Advanced Wireless Communications

lecture notes: section 3

Andrea M. Tonello

Double Master Degree in Electrical Engineering ‐ University of Udine, Italy 

and Information and Communication Engineering ‐ University of Klagenfurt, Austria

Note: these lecture notes have been prepared as part of the material for the joint class “Advanced wireless communications” and “Comunicazioni Wireless” by A. Tonello. The class has been offered in the Spring 2015 term, by 

means of video conferencing in time sharing between two locations.   

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Section Content Topics

oDiversity

oReceive antenna diversity

o Selection combining

oMaximal ratio combining

oMIMO: multiple input – multiple output systems

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Diversity

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System Model

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System Model

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System Model

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Combining

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Distribution of the SNR at the Combiner Output

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SNR for SC

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SNR for SC

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Average SNR in SC (Proof)

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Combining in MRC

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Receiver Structure in MRC

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SNR in MRC

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SNR in MRC

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SNR in MRC (Derivation)

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Comparison of SNR in SC and MRC

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Comparison of SNR in SC and MRCF S

NR(a)

F SNR(a)

a‐Es/N0 (dB) a‐Es/N0 (dB)

SC MRC

This shows the probability that the SNR is less than a certain desired value

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BER Analysis

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Chernov Bound for SC

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Chernov Bound for SC

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Chernov Bound for MRC

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Chernov Bound for MRC

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BER Comparison

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MIMO

Adaptive AntennasReceive antenna combining to gain spatial diversityand cancel co-channel interference.

RX

MS MS

MS

RX

MS

MS

MS

MS Smart AntennasGenerate beams with phased arrays to sectorizecoverage.

Space-Time CodingMultiple transmit and receive antennas to increasecapacity.

RX

TX

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MIMO Channel Capacity

The received signal is the superposition of the NT transmitted signals

All antenna links experience independent fading “in rich scattering”

We keep the average transmitted energy constant

,

1 1,...,

TNr r t t rsk k k k R

tT

Ey x n r N

N

transmitted complex signal by antenna t

channel weight link antenna (t-r)

TX RX

1

NT

1

NR

white Gaussian noise

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MIMO Channel Capacity

The channel capacity conditioned on a channel realization reads

1,1 1,1 1 1

,1 ,

...... ... ... ... ... ...

T

R R R T T R

N

s

N N N N N NT

y x nEN

y x n

+s

T

EN

y Hx n

†02

/log det / /S

HT

E NC bit s Hz

N

I HH

We assume H to have independent complex Gaussian entries (Rayleigh fading)

The Outage Capacity is the distribution of CH

The Ergodic Capacity is the average of CH

HC P C K

HC E C

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Mean Capacity

2 4 6 8 10 12 14 16 18 20 22 240

20

40

60

80

100

120

Cap

acity

(bit/

s/H

z)

Number of Antennas (NT=NR)

0 dB

5 dB

10 dB

SNR=15 dB

20 dB

30 dB

25 dB

Ergodic Capacity is used to characterize fast fading channels

Outage Capacity is used to characterize quasi-static fading channels

Fundamental contribution by Foschini (1996 Bell Labs)

Capacity increases linearly with the number of TX antennas if NR≥ NT

C < 3 bit/s/Hz with NT=NR=1

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Space‐Time Coding

To approach the Shannon Capacity we need to design powerful space-time codes:

joint channel coding, modulation, with transmission over multiple antennas.

Fundamental contribution by Tarokh, Seshadri, and Calderbank (1998 AT&T Labs)

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ST Code Class Three Main ST Coding Aproaches

ST Trellis Codes: extension of the TCM (trellis coded modulation) concept.

ST Block Codes: M-QAM block codes with orthogonal structure.

ST Bit-interleaved Codes

Diversity Gains and Coding Gains are determined by the rank and determinant of certain

matrices constructed from complex codewords:

2

1 1~ LL

T RPe L N NSNR

SNR

Diversity Gain

~ LSNR

SNR

Coding Gain

2~L

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Space‐Time Bit Interleaved Coded Modulation

ST-BICM comprises

coder (block, convolutional, turbo)

bit interleaver space-time mapper (M-PSK / M-QAM)

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Turbo Decoding Principle

The receiver has to separate the overlapping signals and recover the information bits

Iterative (turbo) decoding procedure:

MIMO Demapping at the Detector: A Posteriori Probability Calculator for Each Coded Bit.

Maximum a Posteriori Channel Decoder: Improved Extrinsic Information for the Coded Bits.

,

1( ) ( ) ( ) ( )

TNr t t r

CHt m

y nT x mT g nT mT nT

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Example for GSM‐EDGE1 Bit/s/Hz 2 Bit/s/Hz 3 Bit/s/Hz

1 TX

2 TX

1 TX

2 TX

1 TX

2 TX

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Remarks

Spectral efficiency of wireless channels is significantly increased with MIMO  technology

It is fundamental to

Study and model the MIMO channel

Design good Space‐time codes

Develop simplified decoding algorithms 

Turbo (iterative) processing is the state‐of the art detection/decoding approach