n] =

µ∑

k=0

h[k]x[n − k] =

µ∑

k=0

h[k]x[n − k]N

=x[n] ~ h[n], n = 0, 1, . . . , N − 1 (11)

❐ Therefore,

Y [i] = DFT{y[n] = x[n] ~ h[n]} = X[i]H[i], i = 0, 1, . . . , N − 1 (12)

❐ When {Y [i]} and {H[i]} are given, the transmitted sequence can berecovered as

x[n] = IDFT

{

X[i] =Y [i]

H[i]

}

= IDFT

{DFT{y[n]}DFT{h[n]}

}

, n = 0, 1, . . . , N − 1 (13)

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OFDM Using Cyclic Prefixing - An Example

❐ Consider an OFDM system with total bandwidth B = 1 MHz andusing N = 128 subcarriers, 16QAM modulation, and length µ = 8

of cyclic prefix.

Then

● The subchannel bandwidth is BN = B/128 = 7.812 kHz;

● The symbol duration on each subchannel isTN = 1/BN = 128 µs;

● The total transmission time of each OFDM block isT = TN + 8/B = 136 µs;

● The overhead due to the cyclic prefix is 8/128 = 6.25%;

● The total data rate is128 × log2 16 × 1/(T = 136 × 10−6) = 3.76 Mbps.

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OFDM - System Structure

CP removing

P/S

S/P

IDFT

DFT

Transmitter

processing

processing

Receiver

Signal shaping

Matched-filtering

Channel

CP

XXX

N

xxx

N

yyy

NN

g(t)

g∗(−t)

YYY

Figure 5: Schematic block diagram of the transmitter/receiver for OFDM sys-tems using IDFT/DFT assisted multicarrier modulation/demodulation and cyclic-prefixing (CP).

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OFDM - Transmitter

Serial-to-ParallelConverter

X[N − 1]

Add CyclicPrefix, andParallel-to-SerialConverter

x[0]X[0]

X[1] x[1]

x[N − 1]

×QAM

Modulation

XR bps

D/A s(t)

cos(2πf0t)

x(t)IFFT

Figure 6: Transmitter of OFDM with IFFT/FFT implementation.





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OFDM - Receiver

R bps Prefix, and

Converter

Converter

cos(2πf0t)

× r(t)LPFand A/D

y[n]

Remove

Serial-to-Parallel

y[0]

y[1]

y[N − 1]

FFT

Y [1]

Y [N − 1]

Y [0]

Parallel-to-Serial

YQAMDemod

Figure 7: Receiver of OFDM with IFFT/FFT implementation.

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OFDM - Transmitted Signal

● Let the N data symbols (thought as in the frequency-domain) tobe transmitted on the N subcarriers within a DFT period is givenby

XXX = [X0, X1, . . . , XN−1]T (14)

● After the IDFT on XXX, it generates N time-domain coefficientsexpressed as

xn =1√N

N−1∑

m=0

Xm exp

(

j2πmn

N

)

, n = 0, 1, . . . , N − 1 (15)

● Let FFF be a fast Fourier transform (FFT) matrix given by the nextslide. Then, we can express xxx = [x0, x1, . . . , xN−1]

T as

xxx = FFFHXXX (16)

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FFT/IFFT Matrices

● FFT matrix:

FFF =1√N

1 1 1 · · · 1

1 WN W 2N · · · WN−1

N...

......

. . ....

1 WN−1N W

2(N−1)N · · · W

(N−1)2

N

(17)

where WN = e−j2π/N ;

● IFFT matrix is given by FFFH ;

● Main Properties: FFFHFFF = FFFFFFH = IIIN .

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OFDM - Transmitted Signal

● After adding the cyclic-prefix (CP) of length µ, xxx is modified to xxx

of length N + µ;

● The normalized transmitted base-band OFDM signal is formedas

s(t) =

N+µ−1∑

n=0

xng (t − nTψ) (18)

where

✔ g (t): time-domain pulse defined in [0, Tψ), which isnormalized to satisfy

∫ Tψ0

g2 (t) dt = Tψ;

✔ Tψ: chip-duration and Tψ ≈ 1/B.





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OFDM - Representation of Received Signals

❐ When the OFDM signal of (18) is transmitted over afrequency-selective fading channel with the CIR hn, 0 ≤ n ≤ µ

as well as Gaussian noise, the discrete-time receivedobservation samples in correspondence to x0, x1, . . . , xN−1 aregiven by

yn = xn ∗ hn + vn, n = 0, 1, . . . , N − 1 (19)

❐ Let yyy = [y0, y1, · · · , yN−1]T . Then, it can be shown that yyy can be

expressed as

yyy = HHHxxx + vvv (20)

❐ Here, it is very important to represent the matrix HHH.

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OFDM - Representation of ReceivedSignals (Linear Convalution)

x−µ · · · x−1 x0 x1 x2 x3 x4 · · ·× · · · × × × × × × · · ·

∑hµ · · · h1 h0 0 · · ·

∑0 hµ · · · h1 h0 0 · · ·

∑0 0 hµ · · · h1 h0 0 · · ·

∑0 0 0 hµ · · · h1 h0 0 · · ·

∑0 0 0 0 hµ · · · h1 h0 0 · · ·

+ + + + + · · ·v0 v1 v2 v3 v4 · · ·= = = = = · · ·y0 y1 y2 y3 y4 · · ·

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OFDM - Representation of ReceivedSignals (Another Way)

x−µ · · · x−1 x0 x1 x2 x3 x4 · · ·

h0 h0x0 h0x1 h0x2 h0x3 h0x4 · · ·h1 h1x−1 h1x0 h1x1 h1x2 h1x3 · · ·...

......

......

.... . .

hµ hµx−µ hµx−µ+1 hµx−µ+2 hµx−µ+3 hµx−µ+4 · · ·∑ ∑ ∑ ∑ ∑

· · ·+v0 +v1 +v2 +v3 +v4 · · ·= = = = = · · ·y0 y1 y2 y3 y4 · · ·

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From the previous slide, we can see that

y0

y1

...

yn

...

yN−1

=

hµx−µ + hµ−1x−µ+1 + · · · + h0x0 + v0

hµx−µ+1 + hµ−1x−µ+2 + · · · + h1x0 + h0x1 + v1

...

hµxn−µ + hµ−1xn−µ+1 + · · · + h1xn−1 + h0xn + vn

...

hµxN−µ−1 + hµ−1xN−µ + · · · + h1xN−2 + h0xN−1 + vN−1

(21)





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OFDM - Representation of Received SignalsWhen expressed in matrix form, (21) is

y0

y1

...

yN−1

︸︷︷︸

yyy

=

hµ hµ−1 · · · h0 0 · · · 0 0 · · · 0

0 hµ hµ−1 · · · h0 · · · 0 0 · · · 0...

......

. . ....

. . ....

.... . .

...

0 0 0 · · · 0 · · · hµ hµ−1 · · · h0

︸︷︷︸

HHH

x−µ

...

x−1

x0

...

xN−1

︸︷︷︸

xxx

+

v0

v1

...

vN−1

︸︷︷︸

vvv

(22)

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Therefore, we have

HHH =

hµ hµ−1 · · · h0 0 · · · 0 0 · · · 0

0 hµ hµ−1 · · · h0 · · · 0 0 · · · 0...

......

. . ....

. . ....

.... . .

...

0 0 0 · · · 0 · · · hµ hµ−1 · · · h0

(23)

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OFDM - Representation of Received Signals● In (22), if CP is used and set as x−i = xN−i, i = 1, . . . , µ, then, (22) can be

represented as

y0

y1

...

yN−1

︸︷︷︸

yyy

=

h0 0 · · · 0 · · · 0 · · · h2 h1

h1 h0 · · · 0 · · · 0. . .

......

......

. . ....

. . . 0 · · · 0 hµ

hµ hµ−1 · · · h0 · · · 0 0 · · · 0...

.... . .

.... . .

......

. . ....

0 0 · · · 0 · · · h0 0 · · · 0...

.... . .

.... . .

.... . .

......

0 0 · · · 0 · · · hµ−1 · · · h0 0

0 0 · · · 0 · · · hµ · · · h1 h0

︸︷︷︸

HHH

x0

x1

...

xN−1

︸︷︷︸

xxx

+

v0

v1

...

vN−1

︸︷︷︸

vvv

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HHH =

h0 0 · · · 0 · · · 0 · · · h2 h1

h1 h0 · · · 0 · · · 0. . .

......

......

. . ....

. . . 0 · · · 0 hµ

hµ hµ−1 · · · h0 · · · 0 0 · · · 0...

.... . .

.... . .

......

. . ....

0 0 · · · 0 · · · h0 0 · · · 0...

.... . .

.... . .

.... . .

......

0 0 · · · 0 · · · hµ−1 · · · h0 0

0 0 · · · 0 · · · hµ · · · h1 h0

(25)





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An Example

❐ Let we assume xxx = [x0, x1, x2, x3]T and µ = 2.

❐ Then, we have

HHH =

h2 h1 h0 0 0 0

0 h2 h1 h0 0 0

0 0 h2 h1 h0 0

0 0 0 h2 h1 h0

, HHH =

h0 0 h2 h1

h1 h0 0 h2

h2 h1 h0 0

0 h2 h1 h0

(26)

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OFDM - Signal Detection❐ In (24), HHH is a circulant channel matrix, which can be decomposed into

HHH = FFFHΛΛΛFFF , where ΛΛΛ = diag{λ0, λ1, · · · , λN−1} is a (N ×N) diagonal matrix.

❐ Using xxx = FFFHXXX of (16), we can re-write (24) as

yyy = HHHFFFXXX + vvv = FFFHΛΛΛFFFFFFH︸︷︷︸

=IIIN

XXX + vvv = FFFHΛΛΛXXX + vvv (27)

❐ Carrying out the FFT on yyy gives

YYY = FFFyyy = FFFFFFH︸︷︷︸

=IIIN

ΛΛΛXXX +FFFvvv = ΛΛΛXXX + vvv′ (28)

❐ Therefore, for n = 0, 1, . . . , N − 1,

Yn = λnXn + v′n (29)

based on which {Xn} can be detected.

❐ Explicitly, there is no ISI.

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OFDM - Peak-to-Average Power Ratio

❐ The peak-to-average power ratio (PAPR) is an importantattribute of a communication system;

❐ A low PAPR allows the transmit power amplifier to operateefficiently, whereas a high PAPR forces the transmit poweramplifier to have a large backoff in order to ensure linearamplification of the signal;

❐ A high PAPR requires high resolution for the receiver A/Dconverter, since the dynamic range of the signal is much largerfor high-PAPR signals.

❐ High-resolution A/D conversion places a complexity and powerburden on the receiver front end.

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0 T

Amplitude

Time

Figure 8: Illustration of multicarrier modulated signals.





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OFDM - Peak-to-Average Power Ratio

❐ The PAPR of a continuous-time signal is given by

PAPR ,maxt{|x(t)|2}

Et [|x(t)|2](30)

❐ The PAPR of a discrete-time signal is given by

PAPR ,maxn{|x[n]|2}

En [|x[n]|2](31)

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OFDM - Peak-to-Average Power Ratio❐ In OFDM, the transmitted signal is given by

x[n] =1√N

N−1∑

i=0

X[i] exp

(j2πni

N

)

, 0 ≤ n ≤ N − 1 (32)

❐ Given E[|X[i]|2

]= 1, the average power of x[n] is given by

En

[|x[n]|2

]=

1

N

N−1∑

i=0

E[|X[i]|2

]= 1 (33)

❐ The maximum value occurs when all X[i]’s add coherently, yields

maxn

{|x[n]|2} = max

∣∣∣∣∣

1√N

N−1∑

i=0

X[i]

∣∣∣∣∣

2

=

∣∣∣∣

N√N

∣∣∣∣

2

= N (34)

❐ Therefore, in OFDM systems using N subcarriers, PAPR = N , whichlinearly increases with the number of subcarriers.

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OFDM - Techniques for PAPR Mitigation

❐ Clipping: clip the parts of the signals that are outside theallowed region;

❐ Coding: PAPR reduction can be achieved using coding at thetransmitter to reduce the occurrence probability of the samephase of the N signals;

❐ Peak cancellation with a complementary signal;

❐ · · ·

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OFDM - Frequency and Time Offset

f4 f5 f6 f7f3f2f1f0

Figure 9: Spectrum of the OFDM signal, where the subcarrier signals are orthog-onal to each other.





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❐ OFDM modulation encodes the data symbol {Xi} ontoorthogonal subcarriers, where orthogonality is assumed by thesubcarrier separation ∆f = 1/TN ;

❐ In practice, the frequency separation of subcarriers is imperfectand so ∆f is not exactly equal to 1/TN ;

❐ This is generally caused by mismatched oscillators, Dopplerfrequency shifts, or timing synchronization, etc.;

❐ Consequently, frequency offset generates inter-carrierinterference (ICI).

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❐ Let us assume that the signal transmitted on subcarrier i is

xi(t) = ej2πit/TN (35)

where the data symbol and the main carrier frequency are suppressed;

❐ An ideal signal transmitted on subcarrier (i + m) would by xi+m(t). However,due to the frequency offset of δ/TN , this signal becomes

xi+m(t) = ej2π(i+m+δ)t/TN (36)

❐ Then, the interference imposed by subcarrier (i + m) on subcarrier i is

Im =

∫ TN

0

xi(t)x∗i+m(t)dt =

TN

(1 − e−j2π(δ+m)

)

j2π(δ + m)(37)

❐ Explicitly, when δ = 0, Im = 0.

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❐ It can be shown that the total ICI power on subcarrier i is givenby

ICIi =∑

m6=i

|Im|2 ≈ C0(TNδ)2 (38)

where C0 is a certain constant.

❐ Observations

✔ As TN increases, the subcarriers become narrower andhence more closely spaced, which then results in more ICI;

✔ As predicted, the ICI increases as the frequency offset δ

increases;

✔ The ICI is not directly related to N , but larger N results inlarger TN and, hence, more ICI.

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❐ The effects from timing offset are generally less than those fromthe frequency offset, as long as a full N -sample OFDM symbolis used at the receiver without interference from the previous orsubsequent OFDM symbols;

❐ It can be shown that the ICI power on subcarrier i due to areceiver timing offset τ can be approximated as 2(τ/TN)2;

❐ Since usually τ << TN , the effect from timing offset is typicallynegligible.





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IEEE802.11 Wireless LAN Standard

❐ IEEE802.11a: Bandwidth= 300 MHz, operated in the 5 GHzunlicensed band;

❐ IEEE802.11g: Virtually identical to the IEEE802.11a, butoperated in the 2.4 GHz unlicensed band.

❐ Main Parameters:

✓ 300 MHz bandwidth is divided into 20 MHz channels that canbe assigned to different users;

✓ N = 64, µ = 16 samples;

✓ Convolutional code with one of three possible rates:r = 1/2, 2/3 or 3/4;

✓ Adaptive modulation based on the modulation schemes:BPSK, QPSK, 16-QAM and 64-QAM.

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OFDM - Summary● No interference exists among the transmitted symbols;

● It is a transmission scheme achieving the highest spectral-efficiency;

● No diversity gain is achievable in frequency-selective fading channels;

● Sensitive to the frequency offset and timing jitter;

● The transmitted OFDM signals have a high dynamic range, resulting in thehigh PAPR;

● The high PAPR requires that the OFDM transmitter has a high linear rangefor signal amplification. Otherwise, the OFDM signals conflict non-lineardistortion, which results in out-of-band emissions and co-channelinterference, causing significant degradation of the system’s performance;

● The high PAPR has more harmful effect on the uplink communications thanon the downlink communications, due to the power limit of mobile terminals;

● When OFDM is used for uplink communications, the high PAPR maygenerate severe inter-cell interference in cellular communications.

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Single-Carrier Frequency-DivisionMultiple-Access

❐ In order to take the advantages of multicarrier communicationswhereas circumventing simultaneously the high PAPR problem,the single-carrier frequency-division multiple-access (SC-FDMA)scheme has been proposed for supporting high-speed uplinkcommunications;

❐ In principle, the SC-FDMA can be viewed as a DFT-spreadmulticarrier CDMA scheme, where time-domain data symbolsare transformed to frequency-domain by a DFT before carryingout the multicarrier modulation;

❐ SC-FDMA is also capable of achieving certain diversity gain,when communicating over frequency-selective fading channels.

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SC-FDMA - Transmitter

mappingSubcarrier

(FFT)DFT IDFT

(IFFT)AddCP

Low-passfilter

{xk0, . . . , xk(N−1)}

s(t){Xk0, . . . , Xk(U−1)} {xk0, . . . , xk(U−1)}

T-domain F-domain T-domain

{Xk0, . . . , Xk(N−1)}

Figure 10: Transmitter schematic for the kth user supported by the SC-FDMAuplink.





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SC-FDMA - Receiver

Subcarrier F-domainprocessingdemapping CP filter

T-domain

Matched-RemoveDFT(FFT)

{Y0, . . . , Y(U−1)} {y0, . . . , y(U−1)}{Yk0, . . . , Yk(N−1)}

T-domain

IDFT(IFFT)

{xk0, . . . , xk(N−1)}

F-domainr(t)

Figure 11: Receiver schematic for the kth user supported by the SC-FDMA uplink.


Documents

MC OFDM Principles 4up