Wireless Communication Systems

Wireless Communication Systems

@CS.NCTU

Lecture 5: Multi-User MIMO (MU-MIMO)

Instructor: Kate Ching-Ju Lin (林靖茹)

1

Agenda

• Interference Nulling

• Zero-forcing Beamforming (802.11ac)

• Interference Alignment

• Network MIMO

2

Cross-Link Interference

• Problem:

⎻ Any two nearby links cannot transmit simultaneously on the same frequency

• Solution:

⎻ A transmitter with multiple antennas can actively cancel its interfering signals at nearby receiver(s)

3

Interference Nulling

• Signals cancel each other at Alice’s receiver

• Signals don’t cancel each other at Bob’s receiver

⎻ Because channels are different

⎻ Bob’s receiver can remove Alice’s interference via ZF decoding

Alice

Bob

x

αx' βx'

h₁

h₂

y = hx + (h₁α+h₂β)x’

Nulling: make (h₁α+h₂β)=0 à α = -(h₂/h₁)β

y’ = h’x + (h_1aα+h_1bβ)x’

y” = h”x + (h_2aα+h_2bβ)x’

à

≠ 0

Agenda

• Interference Nulling

• Zero-forcing Beamforming (802.11ac)

• Interference Alignment

• Network MIMO

5

802.11ac

• From 802.11a/b/g, to 802.11n, to 802.11ac

⎻ AP can be more and more powerful à supporting multiple antennas

⎻ But, how about mobile devices? à usually light-

weight and small size à limited number of antennas

6

Cannot leverage multiplexing gains if clients only have a single antenna

802.11ac

• 802.11ac adopts multiuser MIMO (MU-MIMO)

⎻ Involve multiple clients in concurrent transmissions

⎻ Extract the multiplexing gain

⎻ Maximal number of clients (streams) = number of antennas at the AP

⎻ Only support downlink MU-MIMO now

7

Cross-Stream Interference

• Say the AP send x₁, x₂ and x₃ to client 1, 2 and 3, respectively

⎻ If the AP simply uses each antenna to send one stream,

⎻ Each client receives the combined signal of x₁, x₂ and x₃

⎻ x₂ and x₃ are cross-stream interference for client 1

8

x₁ x₂ x₃

Client 1

Client 2

Client 3

Channel Model

9

x₁ x₂ x₃

Client 1

Client 2

Client 3 h₁

h₂ h₃

h₁ = [h₁₁ h₁₂ h₁₃]^T h₂ = [h₂₁ h₂₂ h₂₃]^T h₃ = [h₃₁ h₃₂ h₃₃]^T

y₁ = h₁₁x₁ + (h₁₂x₂ + h₁₃x₃) + n₁

Interference

y₂ = h₂₂x₂ + (h₂₁x₁ + h₂₃x₃) + n₂ y₃ = h₃₃x₃ + (h₃₁x₁ + h₃₂x₂) + n₃

How to Remove Cross-Stream Interference?

• Zero-Forcing Beamforming (ZFBF)

⎻ Also called zero-forcing precoding or null-steering

⎻ Linear precoder that maximizes the output SNR

• The AP uses its antennas to actively cancel the interfering streams at a particular client

⎻ In the previous example, the AP cancel x₂ and x₃ at client 1

cancel x₁ and x₃ at client 2 cancel x₁ and x₂ at client 3

⎻ Steer a beam toward to its intended receiver

• How to suppress all the interference using the limited number of antennas?

10

11

Zero-Forcing Beamforming (ZFBF)

• Use all the antennas to send every stream

• Each stream i is precoded using ZFBF weight vector w_i = [w_i1 w_i2 … w_iN]

• The precoded signal w_ijx_i is sent by the j-th antenna

• The j-th antenna transmit the summation of all the precoded signal (w_1jx₁ + w_2jx₂ + … + w_Njx_N)

12

h₁

h₂ h₃ [w₃₁ w₃₂ w₃₃] * x₃ [w₂₁ w₂₂ w₂₃] * x₂ [w₁₁ w₁₂ w₁₃] * x₁

Zero-Forcing Beamforming (ZFBF)

13

h₁

h₂ h₃

[w₃₁ w₃₂ w₃₃] * x₃ * √P₃ [w₂₁ w₂₂ w₂₃] * x₂ * √P₂ [w₁₁ w₁₂ w₁₃] * x₁ * √P₁

Client 1

Client 2

Client 3

y_i = p

P_ih_iw_ix_i + X

j6=i

pP_jh_iw_jx_j + n_i

Interference

Null the interference:

à

Matrix: ^{y = HWpPx + n} à Let W be the pseudo inverse of H Then, y = p

Px + n⁰

W = H^† = H^⇤(HH^⇤) ¹

P_jh_iw_j = 0, j = i

SNR of ZFBF

• ZFBF is essentially equivalent to ZF, but just performed by the transmitter

• The achievable SNR is determined by the

channel correlation among concurrent clients

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x₂

antenna 1 antenna 2

x₁ x’₁

~h₂ = (h₁₂, h₂₂)

~h₁ = (h₁₁, h₂₁)

~y = (y₁, y₂)

θ

|x⁰1| = |x¹| cos(90 ✓) = |x¹| sin(✓)

MU-MIMO Bit-Rate Selection

AP

A C

B h_A

h_B

h_C

ant. 2 ant. 1

Alice

Bob

ant. 2

Alice

Chris

ant. 1

ant. 2 ant. 1

Bob

Chris

Select a proper rate based on SNR_ZFBF

MU-MIMO User Selection

ant. 2 ant. 1

Alice

Bob

ant. 2

Alice

Chris

ant. 1

ant. 2 ant. 1

Bob

Chris

AP

A C

B h_A

h_B

h_C

Grouping different subsets of clients as concurrent receivers

results in different sum-rates à Need proper user selection

MU-MIMO User Selection

• Exhaustive search:

⎻ Calculate the sum-rate for each of groups

⎻ Pick the one with the maximal sum-rate

• Greedy:

⎻ sequentially add a user producing the maximal rate after projecting on the subspace of the users that have been selected

AP

A C

B h_A

h_B

h_C

N k

Grouping different subsets of clients as concurrent receivers

results in different sum-rates à Need proper user selection

MU-MIMO Power Allocation

• Achievable sum-rate for a set of user S

18

Power allocated to user i R = max

p_i

i S

log(1 + p_i|hⁱw_i|²) subject to

i S

w_i ²p_i P_max

MU-MIMO Power Allocation

• Optimal power allocation: Waterfilling

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p_i = µ

w_i ² 1

+

, where

(x)⁺ = max{x, 0}

µ is the water level satisfying

i S

(µ w_i ²)⁺ = P

[1] Yoo et.al. “On the optimality of multiantenna broadcast scheduling using zero-forcing beamforming,” IEEE JSAC, 24(3):528–541, March 2006.

[2] Huang et.al., "User Selection for Multiuser MIMO Downlink With Zero-Forcing Beamforming," in IEEE TVT, vol. 62, no. 7, pp. 3084-3097, Sept. 2013.

R = max

p_i

i S

log(1 + p_i|hⁱw_i|²) s.t.

i S

w_i ²p_i P_max

user

Waterfilling Power Allocation

i S

(µ w_i ²)⁺ = P

20

water level µ such that

• Good channels get more power than poor channels

• Fairness is a concern

power allocated to user i: ^pi = µ

w_i ² 1

+

w_i ²

Agenda

• Interference Nulling

• Zero-forcing Beamforming (802.11ac)

• Interference Alignment

• Network MIMO

21

Interference Alignment

N-antenna node can only decode N signals

wanted signal I₁

I₂

2-antenna receiver

If I₁ and I₂ are aligned,

à appear as one interferer

à 2-antenna receiver can decode the wanted signal x and the combined interference (I₁+I₂)

à No need to decode I₁ and I₂ since the Rx does not care

Rotate Signal

• A multi-antenna transmitter can rotate the received signal

• To rotate received signal y to y’ = Ry,

the transmitter precodes the transmitted signal by multiplying it with the rotation matrix R

y y’ = Ry

2-antenna receiver

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Rotate Signal (2x2 Example)

• Say an interfering transmitter wants to align its signal at the interfered receiver along the

direction (u,v)

• The interferer precodes its signal x with a weight vector (w₁, w₂)

x x

h₁₁

h₁₂ h₂₁ h₂₂

y₁=(h₁₁+h₁₂)x y₂=(h₂₁+h₂₂)x

(u, v) (h₁₁+h₁₂, h₂₁+h₂₂)

ant1 ant2

Rotate Signal (2x2 Example)

• Find (w₁, w₂) such that

⎻ (w₁h₁₁+w₂h₁₂, w₁h₂₁+w₂h₂₂)∥ (u, v)

w₁x

h₁₁

h₁₂ h₂₁ h₂₂

y₁=(w₁h₁₁+w₂h₁₂)x y₂=(w₁h₂₁+w₂h₂₂)x

(h₁₁+h₁₂, h₂₁+h₂₂)

(u, v) w₂x

(2)

q

w₁² + w₂² = 1 (1) w₁h₁₁ + w₂h₁₂

w₁h₂₁ + w₂h₂₂ = u

v ^Alignment

Power constraint

Interference Alignment

N-antenna node can only decode N signals

wanted signal I₁

I₂

2-antenna receiver

How to align interfering signals?

à Find the direction of any interference (e.g., I₁)

à All the remaining interferers (e.g., I₁ and I₂) rotate their signals to that direction

I₃

Alignment direction

Agenda

• Interference Nulling

• Zero-forcing Beamforming (802.11ac)

• Interference Alignment

• Network MIMO

28

Network MIMO

• Also known as virtual MIMO, cooperative MIMO, distributed MIMO

• Why we need network MIMO?

⎻ Maximal number of concurrent packets is limited by the number of antennas per AP

⎻ It is hard to equip with a large number of antennas in a single AP

• How to build a network MIMO node?

29

Network MIMO

• Combine multiple APs as a giant virtual AP

• Distributed antennas are connected via backhual wired network

• Process signals by one or multiple backend servers

30

vAP

Open Issues of Network MIMO

• Salability

• Latency

• Synchronization

31

Scalability

• Forwarding raw complex signals through the Ethernet requires an extremely large backhual bandwidth

⎻ Ethernet capacity might now become a bottleneck

• Complexity of precoding/decoding a large scale of streams is fairly high

⎻ A single server can only support a limited number of concurrent packets

⎻ Software-based precoding/decoding at the servers is less efficient than hardware-based processing at APs

32

Latency

• Servers need to collect the received signals from distributed antennas

• The latency between antennas and servers might be longer than symbol duration

⎻ For example, the symbol duration of 802.11n is only 4 microseconds (us)

• A packet might not be able to be

acknowledged immediately after data transmission

⎻ The MAC protocol might need to be re-designed

33

Synchronization

• MIMO transmissions require all the antennas to be tightly synchronized

⎻ Otherwise, a small frequency offset could destroy all the concurrent packets

• Potential Solutions

⎻ Connect all the APs to an external clock à scalability would be an issue

⎻ Each AP learn the frequency offset based on a

reference clock and calibrate the offset à hard to achieve a granularity acceptable for network

MIMO

34

Wireless Communication Systems

@CS.NCTU

Lecture 5: Multi-User MIMO (MU-MIMO)

Interference Alignment and Cancellation (SIGCOMM’09) Lecturer: Kate Ching-Ju Lin (林靖茹)

35

Naïve Cooperative MIMO

• Say we combine two 2-antnena APs as a 4–

antenna virtual AP

• Naïve solution:

⎻ Connect the two APs to a server via Ethernet

⎻ Each physical AP sends every received raw signal (complex values) to the server over Ethernet

36

y₂ y₁

y₄ y₃

Raw samples

Naïve Cooperative MIMO

• Say we combine two 2-antnena APs as a 4–

antenna virtual AP

• Naïve solution:

⎻ Connect the two APs to a server via Ethernet

⎻ Each physical AP sends every received raw signal (complex values) to the server over Ethernet

37

y₂ y₁

y₄ y₃

Raw samples

Impractical overhead:

For example, a 3 or 4-antenna system needs 10’s of Gb/s

How to Minimize Ethernet Overhead?

• High-level idea:

1. Decode some packets in certain AP

2. Forward the decoded packets through the Ethernet to other APs

3. Other APs decode the remaining packets 4. Repeat 1-3 until all packets are recovered

38

How to Minimize Ethernet Overhead?

• Advantage:

⎻ The size of data packets is much smaller than the size of raw samples à minimize overhead

• Challenge:

⎻ In theory, an N-antenna AP cannot recover M concurrent transmissions if M>N

⎻ How can an N-antenna AP recover its packet from M concurrent transmissions (M>N)?

à Interference Alignment and Cancellation

39

Interference Alignment and Cancellation

40

p₁

p₃

p₃

p₁

p₂ p₃

p₁

p₂ p₁

p₂

• Align p₃ with p₂ at AP1

• AP1 broadcasts p₁ on Ethernet

• AP2 subtracts/cancels p₁à decodes p₂, p₃

AP1

AP2

Interference Alignment and Cancellation

41

p₁

p₃

p₃

p₁

p₂ p₃

p₁

p₂ p₁

p₂

• AP1 broadcasts p₁ on Ethernet

AP1

AP2

Only forward 1 data packet through the Ethernet!

How to Align?

1. Learn the direction we need to align

⎻ Client 2 aligns p₃ along (h₂₁, h₂₂) at AP1

42

p₃

p₁

p₂ p₁

p₂

AP2

p₁ p₂

h₁₁ AP1

h₁₂ h₂₁ h₂₂

(h₂₁, h₂₂) (h₁₁, h₁₂)

w₁p₃ w₂p₃

How to Align?

43

p₃

p₁

p₂ p₁

p₂

AP2

p₁ p₂

h₃₁ AP1

h₃₂

h₄₁ h₄₂

(h₂₁, h₂₂) (h₁₁, h₁₂)

w₁p₃ w₂p₃

2. Precode p₃ by (w₁, w₂)

3. AP2 receives p₃ along the direction (w₁h₃₁+w₂h₄₁, w₁h₃₂+w₂h₄₂)

(w₁h₃₁+w₂h₄₁, w₁h₃₂+w₂h₄₂)

How to Align?

p₃

p₁

p₂ p₁

p₂

AP2

p₁ p₂

h₃₁ AP1

h₃₂

h₄₁ h₄₂

(h₂₁, h₂₂) (h₁₁, h₁₂)

w₁p₃ w₂p₃

4. Since AP1 tries to decode p₁, we align the interference p₃ along the direction of p₂

à Let (

w

h

+w

h

)/(w

h

+w

h

)=h

/

(w₁h₃₁+w₂h₄₁, w₁h₃₂+w₂h₄₂)

Infinite number of solution?

No! power constraint w₁²+w₂²=P_max

How to Remove Interference?

• For example, how can AP2 remove the interference from p₁?

• Cannot just subtract the bits of p₁ from the received packet

⎻ Should subtract interference signals as received by AP2

• How? à Similar to SIC

⎻ AP2 re-modulates p₁’s bits

⎻ AP2 estimate the channel from client 1 to AP2 and apply the learned channel on the re-

modulated signals of p₁

⎻ Subtract it from the received signal y

45

Theorem

In a M- antenna MIMO system, IAC delivers

• 2M concurrent packets on uplink

• max{2M-2, 3M/2} concurrent packets on downlink

How to Generalize to M-Antenna MIMO?

e.g., M=2 antennas 4 packets on uplink 3 packets on downlink See the paper for the details!

Quiz

• Consider a 2x1 system

• How can the AP (Tx) send a symbol x without being heard by the smartphone?

h₁=4 h₂=-3

x