ELP 4002 LTE_SAE O - 01 Basic Concepts

8/7/2019 ELP 4002 LTE_SAE O - 01 Basic Concepts

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1. Basic ConceptsTable of Contents

Topic Page

1.1. Two way communication ................................................................ 6

1.2. Multiple access ............................................................................... 7 1.2.1. FDMA ...................................................................................................... 7

1.2.2. TDMA ...................................................................................................... 7 1.2.3. CDMA ...................................................................................................... 8 1.2.4. OFDMA .................................................................................................... 9

1.3. Complex numbers ......................................................................... 12

1.4. Fourier analysis ............................................................................ 14 1.4.1. Fourier Transform (FT) .......................................................................... 14 1.4.2. Discrete Fourier Transform (DFT) and Fast Fourier Transform (FFT) ... 15

1.5. OFDM transmitter ......................................................................... 20

1.6. OFDM receiver ............................................................................. 20

1.7. Modulation .................................................................................... 21


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1.1. Two way communicationIn a two way communication, there are two directions of transmission that must beseparated from each other to avoid collisions. This separation process is calledduplex. Transmission from the mobile station to the base station is referred to asUplink (UL), while the transmission from the base station to the mobile station isreferred to as Downlink (DL). The directions of transmission can be separated infrequency or time domain. Frequency Division Duplex (FDD) system uses differentfrequency bands for uplink and downlink, separated by the duplex distance, seeFigure 1.1, while the Time Division Duplex (TDD) system uses the same frequencyband for both uplink and downlink which is time shared as presented in Figure 1.2.

In case of FDD, the uplink is placed on the lower frequency band because thetransmission of lower frequency radio wave requires less energy comparing to thehigher frequency band, on which the downlink is placed. In FDD solution the

transmission and reception may take place continuously or discontinuously. Anexample of the FDD system is GSM.

UL DL

Power

Time

f

Figure 1.1. Frequency Division Duplex (FDD).

Power

Time

f

UL

DL

UL

DL

UL

DL

Figure 1.2. Time Division Duplex (TDD).

TDD requires only one frequency to realize two way communications, which may be

an advantage when the availability of radio resources is a limiting factor. On the


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other hand, to avoid any collisions, TDD system requires a time structure(synchronization) to separate the uplink and downlink transmission, which is alwaysdiscontinuous. An examples of the TDD system is cordless telephony system.

1.2. Multiple accessApart from duplex transmission separation, a harmonized access of multiple mobilestations to the shared radio resources must exist. In uplink direction a number of Mobile Stations (MS) transmit to the base station. Thus the multiple accesstechnology is required, which allows the base station to separate transmissions fromdifferent MSs. In downlink direction a single base station has to keep a connectionwith multiple users. For that reason a multiple access method is applied, whichallows multiplexing of signals at the base station and demultiplexing the signal at thereceiving side.

1G, 2G, 3G and 4G mobile telephony systems use different multiple access methods.

The new Orthogonal Frequency Division Multiple Access (OFDMA) method appliedin LTE and WiMAX has a dramatic impact on the Radio Access Network.

1.2.1. FDMAFrequency Division Multiple Access (FDMA) was the first multiple accesstechnology applied. The available radio resources were divided in frequency domain.For each connection a separate frequency band of equal width was allocated, Figure1.3. The transmission was continuous and no synchronisation in time was required.An example of FDMA system is Advanced Mobile Phone Systems (AMPS) thefirst generation cellular system developed in North America.

User 1

Power

Time

f

User 2 User 3User 4

Figure 1.3. Frequency Division Multiple Access (FDMA).

1.2.2. TDMAAnother solution of a multiple access technology is Time Division Multiple Access(TDMA). The available radio resources are divided in time domain into timeslots,see Figure 1.4. A certain number of timeslots create so called TDMA frame. Thisnumber is system specific. For example in GSM system, which is an example of TDMA system, eight TSs make up a TDMA frame. A single mobile station has a

cyclic access to the common radio resources during the allocated timeslot. Thus the


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transmission is discontinuous and the synchronisation is needed in order to avoidoverlapping of bursts, which are the information content, sent in adjacent timeslots.

Power

Time

f

User 1

User 2

User 3User 4

T i m e s l o t F r a m e User 1

User 2

Figure 1.4. Time Division Multiple Access (TDMA).

In fact GSM system uses a combination of FDMA and TDMA technology. Forexample in GSM 900 system 124 frequency band is divided into TDMA frames,each containing eight timeslots. The same combination of radio access technology isused in other second generation cellular systems, like Digital Advanced MobilePhone Systems (D-AMPS) developed in United States or Personal Digital Cellular(PDC) used in Japan.

1.2.3. CDMACode Division Multiple Access (CDMA) allows for simultaneous transmission of multiple users in the same wide frequency band. Separation of different connectionsis achieved by means of different codes, see Figure 1.5. The codes must have specificproperties. They must be orthogonal (independent of each other).

In UMTS, the Wideband CDMA (WCDMA) method is applied, which uses widefrequency band of 5 MHz. It allows lowering the power density. For example, inFDMA, narrow channels are used and a certain amount of power must be allocated,therefore FDMA results in high spectral power density, that is the average power perbandwidth, compared to WCDMA.


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User 1

Power/Code

Time

f

User 2

User 3User 4

Figure 1.5. Code Division Multiple Access (CDMA).

1.2.4. OFDMAOrthogonal Frequency Division Multiple Access (OFDMA) is an access methodbased on Orthogonal Frequency Division Multiplexing (OFDM).

Theoretical foundation of OFDM had been already laid in 1960', but due to highcosts and lack of appropriate technologies for a long time it remained purelytheoretical. This situation has changed with advent of cheap, small and fastmicrochips capable of processing the Fast Fourier Transform (FFT) and Invert FastFourier Transform (IFFT) algorithms. Nowadays, OFDM is widely used in wirelessnetworking (WLAN), digital television (DVB-T, audio broadcasting (DAB) and

broadband digital communication (WiMAX, LTE).OFDMA is a special type of Frequency Division Multiple Access (FDMA) thetechnology that allows to transfer signals simultaneously, using multiple narrowranges of frequencies, called subcarriers, see Figure 1.6.

Time

f

Power

User 1

User 2User 3

User 4

Figure 1.6. Orthogonal Frequency Division Multiple Access (OFDMA).

To avoid Inter Carrier Interference (ICI), in ordinary FDMA system, all suchsubcarriers are separated in frequency domain with guard bands, therefore some

spectrum is wasted. OFDM provides much better spectrum efficiency, as it doesn't


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need gaps between subcarrier bands. Moreover, the subcarrier bands are overlapping,which allows to additionally save some spectrum. ICI is mitigated here by takingadvantage of the fact that under the following conditions the subcarriers areorthogonal with one another:

The careful choice of subcarrier spacing. The subcarrier spacing f should beexactly equal to the reciprocity of the OFDM symbol duration T s, see Figure1.7, which provides that the subcarriers are mathematically orthogonal andthus independent.

Keeping the synchronization in the frequency domain, providing there are nofrequency shifts, e.g. due to Doppler effects.

f = 1TsBandwidth

fading

f4f3f2f1

f

Spectrum [V/Hz]

Figure 1.7. OFDM subcarriers spectrum.

Multiplexing and demultiplexing of OFDMA symbols into subcarriers can beperformed using Inverse Discrete Fourier Transform (IDFT) and Discrete FourierTransform (DFT). These mathematical procedures, that transform signal fromfrequency to time domain and opposite, can be implemented with Inverse FastFourier Transform (IFFT) and Fast Fourier Transform (FFT) algorithms.

The presented above FDMA, TDMA and CDMA multiple access methods are singlecarrier modulation. The Orthogonal Frequency Division Multiplexing (OFDM) is amulti carrier modulation. In other words, it means that a large number of closelyspaced orthogonal subcarriers are used to carry data. Each sub-carrier is modulatedwith a conventional modulation scheme (such as quadrature amplitude modulation orphase shift keying) at a low symbol rate, maintaining total data rates similar toconventional single carrier modulation schemes in the same bandwidth.

Advantages of OFDMA: OFDMA effectively diminishes the problem of multipath selective fading. Due

to multipath radio waves propagation in typical urban environment, signal at

the receiver can be constructively or destructively interfered by the same signal


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delayed over different path. This effect can dramatically change depending onfrequency used as a signal carrier some of the frequencies will suffer fromdeep fading, while neighbouring ones may not be affected at all. As OFDMAuses very small subcarrier widths, the fading within every subcarrier can beconsidered as relatively flat.

Another problem mitigated by OFDMA is Inter Symbol Interference (ISI).One of the causes of this effect is signal reflection from distant object(typically mountain). The delayed signal, which propagates over much longerpath, interferes with the direct signal because it carries another (older) symbolthan the direct signal and therefore the receiver is unable to detect the correctsymbol. The ISI effect is diminished when the symbol duration is longer, thusonly very far objects will lead to ISI. But the signal reflected from very farobject is usually week enough and does not lead to interference. In OFDMA,the symbol duration can be lengthened, because a few symbols can betransmitted simultaneously on different subcarriers. As already mentioned,longer symbol makes the radio path less vulnerable to ISI.Additionally, to avoid overlapping, the adjacent symbols are always separatedin time by short guard period. In the guard period, from technical reasons, it isnot effective to stop transmission at all, thus Cyclic Prefix (CP) is insertedhere, which is simply a copy of the signal tail end.

OFDMA can achieve a higher MIMO spectral efficiency due to providingflatter frequency channels than a CDMA rake receiver can.

No cell size breathing as more users connect.

Recognized disadvantages of OFDMA Higher sensitivity to frequency offsets and phase noise. Asynchronous data communication services such as web access are

characterized by short communication bursts at high data rate. Few users in abase station cell are transferring data simultaneously at low constant data rate.

The complex OFDMA electronics, including the FFT algorithm and forwarderror correction, is constantly active independent of the data rate, which isinefficient from power consumption point of view, while OFDMA combinedwith data packet scheduling may allow that the FFT algorithm hibernatesduring certain time intervals.

The OFDMA diversity gain, and resistance to frequency-selective fading, maypartly be lost if very few sub-carriers are assigned to each user, and if the samecarrier is used in every OFDMA symbol. Adaptive sub-carrier assignmentbased on fast feedback information about the channel, or sub-carrier frequencyhopping, is therefore desirable.

Dealing with co-channel interference from nearby cells is more complex inOFDMA than in CDMA. It would require dynamic channel allocation withadvanced coordination among adjacent base stations.

The fast channel feedback information and adaptive sub-carrier assignment ismore complex than CDMA fast power control.


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Relation between the two notations is the following:

cosr a = (1.3)

sinr b = (1.4)

Using the above relations the complex number z = a + ib may be expressed asfollows:

)sin(cossincos ir ir r ibaz +=+=+= . (1.5)

Using the below, so called, Eulers formula 1, see also Figure 1.10:

iei =+ sincos (1.6)

the complex iei =+ sincos number z may be noted as follows:

ireir z =+= )sin(cos (1.7)

Re

Im

0

1

i

cos

sinie = cos sin + i

Figure 1.10. Eulers formula.

Using the polar notation a complex number, z and its conjugate z*may be expressedin the following way:

irez = (1.8)

irez =* (1.9)

1

Richard Feynman called Euler's formula one of the most remarkable, almost astounding, formulasin all of mathematics.


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1.4. Fourier analysis

1.4.1. Fourier Transform (FT)Fourier Transform (FT) is an operation that transforms time domain function into

frequency domain function. Therefore FT is often called the frequency domainrepresentation of the original time domain function, see Figure 1.11.

ft

FT

ft

FT

ft

FT

Figure 1.11. Fourier Transform (FT) principles.


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DFT

a

0

1

2

0 1 2 3 4 5 6 7

Signal

r

0

4

8

Amplitude

87

86

85

84

83

82

810 f [Hz]

-

0

Phase

87

86

85

84

83

82

810 f [Hz]

t [s]

Figure 1.12. Example of the Discrete Fourier Transform (DFT).

For the sequence of 8 numbers, the DFT formula may be expressed by the followingmatrix form:

A2

A1

A0

A3A4A5A6A7

=

a 011

1

1

1

1

1

1

1 1

w1 1 1 1 1

w2 w3 w w 5 w6 w7

w2

w3

ww5

w6

w7

w w 6 w8 w10 w12 w14

w6

w8

w10

w12

w14

w9 w12 w15 w18 w21

w12

w15

w18

w21

w16

w20

w24

w28

w20 w24 w28

w25

w30

w35

w35w30

w36

w 9w 2w 2

a 2

a 1

a 3a 4a 5a 6a 7 (1.15)

22

1

4sin

4cos48

2 iieew

ii=

===

. (1.16)

When raising the coefficient w to any integral power, one of eight values is obtained,which are illustrated in Figure 1.13.


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Re

Im

4

w = 2i

21

w = 2 i

w = 3

2i

21

w = 7

2i

21

w = 6 i

w = 4 1

w = 5

2i

21

w = 0 1

Figure 1.13. The coefficient w in the DFT for N = 8.

Let us denote these eight complex values by arrows according to Figure 1.13. Now,

the matrix form of DFT can be noted in the following way:

A2

A1

A0

A3A4A5A6A7

=

0

1

2

1

2

1

0

1(1.17)

We may calculate A numbers from the above matrix notation. As an example A0, A1 and A2 are calculated below:

811011121110111210 =+++++++=A (1.18)

0122

101

22

12)1(

122

10)(1

22

1211

=

+++

+++

+

++

+=

ii

i

ii

iA

(1.19)

410)1(1)(2110)1(1)(212 =+++++++= iiiiA (1.20)

. . . . . . . . . .

You may calculate the remaining A values to confirm that the DFT transforms thesequence ]1,0,1,2,1,0,1,2[=a into the sequence ]0,4,0,0,0,4,0,8[=A . It isimportant to observe that the duration of our signal sample in the time domain was


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8 s, while the shift between transformed signals in frequency domain is equal

Hzs 8

181

= .

IDFT example

We are going show that the IDFT transforms the sequence of N = 8 numbers in thefrequency domain:

]0,4,0,0,0,4,0,8[=A (1.21)

back into the following sequence of numbers in the time domain:

]1,0,1,2,1,0,1,2[=a (1.22)

Values a n may be calculated from formula 1.13, as presented below and value k w

are shown in Figure 1.14:

( )

=

=+++++++==1

00 2040004088

11 N

k k AN

a (1.23)

( )

( )[ ] 144881

448811 1

0

1612101

=++=

=++==

=

ii

wwwwAN

aN

k

k k

(1.24)

( )

( ) ( )[ ] 01414881

448811 1

0

26222022

=++=

=++==

=

N

k

k k wwwwAN

a(1.25)

. . . . . . . . . .

Re

Im

4

w = -7

2i

21

w = -6 i

w = -5

2i

21

w = -1

2

i

2

1

w = -2 i

w = -4 1

w = -3

2

i

2

1

w = 0 1

Figure 1.14. The coefficient w -n

in the IDFT for N = 8. When c omparing with Figure 1.13 notice that w -n is aconjugate of w

n .


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Figure 1.15 shows the graphical presentation of the IDFT example.

t [s]0 1 2 3 4 5 6 7-808

-8

08

-808

-808

-808

-808

-808

-808

a n ,7

f = 0 Hz

81

82

83

84

85

86

87

t [s]

a

210

0 1 2 3 4 5 6 7

Signal

f = Hz

f = Hz

f = Hz

f = Hz

f = Hz

f = Hz

f = Hz

a n ,6

a n ,5

a n ,4

a n ,3

a n ,2

a n ,1

a n ,0

Figure 1.15. Graphical presentation of the IDFT example.


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1.5. OFDM transmitterIn OFDM the carrier signal is a sum of orthogonal subcarriers. In each subcarrierprocessing Quadrature Amplitude Modulation (QAM) or Phase Shift Keying (PSK)can be used. A simplified scheme of an OFDM transmitter has been shown in Figure

1.162

.

D/A

IFFT

A0

A1

AN-2

AN-1

90 O

Im

Re

f cs t ( )

s n[ ]

Serialto parallel

D/A

Digital signal processing Analogue signal processing

a n

Figure 1.16. OFDM transmitter.

s[n] is input bit stream. First, bits are separated into N parallel streams. Streams areassigned for QAM or PSK modulation. Depending on the modulation, subcarriersmay have different transmission bit rate.

Next, Inverse Fast Fourier Transform (IFFT) is computed for the sequence of complex data symbols A0,...,A N-1, which results in a sequence of complex timesymbols a 0,...,a N-1 of the signal. For each symbol, after imaginary and real partseparation, both parts are converted to analogue in Digital-to-Analogue converter(D/A). Next, analogue signals are quadrature modulated (multiplied by cosine andsine functions) and summed up giving the output modulated signal s(t ).

1.6. OFDM receiverFigure 1.17 presents the simplified OFDM receiver model. Receiver is detecting thesignal rx (t ). Besides the wanted signal also signal with 2f frequency is created.Therefore low pass filter is used to filter it out. Next, the signal is sampled andconverted to digital by the Analogue-to-Digital converter (A/D). The series of

complex time symbols is then corrected for frequency drifts and global phase offsets(not shown in the diagram). In the next step Fast Fourier Transform (FFT) is carriedout and frequency symbol detection takes place, which results in N parallel bitstreams, joined finally into one initial bit stream s(n).

2 In the scheme only the main idea of OFDM processing has been shown.


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FFT

B0

90 O

Im

Re

f crx t ( )

Parallelto serial

A/D

A/D

B1

BN-2

BN-1

s n[ ]

Symboldetection

Digital signal processingAnalogue signal processing

bn

Figure 1.17. OFDM receiver.

1.7. ModulationIn telecommunications, modulation is the process of conveying a message signal, forexample digital information bit stream, inside another signal that can be physicallytransmitted. Modulation of a sine waveform is used to transform a baseband messagesignal to a passband signal, for example a radio-frequency (RF) signal. Electricalsignals can only be transferred over a limited passband frequency spectrum, withspecific (non-zero) lower and upper cut-off frequencies. Modulating a sine wavecarrier makes it possible to keep the frequency content of the transferred signal asclose as possible to the centre frequency (typically the carrier frequency) of thepassband.

The modulation techniques used in LTE are based on phase and amplitudemodulation of the carrier frequency: Binary Phase Shift Keying (BPSK) allows for transmission of one

information bit during one modulation symbol. Quadrature Phase Shift Keying (QPSK) allows for transmission of two

information bits during one modulation symbol. 16 Quadrature Phase Keying (16-QPSK) allows for transmission of 4

information bits during one modulation symbol. 64 Quadrature Phase Keying (64-QPSK) is the fastest modulation used in

LTE and allows for transmission of 6 information bits during one modulation

symbol.Figure 1.18 illustrates the modulations used in LTE. Only QPSK, 16-QAM and 64-QAM are used in LTE for user data bit. QPSK is only used for some controlinformation bits, which require robust modulation.


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Re

Im001111

Re

Im

10

11

00

01

Re

Im

0

1

QPSK2 bits/symbol

BPSK1 bit/symbol

64-QAM

6 bits/symbol

111111

101111

011111

Re

Im

1011 1001

1010 1000

0001 0011

0000 0010

1110

1111 1101

1100

0101

0100

0111

0110

16 QAM-

4 bits/symbol

Figure 1.18. Modulations.

ELP 4002 LTE_SAE O - 01 Basic Concepts

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