SYSC 4607 – Lecture 19 Outline

1. SYSC 4607 – Lecture 19 Outline • Capacity of MIMO Channels - Static Channel with CSIR, with and without CSIT - Fading Channel with CSIR, with and without CSIT

2. Capacity of MIMO Channels

3. MIMO Channel Capacity • Depends on what is known at TX and RX and if channel is static or fading • For static channel with perfect CSI at TX and RX, power water-filling over space is optimal: • In fading, water-filling over space (based on short-term power constraint) or space-time (long-term power constraint) • Without transmitter channel knowledge, capacity metric is based on an outage probability (Pout is the probability that the channel capacity given the channel realization is below the transmission rate).

4. Static Channel Capacity

5. Static Channel Capacity

6. Static Channel Capacity (CSIT)

7. Static Channel Capacity (CSIT)

8. Static Channel Capacity (no CSIT)

9. Static Channel Capacity (no CSIT)

10. Fading Channel Capacity

11. Fading Channel Capacity

12. Fading Channel Capacity

13. Fading Channel CapacityMIMO Ergodic Capacity

14. Fading Channel CapacityMIMO Ergodic Capacity (SNR=10dB)

15. Fading Channel CapacityMIMO Outage Capacity

16. Main Points • MIMO capacity is the sum of the capacities of parallel channels. • Depends on: - static or fading - channel knowledge: CSIR, CSIT, channel distribution only • For static channel with perfect channel knowledge at TX and RX, water-filling over space is optimal power allocation • Similar idea in fading, based on short-term or long-term power constraint • Without channel knowledge, capacity metric is based on an outage probability