1. Channel Capacity of MIMO Channels 指導教授：黃文傑 老師 指導教授：黃文傑 老師 學 生：曾凱霖 學 生：曾凱霖 學 號： M9121014 學 號： M9121014 無線通訊實驗室 無線通訊實驗室

2. Outline 1 、 Introduction 2 、 Shannon capacity of MIMO systems 3 、 The ”pipe” interpretation 4 、 To exploit the MIMO channel –BLAST –Space Time Coding 5 、 Conclusion

3. Why multiple antennas ???? Frequency and time processing are at limits. Space processing is interesting because it does not increase bandwidth.

4. Initial Assumptions Flat fading channel (Bcoh>> 1/ Tsymb) Slowly fading channel (Tcoh>> Tsymb) receive and nt transmit antennas Receiver estimates the channel perfectly We consider space diversity only

5. SISO Systems y(t) = h x(t) + n(t) x(t): transmitted signal y(t): received signal h(t): channel transfer function n(t): noise (AWGN,  2 ) Signal to noise ratio : Capacity : C = log 2 (1+  ) x(t) y(t) h

6. Receive Diversity H 11 H 21 = log 2 [1+(P T  2 )·|H| 2 ] [bit/(Hz·s)] H = [ H 11 H 21 ] Capacity increases logarithmically with number of receive antennas...

7. Transmit Diversity / Beamforming H 11 H 12 C diversity = log 2 (1+(P T  2 )·|H| 2 ) [bit/(Hz·s)] Capacity increases logarithmically with n t

8. MIMO Systems H 11 H 22 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

9. 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

10. 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

11. 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) Bell Labs Layered Space Time Architecture {G.J.Foschini, Bell Labs Technical Journal 1996 }

12. 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

13. 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

14. 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

15. 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 =      

16. Conclusion MIMO systems are a promising technique for high data rates. Their efficiency depends on the channel between the transmitters and the receivers (power and correlation). Practical issues need to be resolved.