• 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), multi- carrier 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

= 12 cos(m − n) − 12 cos(m + n)

Both components being sinusoid, integral is zero over one period.

∫02π 12 cos(m − n)ωt − ∫02π 12 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.

OFDM Blocks

OFDM Basics

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 Domain View Frequency Domain View

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

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Am

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Frequency

1.5

1

0.5

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-1 1 2 3 4

-1

-2A

mp

litu

de

Frequency

1.5

1

0.5

0

-1 1 2 3 4

-1

-2

Am

plit

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Frequency

1.5

1

0.5

0

-1 1 2 3 4

-1

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Am

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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.

Fading Effect on OFDM 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.

Fading Effect on OFDM

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.

OFDM Cyclic Prefix, CP

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 symbol Extension

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.

OFDM Synchronization

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 to Wi-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

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, or ASIC .

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

OFDM for LTE - FDD

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_November2014/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: