OFDM for LTE

• Introduction
• Analogy
• Multi-carrier FDM or OFDM
• Orthogonality of subcarriers
• OFDM a special case of FDM
• OFDM Basics
• OFDM Blocks
• FFT/IFFT Basics
• Fading Effect on OFDM
• OFDM Cyclic Prefix, CP
• OFDM Synchronization
• Frequency Offset OFDM
Synchronization
• Clock Offset OFDM
Synchronization
• Advantages of OFDM
• Dis-advantage of OFDM
• OFDM Properties
• OFDM for LTE
• FDD/TDD Sub-Frame
Structure
• Reference
OFDM for LTE

Introduction
 Orthogonal Frequency Division Multiplexing, special case of
FDM.
 It is combination of modulation and multiplexing.
 Multiplexing applied to independent signals, sub-set of one main
signal.
 Signal split into independent channels, modulated by data and re-
multiplexed to create OFDM carrier.
 Less sensitive to frequency selective fading.

Introduction
 OFDM has been adopted in
 Wi-Fi with standards 802.11a, 802.11n.
 Cellular telecommunications with standard LTE / LTE-A,WiMAX
and many more.
 Number of broadcast standards from DAB Digital Radio to Digital
Video Broadcast standards, DVB.
 Other broadcast systems as well including Digital Radio Mondiale
used for the long medium and short wave bands.
 More complicated than earlier forms of signal format.
 Advantageous in terms of high data rates with relatively wide
bandwidths.

Analogy
 1. FDM channel-water flow from tap, water in one big stream .
 Obstruction over faucet hole stops complete water flow.
 OFDM signal- shower, lot of little streams.
 Obstruction stops only one small hole in shower.
 2.Two options for shipment goods via a truck.
 A big truck
 Many smaller trucks.
 Both carry same data but accident damages only 1/4 of data.

Multi-carrier FDM or OFDM
 Four smaller trucks analogous to sub-carriers in an OFDM
system.
 Must be orthogonal for this idea to work.
 The independent sub-channels can be multiplexed by :
 frequency division multiplexing (FDM), multicarrier transmission
 or
 code division multiplexing (CDM), multi-code transmission.

Orthogonality of subcarriers
 The main concept in OFDM is orthogonality of the sub-carriers.
 Sine/cosine wave carriers have area under one period zero.
 Sine wave of frequency m is multiply by sinusoid of frequency n, (m
and n integers).
 The integral or the area under this product is given by
 f ( t ) = sin mwt ×sin nwt
 = 1
2 cos(m − n) − 1
2 cos(m + n)
 Both components being sinusoid, integral is zero over one period.
 ∫0
2π 1
2 cos(m − n)ωt − ∫0
2π 1
2 cos(m + n)ωt = 0 − 0

Orthogonality of subcarriers
 The area under a sine wave multiplied by its own harmonic is
always zero.
 For all integers n and m, sin mx, cos mx, cos nx, sin nx are all
orthogonal to each other.
 These frequencies are called harmonics.
 Orthogonality allows simultaneous transmission on a lot of sub-
carriers in a tight frequency space without interference from each
other.
 Similar to CDMA, where orthogonal codes are used to make data
sequences independent.

OFDM a special case of FDM
 Bandwidth a to b subdivide into four equal spaces.
 Frequencies a and b, and carrier center frequencies (integer or
non-integer) bear no relationship in FDM.
 But if for any n, cn = n ×c1
 c2, c3, c4 are harmonic to c1, hence orthogonal.
 Carriers when added together, do not interfere with each other.
 In FDM,
 It is necessary to receive signal and sidebands to successfully
demodulate data.
 Signals must be spaced so receiver can separate them using a filter.
 There must be a guard band between them for adjacent channel
interference protection.
a
b
c1
c2 c3 c4

OFDM a special case of FDM
 In OFDM
 Carriers orthogonal to each another.
 Overlapping sidebands can still be received without interference.
 Achieved by having carrier spacing equal to reciprocal of the symbol
period.
 Whole number of cycles in the symbol period.
 Their contribution will sum to zero.
 There is no interference contribution.
 OFDM transmitting and receiving systems must be linear.
 Non-linearity causes interference between carriers.
 Inter-modulation distortion introduces unwanted signals causing
interference and impairs orthogonality .
a
b
c1
c2 c3 c4

OFDM Basics
 OFDM has N carriers, from 16 to 1024 depending on the system
environment.
 Example: ODFM signal using 4 sub-carriers.
 The signal has a
 symbol rate of 1
 sampling frequency is 1 sample per symbol,
 so each transition is a bit.
 First few bits are 1, 1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1, -1, 1, -1, -
1, -1, 1,…
 Writing bits in rows of fours (serial to parallel conversion).

OFDM Basics
 Each column has bits carried by one sub-carrier.
 Information rate per carrier is 1/4 symbol per second.
 Nyquist rate will be is 1/2 Hz.
 Let sampling rate is 1 Hz.
 Let modulation scheme is BPSK.
 Carrier 1 to transmit 1, 1, 1 -1, -1, -1 using BPSK carrier of
frequency 1 Hz.
c1 c2 c3 c4
1 1 -1 -1
1 1 1 -1
1 -1 -1 -1
-1 1 -1 -1
-1 1 1 -1
-1 -1 1 1

OFDM Basics
 Carrier 2 is of frequency 2 Hz.
 It is the next orthogonal/harmonic to frequency of the first
carrier of 1 Hz.
 Bits in the second column, 1, 1, -1, 1, 1, -1 modulate this
carrier.
c1 c2 c3 c4
1 1 -1 -1
1 1 1 -1
1 -1 -1 -1
-1 1 -1 -1
-1 1 1 -1
-1 -1 1 1

OFDM Basics
 Carrier 3 frequency is 3 Hz and fourth is 4 Hz.
 Third carrier is modulated with -1, 1, -1, -1, 1, 1.
 Fourth carrier is modulated with -1, -1, -1, -1, -1, 1
c1 c2 c3 c4
1 1 -1 -1
1 1 1 -1
1 -1 -1 -1
-1 1 -1 -1
-1 1 1 -1
-1 -1 1 1

OFDM Basics
 All bits modulated using four independent carriers of orthogonal
frequencies 1 to 4 Hz.
 Bit stream taken, distributed one bit at a time to four sub-
carriers. OFDM signal in time and frequency domain.
c1 c2 c3 c4
1 1 -1 -1
1 1 1 -1
1 -1 -1 -1
-1 1 -1 -1
-1 1 1 -1
-1 -1 1 1
c1
c4
c2
c3

OFDM Basics
 All four modulated carriers added to create OFDM signal.
 The generated OFDM signal.

 Equation for inverse FFT
 c ( t ) = ∑mn ( t )sin(2πnt) from n=1 to N
 Time domain and frequency domain view of a signal:
FFT/IFFT Basics
Time DomainView Frequency DomainView

 FFT converts a random signal into a frequency domain signal.
 Inverse FFT converts spectrum back to time domain signal.
 The two processes are a linear pair.
 Using both in sequence will give the original result back.
 Time domain signal comes out as a spectrum from FFT and IFFT.
FFT/IFFT Basics

 A frequency domain signal comes out as a time domain signal
from IFFT.
 The pair return back the original input.
FFT/IFFT Basics

 The pair return back the input no matter what it is.
 The pair is commutable so they can be reversed and they will
still return the original input.
FFT/IFFT Basics

 Considering original example:
 Each row spectrum has only 4 frequencies 1, 2, 3 and 4 Hz .
 Each spectrums converted to produce a time -domain signal.
 Does what an IFFT does.
 But input is a time domain signal disguising as a spectrum.
OFDM Basics
c1 c2 c3 c4
1 1 -1 -1
1 1 1 -1
1 -1 -1 -1
-1 1 -1 -1
-1 1 1 -1
-1 -1 1 1
1.5
1
0.5
0
-1 1 2 3 4
-1
-2
Amplitude
Frequency
1.5
1
0.5
0
-1 1 2 3 4
-1
-2
Amplitude Frequency
1.5
1
0.5
0
-1 1 2 3 4
-1
-2
Amplitude
Frequency
1.5
1
0.5
0
-1 1 2 3 4
-1
-2
Amplitude
Frequency
Spectrum 1 Spectrum 2
Spectrum 3 Spectrum 4

 The incoming block of bits can be seen as a four bin spectrum.
 The IFFT converts this “spectrum” to a time domain OFDM signal
for one symbol, which actually has four bits in it.
 IFFT computes time-domain signal instead of having to do it one
carrier at time and then adding.
 FFT and IFFT are linear processes and completely reversible, it can
be called a FFT instead of a IFFT.
 The functional block diagram of OFDM link:
OFDM Basics

 If path from transmitter to receiver has reflections or
obstructions, fading results.
 Copy of original signal reaches receiver from different routes.
 Each ray has slightly different delay and gain.
 Time delays result in phase shifts which added to main signal
causes signal degradation.
Fading Effect on OFDM

 In fading, gains in the signal either strength or deep fades.
 Deep fade means signal is nearly wiped out.
 Maximum time delay occurring is called delay spread of signal in that
environment.
 Delay spread can be less than symbol time or larger.
 At some frequencies in the band, channel faces deep fades.
 Called frequency selective fading as occurs at selected frequencies.
 Rayleigh fading has no direct component and all reflected
components.
 Flat fading has delay spread less than one symbol.
 Frequency-selective fading has delay spread much larger than one
symbol.
Іα0І Іα1І
ІαkІ
Δ1
Δ0 Δk

 OFDM signal offers advantage in channel that has frequency
selective fading response.
 Only two sub-carriers are affected, all others are perfectly OK.
 Instead of whole symbol, we lose small subset of (1/N) bits.
 With proper coding, this can be recovered.
Fading
Effect on
OFDM

 The BER performance of OFDM signal in fading channel is
much better than performance of single carrier wideband signal
QPSK/FDM.
 Underlying BER of OFDM signal is same as underlying
modulation in Gaussian channel.
 But in fading channels, OFDM offers far better BER than wide
band signal of same modulation.
 Advantage coming from diversity of multi-carrier as fading
applies only to a small subset.

OFDM Cyclic Prefix, CP
 Key element for OFDM reliability.
 CP acts as buffer region or guard interval between each OFDM
symbol to avoid inter-symbol interference.
 Important even with much lower data rates transmitted in
multicarrier OFDM signal.
 Each OFDM symbol is preceded by copy of end part of that same
symbol.
 Different OFDM cyclic prefix lengths are available in various
systems.
 LTE has normal length and extended length.
 Release 8 has third extended length, although not normally used.

CP Advantages and Dis-advantages
 Advantages
 Provides robustness: Addition of CP adds robustness to
OFDM signal.
 Data that is retransmitted can be used if required.
 Reduces inter-symbol interference: Guard interval
introduced by CP reduces effects of inter-symbol
interference.
 Disadvantages
 Reduces data capacity: As the cyclic prefix re-transmits
data that is already being transmitted, it takes up system
capacity and reduces the overall data rate.

CP mitigates Delay Spread
 Delay spread is like undesired splash from car ahead during rains.
 In fading, front symbol similarly throws a splash backwards.
 Can avoid splash if distance between cars increases.
 The reach of splash is same as the delay spread of a signal.
 Splashes become noise and affect beginning of next symbol.
 The delayed, attenuated signal and composite interference:-
Delayed splash from front symbol
Symbol 1 Symbol 2

CP mitigates Delay Spread
 To mitigate this noise at front of symbol, move symbol away from
region of delay spread.
 Blank space added between symbols to catch delay spread.
 But can not have blank spaces in signals.
 Remedy is to let the symbol run longer.
 Extend symbol into empty space, so symbol is more than one
cycle.
 Front of symbol, important for detecting phase of symbol, still in
danger zone.
 Remedy: slide symbol backwards: symbol-start lands outside this
zone.

CP mitigates Delay Spread- Method
 Slide symbol to start at edge of delay spread time.
 Fill guard space with copy of tail end of the symbol.
 Extended symbol is 1.25 times longer.
Symbol 1 Symbol 2
Portion
added in the
front
Original symbol Original symbolExtension
Copy this
part at front

Adding CP to OFDM
 Cyclic prefix is this superfluous bit of signal added to front of
symbol.
 OFDM, having lot of carriers, theoretically, adds CP to each and
every carrier.
 OFDM, a linear combination, cyclic prefix added just once to
composite OFDM signal.
 The prefix is anywhere from 10% to 25% of the symbol time.

Adding CP to OFDM
 Example: OFDM signal with period equal to 32 samples.Add
25% cyclic shift to this signal.
 First we cut pieces that are 32 samples long.
 Then we take the last 0.25* (32) = 8 samples, copy and append
them to the front as shown.

Adding CP to OFDM
 Prefix added after doing the IFFT just once to composite signal.
 At receiver, first this prefix is removed to get back perfectly
periodic signal.
 FFT done to get back the symbols on each carrier.
 However, addition of cyclic prefix increases the bandwidth.
 Final blocks for OFDM:

OFDM Synchronization
 OFDM advantages of resilience to fading and reflections with high
level of spectrum efficiency possible if OFDM synchronization is
effective.
 Effective OFDM synchronization enables data error rates at
minimum.
 Areas where OFDM synchronisation is critical to operation of the
system:
 OFDM synchronization in terms of frequency offset: It is
necessary that frequencies are accurately tracked to ensure OFDM
orthogonality.
 OFDM synchronisation in terms of clock accuracy: It is
necessary that sampling occurs at the correct time interval to
ensure that samples are synchronized and data errors are
minimised.

Frequency Offset OFDM Synchronization
 Demodulator in OFDM receiver must synchronize with OFDM
carriers.
 Offsets may arise due to:
 Frequency errors between transmitter and receiver.
 Doppler shifts if movement between transmitter and receiver.
 Impaired frequency synchronisation results in reduced carrier
orthogonality.
 Error rates increase.
 Orthogonality necessary to reduce errors and maintain
performance of the link.

Frequency Offset OFDM Synchronization
 With demodulator in synchronisation, all contributions from
other carriers sum to zero. (Fig 1)
 All carriers are orthogonal and error rate is at its minimum.
 Poor frequency synchronisation results in samples away from
signal peak. (Fig 2)
 Contributions from other signals do not sum to zero.
 Lead to signal degradation and increase in number of bit errors.
Fig 1 Fig 2

Clock Offset OFDM Synchronization
 It is also necessary to maintain OFDM synchronization in terms
of clock.
 Otherwise, offset sampling, reduced orthogonality and increase
data errors will occur.
 If receiver clock rate differs from transmitter, even if first carrier
within multiplex is correct, there will be a growing discrepancy
with each carrier away from first one.
 Even small levels of discrepancy will cause error rate to increase.

 Immunity to selective fading: More resistant to frequency selective
fading than single carrier systems.
 Resilience to interference: Interference appearing on a channel
may be bandwidth limited.
 Will not affect all sub-channels, not all data is lost.
 Spectrum efficiency: Using close-spaced overlapping sub-carriers,
makes efficient use of available spectrum.
 Resilient to ISI: Very resilient to inter-symbol and inter-frame
interference.
 Results from low data rate on each of sub-channels.
 Resilient to narrow-band effects: Using adequate channel coding
and interleaving it is possible to recover symbols lost due to
frequency selectivity of channel and narrow band interference.
 Not all the data is lost.
 Simpler channel equalisation: Using multiple sub-channels,
channel equalization becomes much simpler.
Advantages of OFDM

 High peak to average power ratio: OFDM signal has noise like
amplitude variation.
 Has relatively high dynamic range, or peak to average power ratio.
 Impacts RF amplifier efficiency as amplifiers need to be linear and
accommodate large amplitude variations.
 These factors mean amplifier cannot operate with high efficiency
level.
 Sensitive to carrier offset and drift: Sensitive to carrier frequency
offset and drifts.
 Single carrier systems are less sensitive.
Dis-advantages of OFDM

OFDM Properties- Spectrum
 Unshaped QPSK signal produces spectrum with bandwidth (1+ α )Rs.
 In OFDM, adjacent carriers can overlap.
 Addition of two carriers allows transmitting 3Rs over a bandwidth of -
2Rs to 2Rs .
 Bandwidth efficiency of 4/3 Hz per symbol for 3 carriers and 6/5 for 5
carriers.
 With more carriers, bandwidth approaches (N+1)/N bits per Hz.
QPSK
OFDM

OFDM Properties- Bit Error Rate Performance
 The BER of an OFDM is excellent in a fading environment.
 OFDM not used in straight line of sight link such as satellite link.
 OFDM signal due to its amplitude variation does not behave well
in non-linear channel such as created by high power amplifiers on
board satellites.
 Using OFDM for a satellite would require a fairly large backoff
from saturation point, on the order of 3 dB.
 Backoff means PA's maxi output power level must be reduced so
entire signal is within linear region of PA transfer curve.
 This makes use of OFDM just as problematic as Multi-carrier
FDM.
 Not used for moving user.

OFDM Properties- PAPR
 Peak to Average Power Ratio:
 Signal is sum of N signals at a moment.
 The PAPR is defined as
 R = Іx( t )І2 /Pavg
 If OFDM signal has 128 carriers, max PAPR can be as large as log (128)
or 21 dB.
 All 128 carriers combining at their maximum point is unlikely but
possible.
 The RMS PAPR will be around half this number or 10-12 dB.

OFDM Properties- Mitigating large PAPR
 Clipping:
 Clip the signal at desired power level.
 This reduces PAPR but introduces other distortions and ICI.
 Selective Mapping:
 Multiply data signal by set of codes, do IFFT on each and pick one
with least PAPR.
 This is essentially doing process many times using CDMA like code.
 Partial IFFT:
 Divide signal in clusters, do IFFT on each and then combine these.
 Subdivide 128 carrier in to group of four 32 carriers,
 Max PAPR of each will be 12 dB instead of 21 for the full.
 Combine these four sequences to create the transmit signal.
 These keep effect of non-linearity manageable.

OFDM Properties-
 Synchronization.
 Tight synchronization is needed.
 Often pilot tones are sent in sub-carrier space.
 These lock on phase and equalize the channel.
 Coding
 Sub-carriers are typically coded with Convolutional coding
prior to going through IFFT.
 The coded version of OFDM is called COFDM or Coded
OFDM.

 COFDM: Coded Orthogonal frequency division multiplexing.
 A form of OFDM where error correction coding is incorporated into the signal.
 Flash OFDM: Fast hopped form of OFDM developed by Flarion.
 Uses multiple tones and fast hopping to spread signals over given spectrum
band.
 OFDMA: Orthogonal frequency division multiple access.
 Scheme used to provide multiple access capability for applications such as
cellular telecommunications when using OFDM technologies.
 VOFDM: Vector OFDM being developed by CISCO Systems.
 Uses concept of MIMO technology.
 Multi-path effects can be utilised to enhance signal reception and improve
transmission speeds that can be supported.
 WOFDM: Wideband OFDM.
 Uses a degree of spacing between channels that is large enough.
 Any frequency errors between transmitter and receiver do not affect the
performance.
 It is particularly applicable toWi-Fi systems.
OFDM Variants

 Channel spacing is 15 kHz and symbol period is 1/15 kHz = 66.7 µs.
 High-speed serial data is divided into multiple slower streams.
 Each is used to modulate one of the subcarriers.
 Example:
 5-MHz channel: Up to 333 subcarriers, actual number may be 300.
 20-MHz channel: Might use 1024 carriers.
 Modulation QPSK, 16QAM, or 64QAM depending on speed needs.
 OFDM uses frequency and time to spread data.
 Provides high speeds and greater signal reliability.
 For each subcarrier, data sent in sequential symbols, each symbol
represents multiple bits (QPSK 2 bits, 16QAM 4 bits, and 64QAM 6 bits.)
 Basic data rate through a 15-kHz subcarrier channel is 15 kbits/s.
 With higher-level modulation, higher data rates are possible.
OFDM for LTE

 Data is allocated to one or more resource blocks (RBs).
 RB is a segment of OFDM spectrum 12 subcarriers wide for
total of 180 kHz.
 Seven time segments per subcarrier for duration 0.5 ms.
 Data is then transmitted in packets or frames.
 Standard frame contains 20 time slots of 0.5 ms each.
 RB is the minimum basic building block of a transmission.
 Practical way to implement OFDM is software.
OFDM for LTE

 Transmitter uses inverse FFT, while receiver uses FFT.
 Algorithms implemented in DSP, FPGA, orASIC .
 Usual scrambling and adding error-correcting codes are
implemented as well.
 OFDM chosen for LTE primarily due to its reduced sensitivity
to multipath effects.
 Spreading signals in form of multiple subcarriers over a wide
bandwidth reduces these effects.
 Especially if symbol rate on each subcarrier is longer as in
OFDM.
 If multipath effects occur in less than one symbol period, no
equalizer needed.
OFDM for LTE

 Time or frequency shifts by Doppler effect cause frequency
variation of subcarriers at receiver.
 This results in loss of orthogonality and subsequently bit errors.
 LTE mitigates this problem by adding a cyclical prefix (CP) to
each transmitted bit sequence.
 CP allows receiver to recover symbol if time dispersion is
shorter than CP.
 OFDM then can be implemented without complex
equalization.
OFDM for LTE

 LTE downlink uses OFDM, uplink uses SC-FDMA.
 Reason:
 OFDM signals have a high peak to average power ratio (PAPR).
 This requires linear power amplifier with overall low efficiency.
 Good quality achievable for base stations.
 But is a poor quality for battery-operated handsets.
 While complex, SC-FDMA has a lower PAPR.
 Better suited to portable implementation.
OFDM for LTE

 36.211 for FDD LTE - structure of one frame in time domain.
 Time duration for one radio frame is 10 ms.
 100 radio frame per second.
 Number of samples in one frame is 307200 samples.
 Number of samples per second is 307200 x 100 = 30.72 M.
 Number of subframe in one frame is 10.
 Number of slots in one subframe is 2.
 20 slots within one frame.
OFDM for LTE TDD Frame Structure Type 1

 One slot made up of 7 small blocks called 'symbol'.
 Cyclic Prefix at beginning, remaining part is real symbol data.
 Two types of CP –
 Normal Cyclic Prefix
 Extended Cyclic Prefix.
 Length of one slot is fixed.
 In Extended CP, number of symbols within a slot is decreased. 6
symbols.
OFDM for LTE TDD Frame
Type 1

 Length does not vary with the Sampling Rate.
 Number of samples in each symbol and CP varies with sampling
rate.
 The number of samples shown is based on 30.72 Mhz sampling
rate.
OFDM for LTE TDD Frame Type 1

OFDM for LTE TDD Sub-Frame Structure Type 1

OFDM for LTE TDD Sub-Frame Structure Type 1
 First OFDM symbol within a slot is little bit longer than other OFDM
symbols.
 Number of samples based on sampling rate 30.72 M samples/sec and
2048 bins/IFFT.
 Typical values for each system BW is as follows
System BW Number of RBs N IFFT (bins/IFFT)
1.4 6 128
3.0 15 256
5.0 25 512
10.0 50 1024
15.0 75 2048
20.0 100 2048

Overall Sub-Frame Structure Type 1
*NOTE: Channel details in “PPT on LTE”

Sub-Frame Structure Type 1
*NOTE: Channel details in “PPT on LTE”

 http://www.csee.wvu.edu/wcrl/public/jianofdm.pdf
 http://www.drm.org/indexdeuz.htm
 https://en.wikipedia.org/wiki/LTE_(telecommunication)
 http://www.pcadvisor.co.uk/feature/mobile-
phone/whats-difference-between-4g-lte-3605656/
 http://www.in.techradar.com/news/phone-and-
communications/mobile-phones/4G-and-LTE
 http://www.ijarcsse.com/docs/papers/Volume_4/11_N
ovember2014/V4I11-0300.pdf
 http://www.academia.edu
 http://www.radio-electronics.com
Reference:

 http://rfmw.em.keysight.com/wireless/helpfiles/89600b
/webhelp/subsystems/wlan-
ofdm/Content/ofdm_basicprinciplesoverview.htm
 http://complextoreal.com/wp-
content/uploads/2013/01/ofdm2.pdf
 http://www.ni.com/white-paper/3740/en/
Reference:

OFDM for LTE

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