space time codes. 2 attenuation in wireless channels path loss: signals attenuate due to distance...
TRANSCRIPT
Space Time Codes
2
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
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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
r
2
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 N
r
N i
i
11
2
21
2
21
2
2
2
iscz rtrtTtTtE )()()()( 22
Diversity improvement in MRC
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222
2
1
2
1scii TT
Nr
N
Diversity improvement in MRC
Hence γM is a chi-square distribution of 2M Gaussian
random variable with variance 222 N
The resulting pdf for γM is
0for ! )1(
)(1
MM
MM
M M
ep
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
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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