Wireless Communication with Multiple Antennas€¦ · Wireless Communication with Multiple Antennas...

Wireless Communication with

Multiple Antennas

B. Sundar Rajan

Indian Academy of Sciences, Bangalore

Department of Electrical Communication Engineering,

Indian Institute of Science, Bangalore

05 July 2013.

B. Sundar Rajan (ECE) IASc Talk, 05 July 2013 1 / 31

Outline of presentation

1 Information, Uncertainty, and Communication

2 Capacity of multi-antenna systems

3 Codes for multi-antenna systems

4 Well known codes from ECE

5 Recent patents and concluding remarks


Outline







Is ”Information” measurable?

CHANNEL RECEIVERTRANSMITTER

X Y

Figure: A digital communication system transmitting INFORMATION

X can take FINITE values

Y is an observation

Y conveys some information about X ? - How much ?


Is ”Information” measurable?

BEAUTY HEIGHT

TEMPARATURE

STUPIDITY

SMARTNESS

WEIGHT

.....

..........

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

ANGLE

Figure: ”Information” belongs to which one of the above?

”Information” is MEASURABLE


Information and Uncertainty

”Uncertainty” is MEASURABLE - Claude E. Shannon (1948)

Information = Reduction of Uncertainty

Four Axioms of Uncertainty

If X takes M values with probability distribution p1, p2, · · · , pM , then theuncertainty denoted by H(p1, p2, · · · , pM) is given by

H(p1, p2, · · · , pM) = −

M∑

i=1

pi log2(pi ) bits

There is ONLY ONE function of several variables p1, p2, · · · , pM thatsatisfy all the four axioms.


Capacity of a communication system

CHANNEL RECEIVERTRANSMITTER

X Y

Observation Y at the receiver reduces the uncerainty about X .

Observation Y at the receiver conveys information = the reduction inthe uncertainty.

There is an upper limit on the amount of information that can beconveyed/transmitted.

The maximum amount of information that can be conveyed/transmitted iscalled the Shannon Capacity.


Outline







A multiple antenna wireless system

Tx 1

Tx 2

Tx N Rx M

Rx 1

Rx 2

H =

α11 α12 · · · α1M

α21 α22 · · · α2M...

... · · ·...

αN1 αN2 · · · αNM

Multiple input multiple output (MIMO) channel: N transmitters, M

receivers

αij is the complex channel gain from i–th transmit antenna to j–threceive antenna

H is the N × M channel matrix


A 2x2 Access Point

Allows to share 3G connection within home wirelessly to many usersusing WiFi.

(2x2 802.11n access point)


A 3x3 + 3x3 Access Point

This product has 6 antennas;

3 external dipole antennas for 2GHz and there are 3 internal stampedantennas on the board (inside box) for 5 GHz.

(802.11n compliant access point)


A 4x4 Access Point

4x4 IEEE 802.11n compliant access point- coding in 4 streams.


Another 4x4 Access Point

4x4 IEEE 802.11ac complaint access point - coding in 4 streams.


Wireless Channels: Diversity and Capacity

In many cases Spatial Diversity is needed

Wireless Channels: Capacity

Multipath propagation has historically been regarded as animpairment because it causes signal fading.

Information theory has shown that with multipath propagation,multiple antennas at both transmitter and receiver can establishessentially multiple parallel channels that operate simultaneously, onthe same frequency band at the same total radiated power.


Capacity growth with M=Number of Rx; (N=Number of

Tx=1)

0 2 4 6 8 10 120

2

4

6

8

10

12

Capacity vs. M for 0 dB ≤ P ≤ 35 dB (uppermost curve) in 5 dBincrements.

I.Emre Telatar, “Capacity of Multi-antenna Gaussian Channels,” EuropeanTransactions on Telecommunications, vol.10, No.6, pp.585-595, 1999.

Similar diminishing-return behaviour with M fixed.B. Sundar Rajan (ECE) IASc Talk, 05 July 2013 13 / 31

Capacity growth with N=M

00

20

40

60

80

100

120

140

c

5 10 15 20

35

30

25

20

15

10

50

p (in dB)

N=M=

N = M capacity in natsnumber of receive antennasnumber of transmit antennas

p =total transmit power

c =


Possible gains with 2 antennas

IS − 136 +

IS − 136

0

225

200

175

150

125

100

75

50

25

0 5 10 2015

2 Tx 1 Rx Antennas

1 Tx 1 Rx Antennas

1 Tx 2 Rx Antennas

2 Tx 2 Rx Antennas

Achievable Data Rates with Multiple AntennasAc

hiev

able

Dat

e Ra

te (k

bits

/sec

) per

30

kHz

Chan

nal

SNR per Rx Antenna (dB)

We can be here

We are here now

“It is dangerous to put limit on wireless”Guglielmo Marconi (1932)


Outline







Space-Time Codes and System Impacts

The way to achieve the capacity of a communication channel is byCoding and Signal Processing

Space-Time Codes are coding schemes appropriate to multipleantenna systems.

For various TDMA systems, it was shown that STC codes for 2Transmit chains can increase the capacity by about 60% (Winters,Clark).

Ericsson Researchers have shown that the capacity of WCDMAsystems (UMTS) increases (also by around 60%) using STC and 2Transmit chains.


Space–Time Coded Modulation

Information

Source Receiver

Space–Time Encoder

The overall channel is made up of of N × M slowly varyingsub–channels.

At any time interval, N signals are transmitted simultaneously, onefrom each transmit antenna.

Uncoded SISO system (Scalar transmission)

Coded SISO system (Vector transmission)

MIMO quasi-static channel (Matrix transmission)


Space-Time Codes (STC)Signal 2

Signal 1

ConstellationMapper

Constellation

Mapper

InformationSource

ST Block Code

ˆ

c1 c2˜

=

»

c1 −c∗2c2 c∗1

–

→ Idea: (Alamouti code)

[c1 c2] →

[

c1 −c∗2c2 c∗1

]


The problem of designing STCs

A space-time code is a (large) finite set of complex matrices of appropriatesize.

Obtain a matrix of appropriate size with variable entries such that spacetime codes can be generated by letting the variable take values from asmall set of complex numbers. (Such matrices are called Designs)

The designs are required to satisfy several properties !!!


Mathematical tools in MIMO communication

Diversity Gain/Advantage: Can be studied using Division Algebras usingthe Rank Criterion

Coding Gain/Advantage: Studied using Determinants of the differencecodeword matrices

Information Losslessness: The property which assures zero loss in cpacitydue to use of block codes - Studied using Trace-Orthogonality of thecodeword matrices.

low encoding complexity linear space-time codes: Theory of Orthogonaland quasi-orthogonal designs.

Diversity-Multiplexing Trade-off: Part of this property can be studiedusing Non-vanishing determinants (Sufficient condition for optimal tradeoff)

Low/Reduction in Maximum-Likelihood decoding: Completely given byHurwitz-Radon orthogonality for matrices

Ergodic Capacity Calculations: Essential mathematical tool is RandomMatrix Theory

Precoder Design with partial (finite) feedback Theory of ComplexUnitary Matrices.

Precoder Design with perfect (full) feedback Study of behaviour ofB. Sundar Rajan (ECE) IASc Talk, 05 July 2013 20 / 31

Outline







Well known space-time codes from ECE Department !!

”Full-diversity, high-rate space-time block codes from divisionalgebras,” B.A.Sethuraman, B. Sundar Rajan and V. Shashidhar,2003.

”Explicit Space-time codes achieving the diversity-multiplexing gaintradeoff,” P.Elia, K.R.Kumar, S.A.Pawar, P.Vijay Kumar and H.F.Lu,2006.

”Single-symbol maximum likelihood decodable linear STBCs,” Md.Zafar Ali Khan and B. Sundar Rajan, 2006.

”STBC-schemes with nonvanishing determinant for certain number oftransmit antennas,” T. Kiran and B. Sundar Rajan, 2005.

”Perfect space-time codes for any number of antennas,” P. elia,B.A.Sethuraman and P. Vijay Kumar, 2007.

All the above appeared in IEEE Transactions on Information Theory


Practically Important Codes

The three antenna codes accepted for IEEE 802.16e standard is a variationof the codes from ”Single-symbol maximum likelihood decodable linearSTBCs,” Md. Zafar Ali Khan and B. Sundar Rajan, 2006.

The above code was proposed by Beceem Communications whichsuccessfully brought out WiMax chipsets.

Graduate students from ECE department played a critical role in buildingthe Beceem chips.


Beceem Chip

A snapshot of Beceem Chip


A Sprint product with Beceem chip inside


Another Sprint device using Beceem chip


A BSNL product with Beceem chip inside


Outline







Figure: The best code for 4Tx-2Rx system known so far


Figure: A code for wireless relay networks


Figure: A detection technique for LARGE-MIMO systems


Concluding Remarks

6 more US patents have been filed with IISc as assignee.

A project to build a large multi-antenna wireless system for DEALDehradun is going on (with Prof. Chockalingam (PI) and Prof. VinodSharma and B. Sundar Rajan (Co-PIs)


THANK YOU


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