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Space Time Coding and Channel Estimation. By Orhan GAZI. Outline. Spatial Multiplexing Space Time Coding MIMO Channel Capacity MIMO channel estimation Our aim. Spatial Multiplexing. Data is divided into data streams Each stream is sent with an antenna Multiplexing gain is maximum

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space time coding and channel estimation

Space Time Coding and Channel Estimation

By Orhan GAZI

Space Time Coding and Channel Estimation by Orhan Gazi

outline
Outline
  • Spatial Multiplexing
  • Space Time Coding
  • MIMO Channel Capacity
  • MIMO channel estimation
  • Our aim

Space Time Coding and Channel Estimation by Orhan Gazi

spatial multiplexing
Spatial Multiplexing

Space Time Coding and Channel Estimation by Orhan Gazi

slide4
Data is divided into data streams
  • Each stream is sent with an antenna
  • Multiplexing gain is maximum
  • The received symbols are decoded using different techniques
    • Maximum Likelihood (ML) receiver
    • Minimum Mean Square Error receiver
    • ZF receiver

Space Time Coding and Channel Estimation by Orhan Gazi

spatial multiplexing5
Spatial Multiplexing
  • Maximum multiplexing gain
  • Maximum data transmission
  • What about the system performance?

- What about BER vs SNR graph

- Is it the best one?

Space Time Coding and Channel Estimation by Orhan Gazi

slide6

NO !!

Space Time Coding and Channel Estimation by Orhan Gazi

for a better system performance
For a better system performance
  • Increase diversity
  • Increase coding gain

Space Time Coding and Channel Estimation by Orhan Gazi

diversity
Diversity
  • Spatial Diversity

- Transmit diversity

- Receive diversity

  • Path Diversity

- Time diversity

- Frequency Diversity

- Polarization Diversity

Space Time Coding and Channel Estimation by Orhan Gazi

spatial diversity
Spatial Diversity
  • More than one transmit antenna at the transmit side

- Transmit diversity

  • More than one receive antenna at the receiver side
    • Receive diversity

Space Time Coding and Channel Estimation by Orhan Gazi

slide10
Correlation occurs if antennas are spaced at a distance d which is smaller than the half transmit wavelength.

Space Time Coding and Channel Estimation by Orhan Gazi

path diversity
Path Diversity

Frequency diversity

Different frequencies are used to send the same symbol

Space Time Coding and Channel Estimation by Orhan Gazi

delay diversity
Delay Diversity

Symbol and its delayed version are transmitted

Space Time Coding and Channel Estimation by Orhan Gazi

polarization diversity
Polarization Diversity

Antenna polarization is employed for diversity

Space Time Coding and Channel Estimation by Orhan Gazi

how is the effect of diversity gain on the performance
How is the effect of diversity gain on the performance

Diversity increases the slope

Space Time Coding and Channel Estimation by Orhan Gazi

space time block code
Space Time Block Code
  • Alamouti discovered space time block codes

-He used 2 transmit antennas instead of one single antenna.

-1 receive antenna is employed at the receiver side

Space Time Coding and Channel Estimation by Orhan Gazi

alamouti transmit system
Alamouti transmit system

Space Time Coding and Channel Estimation by Orhan Gazi

comparison with the classical one transmit two receive antenna case
Comparison with the classical one transmit two receive antenna case
  • Slopes are the same
  • 3dB loss in performance due to the power division between two transmit antennas

Space Time Coding and Channel Estimation by Orhan Gazi

following studies after alamouti
Following Studies after Alamouti
  • Tarokh worked on Space Time Codes
  • Alamouti code only gives diversity gain
  • Tarokh generalized Alamouti’s work for any number of transmit and receive antennas.
  • Designed space time codes for real and complex signals.

Space Time Coding and Channel Estimation by Orhan Gazi

tarokh discoveries on stbc
Tarokh discoveries on STBC
  • For real signals full rate space time codes exist for only 2,4 and 8 transmit antennas.
  • If transmission rate is not full, then is possible to construct space-time block codes for any number transmit antennas

Space Time Coding and Channel Estimation by Orhan Gazi

for complex signals
for complex signals
  • Full rate space time code exists for only two transmitter antenna case
  • Rate ¾ complex orthogonal codes exists for 3 or 4 transmit antennas.
  • Rate ½ complex orthogonal codes exists for any number of transmit antennas
  • If Tx >4 then it is not possible to find a code with rate >1/2

Space Time Coding and Channel Estimation by Orhan Gazi

examples complex orthogonal codes
Examples¾ complex orthogonal codes

Space Time Coding and Channel Estimation by Orhan Gazi

space time trellis codes
Space Time Trellis Codes
  • Tarokh also designed space time trellis codes
  • Space time trellis codes provides
    • Diversity gain
    • Coding gain
  • Slope increases ( Diversity Gain), curve shifts to left (Coding Gain)

Space Time Coding and Channel Estimation by Orhan Gazi

any space code design
Any Space Code Design
  • Although Tarokh worked on STBC and STTC, his ideas can be generalized for any space time code design.
  • While designing space time code we should try to maximize the diversity and coding gain

Space Time Coding and Channel Estimation by Orhan Gazi

space time code design criteria
Space Time Code Design Criteria
  • The transmitted code matrix is C
  • The received code matrix is C’
  • Error matrix E=(C-C’)(C-C’)T

M is the number of receive antennas

r is the rank of E

is the eigenvalues of E

Space Time Coding and Channel Estimation by Orhan Gazi

slide26

Is called diversity gain

Is called coding gain

Space Time Coding and Channel Estimation by Orhan Gazi

slide27
Rank Criterion
    • To achieve maximum diversity the error matrix E must have full rank for any pair of distinct code words C and C’
  • Determinant Criterion

- For the maximization of the coding gain the determinant of the error matrix must be maximized for a given target diversity order

Space Time Coding and Channel Estimation by Orhan Gazi

slide28

Multi Input Multi Output Communication System

Space Time Coding and Channel Estimation by Orhan Gazi

slide29
N the number of transmit antennas
  • M the number of receive antennas
  • H the channel matrix between transmitter and receiver.
  • S is the transmitted symbol data matrix
  • Y is the received symbol data matrix
  • Y=HS+N
  • N is AWGN

Space Time Coding and Channel Estimation by Orhan Gazi

slide30
Ex N=3 M=4

Space Time Coding and Channel Estimation by Orhan Gazi

mimo channel capacity
MIMO Channel Capacity
  • When channel knowledge is available at the receiver

r is the rank of the channel and is are the positive eigenvalues of the HHT

Space Time Coding and Channel Estimation by Orhan Gazi

slide32

When N=M, the channel capacity is given as

TheMIMO channel capacity is N times SISO channel capacity

Space Time Coding and Channel Estimation by Orhan Gazi

when channel knowledge is available at the transmitter side
When channel knowledge is available at the transmitter side

r is the rank of the channel matrix H

Space Time Coding and Channel Estimation by Orhan Gazi

slide34
This idea is called water pouring
  • Allocate power according to channel eigenvalues
  • Give more power to larger eigenvalues
  • Capacity is greater than the NO CSI at the transmitter but only at the receiver case.

Space Time Coding and Channel Estimation by Orhan Gazi

slide35
The mentioned formulas are for static flat fading channels.

Space Time Coding and Channel Estimation by Orhan Gazi

slide36
What about random channels

Space Time Coding and Channel Estimation by Orhan Gazi

for random channels
For random channels
  • Ergodic Capacity
  • Outage probability
  • Outage Capacity

Space Time Coding and Channel Estimation by Orhan Gazi

slide38
Ergodic capacity is the expected value of the capacity over the distribution of the channel elements
  • Outage probability is the probability that given a transmission rate R and transmit power constraint the channel capacity cannot support reliable communication
  • Given an outage probability, the maximum information rate that can be supported by the communication channel is called the outage capacity of the channel

P{C<Cout}=Pout

Space Time Coding and Channel Estimation by Orhan Gazi

mimo channel estimation methods

MIMO Channel Estimation Methods

*Blind *

*Training Based*

Space Time Coding and Channel Estimation by Orhan Gazi

practical systems use training based channel estimation
Practical systems use training based channel estimation
  • Ex: GSM frame structure

Figure taken from* Tapio Mikael, Channel Estimation, Ms Thesis,Goteborg Sweden

Space Time Coding and Channel Estimation by Orhan Gazi

complete system
Complete System

Space Time Coding and Channel Estimation by Orhan Gazi

channel matrix estimation
Channel Matrix Estimation
  • Using the received signal matrix and knowing the transmitted training signal matrix, the MIMO channel matrix can be found with maximum likelihood method or minimum mean square error method

Y is the received signal matrix, S is the sent training matrix

Space Time Coding and Channel Estimation by Orhan Gazi

slide43

Another approach to estimate the channel is to transform the received data linearly so as to minimize the estimation error and it is given as

Y is the received signal matrix, S is the transmitted training signal matrix, is the average signal to noise ratio, I is the identity matrix

Space Time Coding and Channel Estimation by Orhan Gazi

pilot insertion methods
Pilot Insertion methods

Figure taken from Tapio Mikael, Channel Estimatio, Ms Thesis, Goteborg Sweden

Space Time Coding and Channel Estimation by Orhan Gazi

our initial goal
Our Initial Goal
  • Using superimposed channel estimation technique and space time code design principles, a better MIMO communication system is to be designed

Space Time Coding and Channel Estimation by Orhan Gazi