1. 8: MIMO II: Capacity and Multiplexing Architectures Fundamentals of Wireless Communication, Tse&Viswanath 1 8. MIMO II: Capacity and Multiplexing Architectures

2. 8: MIMO II: Capacity and Multiplexing Architectures Fundamentals of Wireless Communication, Tse&Viswanath 2 Outline Capacity of MIMO fading channels Nature of performance gains Transceiver architectures for fast fading (V-BLAST family) Transceiver architecture for slow fading (D-BLAST) More on performance in slow fading in next section.

3. 8: MIMO II: Capacity and Multiplexing Architectures Fundamentals of Wireless Communication, Tse&Viswanath 3 Transmitter and Receiver CSI Can decompose the MIMO channel into a bunch of orthogonal sub-channels. Can allocate power and rate to each sub-channel according to waterfilling

4. 8: MIMO II: Capacity and Multiplexing Architectures Fundamentals of Wireless Communication, Tse&Viswanath 4 Analogy with OFDM Major difference: In MIMO, the U and V matrices depend on the channel H. In OFDM, the IDFT and DFT matrices do not.

5. 8: MIMO II: Capacity and Multiplexing Architectures Fundamentals of Wireless Communication, Tse&Viswanath 5 Receiver CSI Only The channel matrix H and its singular values i 2 's are random and unknown to the transmitter. Has to fix a Q and a power allocation independent of H. Q = I and uniform power allocation is optimal in many cases. It is not trivial to come up with capacity-achieving architectures.

6. 8: MIMO II: Capacity and Multiplexing Architectures Fundamentals of Wireless Communication, Tse&Viswanath 6 Capacity Can write: Slow fading: Fast fading:

7. 8: MIMO II: Capacity and Multiplexing Architectures Fundamentals of Wireless Communication, Tse&Viswanath 7 Fast Fading Capacity for I.I.D. Rayleigh Fading

8. 8: MIMO II: Capacity and Multiplexing Architectures Fundamentals of Wireless Communication, Tse&Viswanath 8 d.o.f. determines the high SNR slope.

9. 8: MIMO II: Capacity and Multiplexing Architectures Fundamentals of Wireless Communication, Tse&Viswanath 9 Fast Fading Capacity: Low SNR n r – fold power gain at low SNR

10. 8: MIMO II: Capacity and Multiplexing Architectures Fundamentals of Wireless Communication, Tse&Viswanath 10 Nature of Performance Gain At high SNR (d.o.f. limited): min(n t,n r )-fold d.o.f. gain. MIMO is crucial. At low SNR (power limited): n r -fold power gain. Only need multiple receive antennas. At all SNR, min(n t,n r )-fold gain due to a combination of both effects.

11. 8: MIMO II: Capacity and Multiplexing Architectures Fundamentals of Wireless Communication, Tse&Viswanath 11 System Question Should one blindly overlay MIMO technology on CDMA universal reuse systems? These systems operate at low SINR. MIMO gain is mainly receive antenna power gain. Having multiple transmit antennas may not be necessary. Interesting implication on the uplink: expensive to have many antennas at the mobile. However mobile antennas are useful for the downlink. They can also be used to suppress out-of-cell interference and provide diversity.

12. 8: MIMO II: Capacity and Multiplexing Architectures Fundamentals of Wireless Communication, Tse&Viswanath 12 Transceiver Architecture: V-BLAST Can get the performance gain by sending independent coded streams at each of the Tx antennas and joint ML decoding. Is this surprising? Question: –How to get the d.o.f. gain even when streams interfere with each other?

13. 8: MIMO II: Capacity and Multiplexing Architectures Fundamentals of Wireless Communication, Tse&Viswanath 13 Interference Nulling Focusing on Tx antenna 1: Simple strategy: null out the interference from other antennas.

14. 8: MIMO II: Capacity and Multiplexing Architectures Fundamentals of Wireless Communication, Tse&Viswanath 14 Receiver Architecture I: Bank of Decorrelators

15. 8: MIMO II: Capacity and Multiplexing Architectures Fundamentals of Wireless Communication, Tse&Viswanath 15 Bank of Decorrelators: Performance i.i.d. Rayleigh

16. 8: MIMO II: Capacity and Multiplexing Architectures Fundamentals of Wireless Communication, Tse&Viswanath 16 Performance Gap of Decorrelator Achieves the full d.o.f. min( n t,n r ) of the MIMO channel. (Same SNR slope.) But: There is still a substantial constant gap at high SNR. At moderate and low SNR, performance sucks.

17. 8: MIMO II: Capacity and Multiplexing Architectures Fundamentals of Wireless Communication, Tse&Viswanath 17 Interference Nulling vs Match Filtering Interference nulling: remove all interference at the expense of reducing the SNR. Match filtering: projecting onto h 1 to maximize the SNR but SINR may be bad.

18. 8: MIMO II: Capacity and Multiplexing Architectures Fundamentals of Wireless Communication, Tse&Viswanath 18 Optimal Linear Filter:MMSE Seek a linear filter that maximizes the output SINR at all SNR. Offers the optimal compromise between nulling and match filtering. It whitens the interference first and then match filter. This is the linear MMSE filter.

19. 8: MIMO II: Capacity and Multiplexing Architectures Fundamentals of Wireless Communication, Tse&Viswanath 19 MMSE Filter High SNR: MMSE ¼ decorrelator Low SNR: MMSE ¼ matched filter

20. 8: MIMO II: Capacity and Multiplexing Architectures Fundamentals of Wireless Communication, Tse&Viswanath 20 Linear MMSE: Performance

21. 8: MIMO II: Capacity and Multiplexing Architectures Fundamentals of Wireless Communication, Tse&Viswanath 21 Gap at High SNR MMSE improves the performance of decorrelator at moderate and low SNR. Does not remove the gap in performance at high SNR To remove that gap we have to go to non-linear receivers.

22. 8: MIMO II: Capacity and Multiplexing Architectures Fundamentals of Wireless Communication, Tse&Viswanath 22 Successive Interference Cancellation

23. 8: MIMO II: Capacity and Multiplexing Architectures Fundamentals of Wireless Communication, Tse&Viswanath 23 MMSE-SIC Achieves MIMO Capacity

24. 8: MIMO II: Capacity and Multiplexing Architectures Fundamentals of Wireless Communication, Tse&Viswanath 24 Optimality of MMSE-SIC Given a fixed channel H, Why is MMSE-SIC optimal? MMSE is information lossless at each stage. The SIC architecture implements the chain rule of information.

25. 8: MIMO II: Capacity and Multiplexing Architectures Fundamentals of Wireless Communication, Tse&Viswanath 25 Fast vs Slow Fading So far we have focused on the fast fading scenario. Can V- BLAST achieve the outage capacity of the slow fading channel? No, cannot achieve transmit diversity. In fast fading channels, transmit diversity is not important since there is already plenty of time diversity. In slow fading channels, there is no time diversity so coding across transmit antennas becomes important. Challenge is to combine this with SIC.

26. 8: MIMO II: Capacity and Multiplexing Architectures Fundamentals of Wireless Communication, Tse&Viswanath 26 D-BLAST MMSE

27. 8: MIMO II: Capacity and Multiplexing Architectures Fundamentals of Wireless Communication, Tse&Viswanath 27 Parallel Channel Conversion D-BLAST converts the MIMO channel into a parallel channel. Any good time-diversity code can be used in conjunction with D-BLAST to achieve good outage performance.

28. 8: MIMO II: Capacity and Multiplexing Architectures Fundamentals of Wireless Communication, Tse&Viswanath 28 Uplink Architectures So far we have considered point-to-point communication. But since we are sending independent streams from each transmit antennas, we can use the receiver structures for the uplink with multiple users. This is called space-division multiple access (SDMA) Several simultaneous users can be supported. Linear MMSE also called receive beamforming.

29. 8: MIMO II: Capacity and Multiplexing Architectures Fundamentals of Wireless Communication, Tse&Viswanath 29 SDMA vs Orthogonal MA Many wireless systems use orthogonal multiple access. How does SDMA compared to just using the receive antenna array to provide a power gain for each user? At high SINR, the system is d.o.f. limited and SDMA provides significant gain. At low SINR, system is power-limited and SDMA provides limited gain. This suggests that SDMA is useful in sparse frequency reuse system or when some of the antennas are used to suppress interference from nearby cells.

30. 8: MIMO II: Capacity and Multiplexing Architectures Fundamentals of Wireless Communication, Tse&Viswanath 30 Downlink In the uplink, transmitters cannot cooperate, but receiver can jointly process the received signal at all the antennas. In the downlink, it is the receivers that cannot cooperate. If the transmitter does not track the channel, cannot do SDMA on the downlink. If it does, can use techniques reciprocal to the uplink.

31. 8: MIMO II: Capacity and Multiplexing Architectures Fundamentals of Wireless Communication, Tse&Viswanath 31 Uplink-Downlink Reciprocity The total power to achieve given SINR requirements is the same in the two links. Can use MMSE filters in the “virtual” uplink for downlink transmit beamforming.

32. 8: MIMO II: Capacity and Multiplexing Architectures Fundamentals of Wireless Communication, Tse&Viswanath 32 Downlink Transmit Beamforming Can use transmit filter for user 1 that nulls out interference to other users. (downlink decorrelator.) More generally, can optimally balance the energy transferred to the users and the inter-user interference (downlink MMSE)

33. 8: MIMO II: Capacity and Multiplexing Architectures Fundamentals of Wireless Communication, Tse&Viswanath 33 Example: ArrayComm SDMA overlay on Japan’s PHS system, also a newer data system (iBurst) Up to 12 antennas at BS, with up to 4 users simultaneously in SDMA. Antennas also used to null out inter-cell interference, increasing frequency-reuse factor (from 1/8 to 1 in PHS) System is TDD. Channel is measured from pilot in uplink, and used in downlink transmit beamforming.

34. 8: MIMO II: Capacity and Multiplexing Architectures Fundamentals of Wireless Communication, Tse&Viswanath 34 Uplink-Downlink Duality Linear receive beamforming strategies for the uplink map to linear transmit beamforming strategies in the downlink. But in the uplink we can improve performance by doing successive interference cancellation at the receiver Is there a dual to this strategy in the downlink?

35. 8: MIMO II: Capacity and Multiplexing Architectures Fundamentals of Wireless Communication, Tse&Viswanath 35 Transmit Precoding In downlink transmit beamforming, signals for different users are superimposed and interfere with each other. With a single transmit antenna, users are ordered in terms of signal strength. A user can decode and cancel all the signals intended for the weaker user before decoding its own. With multiple Tx antennas, no such ordering exists and no user may be able to decode information beamformed to other users. However, the base station knows the information to be transmitted to every user and can precode to cancel at the transmitter.

36. 8: MIMO II: Capacity and Multiplexing Architectures Fundamentals of Wireless Communication, Tse&Viswanath 36 Symbol-by-Symbol Precoding Generic problem: Interference s is known at the transmitter, not at the receiver. Applications: –downlink: s is signal for another user. –information embedding: s is the host signal. –ISI precoding: s is the intersymbol interference.

37. 8: MIMO II: Capacity and Multiplexing Architectures Fundamentals of Wireless Communication, Tse&Viswanath 37 Naïve Pre-cancellation Strategy Want to send point u in a 4-PAM constellation. Transmit to pre-cancel the effect of s. But this is very power inefficient if s is large.

38. 8: MIMO II: Capacity and Multiplexing Architectures Fundamentals of Wireless Communication, Tse&Viswanath 38 Tomlinson-Harashima Precoding (I) Replicate the PAM constellation to tile the whole real line. Represent information u by an equivalence class of constellation points instead of a single point.

39. 8: MIMO II: Capacity and Multiplexing Architectures Fundamentals of Wireless Communication, Tse&Viswanath 39 Tomlinson-Harashima Precoding (II) Given u and s, find the point in its equivalence class closest to s and transmit the difference.

40. 8: MIMO II: Capacity and Multiplexing Architectures Fundamentals of Wireless Communication, Tse&Viswanath 40 Writing on Dirty Paper Can extend this idea to block precoding. Problem is to design codes which are simultaneously good source codes (vector quantizers) as well as good channel codes. Somewhat surprising, information theory guarantees that one can get to the capacity of the AWGN channel with the interference completely removed. Applying this to the downlink, can perform SIC at the transmitter.