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

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

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)

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

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

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)

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

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

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.

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

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

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.

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

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.

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

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

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

Simulation Results of Alamouti Scheme Simulation Parameters Number of Antennas – 1x1, 2x1, 3x1, 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

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.

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

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

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

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

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

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

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 ]

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

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

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.

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

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……………

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. 311-335, 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. 14-16, January 1999 Benjebbour, A., Murata, H. and Yoshida, S., “Comparison of ordered successive receivers for space-time transmission,” Vehicular Technology Conference, 2001. VTC 2001 Fall. IEEE VTS 54th , Vol. 4 , pp. 2053 - 2057 , 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. 744-765, 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, 18-21 Sept. 2000

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. 14-16, 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