Mattias Wennström Uppsala University Sweden

1. Promises of Wireless MIMO Systems Mattias Wennström Uppsala University Sweden

2. Outline • Introduction...why MIMO?? • Shannon capacity of MIMO systems • The ”pipe” interpretation • To exploit the MIMO channel • BLAST • Space Time Coding • Beamforming • Comparisons & hardware issues • Space time coding in 3G & EDGE Telatar, AT&T 1995 Foschini, Bell Labs 1996 Tarokh, Seshadri & Calderbank 1998 Release ’99

3. outdoor indoor ”Specular” channels ”Scattering” channels Why multiple antennas ???? • Frequency and time processing are at limits • Space processing is interesting because it • does not increase bandwidth Phased array range extension, interference reduction MIMO Systems (diversity) Adaptive Antennas interference cancellation

4. Initial Assumptions • Flat fading channel (Bcoh>> 1/ Tsymb) • Slowly fading channel (Tcoh>> Tsymb) • nr receive and nt transmit antennas • Noise limited system (no CCI) • Receiver estimates the channel perfectly • We consider space diversity only

5. = log2[1+(PT/s2)·|H|2] [bit/(Hz·s)] H = [ H11 H21] Capacity increases logarithmically with number of receive antennas... ”Classical” receive diversity H11 H21

6. H11 H12 • 3 dB SNR increase if transmitter knows H • Capacity increases logarithmically with nt Transmit diversity / beamforming Cdiversity = log2(1+(PT/2s2)·|H|2) [bit/(Hz·s)] Cbeamforming = log2(1 +(PT/s2 )·|H|2) [bit/(Hz·s)]

7. Interpretation: l1 Receiver Transmitter l2 m=min(nr, nt) parallel channels, equal power allocated to each ”pipe” Multiple Input Multiple Output systems H11 H21 H12 H22 Cdiversity = log2det[I +(PT/2s2 )·HH†]= Where the i are the eigenvalues to HH†

8. H known at TX Where the power distribution over ”pipes” are given by a water filling solution l1 p1 l2 p2 l3 p3 l4 p4 MIMO capacity in general H unknown at TX

9. The Channel Eigenvalues Orthogonal channelsHH† =I,1=2=…= m=1 • Capacity increases linearly with min( nr , nt ) • An equal amount of power PT/nt is allocated • to each ”pipe” Transmitter Receiver

10. Random channel models and Delay limited capacity • In stochastic channels, • the channel capacity becomes a random variable Define : Outage probability Pout = Pr{ C < R } Define : Outage capacity R0 given a outage probability Pout = Pr{ C < R0 }, this is the delay limited capacity. Outage probability approximates the Word error probability for coding blocks of approx length100

11. Example : Rayleigh fading channel Hij CN (0,1) Ordered eigenvalue distribution for nr= nt = 4 case. nr=1 nr= nt

12. Time s1 s1 s1 s1 s1 s1 V-BLAST Antenna s2 s2 s2 s2 s2 s2 s3 s3 s3 s3 s3 s3 s0 s1 s2 s0 s1 s2 D-BLAST s0 s1 s2 s0 s1 s0 s1 s2 s0 To Exploit the MIMO Channel Bell Labs Layered Space Time Architecture • nr  nt required • Symbol by symbol detection. Using nulling and symbol cancellation • V-BLAST implemented -98 by Bell Labs (40 bps/Hz) • If one ”pipe” is bad in BLAST we get errors ... {G.J.Foschini, Bell Labs Technical Journal 1996 }

13. Space Time Coding • Use parallel channel to obtain diversity not • spectral efficiency as in BLAST • Space-Time trellis codes : coding and diversity gain (require Viterbi detector) • Space-Time block codes : diversity gain • (use outer code to get coding gain) • nr= 1 is possible • Properly designed codes acheive diversity of nr nt *{V.Tarokh, N.Seshadri, A.R.Calderbank Space-time codes for high data rate wireless communication: Performance Criterion and Code Construction , IEEE Trans. On Information Theory March 1998 }

14. Orthogonal Space-time Block Codes Block of T symbols Constellation mapper STBC Data in nt transmit antennas • K input symbols, T output symbols T K • R=K/T is the code rate • If R=1 the STBC has full rate • If T= ntthe code has minimum delay • Detector is linear !!! Block of K symbols *{V.Tarokh, H.Jafarkhani, A.R.Calderbank Space-time block codes from orthogonal designs, IEEE Trans. On Information Theory June 1999 }

15. STBC for 2 Transmit Antennas Full rate and minimum delay [ c0 c1 ]  Antenna Time Assume 1 RX antenna: Received signal at time 0 Received signal at time 1

16. The MIMO/ MISO system is in fact transformed to an equivalent SISO system with SNR SNReq = ||H ||F2SNR/nt l1+l2 ||H ||F2 = l1+l2 Diagonal matrix due to orthogonality

17. Example: nt =4, K=3, T=4  R=3/4 The existence of Orthogonal STBC • Real symbols : For nt =2,4,8 exists delay optimal • full rate codes. • For nt =3,5,6,7,>8 exists full rate • codes with delay (T>K) • Complex symbols : For nt =2 exists delay optimal • full rate codes. • For nt =3,4 exists rate 3/4 codes • For nt > 4 exists (so far) • rate 1/2 codes

18. Outage capacity of STBC Optimal capacity • STBC is optimal • wrt capacity if • HH† = || H ||F2 • which is the case for • MISO systems • Low rank channels 

19. Performance of the STBC… (Rayleigh faded channel) The PDF of Assume BPSK modulation BER is then given by ||H ||F2 = l1+l2+ .. + lm Diversity gain nrnt which is same as for orthogonal channels nt=4 transmit antennas and nr is varied.

20. MIMO With Beamforming Requires that channel H is known at the transmitter Is the capacity-optimal transmission strategy if Which is often true for line of sight (LOS) channels Only one ”pipe” is used Cbeamforming = log2(1+SNR·1) [bit/(Hz·s)]

21. Comparisons... 2 * 2 system. With specular component (Ricean fading) One dominating eigenvalue. BF puts all energy into that ”pipe”

22. Correlated channels / Mutual coupling ... When angle spread (D) is small, we have a dominating eigenvalue. The mutual coupling actually improves the performance of the STBC by making the eigenvalues ”more equal” in magnitude.

23. Open loop mode is exactly the 2 antenna STBC The feedback bits (1500 Hz) determines the beamformer weights Submode 1 Equal power and bit chooses phase between {0,180} / {90/270} Submode 2 Bit one chooses power division {0.8 , 0.2} / {0.2 , 0.8} and 3 bits chooses phase in an 8-PSK constellation WCDMA Transmit diversity concept (3GPP Release ’99 with 2 TX antennas) • 2 modes • Open loop (STTD) • Closed loop (1 bit / slot feedback) • Submode 1 (1 phase bit) • Submode 2 (3 phase bits / 1 gain bit)

24. Time reversal Complex conjugate Time reversal Complex conjugate -1 GSM/EDGE Space time coding proposal • Frequency selective channel … • Require new software in terminals .. • Invented by Erik Lindskog Time Reversal Space Time Coding (works for 2 antennas) Block S1(t) S(t) S2(t)

25. ”Take- home message” • Channel capacity increases linearly • with min(nr, nt) • STBC is in the 3GPP WCDMA proposal