ECE 598HH: Advanced Wireless Networks and Sensing Systems. Lecture 8: MIMO Part 1 Haitham Hassanieh

Transcription

1 ECE 598HH: Advanced Wireless Networks and Sensing Systems Lecture 8: MIMO Part 1 Haitham Hassanieh

2 MIMO: Multiple Input Multiple Output So far: single input single output This lecture: multiple input multiple output Increase capacity of channel using multiple transmit and receive antennas.

3 MIMO: Multiple TX-RX streams h #" h "# h ## h "" $ " = h "" + h "# = h #" + h ## $ " = h "" h #" h "# h ## + ) " ) # * = +, + - How to recover and? Estimate +, compute +." and invert the channel!,/ = +.0 * = +.0 +, =, Transmit 2 packets at the same time!

4 MIMO: Multiple TX-RX streams h #" h "# h ## h "" $ " = h "" + h "# = h #" + h ## $ " = h "" h #" h "# h ## + How to recover and? ) " ) # * = +, + - Estimate +, compute +." and invert the channel!,/ = +.0 * = +.0 +, =, For 1 antennas, + is 1 1 matrix à Noise amplification

5 MIMO: Vector Representation h #" h "# h ## h "" $ " = h "" + h "# = h #" + h ## $ " = h "" h #" h "# h ## + ) " ) # * = +, + - How to recover and? h "" * = + =. " +. # h #" h "# h ##

6 MIMO: Antenna Space! = $ % & % + $ ( & ( Ant. 2: ) ( $ ( & (! $ % & % Ant. 1: ) %

7 MIMO: Antenna Space! = $ % & % + $ ( & ( Ant. 2: ) ( To decode & %, project on a vector $ ( * orthogonal to $( $ ( & (! $ ( *! = $( * $% & % + $ ( * $( & ( = $ ( * $% & % $ % & % h %%! = & % + & ( h (% h %( h (( $ ( *! = h(( h %% & % h %( h (% & % Ant. 1: ) % + h (( h %( & ( h %( h (( & ( $ ( * = h(( h %( = h (( h %% h %( h (% & %

8 MIMO: Antenna Space! = $ % & % + $ ( & ( Ant. 2: ) ( To decode & (, project on a vector $ % * orthogonal to $% $ ( & (! $ % *! = $% * $% & % + $ % * $( & ( = $ % * $( & ( $ % & % h %%! = & % + & ( h (% h %( h (( $ % *! = h(% h %% & % h (% h %% & % Ant. 1: ) % + h (% h %( & ( h %% h (( & ( $ % * = h(% h %% = h (% h %( h %% h (( & (

9 MIMO: Antenna Space What about MIMO with more antennas?! = $ % & % + $ ( & ( Ant. 2: ) ( +$ * & * To decode & %, project on a vector $ (* + orthogonal to the plane formed by $ ( and $ * $ ( & ( $ (* + = $( $ * $ * & * $ % & % Ant. 1: ) % Ant. 3: ) *

10 MIMO: Antenna Space What about MIMO with more antennas?! = $ % & % + $ ( & ( + $ ) & ) Ant. 2: * ( To decode & %, project on a vector $ () + orthogonal to the plane formed by $ ( and $ ) $ ( & ( $ () + = $( $ ) $ ) & ) $ % & % - antenna MIMO, receives signals in - dimensional Ant. space 1: * % à Can decode - parallel signals Decoding complexity scales.(- ( ) operations with the number Ant. of antennas 3: * )

11 MIMO Channel h #" h "# h ## h "" $ " = h "" + h "# = h #" + h ## How to estimate the channels: h "", h "#, h #", h ##? TX 1: TX 2: Preamble Preamble

12 MIMO Channel h #" h "# h ## h "" $ " = h "" + h "# = h #" + h ## How to estimate the channels: h "", h "#, h #", h ##? TX 1: TX 2: Preamble Preamble

13 MIMO Gains Multiplexing Gain: Send multiple packets at the same time!! MIMO à! more packets Diversity Gain: Send/Receive the same packet on multiple antennas Increase SNR of the received packets à transmit at higher data rates

14 Receiver Diversity h # # = h #! + ( # " $ =! + ( $ How to best decode!? Option 1: Add the received signals " # + " $ = h #! + ( # +! + ( $ = h # +! + ( # + ( $ Channels can sum up destructively! h # + 0

15 Receiver Diversity h # # = h #! + ( # " $ =! + ( $ How to best decode!? Option 1: Add the received signals Option 2: Decode independently Sub-optimal!

16 Receiver Diversity h # # = h #! + ( # " $ =! + ( $ How to best decode!? Option 1: Add the received signals Option 2: Decode independently Optimal Solution: Maximum Ratio Combining (MRC)

17 Maximum Ratio Combining h # # = h #! + ( # " $ =! + ( $ 7 # " # + 7 $ " $ = h # " # + " $ = h # h #! + h # ( # +! + ( $ = h + $! + h # ( # + h $ ( $ Let 0 = 5! $ and 6 $ = 5 ( $ = 5 ( $ +,-(./ = 5 h + $! $ = h + h $ $ $ 5! $ = $ + 0

18 Maximum Ratio Combining h # # = h #! + ( # " $ =! + ( $ 9 # " # + 9 $ " $ = h # " # + " $ = h # h #! + h # ( # +! + ( $ = h + $! + h # ( # + h $ ( $ Let 1 = )! $ and 8 $ = ) ( $ = ) ( $ +,-(./ = $ , = ) h # ( # + h $ $ ( $ = ) h # ( + ) h $ $ ( $ = h ) ( + $ ) ( $ $ = h + $ 8 $

19 Maximum Ratio Combining h # # = h #! + ( # " $ =! + ( $ : # " # + : $ " $ = h # " # + " $ = h # h #! + h # ( # +! + ( $ Let / = 7! $ and 6 $ = 7 ( # $ = 7 ( $ $ )*+(,- /0123 = h # $ + $ $ / 40*52 /0123 = h # $ + $ 6 $ )48 = h # $ + $ $ / h # $ + $ 6 $ = h # $ + $ / 6 $ = h # $ + $! + h # ( # + ( $

20 Maximum Ratio Combining h # # = h #! + ( # " $ =! + ( $ 0 # " # + 0 $ " $ = h # " # + " $ = h # h #! + h # ( # +! + ( $ = h # $ + $! + h # ( # + ( $ With Receiver Diversity: )*+ = h # $ + $ -. $ Single Receiver: )*+ = h # $ -. $

21 Receiver Diversity Gain h # # = h #! + ( # " $ =! + ( $ With Receiver Diversity: )*+ = h # $ + $ -. $ Single Receiver: )*+ = h # $ -. $ h # $ $ à Can double SNR!

22 Receiver Diversity Gain Do we care about doubling the SNR?!"#"$%&' log,-. Rate SNR

23 Receiver Diversity Gain h # # = h #! + ( # " $ =! + ( $ With Receiver Diversity: )*+ $,- = h # $ + $ / 0 $ Single Receiver: )*+ #,- = h # $ / 0 $ h # $ $ h # $ $ h # $ $ à Can double SNR! à Huge Gain in SNR à Little Gain in SNR It is unlikely that both antennas experience channel fading.

24 Transmitter Diversity % $! = % $ + h ' % ' + ( % ' h ' What should we transmit on each antenna? Option 1: transmit the same thing % on both antennas! = + h ' % + ( Channels can sum up destructively! + h ' 0 Total transmit power = 2,à Doubled TX power à Why not use 1 TX with 2,

25 Transmitter Diversity % $! = % $ + h ' % ' + ( % ' h ' What should we transmit on each antenna? Option 1: transmit the same thing % on both antennas! = + h ' % + ( Must ensure signals sum up constructively. Channels can sum up destructively! + h ' 0 Total Must transmit ensure total power TX = power 2,à = Doubled - % ' $ TX + power - % ' ' à = Why - not % ' use =, 1 TX with 2,

26 Transmitter Diversity % $! = % $ + h ' % ' + ( % ' h ' What should we transmit on each antenna? Option 2: Maximum Ratio Combining (MRC) % $ = ) $ %! = ) $ + ) ' h ' % + ( % ' = ) ' % Set: ) $ =, ) ' = h ' à! = + h ' h ' % + ( = ' + h ' ' % + (

27 Transmitter Diversity % $! = % $ + h ' % ' + ( % ' h ' What should we transmit on each antenna? Option 2: Maximum Ratio Combining (MRC) % $ = ' + h ' ' % % ' = +,-./ +0 1,234 = 5 % $ ' + 5 % $ ' = ' ' + h ' ' 1 + h ' ' + h ' ' % h ' ' ' + h ' ' 1 = 1

28 Transmitter Diversity % $! = % $ + h ' % ' + ( % ' h ' What should we transmit on each antenna? Option 2: Maximum Ratio Combining (MRC) % $ = ' + h ' ' % % ' = h ' ' + h ' ' %! = ' + h ' ' % + h ' h ' ' + h ' ' % + (

29 Transmitter Diversity % $! = % $ + h ' % ' + ( % ' h ' What should we transmit on each antenna? Option 2: Maximum Ratio Combining (MRC) % $ = ' + h ' ' % % ' = h ' ' + h ' ' %! = ' + h ' ' ' + h ' ' % + ( = ' + h ' ' % + (

30 Transmitter Diversity % $! = % $ + h ' % ' + ( % ' h ' What should we transmit on each antenna? Option 2: Maximum Ratio Combining (MRC)! = ' + h ' ' % + ( )*+ = h ' $ + h ', ' à Similar SNR Gain to RX Diversity -' Caveat: MRC at TX Requires Feedback from the Receiver!

31 Transmitter Diversity % $! = % $ + h ' % ' + ( % ' h ' What should we transmit on each antenna? Solution: Use Space-Time Codes MRC codes across space only (Requires Channel Feedback): TX1: % $, $ % 1, $ % 2, $ = TX2: % ', ' % 1, ' % 2, ' = ) = 1 ) = 2 ' + h ' ' h ' ' + h ' '

32 Transmitter Diversity % $! = % $ + h ' % ' + ( % ' h ' What should we transmit on each antenna? Solution: Use Space-Time Codes Alamouti Codes: TX1: % $ % 1 % 2![1] = %[1] + h ' %[2] TX2: % ' % 2 % 1! 2 = % [2] + h ' % [1] ) = 1 ) = 2

33 Transmitter Diversity % $! = % $ + h ' % ' + ( % ' h ' What should we transmit on each antenna? Solution: Use Space-Time Codes Alamouti Codes:![1] = %[1] + h ' %[2]! 2 = % [2] + h ' % [1] h $! 1 + h '! 2 = h $ % 1 + h $ h ' % 2 h ' h $ % 2 + h ' h ' % 1 = h ' $ + h ' ' % 1

34 Transmitter Diversity % $! = % $ + h ' % ' + ( % ' h ' What should we transmit on each antenna? Solution: Use Space-Time Codes Alamouti Codes:![1] = %[1] + h ' %[2]! 2 = % [2] + h ' % [1] h '! 1! 2 = h ' % 1 + h ' h ' % 2 + h $ % 2 h ' % 1 = h ' $ + h ' ' % 2

35 Transmitter Diversity % $! = % $ + h ' % ' + ( % ' h ' What should we transmit on each antenna? Solution: Use Space-Time Codes Alamouti Codes: TX1: % $ % 1 % 2! 1 + h '! 2 = ' + h ' ' % 1 TX2: % ' % 2 % 1 ) = 1 ) = 2 h '! 1! 2 = ' + h ' ' % 2

36 MIMO Gains Multiplexing Gain: Send multiple packets at the same time!! MIMO à! more packets Data Rate:! log '!(/! Diversity Gain: Increase SNR of the received packets!! MIMO à log! * data rate Data Rate log '!(! *

37 MIMO h #" h "# h ## h "" $ " = h "" + h "# = h #" + h ## ) = *+ +, +- = *./ ) = *./ *+ + *./, = + + *./,

38 Multi-User MIMO h #" h "# h ## h "" $ " = h "" + h "# = h #" + h ## ) = *+ +, +- = *./ ) = *./ *+ + *./, = + + *./, Does not work. Receivers do not have access to each other s signals

39 Precoding h #" h "# h ## h "" $ " = h "" + h "# = h #" + h ## Send: +, = *./ + Receive: ) = *+, + - = **./ = Also known as Beamforming or Zero-Forcing

40 What about distributed transmitters? h #" h "# h ## h "" $ " = h "" + h "# = h #" + h ## Send: +, = *./ + Receive: ) = *+, + - = **./ = Does not work. Transmitters do not have access to each other s signals False: what if transmitters are APs connected over Ethernet?

41 Clock Synchronization in MIMO h "" $ h " #" h "# h ## $ " = h "" ' ()#*+, h "# ' ()#*+, -1. = h #" ' ()#*+, h ## ' ()#*+, 11. $ " = h "" h #" h "# h ## + 2 " 2 #

42 Clock Synchronization in MIMO h "" $ h " #" h "# h ## $ " = h "" ' ()#*+, --. h #" ' ()#*+, /-. h "# ' ()#*+, -/. h ## ' ()#*+, //. + 1 " 1 # On chip MIMO: Δ3 "" = Δ3 #" = Δ3 "# = Δ3 ## = Δ3 $ " = h "" h #" h "# h ## ' ()#*+,. + 1 " 1 #

43 Clock Synchronization in MIMO h "" $ h " #" h "# h ## $ " = h "" ' ()#*+, --. h #" ' ()#*+, /-. h "# ' ()#*+, -/. h ## ' ()#*+, //. + 1 " 1 # MU-MIMO: Δ3 "" = Δ3 "# and Δ3 #" = Δ3 ## $ " = h "" ' ()#*+, -. h #" ' ()#*+, /. h "# ' ()#*+, -. h ## ' ()#*+, /. + 1 " 1 #

44 Clock Synchronization in MIMO h "" $ h " #" h "# h ## $ " = h "" ' ()#*+, --. h #" ' ()#*+, /-. h "# ' ()#*+, -/. h ## ' ()#*+, //. + 1 " 1 # MU-MIMO: Δ3 "" = Δ3 "# and Δ3 #" = Δ3 ## $ " = ' ()#*+, ' ()#*+, /. h "" h #" h "# h ## + 1 " 1 #

45 Clock Synchronization in MIMO h "" $ h " #" h "# h ## $ " = h "" ' ()#*+, --. h #" ' ()#*+, /-. h "# ' ()#*+, -/. h ## ' ()#*+, //. + 1 " 1 # Distributed MIMO: Δ3 "" Δ3 "# Δ3 #" Δ3 ## Next Lecture!