Mattias Wennström Signals & Systems Group Mattias Wennström Uppsala University Sweden Promises of Wireless MIMO Systems

Mattias Wennström Signals & Systems Group 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

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

Mattias Wennström Signals & Systems Group Initial Assumptions Flat fading channel (B coh >> 1/ T symb ) Slowly fading channel (T coh >> T symb ) n r receive and n t transmit antennas Noise limited system (no CCI) Receiver estimates the channel perfectly We consider space diversity only

Mattias Wennström Signals & Systems Group H 11 H 21 ”Classical” receive diversity = log 2 [1+(P T  2 )·|H| 2 ] [bit/(Hz·s)] H = [ H 11 H 21 ] Capacity increases logarithmically with number of receive antennas...

Mattias Wennström Signals & Systems Group Transmit diversity / beamforming H 11 H 12 C diversity = log 2 (1+(P T  2 )·|H| 2 ) [bit/(Hz·s)] C beamforming = log 2 (1 +(P T  2 )·|H| 2 ) [bit/(Hz·s)] 3 dB SNR increase if transmitter knows H Capacity increases logarithmically with n t

Mattias Wennström Signals & Systems Group H 11 H 22 Multiple Input Multiple Output systems H 12 H 21 C diversity = log 2 det[I +(P T  2 )·HH † ]= Where the i are the eigenvalues to HH †   m=min(n r, n t ) parallel channels, equal power allocated to each ”pipe” Interpretation: Receiver Transmitter

Mattias Wennström Signals & Systems Group MIMO capacity in general H unknown at TX H known at TX Where the power distribution over ”pipes” are given by a water filling solution     p1p1 p2p2 p3p3 p4p4

Mattias Wennström Signals & Systems Group The Channel Eigenvalues Orthogonal channels HH † = I, 1 = 2 = …= m = 1 Capacity increases linearly with min( n r, n t ) An equal amount of power P T /n t is allocated to each ”pipe” Transmitter Receiver

Mattias Wennström Signals & Systems Group Random channel models and Delay limited capacity In stochastic channels, the channel capacity becomes a random variable Define : Outage probability P out = Pr{ C < R } Define : Outage capacity R 0 given a outage probability P out = Pr{ C < R 0 }, this is the delay limited capacity. Outage probability approximates the Word error probability for coding blocks of approx length100

Mattias Wennström Signals & Systems Group Example : Rayleigh fading channel H ij  CN (0,1) n r =1n r = n t Ordered eigenvalue distribution for n r = n t = 4 case.

Mattias Wennström Signals & Systems Group To Exploit the MIMO Channel Time s0 s1 s2 V-BLAST D-BLAST Antenna s1 s2 s3 n r  n t 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... Bell Labs Layered Space Time Architecture {G.J.Foschini, Bell Labs Technical Journal 1996 }

Mattias Wennström Signals & Systems Group Space Time Coding diversity Use parallel channel to obtain diversity not spectral efficiency as in BLAST trellisand Space-Time trellis codes : coding and diversity gain (require Viterbi detector) block Space-Time block codes : diversity gain (use outer code to get coding gain) n r = 1 is possible Properly designed codes acheive diversity of n r n t *{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 }

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

Mattias Wennström Signals & Systems Group STBC for 2 Transmit Antennas [ c 0 c 1 ]  Time Antenna Full rate Full rate and minimum delay Assume 1 RX antenna: Received signal at time 0 Received signal at time 1

Mattias Wennström Signals & Systems Group Diagonal matrix due to orthogonality The MIMO/ MISO system is in fact transformed to an equivalent SISO system with SNR SNR eq = || H || F 2 SNR/n t || H || F 2 =      

Mattias Wennström Signals & Systems Group The existence of Orthogonal STBC Real symbols : Real symbols : For n t =2,4,8 exists delay optimal full rate codes. For n t =3,5,6,7,>8 exists full rate codes with delay (T>K) Complex symbols : Complex symbols : For n t =2 exists delay optimal full rate codes. For n t =3,4 exists rate 3/4 codes For n t > 4 exists (so far) rate 1/2 codes Example: n t =4, K=3, T=4  R=3/4

Mattias Wennström Signals & Systems Group Outage capacity of STBC Optimal capacity STBC is optimal wrt capacity if HH † = || H || F 2 which is the case for MISO systems Low rank channels 

Mattias Wennström Signals & Systems Group Performance of the STBC… (Rayleigh faded channel) || H || F 2 =     m n t =4 transmit antennas and n r is varied. The PDF of Assume BPSK modulation BER is then given by Diversity gain n r n t which is same as for orthogonal channels

Mattias Wennström Signals & Systems Group MIMO With Beamforming Requires that channel H is known at the transmitter Is the capacity-optimal transmission strategy if C beamforming = log 2 (1+SNR· 1 ) [bit/(Hz·s)] Which is often true for line of sight (LOS) channels Only one ”pipe” is used

Mattias Wennström Signals & Systems Group Comparisons... 2 * 2 system. With specular component (Ricean fading) One dominating eigenvalue. BF puts all energy into that ”pipe”

Mattias Wennström Signals & Systems Group Correlated channels / Mutual coupling... When angle spread (  ) is small, we have a dominating eigenvalue. The mutual coupling actually improves improves the performance of the STBC by making the eigenvalues ”more equal” in magnitude.

Mattias Wennström Signals & Systems Group 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) 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

Mattias Wennström Signals & Systems Group 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) Time reversalComplex conjugate Time reversalComplex conjugate S(t) S 1 (t) S 2 (t) Block

Mattias Wennström Signals & Systems Group ”Take- home message” linearly Channel capacity increases linearly with min(n r, n t ) STBC is in the 3GPP WCDMA proposal