Prakshep Mehta (03307909) Guided By: Prof. R.K. Shevgaonkar

1. MIMO Antenna Systems for Wireless Communication Prakshep Mehta (03307909) Guided By: Prof. R.K. Shevgaonkar

2. Outline • Introduction...Why MIMO?? • What is MIMO ?? • From SISO to MIMO • The ”pipe” interpretation • To exploit the MIMO channel • BLAST • Space Time Coding • Special Cases • Still to Conquer Foschini, Bell Labs 1996 Tarokh, Seshadri & Calderbank 1998

3. Whatis MIMO ??

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. 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 C = log2det[I +(PT/2s2 )·HH†]= Where the i are the eigenvalues to HH†

7. 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

8. 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

9. 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 }

10. Solution: BLAST algorithm • Idea: NON-LINEAR DETECTOR • Step 1: H+ = (HHH)-1HH • Step 2: Find the strongest signal (Strongest = the one with the highest post detection SNR) • Step 3: Detect it (Nearest neighbor among Q) • Step 4: Subtract it • Step 5: if not all yet detected, go to step 2

11. 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 MMSE at Decoder) *{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 }

12. 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 }

13. 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

14. Still to Conquer !! • Backward Compatibility • Antenna Spacing • Complexity at Receiver

15. ”Take- home message” • MIMO is the FUTURE