1. Multiple Input Multiple Output (MIMO) Communications System
Madhup Khatiwada
(M.E. Student)
University of Canterbury, Christchurch, New Zealand
Supervisor – Dr. P. J. Smith

2. MIMO Wireless System Introduction I
Multiple Input Multiple Output (MIMO)
Multiple antennas at source and destination.
Motivation : Current wireless systems
Capacity constrained networks.
Issues related to quality and coverage
Coding
Modulation
Demodulation
Decoding
N TXers
M RXers
Channel H

3. Introduction II MIMO increases capacity
MIMO uses independent channel fading due to multipath propagation to increase capacity.
No extra expen$ive bandwidth required !!
MIMO gives reliable communication
Multiple independent samples of the same signal at the receiver give rise to “diversity”.
C  NT log2(1 + SNR)

4. Introduction III Diversity exhibited : Spatial diversity
spacing between antennas
Transmit diversity
space – time coding
Receive diversity
receive antennas

5. System Model I MIMO system with N transmit and M receive antennas
R : received vector
H : quasi-static channel matrix
s : transmitted vector
n : white Gaussian noise vector

6. System Model II Rayleigh channel model : multi-path
Channel between any two pair of antennas is independent
Each hik is complex Gaussian with unit variance
Ricean channel model : line of sight (K = 0dB)

7. What led us to MIMO?
Courtesy- AT&T Labs

8. Shortcoming of SISO channels
SISO Channel Equation
r(t) = H(t)*s(t)+n(t)
Problems with SISO channels:
High Pathloss.
Interference of multipaths.
Inefficient bandwidth utilisation.
Low gain.
Capacity of the SISO channel:
Where ρ is the SNR at any RX antenna

9. Exploring Ideas on Diversity
Make use of Multipath propagation, than mitigate it.
Improves the performance in fading.
Frequency Diversity: Signal transmitted in several frequency bands (coherence BW).
Time Diversity: Signal is transmitted in different time slots.
Polarization Diversity: Two antennas with different polarisation for reception/transmission.
Space Diversity: Multiple antennas to receive signal.

10. Receive Diversity H11 H21 SIMO channel H = [ H11 H21]
Use of well separated multiple receive antennas to generate independent reception of symbols.
Selection Diversity: Choose signal with largest received power or SNR.
Switched Diversity: Choose alternate antenna if signal falls below certain threshold.
Linear Combining: Linearly combine weight replica of all received signal.
Capacity increases logarithmically with number of receive antennas

11. Transmit Diversity H11 H12 MISO channel
Improves signal quality at Rx by simple processing across two transmit antennas.
Tx Diversity order = Rx Diversity order (MRRC).(Alamouti scheme)
No feedback from Tx to Rx.
No bandwidth expansion needed.
Improves error performance, data rate or capacity.
Allows to use higher level modulation schemes.
Capacity increases logarithmically with number of transmit antenna

12. Multiple Input Multiple Output system
H11
H22
H12
H21
MIMO channel
Transmitting Tx and receiving Rx ends equipped with multiple antenna system.
Two dimensional channel: Spatial and Temporal
Often described as independent channels.
Multiple independent samples of the same signal at the receiver gives rise to “diversity”. MIMO channels transfer function is a complex matrix H for N Tx and M Rx antennas.
MIMO uses independent channel fading due to multipath propagation to increase capacity.

13. Comparison of Capacity
Probability (capacity > abscissa)
Capacity (bits/sec/Hz)
Increased MIMO channel capacity compared to SISO, SIMO or MISO.

14. Space- Time Coding I
Space- Time Coding scheme allows for the adjusting and optimization of joint encoding across space and time in order to maximize the reliability of a wireless link.
Space- Time Coding provides diversity gain and coding gain by introducing spatial and temporal correlation into the signals.
Space- Time Coding also
Improves Downlink performance.
Does not require CSI at the Tx.
Robust again non-ideal connections.

15. Space- Time Coding II
For each input symbol, space time encoder chooses the constellation points to simultaneously transmit from each antenna, achieving coding gain and diversity
A Typical ST Coding Model may include
N Tx and M Rx antennas.
Overall channel made up of N*M slowly varying subchannels.
Each sub-channel is modelled as Rayleigh fading.
At any time N signals are transmitted simultaneously one from each Tx antenna.
The sub-channels undergo independent fading.
Fading coefficients are assumed to be fixed and independent.
V.Tarokh, H.Jafarkhani, A.R.Calderbank Space-time block codes from orthogonal designs, IEEE Trans. On Information Theory June 1999

16. Space- Time Coding III Space-Time Block Codes:
These codes are transmitted using an orthogonal block structure which enables simple decoding at the receiver.
diversity gain (use outer code to get coding gain)
simple detection
Space-Time Trellis Codes:
These are convolutional codes extended to the case of multiple transmit and receive antennas.
coding and diversity gain
require Viterbi detector, which is complex

17. Space- Time Block Code – Alamouti Scheme
Decoding:
Linearly combine received symbols.
Perform Maximum Likelihood (ML) detection.
Alamouti, S. M., “A simple transmit diversity technique for wireless communications” Selected Areas in Communications, IEEE Journal,16(8):1451–1458, 1998

18. Simulation Results of Alamouti Scheme
Simulation Parameters
Number of Antennas – 1x1, 2x1, x1, 4x1.
Modulation Scheme – BPSK
Channel Model – Flat Rayleigh Fading
Increase in number of antennas leads to increase in diversity which consequently leads to better system performance.
Courtesy- Hoo-Jin Lee, Shailesh Patil, and Raghu G. Raj, Univ. of Texas

19. Spatial Multiplexing Technique – An Overview
Multiple data streams are transmitted simultaneously and on the same frequency using a transmit array
Different data sub-streams are transmitted from different antennas
The transmitter needs no channel state information
No need for fast feedback links.

20. Spatial Multiplexing Detection
Maximum Likelihood (ML): optimum and most time consuming detection method
Linear detection
Zero-Forcing (ZF): pseudo inverse of the channel, simple
Minimum mean-squared error (MMSE) : simple detection with intermediate performance

21. Comparison of Detection Methods
Simulation Parameters
Number of Antennas – 4 x 4
Modulation Scheme – BPSK
Channel Model – Flat Rayleigh Fading

22. Comparison for different systems
Simulation Parameters
Number of Antennas – 2 x 2, 6 x 6, 8 x 8
Modulation Scheme – BPSK
Channel Model – Flat Rayleigh Fading

23. V-BLAST V-BLAST (Vertical Bell Labs Layered Space-Time)
extracts data streams by ZF or MMSE filter with ordered successive interference cancellation (SIC)
Steps for V-BLAST detection
Ordering: choosing the “best” channel
Interference Nulling/ Reduction : using ZF or MMSE
Slicing: making a symbol decision
Canceling: subtracting the detected symbol
Iteration: going to the first step to
detect the next symbol
G.J.Foschini, Bell Labs Technical Journal 1996

24. Performance of V-BLAST
Simulation Parameters
Number of Antennas – 4 x 4
Modulation Scheme – BPSK
Channel Model – Flat Rayleigh Fading

25. Comparison among Spatial Multiplexing Receivers in Rayleigh Channel
Simulation Parameters
Number of Antennas – 2 x 3
Modulation Scheme – 4 QAM
Channel Model – Flat Rayleigh Fading
Performance and Complexity:
ML receiver > MMSE V-BLAST (SIC) receiver
> ZF V-BLAST (SIC) receiver > MMSE receiver > ZF receiver
Courtesy- Hoo-Jin Lee, Shailesh Patil, and Raghu G. Raj, Univ. of Texas

26. Issues of Ordering and Speed I
Optimal ordering plays a significant role in achieving high performance
In V-BLAST, the best channel is picked based on highest SINR, but picking up channels based on highest SINR value doesn’t seem to be the optimal way of ordering.
[ In the initial V-BLAST paper, Foschini et al. have proposed a optimal method for ordering for ZF detection. But for MMSE detection (which is proved to be better than ZF), no such optimal ordering scheme has been proposed. So it has been a practice to order based on highest SINR in MMSE detection ]

27. Significance of Optimal Ordering
Simulation Parameters
Number of Antennas – 4 x 4
Modulation Scheme – BPSK
Channel Model – Flat Rayleigh Fading
Picking the first best channel can effect significantly in the whole system performance

28. Issues of Ordering and Speed II
Switching
Switching based on SINR or Eigenvalues of the channel helps in reducing the computational time by adding very little complexity to the system.
Switching is a scheme in which the receiver switches its detection technique from V-BLAST MMSE to simple MMSE depending upon the channel condition (either SINR values or eigenvalues of the channel).
Switching allows us to trade off performance with time

29. Significance of Switching
Simulation time reduced by nearly 60% at 10 db SNR case
Simulation Parameters
Number of Antennas – 4 x 4
Modulation Scheme – BPSK
Channel Model – Flat Rayleigh Fading
The position of the blue curve may vary anywhere between the black and red curves depending upon performance we require trading off with the processing time.

30. Significance of Ordering and Switching in Overloaded system
Simulation Parameters
Number of Antennas – 4 x 2
Modulation Scheme – BPSK
Channel Model – Flat Rayleigh Fading
For systems with less receive antennas, optimal ordering can be a crucial issue for system performance

31. This research project is still on progress……………
“Take- home Message”
Channel capacity increases linearly with min(M, N) antennas.
Optimal ordering plays a vital role in increasing the performance of V-BLAST systems with MMSE.
Switching techniques may be useful in reducing processing time while adding very little complexity to the system.
This research project is still on progress……………

32. Key references I
Foschini, G. J. and Gans, M. J., “ On limits of wireless communications in a fading environment when using multiple antennas,” Wireless Personal Communications, Vol. 6, pp , 1998
Golden, G. D., Foschini, G. J., Valenzuela, R. A., and Wolniansky, P. W., “ Detection algorithm and initial laboratory results using V-BLAST space-time communication architecture,” IEE Lett., Vol. 35, No. 1, pp , January 1999
Benjebbour, A., Murata, H. and Yoshida, S., “Comparison of ordered successive receivers for space-time transmission,” Vehicular Technology Conference, VTC 2001 Fall. IEEE VTS 54th , Vol. 4 , pp , 7-11 Oct. 2001
Tarokh, V., Jafarkhani, H., and Calderbank, A. R., “Space-time Codes for High Data Rate Wireless Communication: Performance Criterion and Code Construction,” IEEE Trans. Inform. Theory, Vol. 44, No. 2, pp , July 1998
Hassell, C.Z.W., Thompson, J., Mulgrew, B. and Grant, P.M., “A comparison of detection algorithms including BLAST for wireless communication using multiple antennas” The 11th IEEE International Symposium on Personal, Indoor and Mobile Radio Communications, Vol. 1 , pp. 698 – 703, Sept. 2000

33. Key references II
Alamouti, S. M., “A simple transmit diversity technique for wireless communications,” Selected Areas in Communications, IEEE Journal,16(8):1451–1458, 1998
Gore, D. A., Heath, R. W. Jr., and Paulraj, A. J., “Performance Analysis of Spatial Multiplexing in Correlated Channels,” submitted to Communications, IEEE Transactions March 2002
Golden, G. D., Foschini, C. J., Valenzuela, R. A., and Wolniansky, P. W., “ Detection algorithm and initial laboratory results using V-BLAST space-time communication architecture,” IEEE Lett., Vol. 35, No. 1, pp , January 1999
Gesbert, D.; Shafi, M.; Da-shan Shiu; Smith, P.J.; Naguib, A .,“From theory to practice: an overview of MIMO space-time coded wireless systems”, Selected Areas in Communications, IEEE Journal on , Vol. 21 , Issue. 3,pp.281 – 302, April 2003