![MEMO capacity on fading channels
1. The capacity increase can be seen by comparing MEMO systems
with SISO, SIMO, and MISO systems
• SISO:capacity is given by Shannon’s classical formula:
Where B is the BW and h is the fading gain
• SIMO (with M transmitting antennas), the capacity is given by
[2]
)
2
1(
2
log hsnrBC ⋅+=
)
1
2
1(
2
log ∑
=
⋅+=
m
n
n
hsnrBC](https://image.slidesharecdn.com/sandhyappt-copy-170214154349/85/MULTIPLE-INPUT-MULTIPLE-OUTPUT-BY-SAIKIRAN-PANJALA-7-320.jpg)
![Average capacity of a MIMO Rayleigh
fading channel
0
5
10
15
20
25
30
35
40
45
50
55
60
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
SNR [dB]
AverageCapacity[bits/sec/Hz]
N=1 M=1 N=2 M=1 N=1 M=2 N=2 M=2 N=2 M=4 N=2 M=6 N=4 M=4 N=8 M=8](https://image.slidesharecdn.com/sandhyappt-copy-170214154349/85/MULTIPLE-INPUT-MULTIPLE-OUTPUT-BY-SAIKIRAN-PANJALA-10-320.jpg)
![MIMO Diversity and Reliability
The performance improvement in SNR and error probability for
MIMO can be compared with SISO, SIMO, and MISO
The detailed calculation for SNR and Pe is shown in [1]
SISO:
Receive Diversity (SIMO):
Ninxhy iii ,2,1, =+=
∑=
N
i
hSNRhSNR
2
)(
2
1
1
SNR
Pe
+
≤
nhxy +=
2
2
2
)( hSNR
nE
hxE
hSNR == and
N
SNR
Pe
+
≤
2
1
1
and](https://image.slidesharecdn.com/sandhyappt-copy-170214154349/85/MULTIPLE-INPUT-MULTIPLE-OUTPUT-BY-SAIKIRAN-PANJALA-12-320.jpg)
![References
[1] MIMO Architecture for Wireless Communication:
Intel Technology Journal, vol. 10, Issue 02, May
2006
[2] MIMO Systems and Transmit Diversity,
www.comm.utoronto.ca/~rsadve/Notes/DiversityT
ransmit.pdf
[3] R.A. Carrasco, Space-time Diversity Codes for
fading Channel,
Staffordshire University](https://image.slidesharecdn.com/sandhyappt-copy-170214154349/85/MULTIPLE-INPUT-MULTIPLE-OUTPUT-BY-SAIKIRAN-PANJALA-15-320.jpg)
MULTIPLE INPUT MULTIPLE OUTPUT BY SAIKIRAN PANJALA
- 1. MULTIPLE INPUT MULTIPLE OUTPUT By XXXXX (12XXXXXXX) Under the guidance of XXXXXX, XXXX Lecturer
- 2. 1. INTRODUCTION MIMO Systems: • use multiple inputs and multiple outputs from a single channel.
- 3. SPATIAL DIVERSITY AND SPATIAL MULTIPLEXING 1. Spatial Diversity • Signal copies are transferred from multiple antennas or received at more than one antenna 1. Spatial Multiplexing • the system is able to carry more than one data stream over one frequency, simultaneously
- 4. Why MIMO....? 1. There is always a need for increase in performance in wireless systems • Significant increase in spectral efficiency and data rates • Wide coverage, etc. 1. Wireless channel that we are using is very unfriendly • Suffers from Co–channel interference and signal level fading • power falls off with distance
- 5. MIMO System solutions 1. By using Multiple Output Multiple Input (MIMO) systems • Diversity gain mitigates the fading and increases coverage and improves QOS • Array gain results in an increase in average receive SNR. 1. Spatial Diversity and Spatial Multiplexing can be conflicting goals
- 6. Spatial Multiplexing 1. MIMO channels can be decomposed into a number of R parallel independent channels Multiplexing Gain→ • Principle: Transmit independent data signals from different antennas to increase the throughput, capacity.
- 7. MEMO capacity on fading channels 1. The capacity increase can be seen by comparing MEMO systems with SISO, SIMO, and MISO systems • SISO:capacity is given by Shannon’s classical formula: Where B is the BW and h is the fading gain • SIMO (with M transmitting antennas), the capacity is given by [2] ) 2 1( 2 log hsnrBC ⋅+= ) 1 2 1( 2 log ∑ = ⋅+= m n n hsnrBC
- 8. MEMO capacity on fading channels • The capacity for MIMO systems can have the following forms (Assuming Tx antennas = Rx antennas = N): A) If the channel is not known at the transmitter: Where Es is the total power, σ2 is noise level of AWGN B) If the channel is known at the transmitter ) 2 2 1( 2 log n h N s E NC ⋅ += σ ∑= ⋅ += N n n hn E C 1 ) 2 2 1( 2 log σ
- 9. MEMO capacity on fading channels • With the channel known at the transmitter, the total power allocation the each channel will be based on watterfilling. Where σN 2 = σ2 / h│ n 2 │
- 10. Average capacity of a MIMO Rayleigh fading channel 0 5 10 15 20 25 30 35 40 45 50 55 60 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 SNR [dB] AverageCapacity[bits/sec/Hz] N=1 M=1 N=2 M=1 N=1 M=2 N=2 M=2 N=2 M=4 N=2 M=6 N=4 M=4 N=8 M=8
- 11. Spatial Diversity • Improves the signal quality and achieves a higher SNR at the receiver-side xi yi
- 12. MIMO Diversity and Reliability The performance improvement in SNR and error probability for MIMO can be compared with SISO, SIMO, and MISO The detailed calculation for SNR and Pe is shown in [1] SISO: Receive Diversity (SIMO): Ninxhy iii ,2,1, =+= ∑= N i hSNRhSNR 2 )( 2 1 1 SNR Pe + ≤ nhxy += 2 2 2 )( hSNR nE hxE hSNR == and N SNR Pe + ≤ 2 1 1 and
- 13. MIMO Diversity and Reliability • The values for SNR and Pe for: Transmit Diversity (MISO): • Transmit/Receive Diversity (MIMO): The received signal at antenna i will be: ijij M j i nxhy += ∑=1 2 2 )( },min{ HSNRHSNR MN HSNR ≤≤ M SNR Pe + ≤ 2 1 1 nxhy j M j j += ∑=1 ∑= = M j jhSNRhSNR 1 2 )( and MN MN SNR Pe + ≤ },min{2 1 1 and
- 14. Conclusion • The capacity of Receive or Transmit Diversity grows logarithmically with the number of antennas • Capacity of MEMO increases linearly with the number of antennas • Using Spatial Diversity: • The SNR increases and Pe decreases when using MIMO
- 15. References [1] MIMO Architecture for Wireless Communication: Intel Technology Journal, vol. 10, Issue 02, May 2006 [2] MIMO Systems and Transmit Diversity, www.comm.utoronto.ca/~rsadve/Notes/DiversityT ransmit.pdf [3] R.A. Carrasco, Space-time Diversity Codes for fading Channel, Staffordshire University