Space Time Codes

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Attenuation in Wireless Channels

Path loss: Signals attenuate due to distance Shadowing loss : absorption of radio waves by scattering

structures Fading loss :constructive and destructive interference of multiple

reflected radio wave paths Channel parameters: coherence time, coherence bandwidth If symbol period>coherence time, the channel is time selective If symbol period< channel delay spread, the channel is frequency

selective

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Diversity techniques Powerful technique that provides

wireless link improvement at relatively low cost.

Unlike equalization, diversity requires no training overhead.

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…Principle of diversity Receiving the same information

bearing signal over 2 or more fading channels.

Eg. If we space 2 antennas at 0.5 m, one may receive a null while the other receives a strong signal. By selecting the best signal at all times, a receiver can mitigate or reduce small-scale fading. This concept is Antenna Diversity.

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Types of diversity Space Diversity

Transmission using multiple transmit/receive antennas

Either at the mobile or base station. At base station, separation on order of

several tens of wavelength are required. Polarization Diversity

Orthogonal Polarization to exploit diversity High art of space diversity is avoided.

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…Types of diversity Frequency Diversity :

More than one carrier frequency is used Multiple frequency channels separated by at

least the coherence bandwidth

Time Diversity : Information is sent at time spacings Greater than the coherence time of channel,

so that multiple repetitions can be resolved

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Spatial diversity Single-input, single-output (SISO) channel

No spatial diversity Single-input, multiple-output (SIMO) channel

Receive diversity Multiple-input, single-output (MISO) channel

Transmit diversity Multiple-input, multiple-output (MIMO)

channelCombined transmit and receive diversity

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Spatial diversity (cont’d)•Selection combining (SC)

h1

h2

yx

MonitorSNR

Selectbranch

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Spatial diversity (cont’d) Switched diversity

Switch-and-stay combining (SSC) Switch-and-examine combining (SEC)

h1

h2

x

ComparatorChannelestimator

switchingthreshold

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Spatial diversity (cont’d) •Maximum ratio combining (MRC)

•Combining all the signals in a co-phased and weighted manner so as to have the highest achievable SNR at the receiver at all times.

h1

h2

h1*

h2*

yx

11

Spatial diversity (cont’d) •Equal Gain Combining (EQC)

•Combining all the signals in a co-phased manner with unity weights for all signals so as to improve achievable SNR at the receiver at all times.

h1

h2

h1*

h2*

yx

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Diversity Improvement• Consider a fading channel (Rayleigh)

Input s(t) Output r(t)

• Input-output relation

r (t) = (t) e -j (t) s (t) + n (t)

Average value of signal to noise ratio ___SNR = = (Eb / No) 2 (t)

Channel

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Diversity improvement in MRC

Assumptions:

The voltage signal γi from each of the M diversity branches are co-phased to provide coherent voltage addition and are individually weighted to provide optimal SNR.

Each branch has gain Gi Each branch has same average noise power N

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Resulting signal envelope applied to the detector is

Assuming that all amplifiers have additive noise at their input and that the noise is uncorrelated between different amplifiers.

M

iiiM rGr

1

M

iiT GNN

1

2

Diversity improvement in MRC

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Which results in a SNR applied to the detector γM

Using Chebychev’s inequality γM is maximized when

T

MM N

r2

2

NrG i

i

Diversity improvement in MRC

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The Maximized value is

The received signal envelope for a fading mobile radio signal can be modeled from two independent Gaussian random variables Tc and Ts each having zero mean and equal variance σ2 .

M

ii

M

i

i

Nr

Nr

M Nr

N i

i

11

2

21

2

21

2

2

2

iscz rtrtTtTtE )()()()( 22

Diversity improvement in MRC

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222

21

21

scii TTN

rN

Diversity improvement in MRC

Hence γM is a chi-square distribution of 2M Gaussian random variable with variance 22

2 N

The resulting pdf for γM is

0for ! )1(

)(1

MM

MM

M Mep

M

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The probability that γM is less than some

SNR threshold γ is

M

k

k

MMMr kedpP

1

1

0 ! 11)(

Diversity improvement in MRC

Hence the mean SNR is

MM

i

M

iiM

11

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Maximizing diversity with Space-Time Codes

Space–Time Trellis Codes (STTC) often better performance at the cost of increased complexity

Complex decoding (vector version of the Viterbi algorithm) —increases exponentially with the transmission rate

Full diversity. Coding gain Space–Time Block Codes (STBC)

Simple maximum–likelihood (ML) decoding based on linear processing

Full diversity. Minimal or no coding gain

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Scope of MIMO MIMO channels offer multiplexing gain, diversity

gain, power gain (array gain) and a co–channel interference cancellation gain

Tradeoff between diversity gain and multiplexing gain: Careful balancing between those gains is required

Space-Time Coding: Space-Time block codes (STBC) and Space-Time Trellis Codes

Easy to combine with error control codes MIMO systems offer a solution choice for future

generation wireless networks Distributed MIMO: Cooperative wireless

networks