Promises of Wireless MIMO Systems Mattias Wennstrm Uppsala

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

Outline • • Introduction. . . why MIMO? ? Shannon capacity of MIMO systems Telatar, AT&T 1995 The ”pipe” interpretation To exploit the MIMO channel – BLAST Foschini, Bell Labs 1996 – Space Time Coding Tarokh, Seshadri & Calderbank 1998 – Beamforming • Comparisons & hardware issues • Space time coding in 3 G & EDGE 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 outdoor ”Specular” ”Scattering” channels indoor Phased array range extension, interference reduction Mattias Wennström Signals & Systems Group Adaptive Antennas interference cancellation MIMO Systems (diversity)

Initial Assumptions • • • Mattias Wennström Signals & Systems Group 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

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

Transmit diversity / beamforming H 11 H 12 Cdiversity = log 2(1+(PT/2 s 2)·|H|2) [bit/(Hz·s)] Cbeamforming = log 2(1 +(PT/s 2 )·|H|2) • 3 d. B SNR increase if transmitter knows H • Capacity increases logarithmically with nt Mattias Wennström Signals & Systems Group [bit/(Hz·s)]

Multiple Input Multiple Output systems H 12 H 21 H 11 H 22 Cdiversity = log 2 det[I +(PT/2 s 2 )·HH†]= Interpretation: Transmitter Mattias Wennström Signals & Systems Group 1 2 m=min(nr, nt) parallel channels, equal power allocated to each ”pipe” Where the i are the eigenvalues to HH† Receiver

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 Mattias Wennström Signals & Systems Group p 1 1 p 2 2 p 3 p 4 3 4

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

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 R 0 given a outage probability Pout = Pr{ C < R 0 }, this is the delay limited capacity. Mattias Wennström Signals & Systems Group Outage probability approximates the Word error probability for coding blocks of approx length 100

Example : Rayleigh fading channel Hij CN (0, 1) Ordered eigenvalue distribution for nr= nt = 4 case. Mattias Wennström Signals & Systems Group nr=1 nr= nt

To Exploit the MIMO Channel Bell Labs Layered Space Time Architecture Antenna Time s 1 s 1 s 1 s 2 s 2 s 2 s 3 s 3 s 3 s 0 s 1 s 2 s 0 s 1 s 2 s 0 Mattias Wennström Signals & Systems Group V-BLAST D-BLAST • 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 }

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 Mattias Wennström Signals & Systems Group *{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 }

Orthogonal Space-time Block Codes Block of T symbols Constellation mapper Data in STBC Block of K symbols Mattias Wennström Signals & Systems Group 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= nt the code has minimum delay • Detector is linear !!! *{V. Tarokh, H. Jafarkhani, A. R. Calderbank Space-time block codes from orthogonal designs, IEEE Trans. On Information Theory June 1999 }

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

Diagonal matrix due to orthogonality The MIMO/ MISO system is in fact transformed to an equivalent SISO system with SNReq = || H ||F 2 SNR/nt Mattias Wennström Signals & Systems Group || H ||F 2 = 1+ 2

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 Example: nt =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) The PDF of || H ||F 2 = 1+ 2+. . + m Assume BPSK modulation BER is then given by Diversity gain nrnt which is same as for orthogonal channels Mattias Wennström Signals & Systems Group nt=4 transmit antennas and nr is varied.

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 Mattias Wennström Signals & Systems Group Cbeamforming = log 2(1+SNR· 1) [bit/(Hz·s)]

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 (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. Mattias Wennström Signals & Systems Group

WCDMA Transmit diversity concept (3 GPP Release ’ 99 with 2 TX antennas) • 2 modes Open loop mode is exactly the 2 antenna STBC • Open loop (STTD) • Closed loop (1 bit / slot feedback) • Submode 1 (1 phase bit) • Submode 2 (3 phase bits / 1 gain bit) 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) Block S 1(t) Time reversal Complex conjugate S(t) S 2(t) Mattias Wennström Signals & Systems Group -1

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