ECE 598HH: Advanced Wireless Networks and Sensing Systems

59
ECE 598HH: Advanced Wireless Networks and Sensing Systems Lecture 6: MIMO Part 1 Haitham Hassanieh

Transcript of ECE 598HH: Advanced Wireless Networks and Sensing Systems

Page 1: ECE 598HH: Advanced Wireless Networks and Sensing Systems

ECE 598HH: Advanced Wireless Networks and Sensing Systems

Lecture 6: MIMO Part 1Haitham Hassanieh

Page 2: ECE 598HH: Advanced Wireless Networks and Sensing Systems

Version Year Technology Modulation Freq. Bandwidth Maximum Data Rate

WiFi 1 (802.11b) 1999 DSSS DBPSK, DQPSK, 2.4 GHz 22 MHz 11 Mb/s

WiFi Standards from WiFi 1 to WiFi 6

Page 3: ECE 598HH: Advanced Wireless Networks and Sensing Systems

Version Year Technology Modulation Freq. Bandwidth Maximum Data Rate

WiFi 1 (802.11b) 1999 DSSS DBPSK, DQPSK, 2.4 GHz 22 MHz 11 Mb/s

WiFi Standards from WiFi 1 to WiFi 6

Page 4: ECE 598HH: Advanced Wireless Networks and Sensing Systems

Version Year Technology Modulation Freq. Bandwidth Maximum Data Rate

WiFi 1 (802.11b) 1999 DSSS DBPSK, DQPSK, 2.4 GHz 22 MHz 11 Mb/s

WiFi 3 (802.11g) 2003 OFDM (N=64)BPSK, QPSK, 16-QAM, 64-QAM 2.4 GHz 20 MHz 54 Mb/s

WiFi Standards from WiFi 1 to WiFi 6

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Version Year Technology Modulation Freq. Bandwidth Maximum Data Rate

WiFi 1 (802.11b) 1999 DSSS DBPSK, DQPSK, 2.4 GHz 22 MHz 11 Mb/s

WiFi 3 (802.11g) 2003 OFDM (N=64)BPSK, QPSK, 16-QAM, 64-QAM 2.4 GHz 20 MHz 54 Mb/s

WiFi 4 (802.11n) 2009 OFDM (N=64)MIMO (4x4)

BPSK, QPSK, 16-QAM, 64-QAM

2.4 GHz 5 GHz

20 MHz 40 MHz 600 Mb/s

WiFi Standards from WiFi 1 to WiFi 6

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Version Year Technology Modulation Freq. Bandwidth Maximum Data Rate

WiFi 1 (802.11b) 1999 DSSS DBPSK, DQPSK, 2.4 GHz 22 MHz 11 Mb/s

WiFi 3 (802.11g) 2003 OFDM (N=64)BPSK, QPSK, 16-QAM, 64-QAM 2.4 GHz 20 MHz 54 Mb/s

WiFi 4 (802.11n) 2009 OFDM (N=64)MIMO (4x4)

BPSK, QPSK, 16-QAM, 64-QAM

2.4 GHz 5 GHz

20 MHz 40 MHz 600 Mb/s

WiFi Standards from WiFi 1 to WiFi 6

Page 7: ECE 598HH: Advanced Wireless Networks and Sensing Systems

Version Year Technology Modulation Freq. Bandwidth Maximum Data Rate

WiFi 1 (802.11b) 1999 DSSS DBPSK, DQPSK, 2.4 GHz 22 MHz 11 Mb/s

WiFi 3 (802.11g) 2003 OFDM (N=64)BPSK, QPSK, 16-QAM, 64-QAM 2.4 GHz 20 MHz 54 Mb/s

WiFi 4 (802.11n) 2009 OFDM (N=64)MIMO (4x4)

BPSK, QPSK, 16-QAM, 64-QAM

2.4 GHz 5 GHz

20 MHz 40 MHz 600 Mb/s

WiFi 5 (802.11ac) 2014OFDM (N=64, 128, 256, 512)MIMO (8x8)MU-MIMO (Downlink)

BPSK, QPSK, 16-QAM, 64-QAM256-QAM

5 GHz20 MHz 40 MHz80 MHz160 MHz

6.933 Gb/s

WiFi Standards from WiFi 1 to WiFi 6

Page 8: ECE 598HH: Advanced Wireless Networks and Sensing Systems

Version Year Technology Modulation Freq. Bandwidth Maximum Data Rate

WiFi 1 (802.11b) 1999 DSSS DBPSK, DQPSK, 2.4 GHz 22 MHz 11 Mb/s

WiFi 3 (802.11g) 2003 OFDM (N=64)BPSK, QPSK, 16-QAM, 64-QAM 2.4 GHz 20 MHz 54 Mb/s

WiFi 4 (802.11n) 2009 OFDM (N=64)MIMO (4x4)

BPSK, QPSK, 16-QAM, 64-QAM

2.4 GHz 5 GHz

20 MHz 40 MHz 600 Mb/s

WiFi 5 (802.11ac) 2014OFDM (N=64, 128, 256, 512)MIMO (8x8)MU-MIMO (Downlink)

BPSK, QPSK, 16-QAM, 64-QAM256-QAM

5 GHz20 MHz 40 MHz80 MHz160 MHz

6.933 Gb/s

WiFi 6 (802.11ax) 2019

OFDM (N=256, 512, 1024, 2048)MIMO (8x8)MU-MIMO (Up & Down)OFDMA

BPSK, QPSK, 16-QAM, 64-QAM256-QAM, 1024-QAM

2.4 GHz5 GHz

20 MHz 40 MHz80 MHz160 MHz

9.608 Gb/s

WiFi Standards from WiFi 1 to WiFi 6

Page 9: ECE 598HH: Advanced Wireless Networks and Sensing Systems

Version Year Technology Modulation Freq. Bandwidth Maximum Data Rate

WiFi 1 (802.11b) 1999 DSSS DBPSK, DQPSK, 2.4 GHz 22 MHz 11 Mb/s

WiFi 3 (802.11g) 2003 OFDM (N=64)BPSK, QPSK, 16-QAM, 64-QAM 2.4 GHz 20 MHz 54 Mb/s

WiFi 4 (802.11n) 2009 OFDM (N=64)MIMO (4x4)

BPSK, QPSK, 16-QAM, 64-QAM

2.4 GHz 5 GHz

20 MHz 40 MHz 600 Mb/s

WiFi 5 (802.11ac) 2014OFDM (N=64, 128, 256, 512)MIMO (8x8)MU-MIMO (Downlink)

BPSK, QPSK, 16-QAM, 64-QAM256-QAM

5 GHz20 MHz 40 MHz80 MHz160 MHz

6.933 Gb/s

WiFi 6 (802.11ax)WiFi 6E 2020

OFDM (N=256, 512, 1024, 2048)MIMO (8x8)MU-MIMO (Up & Down)OFDMA

BPSK, QPSK, 16-QAM, 64-QAM256-QAM, 1024-QAM

2.4 GHz5 GHz6 GHz

20 MHz 40 MHz80 MHz160 MHz

9.608 Gb/s

WiFi Standards from WiFi 1 to WiFi 6

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WiFi Standards from WiFi 1 to WiFi 6

WiFi 1 More MIMO Antennas WiFi 5/6

More Channels &

Bandw

idth

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So far: single input single output

MIMO: multiple input multiple output

Increase capacity of channel using multiple transmit and receive antennas.

MIMO: Multiple Input Multiple Output

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So far: single input single output

MIMO: multiple input multiple output

Increase capacity of channel using multiple transmit and receive antennas.

MIMO: Multiple Input Multiple Output

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MIMO: Multiple TX-RX streamsπ‘₯!

π‘₯"

𝑦!

𝑦"

β„Ž!! = β„Ž!!π‘₯! + β„Ž!"π‘₯"

= β„Ž"!π‘₯! + β„Ž""π‘₯"β„Ž!"β„Ž""

β„Ž"!

𝑦!

𝑦"=

β„Ž!!

β„Ž"!

β„Ž!"

β„Ž""

π‘₯!

π‘₯"+

𝑛!

𝑛"𝐲 = 𝐇𝐱 + 𝐧

How to recover π‘₯" and π‘₯#?

Estimate 𝐇, compute 𝐇$" and invert the channel!

+𝐱 = 𝐇#𝟏𝐲 = 𝐇#πŸπ‡π± + 𝐇#𝟏𝐧 = 𝐱 + 𝐇#𝟏𝐧

Transmit 2 packets at the same time!

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MIMO: Multiple TX-RX streamsπ‘₯!

π‘₯"

𝑦!

𝑦"

β„Ž!! = β„Ž!!π‘₯! + β„Ž!"π‘₯"

= β„Ž"!π‘₯! + β„Ž""π‘₯"β„Ž!"β„Ž""

β„Ž"!

𝑦!

𝑦"=

β„Ž!!

β„Ž"!

β„Ž!"

β„Ž""

π‘₯!

π‘₯"+

𝑛!

𝑛"𝐲 = 𝐇𝐱 + 𝐧

How to recover π‘₯" and π‘₯#?

Estimate 𝐇, compute 𝐇$" and invert the channel!

+𝐱 = 𝐇#𝟏𝐲 = 𝐇#πŸπ‡π± + 𝐇#𝟏𝐧 = 𝐱 + 𝐇#𝟏𝐧

Noise amplification

For 𝑁 antennas, 𝐇 is 𝑁×𝑁 matrix Γ  𝑂 𝑁%

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MIMO: Vector Representationπ‘₯!

π‘₯"

𝑦!

𝑦"

β„Ž!! = β„Ž!!π‘₯! + β„Ž!"π‘₯"

= β„Ž"!π‘₯! + β„Ž""π‘₯"β„Ž!"β„Ž""

β„Ž"!

𝑦!

𝑦"=

β„Ž!!

β„Ž"!

β„Ž!"

β„Ž""

π‘₯!

π‘₯"+

𝑛!

𝑛"𝐲 = 𝐇𝐱 + 𝐧

How to recover π‘₯" and π‘₯#?

=β„Ž!!

β„Ž"!

β„Ž!"

β„Ž""π‘₯! π‘₯"𝐲 + = 𝐑!π‘₯! + 𝐑"π‘₯"

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MIMO: Antenna Space𝐲 = 𝐑!π‘₯! + 𝐑"π‘₯"

Ant. 2: 𝑦#

Ant. 1: 𝑦"

𝐑"π‘₯"

𝐑!π‘₯!

𝐲

Page 17: ECE 598HH: Advanced Wireless Networks and Sensing Systems

MIMO: Antenna Space𝐲 = 𝐑!π‘₯! + 𝐑"π‘₯"

Ant. 2: 𝑦#

Ant. 1: 𝑦"

𝐑"π‘₯"

𝐑!π‘₯!

𝐲To decode π‘₯!, project on a vector 𝐑"

%orthogonal to 𝐑"

𝐑"%𝐲 = 𝐑"

%𝐑!π‘₯! + 𝐑"

%𝐑"π‘₯"

= 𝐑"%𝐑!π‘₯!

=β„Ž!!

β„Ž"!

β„Ž!"

β„Ž""π‘₯! π‘₯"𝐲 +

𝐑"%= β„Ž"" βˆ’ β„Ž!"

𝐑"%𝐲 = β„Ž""β„Ž!!π‘₯! βˆ’ β„Ž!"β„Ž"!π‘₯!+ β„Ž""β„Ž!"π‘₯"βˆ’ β„Ž!"β„Ž""π‘₯"

= β„Ž""β„Ž!! βˆ’ β„Ž!"β„Ž"! π‘₯!

0

0

Page 18: ECE 598HH: Advanced Wireless Networks and Sensing Systems

MIMO: Antenna Space𝐲 = 𝐑!π‘₯! + 𝐑"π‘₯"

Ant. 2: 𝑦#

Ant. 1: 𝑦"

𝐑"π‘₯"

𝐑!π‘₯!

𝐲To decode π‘₯", project on a vector 𝐑!

%orthogonal to 𝐑!

𝐑!%𝐲 = 𝐑!

%𝐑!π‘₯! + 𝐑!

%𝐑"π‘₯"

= 𝐑!%𝐑"π‘₯"

=β„Ž!!

β„Ž"!

β„Ž!"

β„Ž""π‘₯! π‘₯"𝐲 +

𝐑!%= β„Ž"! βˆ’ β„Ž!!

𝐑!%𝐲 = β„Ž"!β„Ž!!π‘₯! βˆ’ β„Ž"!β„Ž!!π‘₯!+ β„Ž"!β„Ž!"π‘₯"βˆ’ β„Ž!!β„Ž""π‘₯"

= β„Ž"!β„Ž!" βˆ’ β„Ž!!β„Ž"" π‘₯"

0

0

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MIMO: Antenna Space

𝐲 = 𝐑!π‘₯! + 𝐑"π‘₯"Ant. 2: 𝑦#

Ant. 1: 𝑦"

𝐑"π‘₯"

𝐑!π‘₯!

To decode π‘₯!, project on a vector 𝐑"&

%orthogonal to the

plane formed by 𝐑" and 𝐑&

What about MIMO with more antennas?

Ant. 3: 𝑦%

𝐑&π‘₯&𝐑"&%= 𝐑" Γ— 𝐑&

+𝐑&π‘₯&

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MIMO: Antenna Space

𝐲 = 𝐑!π‘₯! + 𝐑"π‘₯" + 𝐑&π‘₯&Ant. 2: 𝑦#

Ant. 1: 𝑦"

𝐑"π‘₯"

𝐑!π‘₯!

To decode π‘₯!, project on a vector 𝐑"&

%orthogonal to the

plane formed by 𝐑" and 𝐑&

What about MIMO with more antennas?

Ant. 3: 𝑦%

𝐑&π‘₯&𝐑"&%= 𝐑" Γ— 𝐑&

𝑁 antenna MIMO, receives signals in 𝑁 dimensional spaceΓ  Can decode 𝑁 parallel signals

Decoding complexity scales 𝑂(𝑁#) operations with the number of antennas

Page 21: ECE 598HH: Advanced Wireless Networks and Sensing Systems

MIMO Channelπ‘₯!

π‘₯"

𝑦!

𝑦"

β„Ž!! = β„Ž!!π‘₯! + β„Ž!"π‘₯"

= β„Ž"!π‘₯! + β„Ž""π‘₯"β„Ž!"β„Ž""

β„Ž"!

How to estimate the channels: β„Ž"", β„Ž"#, β„Ž#", β„Ž##?

TX 1:

TX 2:

Preamble π‘₯!Preamble π‘₯"

Page 22: ECE 598HH: Advanced Wireless Networks and Sensing Systems

MIMO Channelπ‘₯!

π‘₯"

𝑦!

𝑦"

β„Ž!! = β„Ž!!π‘₯! + β„Ž!"π‘₯"

= β„Ž"!π‘₯! + β„Ž""π‘₯"β„Ž!"β„Ž""

β„Ž"!

How to estimate the channels: β„Ž"", β„Ž"#, β„Ž#", β„Ž##?

TX 1:

TX 2:

Preamble π‘₯!Preamble π‘₯"

Page 23: ECE 598HH: Advanced Wireless Networks and Sensing Systems

MIMO Gains

Multiplexing Gain: β€’ Send multiple packets at the same timeβ€’ 𝑁×𝑁 MIMO Γ  𝑁× more packets

Diversity Gain: β€’ Send/Receive the same packet on

multiple antennas β€’ Increase SNR of the received packets

Γ  transmit at higher data rates

Page 24: ECE 598HH: Advanced Wireless Networks and Sensing Systems

Receiver Diversity

π‘₯ 𝑦!

𝑦"

= β„Ž!π‘₯ + 𝑛!

𝑦! + 𝑦" = β„Ž!π‘₯ + 𝑛! + β„Ž"π‘₯ + 𝑛"

How to best decode π‘₯?

Option 1: Add the received signals

= β„Ž! + β„Ž" π‘₯ + 𝑛! + 𝑛"

Channels can sum up destructively! β„Ž! + β„Ž" β‰ˆ 0

= β„Ž"π‘₯ + 𝑛"

β„Ž!

β„Ž"

Page 25: ECE 598HH: Advanced Wireless Networks and Sensing Systems

Receiver Diversity

π‘₯ 𝑦!

𝑦"

= β„Ž!π‘₯ + 𝑛!

How to best decode π‘₯?

Option 1: Add the received signals

= β„Ž"π‘₯ + 𝑛"

β„Ž!

β„Ž"

Option 2: Decode independently

Sub-optimal!

Page 26: ECE 598HH: Advanced Wireless Networks and Sensing Systems

Receiver Diversity

π‘₯ 𝑦!

𝑦"

= β„Ž!π‘₯ + 𝑛!

How to best decode π‘₯?

Option 1: Add the received signals

= β„Ž"π‘₯ + 𝑛"

β„Ž!

β„Ž"

Option 2: Decode independently

Optimal Solution: Maximum Ratio Combining (MRC)

Page 27: ECE 598HH: Advanced Wireless Networks and Sensing Systems

Maximum Ratio Combining

π‘₯ 𝑦!

𝑦"

= β„Ž!π‘₯ + 𝑛!

= β„Ž"π‘₯ + 𝑛"

β„Ž!

β„Ž"

= β„Ž!βˆ—π‘¦! + β„Ž"βˆ—π‘¦" = β„Ž!βˆ—β„Ž!π‘₯ + β„Ž!βˆ—π‘›! + β„Ž"βˆ—β„Ž"π‘₯ + β„Ž"βˆ—π‘›"

= β„Ž! " + β„Ž" " π‘₯ + β„Ž!βˆ—π‘›! + β„Ž"βˆ—π‘›"

π‘†π‘–π‘”π‘›π‘Žπ‘™ π‘ƒπ‘œπ‘€π‘’π‘Ÿ = 𝔼 β„Ž! " + β„Ž" " π‘₯ "

= β„Ž! " + β„Ž" " " 𝔼 π‘₯ "

= β„Ž! " + β„Ž" " " 𝑃

Let 𝑃 = 𝔼 π‘₯ " and 𝜎" = 𝔼 𝑛! " = 𝔼 𝑛" "

𝛼!𝑦!+ 𝛼"𝑦"

Page 28: ECE 598HH: Advanced Wireless Networks and Sensing Systems

Maximum Ratio Combining

π‘₯ 𝑦!

𝑦"

= β„Ž!π‘₯ + 𝑛!

= β„Ž"π‘₯ + 𝑛"

β„Ž!

β„Ž"

= 𝔼 β„Ž!βˆ—π‘›! " + 𝔼 β„Ž"βˆ—π‘›" "

π‘†π‘–π‘”π‘›π‘Žπ‘™ π‘ƒπ‘œπ‘€π‘’π‘Ÿ = β„Ž! " + β„Ž" " " 𝑃

π‘π‘œπ‘–π‘ π‘’ π‘ƒπ‘œπ‘€π‘’π‘Ÿ = 𝔼 β„Ž!βˆ—π‘›! + β„Ž"βˆ—π‘›" "

= β„Ž! "𝔼 𝑛! " + β„Ž" "𝔼 𝑛" " = β„Ž! " + β„Ž" " 𝜎"

Let 𝑃 = 𝔼 π‘₯ " and 𝜎" = 𝔼 𝑛! " = 𝔼 𝑛" "

= β„Ž!βˆ—π‘¦! + β„Ž"βˆ—π‘¦" = β„Ž!βˆ—β„Ž!π‘₯ + β„Ž!βˆ—π‘›! + β„Ž"βˆ—β„Ž"π‘₯ + β„Ž"βˆ—π‘›"

= β„Ž! " + β„Ž" " π‘₯ + β„Ž!βˆ—π‘›! + β„Ž"βˆ—π‘›"

𝛼!𝑦!+ 𝛼"𝑦"

Page 29: ECE 598HH: Advanced Wireless Networks and Sensing Systems

Maximum Ratio Combining

π‘₯ 𝑦!

𝑦"

= β„Ž!π‘₯ + 𝑛!

= β„Ž"π‘₯ + 𝑛"

β„Ž!

β„Ž"

π‘†π‘–π‘”π‘›π‘Žπ‘™ π‘ƒπ‘œπ‘€π‘’π‘Ÿ = β„Ž! " + β„Ž" " " 𝑃

π‘π‘œπ‘–π‘ π‘’ π‘ƒπ‘œπ‘€π‘’π‘Ÿ = β„Ž! " + β„Ž" " 𝜎"

Let 𝑃 = 𝔼 π‘₯ " and 𝜎" = 𝔼 𝑛! " = 𝔼 𝑛" "

𝑆𝑁𝑅 =β„Ž! " + β„Ž" " " π‘ƒβ„Ž! " + β„Ž" " 𝜎" = β„Ž! " + β„Ž" " 𝑃

𝜎"

= β„Ž!βˆ—π‘¦! + β„Ž"βˆ—π‘¦" = β„Ž!βˆ—β„Ž!π‘₯ + β„Ž!βˆ—π‘›! + β„Ž"βˆ—β„Ž"π‘₯ + β„Ž"βˆ—π‘›"

= β„Ž! " + β„Ž" " π‘₯ + β„Ž!βˆ—π‘›! + β„Ž"βˆ—π‘›"

𝛼!𝑦!+ 𝛼"𝑦"

Page 30: ECE 598HH: Advanced Wireless Networks and Sensing Systems

Maximum Ratio Combining

π‘₯ 𝑦!

𝑦"

= β„Ž!π‘₯ + 𝑛!

= β„Ž"π‘₯ + 𝑛"

β„Ž!

β„Ž"

With Receiver Diversity: 𝑆𝑁𝑅 = β„Ž! " + β„Ž" " π‘ƒπœŽ"

Single Receiver: 𝑆𝑁𝑅 = β„Ž! " π‘ƒπœŽ"

= β„Ž!βˆ—π‘¦! + β„Ž"βˆ—π‘¦" = β„Ž!βˆ—β„Ž!π‘₯ + β„Ž!βˆ—π‘›! + β„Ž"βˆ—β„Ž"π‘₯ + β„Ž"βˆ—π‘›"

= β„Ž! " + β„Ž" " π‘₯ + β„Ž!βˆ—π‘›! + β„Ž"βˆ—π‘›"

𝛼!𝑦!+ 𝛼"𝑦"

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Receiver Diversity Gain

π‘₯ 𝑦!

𝑦"

= β„Ž!π‘₯ + 𝑛!

= β„Ž"π‘₯ + 𝑛"

β„Ž!

β„Ž"

With Receiver Diversity: 𝑆𝑁𝑅 = β„Ž! " + β„Ž" " π‘ƒπœŽ"

Single Receiver: 𝑆𝑁𝑅 = β„Ž! " π‘ƒπœŽ"

β€’ β„Ž! " β‰ˆ β„Ž" " Γ  Can double SNR!

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Receiver Diversity GainDo we care about doubling the SNR?

πΆπ‘Žπ‘π‘Žπ‘π‘–π‘‘π‘¦ ∝ log 𝑆𝑁𝑅

Rate

SNR

Page 33: ECE 598HH: Advanced Wireless Networks and Sensing Systems

Receiver Diversity Gain

π‘₯ 𝑦!

𝑦"

= β„Ž!π‘₯ + 𝑛!

= β„Ž"π‘₯ + 𝑛"

β„Ž!

β„Ž"

With Receiver Diversity: 𝑆𝑁𝑅"() = β„Ž! " + β„Ž" " π‘ƒπœŽ"

Single Receiver: 𝑆𝑁𝑅!() = β„Ž! " π‘ƒπœŽ"

β€’ β„Ž! " β‰ˆ β„Ž" "

β€’ β„Ž! " β‰ͺ β„Ž" "

β€’ β„Ž! " ≫ β„Ž" "

Γ  Huge Gain in SNR

Γ  Little Gain in SNR

Γ  Can double SNR!It is unlikely that both antennas experiencechannel fading.

Page 34: ECE 598HH: Advanced Wireless Networks and Sensing Systems

Transmitter Diversity

𝑦 = β„Ž!π‘₯! + β„Ž"π‘₯" + 𝑛

What should we transmit on each antenna?

Option 1: transmit the same thing π‘₯ on both antennas

𝑦 = β„Ž! + β„Ž" π‘₯ + 𝑛

Channels can sum up destructively! β„Ž! + β„Ž" β‰ˆ 0

β„Ž!

β„Ž"

π‘₯!

π‘₯"

Total transmit power = 2𝑃à Doubled TX powerΓ  Why not use 1 TX with 2𝑃

Page 35: ECE 598HH: Advanced Wireless Networks and Sensing Systems

Transmitter Diversity

𝑦 = β„Ž!π‘₯! + β„Ž"π‘₯" + 𝑛

What should we transmit on each antenna?

Option 1: transmit the same thing π‘₯ on both antennas

𝑦 = β„Ž! + β„Ž" π‘₯ + 𝑛

Channels can sum up destructively! β„Ž! + β„Ž" β‰ˆ 0

β„Ž!

β„Ž"

π‘₯!

π‘₯"

Total transmit power = 2𝑃à Doubled TX powerΓ  Why not use 1 TX with 2𝑃

β€’ Must ensure signals sum up constructively.

β€’ Must ensure total TX power = 𝔼 π‘₯! " + 𝔼 π‘₯" "

= 𝔼 π‘₯ " = 𝑃

Page 36: ECE 598HH: Advanced Wireless Networks and Sensing Systems

Transmitter Diversity

𝑦 = β„Ž!π‘₯! + β„Ž"π‘₯" + 𝑛

What should we transmit on each antenna?

Option 2: Maximum Ratio Combining (MRC)

π‘₯! = 𝛼!π‘₯

β„Ž!

β„Ž"

π‘₯!

π‘₯"

π‘₯" = 𝛼" π‘₯𝑦 = 𝛼!β„Ž! + 𝛼"β„Ž" π‘₯ + 𝑛

Set: 𝛼! = β„Ž!βˆ— , 𝛼" = β„Ž"βˆ— Γ  𝑦 = β„Ž!βˆ—β„Ž! + β„Ž"βˆ—β„Ž" π‘₯ + 𝑛

= β„Ž! " + β„Ž" " π‘₯ + 𝑛

Page 37: ECE 598HH: Advanced Wireless Networks and Sensing Systems

Transmitter Diversity

𝑦 = β„Ž!π‘₯! + β„Ž"π‘₯" + 𝑛

What should we transmit on each antenna?

Option 2: Maximum Ratio Combining (MRC)

π‘₯! =β„Ž!βˆ—

β„Ž! " + β„Ž" "π‘₯

β„Ž!

β„Ž"

π‘₯!

π‘₯"

π‘₯" =β„Ž"βˆ—

β„Ž! " + β„Ž" "π‘₯

π‘‡π‘œπ‘‘π‘Žπ‘™ 𝑇𝑋 π‘ƒπ‘œπ‘€π‘’π‘Ÿ = 𝔼 π‘₯! " + 𝔼 π‘₯! "

=β„Ž! "

β„Ž! " + β„Ž" " 𝑃 +β„Ž" "

β„Ž! " + β„Ž" " 𝑃 = 𝑃

Page 38: ECE 598HH: Advanced Wireless Networks and Sensing Systems

Transmitter Diversity

𝑦 = β„Ž!π‘₯! + β„Ž"π‘₯" + 𝑛

What should we transmit on each antenna?

Option 2: Maximum Ratio Combining (MRC)

π‘₯! =β„Ž!βˆ—

β„Ž! " + β„Ž" "π‘₯

β„Ž!

β„Ž"

π‘₯!

π‘₯"

π‘₯" =β„Ž"βˆ—

β„Ž! " + β„Ž" "π‘₯

𝑦 =β„Ž!β„Ž!βˆ—

β„Ž! " + β„Ž" "π‘₯ +

β„Ž"β„Ž"βˆ—

β„Ž! " + β„Ž" "π‘₯ + 𝑛

Page 39: ECE 598HH: Advanced Wireless Networks and Sensing Systems

Transmitter Diversity

𝑦 = β„Ž!π‘₯! + β„Ž"π‘₯" + 𝑛

What should we transmit on each antenna?

Option 2: Maximum Ratio Combining (MRC)

π‘₯! =β„Ž!βˆ—

β„Ž! " + β„Ž" "π‘₯

β„Ž!

β„Ž"

π‘₯!

π‘₯"

π‘₯" =β„Ž"βˆ—

β„Ž! " + β„Ž" "π‘₯

𝑦 =β„Ž! " + β„Ž" "

β„Ž! " + β„Ž" "π‘₯ + 𝑛 = β„Ž! " + β„Ž" " π‘₯ + 𝑛

Page 40: ECE 598HH: Advanced Wireless Networks and Sensing Systems

Transmitter Diversity

𝑦 = β„Ž!π‘₯! + β„Ž"π‘₯" + 𝑛

What should we transmit on each antenna?

Option 2: Maximum Ratio Combining (MRC)

β„Ž!

β„Ž"

π‘₯!

π‘₯"

𝑦 = β„Ž! " + β„Ž" " π‘₯ + 𝑛

𝑆𝑁𝑅 = β„Ž! " + β„Ž" " π‘ƒπœŽ"

Γ  Similar SNR Gain to RX Diversity

Caveat: MRC at TX Requires Feedback from the Receiver!

Page 41: ECE 598HH: Advanced Wireless Networks and Sensing Systems

Transmitter Diversity

𝑦 = β„Ž!π‘₯! + β„Ž"π‘₯" + 𝑛

What should we transmit on each antenna?

Solution: Use Space-Time Codes

β„Ž!

β„Ž"

π‘₯!

π‘₯"

TX1: π‘₯!

TX2: π‘₯"

𝑑 = 1 𝑑 = 2

π‘₯ 1

π‘₯ 1

π‘₯ 2

π‘₯ 2

MRC codes across space only (Requires Channel Feedback):

𝛼! =β„Ž!βˆ—

β„Ž! " + β„Ž" "

𝛼" =β„Ž"βˆ—

β„Ž! " + β„Ž" "

𝛼" 𝛼"

𝛼! 𝛼!

Page 42: ECE 598HH: Advanced Wireless Networks and Sensing Systems

Transmitter Diversity

𝑦 = β„Ž!π‘₯! + β„Ž"π‘₯" + 𝑛

What should we transmit on each antenna?

β„Ž!

β„Ž"

π‘₯!

π‘₯"

TX1: π‘₯!

TX2: π‘₯"

𝑑 = 1 𝑑 = 2

π‘₯ 1

π‘₯ 2

βˆ’π‘₯βˆ— 2

π‘₯βˆ— 1

Alamouti Codes:

𝑦[1] = β„Ž!π‘₯[1] + β„Ž"π‘₯[2]

𝑦 2 = βˆ’β„Ž!π‘₯βˆ—[2] + β„Ž"π‘₯βˆ—[1]

Solution: Use Space-Time Codes

Page 43: ECE 598HH: Advanced Wireless Networks and Sensing Systems

Transmitter Diversity

𝑦 = β„Ž!π‘₯! + β„Ž"π‘₯" + 𝑛

What should we transmit on each antenna?

β„Ž!

β„Ž"

π‘₯!

π‘₯"

Alamouti Codes:

𝑦[1] = β„Ž!π‘₯[1] + β„Ž"π‘₯[2] 𝑦 2 = βˆ’β„Ž!π‘₯βˆ—[2] + β„Ž"π‘₯βˆ—[1]

β„Ž!βˆ—π‘¦ 1 + β„Ž"π‘¦βˆ— 2 = β„Ž!βˆ—β„Ž!π‘₯ 1 + β„Ž!βˆ—β„Ž"π‘₯ 2βˆ’β„Ž"β„Ž!βˆ—π‘₯ 2 + β„Ž"β„Ž"βˆ—π‘₯ 1= β„Ž! " + β„Ž" " π‘₯ 1

Solution: Use Space-Time Codes

Page 44: ECE 598HH: Advanced Wireless Networks and Sensing Systems

Transmitter Diversity

𝑦 = β„Ž!π‘₯! + β„Ž"π‘₯" + 𝑛

What should we transmit on each antenna?

β„Ž!

β„Ž"

π‘₯!

π‘₯"

Alamouti Codes:

𝑦[1] = β„Ž!π‘₯[1] + β„Ž"π‘₯[2] 𝑦 2 = βˆ’β„Ž!π‘₯βˆ—[2] + β„Ž"π‘₯βˆ—[1]

β„Ž"βˆ—π‘¦ 1 βˆ’ β„Ž!π‘¦βˆ— 2 = β„Ž"βˆ—β„Ž!π‘₯ 1 + β„Ž"βˆ—β„Ž"π‘₯ 2+β„Ž!β„Ž!βˆ—π‘₯ 2 βˆ’ β„Ž!β„Ž"βˆ—π‘₯ 1= β„Ž! " + β„Ž" " π‘₯ 2

Solution: Use Space-Time Codes

Page 45: ECE 598HH: Advanced Wireless Networks and Sensing Systems

Transmitter Diversity

𝑦 = β„Ž!π‘₯! + β„Ž"π‘₯" + 𝑛

What should we transmit on each antenna?

β„Ž!

β„Ž"

π‘₯!

π‘₯"

TX1: π‘₯!

TX2: π‘₯"

𝑑 = 1 𝑑 = 2

π‘₯ 1

π‘₯ 2

βˆ’π‘₯βˆ— 2

π‘₯βˆ— 1

Alamouti Codes: β„Ž!βˆ—π‘¦ 1 + β„Ž"π‘¦βˆ— 2

= β„Ž! " + β„Ž" " π‘₯ 1

β„Ž"βˆ—π‘¦ 1 βˆ’ β„Ž!π‘¦βˆ— 2

= β„Ž! " + β„Ž" " π‘₯ 2

Solution: Use Space-Time Codes

Page 46: ECE 598HH: Advanced Wireless Networks and Sensing Systems

MIMO Gains

Multiplexing Gain: β€’ Send multiple packets at the same timeβ€’ 𝑁×𝑁 MIMO à×𝑁 more packetsβ€’ Data Rate: ∝ 𝑁 log 𝑆𝑁𝑅/𝑁

Diversity Gain: β€’ Increase SNR of the received packetsβ€’ 𝑁×𝑁 MIMO Γ  Γ— log𝑁" data rateβ€’ Data Rate ∝ log 𝑆𝑁𝑅×𝑁"

Page 47: ECE 598HH: Advanced Wireless Networks and Sensing Systems

47

WiFi 802.11ac MCS (Modulations and Coding Schemes)

Page 48: ECE 598HH: Advanced Wireless Networks and Sensing Systems

48

WiFi 802.11ac MCS (Modulations and Coding Schemes)

Page 49: ECE 598HH: Advanced Wireless Networks and Sensing Systems

49

WiFi 802.11ac MCS (Modulations and Coding Schemes)

Page 50: ECE 598HH: Advanced Wireless Networks and Sensing Systems

MIMO: Multiple TX-RX streamsWiFi Access Points 2 to 8 MIMO WiFi Devices 1 to 2 MIMO

β€’ Powerβ€’ Form Factor & Antenna

Separationβ€’ Most mobile phones

support 2 MIMO

Page 51: ECE 598HH: Advanced Wireless Networks and Sensing Systems

MIMOπ‘₯!

π‘₯"

𝑦!

𝑦"

β„Ž!! = β„Ž!!π‘₯! + β„Ž!"π‘₯"

= β„Ž"!π‘₯! + β„Ž""π‘₯"β„Ž!"β„Ž""

β„Ž"!

𝐲 = 𝐇𝐱 + 𝐧

N𝐱 = 𝐇%𝟏𝐲 = 𝐇%πŸπ‡π± + 𝐇%𝟏𝐧 = 𝐱 + 𝐇%𝟏𝐧

Page 52: ECE 598HH: Advanced Wireless Networks and Sensing Systems

Multi-User MIMOπ‘₯!

π‘₯"

𝑦!

𝑦"

β„Ž!! = β„Ž!!π‘₯! + β„Ž!"π‘₯"

= β„Ž"!π‘₯! + β„Ž""π‘₯"β„Ž!"β„Ž""

β„Ž"!

𝐲 = 𝐇𝐱 + 𝐧

N𝐱 = 𝐇%𝟏𝐲 = 𝐇%πŸπ‡π± + 𝐇%𝟏𝐧 = 𝐱 + 𝐇%𝟏𝐧

Does not work. Receivers do not have access to each other’s signals

Page 53: ECE 598HH: Advanced Wireless Networks and Sensing Systems

Precoding π‘₯!

π‘₯"

𝑦!

𝑦"

β„Ž!! = β„Ž!!π‘₯! + β„Ž!"π‘₯"

= β„Ž"!π‘₯! + β„Ž""π‘₯"β„Ž!"β„Ž""

β„Ž"!

Receive: 𝐲 = 𝐇.𝐱 + 𝐧 = 𝐇𝐇#𝟏𝐱 + 𝐧 = 𝐱 + 𝐧

Send: .𝐱 = 𝐇#𝟏𝐱

Also known as Beamforming or Zero-Forcing

Requires Channel Feedback!

Page 54: ECE 598HH: Advanced Wireless Networks and Sensing Systems

What about distributed transmitters?π‘₯!

π‘₯"

𝑦!

𝑦"

β„Ž!! = β„Ž!!π‘₯! + β„Ž!"π‘₯"

= β„Ž"!π‘₯! + β„Ž""π‘₯"β„Ž!"β„Ž""

β„Ž"!

Receive: 𝐲 = 𝐇.𝐱 + 𝐧 = 𝐇𝐇#𝟏𝐱 + 𝐧 = 𝐱 + 𝐧

Send: .𝐱 = 𝐇#𝟏𝐱

Does not work. Transmitters do not have access to each other’s signals

False: what if transmitters are APs connected over Ethernet?

Page 55: ECE 598HH: Advanced Wireless Networks and Sensing Systems

Clock Synchronization in MIMOπ‘₯!

π‘₯"

𝑦!

𝑦"

β„Ž!!

= β„Ž!!π‘₯!𝑒#*"+,-!!. + β„Ž!"π‘₯"𝑒#*"+,-!".

= β„Ž"!π‘₯!𝑒#*"+,-"!. + β„Ž""π‘₯"𝑒#*"+,-"".

β„Ž!"β„Ž""

β„Ž"!

𝑦!

𝑦"

𝑦!

𝑦"=

β„Ž!!

β„Ž"!

β„Ž!"

β„Ž""

π‘₯!

π‘₯"+

𝑛!

𝑛"

Page 56: ECE 598HH: Advanced Wireless Networks and Sensing Systems

Clock Synchronization in MIMOπ‘₯!

π‘₯"

𝑦!

𝑦"

β„Ž!!

β„Ž!"β„Ž""

β„Ž"!

𝑦!

𝑦"=

β„Ž!! 𝑒#*"+,-!!.

β„Ž"!𝑒#*"+,-"!.

β„Ž!"𝑒#*"+,-!".

β„Ž""𝑒#*"+,-"".

π‘₯!

π‘₯"+

𝑛!

𝑛"

On chip MIMO: Δ𝑓!!= Δ𝑓"!= Δ𝑓!"= Δ𝑓""= Δ𝑓

𝑦!

𝑦"=

β„Ž!!

β„Ž"!

β„Ž!"

β„Ž""

π‘₯!

π‘₯"+

𝑛!

𝑛"𝑒#*"+,-.

Page 57: ECE 598HH: Advanced Wireless Networks and Sensing Systems

Clock Synchronization in MIMOπ‘₯!

π‘₯"

𝑦!

𝑦"

β„Ž!!

β„Ž!"β„Ž""

β„Ž"!

𝑦!

𝑦"=

β„Ž!! 𝑒#*"+,-!!.

β„Ž"!𝑒#*"+,-"!.

β„Ž!"𝑒#*"+,-!".

β„Ž""𝑒#*"+,-"".

π‘₯!

π‘₯"+

𝑛!

𝑛"

MU-MIMO: Δ𝑓!!= Δ𝑓!" and Δ𝑓"!= Δ𝑓""

𝑦!

𝑦"=

β„Ž!! 𝑒#*"+,-!.

β„Ž"!𝑒#*"+,-".

β„Ž!"𝑒#*"+,-!.

β„Ž""𝑒#*"+,-".

π‘₯!

π‘₯"+

𝑛!

𝑛"

Page 58: ECE 598HH: Advanced Wireless Networks and Sensing Systems

Clock Synchronization in MIMOπ‘₯!

π‘₯"

𝑦!

𝑦"

β„Ž!!

β„Ž!"β„Ž""

β„Ž"!

𝑦!

𝑦"=

β„Ž!! 𝑒#*"+,-!!.

β„Ž"!𝑒#*"+,-"!.

β„Ž!"𝑒#*"+,-!".

β„Ž""𝑒#*"+,-"".

π‘₯!

π‘₯"+

𝑛!

𝑛"

MU-MIMO: Δ𝑓!!= Δ𝑓!" and Δ𝑓"!= Δ𝑓""

𝑦!

𝑦"=

β„Ž!!

β„Ž"!

β„Ž!"

β„Ž""

π‘₯!

π‘₯"+

𝑛!

𝑛"

𝑒#*"+,-!.

0

0

𝑒#*"+,-".

Page 59: ECE 598HH: Advanced Wireless Networks and Sensing Systems

Clock Synchronization in MIMOπ‘₯!

π‘₯"

𝑦!

𝑦"

β„Ž!!

β„Ž!"β„Ž""

β„Ž"!

𝑦!

𝑦"=

β„Ž!! 𝑒#*"+,-!!.

β„Ž"!𝑒#*"+,-"!.

β„Ž!"𝑒#*"+,-!".

β„Ž""𝑒#*"+,-"".

π‘₯!

π‘₯"+

𝑛!

𝑛"

Distributed MIMO: Δ𝑓!! β‰  Δ𝑓!" β‰  Δ𝑓"! β‰  Δ𝑓""

Next Lecture!