David versus Goliath:Small Cells versus Massive MIMO Jakob Hoydis - - PowerPoint PPT Presentation

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David versus Goliath:Small Cells versus Massive MIMO Jakob Hoydis and Mrouane Debbah 1948: Cybernetics and Theory of Communications A Mathematical Theory of Communication, Bell System Technical Journal, 1948, C. E. Shannon

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SLIDE 1

David versus Goliath:Small Cells versus Massive MIMO

Jakob Hoydis and Mérouane Debbah

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SLIDE 2

1948: Cybernetics and Theory of Communications

  • ”A Mathematical Theory of Communication”, Bell System Technical

Journal, 1948, C. E. Shannon

  • ”Cybernetics, or Control and Communication in the Animal and the

Machine”, Herman et Cie/The Technology Press, 1948, N. Wiener

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SLIDE 3

60 years later... MIMO Flexible Networks

We must learn and control the black box

  • within a fraction of time
  • with finite energy.

In many cases, the number of inputs/outputs (the dimensionality of the system) is of the same order as the time scale changes of the box.

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SLIDE 4
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SLIDE 5
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SLIDE 6

“David vs Goliath“ or ”Small Cells vs Massive MIMO“

How to densify: “More antennas or more BSs?” Questions:

◮ Should we install more base stations or simply more antennas per base? ◮ How can massively many antennas be efficiently used? ◮ Can massive MIMO simplify the signal processing?

4 / 25

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SLIDE 7

Vision

Bell Labs lightradio antenna module – the next generation small cell (picture from www.washingtonpost.com)

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SLIDE 8

A thought experiment

Consider an infinite large network of randomly uniformly distributed base stations and user terminals. What would be better? A 2 × more base stations B 2 × more antennas per base station

5 / 25

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SLIDE 9

A thought experiment

Consider an infinite large network of randomly uniformly distributed base stations and user terminals. What would be better? A 2 × more base stations B 2 × more antennas per base station Stochastic geometry can provide an answer.

5 / 25

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SLIDE 10

System model: Downlink

Received signal at a tagged UT at the origin: y = 1 r α/2 hH

0 x0

  • desired signal

+

∞

  • i=1

1 r α/2

i

hH

i xi

  • interference

+ n

◮ hi ∼ CN(0, IN): fast fading channel vectors ◮ ri: distance to ith closest BS ◮ P = E

  • xH

i xi

  • : average transmit power constraint per BS

6 / 25

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SLIDE 11

System model: Downlink

Received signal at a tagged UT at the origin: y = 1 r α/2 hH

0 x0

  • desired signal

+

∞

  • i=1

1 r α/2

i

hH

i xi

  • interference

+ n

◮ hi ∼ CN(0, IN): fast fading channel vectors ◮ ri: distance to ith closest BS ◮ P = E

  • xH

i xi

  • : average transmit power constraint per BS

Assumptions:

◮ infinitely large network of uniformly randomly distributed BSs and UTs

with densities λBS and λUT, respectively

◮ single-antenna UTs, N antennas per BS ◮ each UT is served by its closest BS ◮ distance-based path loss model with path loss exponent α > 2 ◮ total bandwidth W , re-used in each cell

6 / 25

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SLIDE 12

Transmission strategy: Zero-forcing

Assumptions:

◮ K = λUT λBS UTs need to be served by each BS on average ◮ total bandwidth W divided into L ≥ 1 sub-bands ◮ K = K/L ≤ N UTs are simultaneously served on each sub-band

7 / 25

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SLIDE 13

Transmission strategy: Zero-forcing

Assumptions:

◮ K = λUT λBS UTs need to be served by each BS on average ◮ total bandwidth W divided into L ≥ 1 sub-bands ◮ K = K/L ≤ N UTs are simultaneously served on each sub-band

Transmit vector of BS i: xi =

  • P

K

K

  • k=1

wi,ksi,k

◮ si,k ∼ CN(0, 1): message determined for UT k from BS i ◮ wi,k ∈ C N×1: ZF-beamforming vectors

7 / 25

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SLIDE 14

Performance metric: Average throughput

Received SINR at tagged UT: γ = r −α

  • hH

0 w0,1

  • 2

∞

i=1 r −α i

K

k=1

  • hH

i wi,k

  • 2 + K

P

= r −α S ∞

i=1 r −α i

gi + K

P

Coverage probability: Pcov(T) = P (γ ≥ T) Average throughput per UT: C = W L × E [log(1 + γ)] = W L × ∞ Pcov (ez − 1) dz

8 / 25

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SLIDE 15

Performance metric: Average throughput

Received SINR at tagged UT: γ = r −α

  • hH

0 w0,1

  • 2

∞

i=1 r −α i

K

k=1

  • hH

i wi,k

  • 2 + K

P

= r −α S ∞

i=1 r −α i

gi + K

P

Coverage probability: Pcov(T) = P (γ ≥ T) Average throughput per UT: C = W L × E [log(1 + γ)] = W L × ∞ Pcov (ez − 1) dz Remarks:

◮ expectation with respect to fading and BSs locations ◮ S =

  • hH

0 w0,1

  • 2 ∼ Γ(N − K + 1, 1),

gi = K

k=1

  • hH

i wi,k

  • 2 ∼ Γ(K, 1)

◮ K impacts the interference distribution, N impacts the desired signal ◮ for P → ∞, the SINR becomes independent of λBS

8 / 25

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SLIDE 16

A closed-form result

Theorem (Combination of Baccelli’09, Andrews’10)

Pcov(T) =

  • r0>0

∞

−∞

LIr0 (i2πrα

0 Ts) exp

  • − i2πrα

0 TK

P s LS (−i2πs) − 1 i2πs fr0(r0)dsdr0 where LIr0 (s) = exp

  • −2πλBS

∞

r0

  • 1 −

1 (1 + sv−α)K

  • vdv
  • LS(s) =
  • 1

1 + s N−K+1 fr0(r0) = 2πλBSr0e−λBSπr2 The computation of Pcov(T) requires in general three numerical integrals.

  • J. G. Andrews, F. Baccelli, R. K. Ganti, “A Tractable Approach to Coverage and Rate in Cellular Networks” IEEE
  • Trans. Wireless Commun., submitted 2010.
  • F. Baccelli, B. B

laszczyszyn, P. M¨ uhlethaler, “Stochastic Analysis of Spatial and Opportunistic Aloha” Journal on Selected Areas in Communications, 2009

9 / 25

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SLIDE 17

Example

◮ Density of UTs: λUT = 16 ◮ Constant transmit power density: P × λBS = 10 ◮ Number of BS-antennas: N = λUT/λBS ◮ Path loss exponent: α = 4 ◮ UT simultaneously served on each band: K = λUT/(λBS × L)

⇒ Only two parameters: λBS and L

10 / 25

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SLIDE 18

Example

◮ Density of UTs: λUT = 16 ◮ Constant transmit power density: P × λBS = 10 ◮ Number of BS-antennas: N = λUT/λBS ◮ Path loss exponent: α = 4 ◮ UT simultaneously served on each band: K = λUT/(λBS × L)

⇒ Only two parameters: λBS and L

Table: Average spectral efficiency C/W in (bits/s/Hz)

sub-bands L λBS = 1 λBS = 2 λBS = 4 λBS = 8 λBS = 16 1 0.6209 0.8188 1.1964 1.5215 2.1456 2 1.1723 1.2414 1.3404 1.5068 x 4 0.8882 0.8973 1.1964 x x 8 0.5689 0.5952 x x 16 0.3532 x x x x Fully distributing the antennas gives highest throughput gains!

10 / 25

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SLIDE 19

First conclusions

◮ Distributed network densification is preferable over massive MIMO if the

average throughput per UT should be increased.

◮ More antennas increase the coverage probability, but more BSs lead to a

linear increase in area spectral efficiency (with constant total transmit power).

◮ If we use other metrics such as coverage probability or goodput, the

picture might change.

11 / 25

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SLIDE 20
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SLIDE 21
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SLIDE 22
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SLIDE 23

Beyond LTE: The 400-Antenna Base Station

Thomas L. Marzetta Bell Laboratories Alcatel-Lucent 28 May, 2010

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SLIDE 24

Large Excess of Base Station Antennas Over Terminals Yields Energy Efficiency + Reliably High Throughput

  • M~400 base station antennas serve K~40 terminals via multi-user MIMO
  • Doubling M permits a reduction in total transmit power by factor-of-two
  • Extra base station antennas always help (even wit h noisy CS

I)

 Eventually produce inter-cellular interference-limited operation: everybody can

now reduce power arbitrarily!

 reduce effects of uncorrelated noise and fast fading  compensate for poor-quality channel-state information

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SLIDE 25

Multiple Cells: No Cooperation

  • If we could assign an orthogonal pilot sequence to every terminal in

every cell then nothing bad would happen!

 Ever greater numbers of base station antennas would eventually defeat all

noise, and eliminate both intra- and inter-cell interference

  • But there aren’ t enough orthogonal pilot sequences for everyone!

 Pilot sequences have to be re-used

  • Pilot contamination: the base station inadvertently learns the

channel to mobiles in other cells

 Forward link: base station transmits interference to mobiles in other cells  Reverse link: base station processing enhances his reception of

transmission from mobiles in other cells

  • Inter-cell interference due to pilot contamination persists, even

with an infinite number of antennas!

 This is the only remaining impairment

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SLIDE 26

Limiting Case: Infinite Number of Antennas

  • Greatly simplifies multi-cellular analysis: all effects

accounted for near-analytically

  • Acquisition of CS

I

  • Imperfections in CS

I

  • Inter-cellular interference
  • Propagation
  • Fast (either line-of-sight, or independent Rayleigh, or something

intermediate)

  • S

low (geometric, log-normal shadow)

  • Far-reaching and comprehensive conclusions ensue
  • Indicates a new direction in which the macro-cellular

world can go: vastly improved energy efficiency and throughput compared with LTE

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SLIDE 27

Summary of Limit Analysis

  • Multi-cellular TDD scenario, 42 terminals served per cell

 500 sec coherence interval (7 OFDM symbols): 3 reverse-link pilots, 1 idle,

3 data

 OFDM: 20 MHz bandwidth, cyclic prefix 4.76 sec  Fading: Fast + log-normal shadow (8 dB) + geometric (3.8 power)  No inter-cellular cooperation

  • Net downlink throughput (comparable uplink) for frequency re-use 7

 mean

– 730 Mbits/ sec/ cell – 17 Mbits/ sec/ terminal

 95%

likely: 3.6 Mbits/ sec/ terminal

 spectral efficiency constant with respect to bandwidth  throughput constant with respect to cell-size  number of terminals per cell proportional to coherence interval  performance independent of power

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SLIDE 28

Cells Operate Independently, Each Serving Single- Antenna Terminals via Multi-User MIMO: TDD Only!

  • Maximum number of terminals limited by the time that it takes to

send reverse pilots: pilot-interval divided by the channel delay- spread

  • Coherence interval: 500 sec (7 LTE OFDM symbols) – TGV speeds!

 3 symbols for reverse-link pilots  3 symbols for data  1 symbol for computations and dead time

  • 42 terminals per cell served simultaneously
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SLIDE 29

Infinitely Many Antennas: Forward-Link Capacity For 20 MHz Bandwidth, 42 Terminals per Cell, 500 sec Slot

Frequency Reuse .95-Likely SIR (dB) .95-Likely Capacity per Terminal (Mbits/s) Mean Capacity per Terminal (Mbits/s) Mean Capacity per Cell (Mbits/s) 1

  • 29

.016 44 1800 3

  • 5.8

.89 28 1200 7 8.9 3.6 17 730

Interference-limited: energy-per-bit can be made arbitrarily small!

Mean Capacity per Cell (Mbits/s) LTE Advanced (>= Release 10) 74

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SLIDE 30

Infinitely Many Antennas: Forward-Link Capacity For 20 MHz Bandwidth, 42 Terminals per Cell, 500 sec Slot

Frequency Reuse .95-Likely SIR (dB) .95-Likely Capacity per Terminal (Mbits/s) Mean Capacity per Terminal (Mbits/s) Mean Capacity per Cell (Mbits/s) 1

  • 29

.016 44 1800 3

  • 5.8

.89 28 1200 7 8.9 3.6 17 730

Interference-limited: energy-per-bit can be made arbitrarily small!

Mean Capacity per Cell (Mbits/s) LTE Advanced (>= Release 10) 74

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SLIDE 31

Motivation of massive MIMO

Consider a N × K MIMO MAC: y =

K

  • k=1

hkxk + n where hk, n are i.i.d. with zero mean and unit variance.

Jakob Hoydis (Sup´ elec) Massive MIMO: How many antennas do we need? 4 / 30

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SLIDE 32

Motivation of massive MIMO

Consider a N × K MIMO MAC: y =

K

  • k=1

hkxk + n where hk, n are i.i.d. with zero mean and unit variance. By the strong law of large numbers: 1 N hm

Hy a.s.

− − − − − − − − − − →

N→∞, K=const. xm

Jakob Hoydis (Sup´ elec) Massive MIMO: How many antennas do we need? 4 / 30

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SLIDE 33

Motivation of massive MIMO

Consider a N × K MIMO MAC: y =

K

  • k=1

hkxk + n where hk, n are i.i.d. with zero mean and unit variance. By the strong law of large numbers: 1 N hm

Hy a.s.

− − − − − − − − − − →

N→∞, K=const. xm

With an unlimited number of antennas, uncorrelated interference and noise vanish, the matched filter is optimal, the transmit power can be made arbitrarily small.

  • T. Marzetta, “Noncooperative cellular wireless with unlimited numbers of base station antennas” IEEE Trans. Wireless Commun.,
  • vol. 9, no. 11, pp. 35903600, Nov. 2010.

Jakob Hoydis (Sup´ elec) Massive MIMO: How many antennas do we need? 4 / 30

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SLIDE 34

About some fundamental assumptions

The receiver has perfect channel state information (CSI). What happens if the channel must be estimated?

Jakob Hoydis (Sup´ elec) Massive MIMO: How many antennas do we need? 5 / 30

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SLIDE 35

About some fundamental assumptions

The receiver has perfect channel state information (CSI). What happens if the channel must be estimated? The number of interferers K is small compared to N. What does small mean?

Jakob Hoydis (Sup´ elec) Massive MIMO: How many antennas do we need? 5 / 30

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SLIDE 36

About some fundamental assumptions

The receiver has perfect channel state information (CSI). What happens if the channel must be estimated? The number of interferers K is small compared to N. What does small mean? The channel provides infinite diversity, i.e., each antenna gives an independent look

  • n the transmitted signal.

What if the degrees of freedom are limited?

Jakob Hoydis (Sup´ elec) Massive MIMO: How many antennas do we need? 5 / 30

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SLIDE 37

About some fundamental assumptions

The receiver has perfect channel state information (CSI). What happens if the channel must be estimated? The number of interferers K is small compared to N. What does small mean? The channel provides infinite diversity, i.e., each antenna gives an independent look

  • n the transmitted signal.

What if the degrees of freedom are limited? The received energy grows without bounds as N → ∞. Clearly wrong, but might hold up to very large antenna arrays if the aperture scales with N.

Jakob Hoydis (Sup´ elec) Massive MIMO: How many antennas do we need? 5 / 30

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SLIDE 38

On channel estimation and pilot contamination

1

The receiver estimates the channels based on pilot sequences.

2

The number of orthogonal sequences is limited by the coherence time.

3

Thus, the pilot sequences must be reused.

Jakob Hoydis (Sup´ elec) Massive MIMO: How many antennas do we need? 6 / 30

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SLIDE 39

On channel estimation and pilot contamination

1

The receiver estimates the channels based on pilot sequences.

2

The number of orthogonal sequences is limited by the coherence time.

3

Thus, the pilot sequences must be reused. Assume that transmitter m and j use the same pilot sequence: ˆ hm = hm + hj

  • pilot contamination

+ nm

  • estimation noise

Jakob Hoydis (Sup´ elec) Massive MIMO: How many antennas do we need? 6 / 30

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SLIDE 40

On channel estimation and pilot contamination

1

The receiver estimates the channels based on pilot sequences.

2

The number of orthogonal sequences is limited by the coherence time.

3

Thus, the pilot sequences must be reused. Assume that transmitter m and j use the same pilot sequence: ˆ hm = hm + hj

  • pilot contamination

+ nm

  • estimation noise

Thus, 1 N ˆ hm

Hy a.s

− − − − − − − − − →

N→∞,K=const. xm + xj

Jakob Hoydis (Sup´ elec) Massive MIMO: How many antennas do we need? 6 / 30

slide-41
SLIDE 41

On channel estimation and pilot contamination

1

The receiver estimates the channels based on pilot sequences.

2

The number of orthogonal sequences is limited by the coherence time.

3

Thus, the pilot sequences must be reused. Assume that transmitter m and j use the same pilot sequence: ˆ hm = hm + hj

  • pilot contamination

+ nm

  • estimation noise

Thus, 1 N ˆ hm

Hy a.s

− − − − − − − − − →

N→∞,K=const. xm + xj

With an unlimited number of antennas, uncorrelated interference, noise and estimation errors vanish, the matched filter is optimal, the transmit power can be made arbitrarily small (∼ 1/ √ N [Ngo’11]), but the performance is limited by pilot contamination.

  • T. Marzetta, “Noncooperative cellular wireless with unlimited numbers of base station antennas” IEEE Trans. Wireless Commun.,
  • vol. 9, no. 11, pp. 35903600, Nov. 2010.

Jakob Hoydis (Sup´ elec) Massive MIMO: How many antennas do we need? 6 / 30

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SLIDE 42

Uplink

Jakob Hoydis (Sup´ elec) Massive MIMO: How many antennas do we need? 7 / 30

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SLIDE 43

System model and channel estimation

Uplink: L BSs with N antennas, K UTs per cell. Received signal at BS j: yj = √ρ

L

  • l=1

Hjlxl + nj

Jakob Hoydis (Sup´ elec) Massive MIMO: How many antennas do we need? 8 / 30

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SLIDE 44

System model and channel estimation

Uplink: L BSs with N antennas, K UTs per cell. Received signal at BS j: yj = √ρ

L

  • l=1

Hjlxl + nj The columns of Hjl (N × K) are modeled as hjlk = R

1 2

jlkwjlk,

wjlk ∼ CN(0, IN)

Jakob Hoydis (Sup´ elec) Massive MIMO: How many antennas do we need? 8 / 30

slide-45
SLIDE 45

System model and channel estimation

Uplink: L BSs with N antennas, K UTs per cell. Received signal at BS j: yj = √ρ

L

  • l=1

Hjlxl + nj The columns of Hjl (N × K) are modeled as hjlk = R

1 2

jlkwjlk,

wjlk ∼ CN(0, IN) Channel estimation: yτ

jk = hjjk +

  • l=j

hjlk + 1 √ρτ njk

Jakob Hoydis (Sup´ elec) Massive MIMO: How many antennas do we need? 8 / 30

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SLIDE 46

System model and channel estimation

Uplink: L BSs with N antennas, K UTs per cell. Received signal at BS j: yj = √ρ

L

  • l=1

Hjlxl + nj The columns of Hjl (N × K) are modeled as hjlk = R

1 2

jlkwjlk,

wjlk ∼ CN(0, IN) Channel estimation: yτ

jk = hjjk +

  • l=j

hjlk + 1 √ρτ njk MMSE estimate: hjjk = ˆ hjjk + ˜ hjjk

Jakob Hoydis (Sup´ elec) Massive MIMO: How many antennas do we need? 8 / 30

slide-47
SLIDE 47

System model and channel estimation

Uplink: L BSs with N antennas, K UTs per cell. Received signal at BS j: yj = √ρ

L

  • l=1

Hjlxl + nj The columns of Hjl (N × K) are modeled as hjlk = R

1 2

jlkwjlk,

wjlk ∼ CN(0, IN) Channel estimation: yτ

jk = hjjk +

  • l=j

hjlk + 1 √ρτ njk MMSE estimate: hjjk = ˆ hjjk + ˜ hjjk ˆ hjjk ∼ CN (0, Φjjk) , ˜ hjjk ∼ CN (0, Rjjk − Φjjk) Φjlk = RjjkQjkRjlk, Qjk =

  • 1

ρτ IN +

  • l

Rjlk −1

Jakob Hoydis (Sup´ elec) Massive MIMO: How many antennas do we need? 8 / 30

slide-48
SLIDE 48

Achievable rates with linear detectors

Ergodic achievable rate of UT m in cell j: Rjm = Eˆ

Hjj [log2 (1 + γjm)]

γjm =

  • rH

jmˆ

hjjm

  • 2

E

  • rH

jm

  • 1

ρIN + ˜

hjjm˜ hH

jjm − hjjmhH jjm + l HjlHH jl

  • rjm
  • ˆ

Hjj

  • with an arbitrary receive filter rjm.
  • B. Hassibi and B. M. Hochwald, “How much training is needed in multiple-antenna wireless links?” IEEE Trans. Inf. Theory., vol.

49, no. 4, pp. 951–963, Nov. 2003.

Jakob Hoydis (Sup´ elec) Massive MIMO: How many antennas do we need? 9 / 30

slide-49
SLIDE 49

Achievable rates with linear detectors

Ergodic achievable rate of UT m in cell j: Rjm = Eˆ

Hjj [log2 (1 + γjm)]

γjm =

  • rH

jmˆ

hjjm

  • 2

E

  • rH

jm

  • 1

ρIN + ˜

hjjm˜ hH

jjm − hjjmhH jjm + l HjlHH jl

  • rjm
  • ˆ

Hjj

  • with an arbitrary receive filter rjm.

Two specific linear detectors rjm: rMF

jm = ˆ

hjjm rMMSE

jm

=

  • ˆ

Hjj ˆ HH

jj + Zj + NλIN

−1 ˆ hjjm where λ > 0 is a design parameter and Zj = E  ˜ Hjj ˜ HH

jj +

  • l=j

HjlHjl   =

  • k

(Rjjk − Φjjk) +

  • l=j
  • k

Rjlk.

  • B. Hassibi and B. M. Hochwald, “How much training is needed in multiple-antenna wireless links?” IEEE Trans. Inf. Theory., vol.

49, no. 4, pp. 951–963, Nov. 2003.

Jakob Hoydis (Sup´ elec) Massive MIMO: How many antennas do we need? 9 / 30

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SLIDE 50

Large system analysis based on random matrix theory

Assume N, K → ∞ at the same speed. Then, γjm − ¯ γjm

a.s.

− − → 0 Rjm − log2 (1 + ¯ γjm)

a.s.

− − → 0

Jakob Hoydis (Sup´ elec) Massive MIMO: How many antennas do we need? 10 / 30

slide-51
SLIDE 51

Large system analysis based on random matrix theory

Assume N, K → ∞ at the same speed. Then, γjm − ¯ γjm

a.s.

− − → 0 Rjm − log2 (1 + ¯ γjm)

a.s.

− − → 0 where ¯ γMF

jm =

1

N tr Φjjm

2

1 ρN2 tr Φjjm + 1 N

  • l,k

1 N tr RjlkΦjjm + l=j

  • 1

N tr Φjlm

  • 2

¯ γMMSE

jm

= δ2

jm 1 ρN2 tr Φjjm ¯

T′

j + 1 N

  • l,k µjlkm +

l=j |ϑjlm|2

and δjm, µjlkm, θjlm, ¯ T′

j can be calculated numerically.

Jakob Hoydis (Sup´ elec) Massive MIMO: How many antennas do we need? 10 / 30

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SLIDE 52

A simple multi-cell scenario

Jakob Hoydis (Sup´ elec) Massive MIMO: How many antennas do we need? 11 / 30

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SLIDE 53

A simple multi-cell scenario

intercell interference factor α ∈ [0, 1] transmit power per UT: ρ Hjl = [hjl1 · · · hjlK] =

  • N/PAWjl

A ∈ C

N×P composed of P ≤ N columns of a unitary matrix

Wij ∈ C

P×K have i.i.d. elements with zero mean and unit variance

Jakob Hoydis (Sup´ elec) Massive MIMO: How many antennas do we need? 11 / 30

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SLIDE 54

A simple multi-cell scenario

intercell interference factor α ∈ [0, 1] transmit power per UT: ρ Hjl = [hjl1 · · · hjlK] =

  • N/PAWjl

A ∈ C

N×P composed of P ≤ N columns of a unitary matrix

Wij ∈ C

P×K have i.i.d. elements with zero mean and unit variance

Assumptions: P channel degrees of freedom, i.e., rank (Hjl) = min(P, K) [Ngo’11] energy scales linearly with N, i.e., E

  • tr HjlHH

jl

  • = KN
  • nly pilot contamination, i.e., no estimation noise:

ˆ hjjk = hjjk + √α

  • l=j

hjlk

Jakob Hoydis (Sup´ elec) Massive MIMO: How many antennas do we need? 11 / 30

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SLIDE 55

Asymptotic performance of the matched filter

Assume that N, K and P grow infinitely large at the same speed: SINRMF ≈ 1 ¯ L ρN

  • noise

+ K P ¯ L2

  • multi-user interference

+ α(¯ L − 1)

  • pilot contamination

where ¯ L = 1 + α(L − 1).

Jakob Hoydis (Sup´ elec) Massive MIMO: How many antennas do we need? 12 / 30

slide-56
SLIDE 56

Asymptotic performance of the matched filter

Assume that N, K and P grow infinitely large at the same speed: SINRMF ≈ 1 ¯ L ρN

  • noise

+ K P ¯ L2

  • multi-user interference

+ α(¯ L − 1)

  • pilot contamination

where ¯ L = 1 + α(L − 1). Observations: The effective SNR ρN increases linearly with N. The multiuser interference depends on P/K and not on N. Ultimate performance limit: SINRMF

a.s

− − − − − − − − − − − →

N,P→∞, K=const. SINR∞ =

1 α(¯ L − 1)

  • J. Hoydis, S. ten Brink, and M. Debbah, “Massive MIMO: How many antennas do we need”, Allerton Conference,

Urbana-Champaing, Illinois, US, Sep. 2011. [Online] http://arxiv.org/abs/1107.1709

Jakob Hoydis (Sup´ elec) Massive MIMO: How many antennas do we need? 12 / 30

slide-57
SLIDE 57

Asymptotic performance of the MMSE detector

Assume that N, K and P grow infinitely large at the same speed: SINRMMSE ≈ 1 ¯ L ρN X

noise

+ K P ¯ L2Y

multi-user interference

+ α(¯ L − 1)

  • pilot contamination

where ¯ L = 1 + α(L − 1) and X, Y are given in closed-form.

Jakob Hoydis (Sup´ elec) Massive MIMO: How many antennas do we need? 13 / 30

slide-58
SLIDE 58

Asymptotic performance of the MMSE detector

Assume that N, K and P grow infinitely large at the same speed: SINRMMSE ≈ 1 ¯ L ρN X

noise

+ K P ¯ L2Y

multi-user interference

+ α(¯ L − 1)

  • pilot contamination

where ¯ L = 1 + α(L − 1) and X, Y are given in closed-form. Observations: As for the MF, the performance depends only on ρN and P/K. The ultimate performance of MMSE and MF coincide: SINRMMSE

a.s

− − − − − − − − − − − →

N,P→∞, K=const. SINR∞ =

1 α(¯ L − 1)

  • J. Hoydis, S. ten Brink, and M. Debbah, “Massive MIMO: How many antennas do we need”, Allerton Conference,

Urbana-Champaing, Illinois, US, Sep. 2011. [Online] http://arxiv.org/abs/1107.1709

Jakob Hoydis (Sup´ elec) Massive MIMO: How many antennas do we need? 13 / 30

slide-59
SLIDE 59

Numerical results 100 200 300 400 1 2 3 4 5 R∞

P = N P = N/3 ρ = 1, K = 10, α = 0.1, L = 4

Number of antennas N Ergodic achievable rate (b/s/Hz)

MF approx. MMSE approx. Simulations

Jakob Hoydis (Sup´ elec) Massive MIMO: How many antennas do we need? 14 / 30

slide-60
SLIDE 60

Conclusions (I) - Uplink

Massive MIMO can be seen as a particular operating condition where noise + interference ≪ pilot contamination.

Jakob Hoydis (Sup´ elec) Massive MIMO: How many antennas do we need? 18 / 30

slide-61
SLIDE 61

Conclusions (I) - Uplink

Massive MIMO can be seen as a particular operating condition where noise + interference ≪ pilot contamination. If this condition is satisfied depends on: P/K : degrees of freedom per UT ρN : effective SNR (transmit power × number of antennas) α : path loss (or intercell interference)

Jakob Hoydis (Sup´ elec) Massive MIMO: How many antennas do we need? 18 / 30

slide-62
SLIDE 62

Conclusions (I) - Uplink

Massive MIMO can be seen as a particular operating condition where noise + interference ≪ pilot contamination. If this condition is satisfied depends on: P/K : degrees of freedom per UT ρN : effective SNR (transmit power × number of antennas) α : path loss (or intercell interference) Connection between N and P is crucial, but unclear for real channels.

Jakob Hoydis (Sup´ elec) Massive MIMO: How many antennas do we need? 18 / 30

slide-63
SLIDE 63

Conclusions (I) - Uplink

Massive MIMO can be seen as a particular operating condition where noise + interference ≪ pilot contamination. If this condition is satisfied depends on: P/K : degrees of freedom per UT ρN : effective SNR (transmit power × number of antennas) α : path loss (or intercell interference) Connection between N and P is crucial, but unclear for real channels. As N → ∞, MF and MMSE detector achieve identical performance. For finite N, the MMSE detector largely outperforms the MF.

Jakob Hoydis (Sup´ elec) Massive MIMO: How many antennas do we need? 18 / 30

slide-64
SLIDE 64

Conclusions (I) - Uplink

Massive MIMO can be seen as a particular operating condition where noise + interference ≪ pilot contamination. If this condition is satisfied depends on: P/K : degrees of freedom per UT ρN : effective SNR (transmit power × number of antennas) α : path loss (or intercell interference) Connection between N and P is crucial, but unclear for real channels. As N → ∞, MF and MMSE detector achieve identical performance. For finite N, the MMSE detector largely outperforms the MF. The number of antennas needed for massive MIMO depends on all these parameters!

Jakob Hoydis (Sup´ elec) Massive MIMO: How many antennas do we need? 18 / 30

slide-65
SLIDE 65

Downlink

Jakob Hoydis (Sup´ elec) Massive MIMO: How many antennas do we need? 19 / 30

slide-66
SLIDE 66

System model: Downlink

L BSs with N antennas, K UTs per cell. Received signal at mth UT in cell j: yjm = √ρ

L

  • l=1

hH

ljmsl + qjm

Jakob Hoydis (Sup´ elec) Massive MIMO: How many antennas do we need? 20 / 30

slide-67
SLIDE 67

System model: Downlink

L BSs with N antennas, K UTs per cell. Received signal at mth UT in cell j: yjm = √ρ

L

  • l=1

hH

ljmsl + qjm

where sl =

  • λl

K

  • m=1

wlmxlm =

  • λlWlxl

λl = 1 tr WlWH

l

= ⇒ E

  • ρsH

l sl

  • = ρ

Jakob Hoydis (Sup´ elec) Massive MIMO: How many antennas do we need? 20 / 30

slide-68
SLIDE 68

System model: Downlink

L BSs with N antennas, K UTs per cell. Received signal at mth UT in cell j: yjm = √ρ

L

  • l=1

hH

ljmsl + qjm

where sl =

  • λl

K

  • m=1

wlmxlm =

  • λlWlxl

λl = 1 tr WlWH

l

= ⇒ E

  • ρsH

l sl

  • = ρ

Channel estimation through uplink pilots (as before): hjjk = ˆ hjjk + ˜ hjjk ˆ hjjk ∼ CN (0, Φjjk) , ˜ hjjk ∼ CN (0, Rjjk − Φjjk) Φjlk = RjjkQjkRjlk, Qjk =

  • 1

ρτ IN +

  • l

Rjlk −1

Jakob Hoydis (Sup´ elec) Massive MIMO: How many antennas do we need? 20 / 30

slide-69
SLIDE 69

Achievable rates with linear precoders

Ergodic achievable rate of UT m in cell j: Rjm = log2 (1 + γjm) γjm =

  • E
  • λjhH

jjmwjm

  • 2

1 ρ + var

  • λjhH

jjmwjm

  • +

(l,k)=(j,m) E

  • √λlhH

ljmwlk

  • 2.
  • J. Jose, A. Ashikhmin, T. Marzetta, and S. Vishwanath, “Pilot contamination and precoding in multi-cell TDD systems,” IEEE
  • Trans. Wireless Commun., no. 99, pp. 1–12, 2011.

Jakob Hoydis (Sup´ elec) Massive MIMO: How many antennas do we need? 21 / 30

slide-70
SLIDE 70

Achievable rates with linear precoders

Ergodic achievable rate of UT m in cell j: Rjm = log2 (1 + γjm) γjm =

  • E
  • λjhH

jjmwjm

  • 2

1 ρ + var

  • λjhH

jjmwjm

  • +

(l,k)=(j,m) E

  • √λlhH

ljmwlk

  • 2.

Two specific precoders Wj: WBF

j

△

= ˆ Hjj WRZF

j

△

=

  • ˆ

Hjj ˆ HH

jj + Fj + NαIN

−1 ˆ Hjj where α > 0 and Fj are design parameters.

  • J. Jose, A. Ashikhmin, T. Marzetta, and S. Vishwanath, “Pilot contamination and precoding in multi-cell TDD systems,” IEEE
  • Trans. Wireless Commun., no. 99, pp. 1–12, 2011.

Jakob Hoydis (Sup´ elec) Massive MIMO: How many antennas do we need? 21 / 30

slide-71
SLIDE 71

Large system analysis based on random matrix theory

Assume N, K → ∞ at the same speed. Then, γjm − ¯ γjm

a.s.

− − → 0 Rjm − log2 (1 + ¯ γjm)

a.s.

− − → 0

  • J. Hoydis, S. ten Brink, M. Debbah, “Comparison of linear precoding schemes for downlink Massive MIMO”, ICC’12, 2011.

Jakob Hoydis (Sup´ elec) Massive MIMO: How many antennas do we need? 22 / 30

slide-72
SLIDE 72

Large system analysis based on random matrix theory

Assume N, K → ∞ at the same speed. Then, γjm − ¯ γjm

a.s.

− − → 0 Rjm − log2 (1 + ¯ γjm)

a.s.

− − → 0 where ¯ γBF

jm =

¯ λj 1

N tr Φjjm

2

K Nρ + 1 N

  • l,k ¯

λl 1

N tr RljmΦllk + l=j ¯

λj

  • 1

N tr Φljm

  • 2

¯ γRZF

jm

= ¯ λjδ2

jm K Nρ (1 + δjm)2 + 1 N

  • l,k ¯

λl

  • 1+δjm

1+δlk

2 µljmk +

l=j ¯

λl

  • 1+δjm

1+δlm

2 |ϑljm|2 and ¯ λj, δjm, µjlkm and ϑjlm can be calculated numerically.

  • J. Hoydis, S. ten Brink, M. Debbah, “Comparison of linear precoding schemes for downlink Massive MIMO”, ICC’12, 2011.

Jakob Hoydis (Sup´ elec) Massive MIMO: How many antennas do we need? 22 / 30

slide-73
SLIDE 73

Downlink: Numerical results

−3 −2 −1 1 2 3 −3 −2 −1 1 2 3

Base stations User terminals cell l UT k djlk 2 cell j

3 4

7 cells, K = 10 UTs distributed on a circle of radius 3/4

Jakob Hoydis (Sup´ elec) Massive MIMO: How many antennas do we need? 23 / 30

slide-74
SLIDE 74

Downlink: Numerical results

−3 −2 −1 1 2 3 −3 −2 −1 1 2 3

Base stations User terminals cell l UT k djlk 2 cell j

3 4

7 cells, K = 10 UTs distributed on a circle of radius 3/4 path loss exponent β = 3.7, ρτ = 6 dB, ρ = 10 dB

Jakob Hoydis (Sup´ elec) Massive MIMO: How many antennas do we need? 23 / 30

slide-75
SLIDE 75

Downlink: Numerical results

−3 −2 −1 1 2 3 −3 −2 −1 1 2 3

Base stations User terminals cell l UT k djlk 2 cell j

3 4

7 cells, K = 10 UTs distributed on a circle of radius 3/4 path loss exponent β = 3.7, ρτ = 6 dB, ρ = 10 dB Two channel models:

◮ No correlation ◮ ˜

Rjlk = d−β/2

jlk

[A 0N×N−P], where A = [a(φ1) · · · a(φP)] ∈ C

N×P with

a(φp) = 1 √ P

  • 1, e−i2πc sin(φ), . . . , e−i2πc(N−1) sin(φ)T

Jakob Hoydis (Sup´ elec) Massive MIMO: How many antennas do we need? 23 / 30

slide-76
SLIDE 76

Downlink: Numerical results 100 200 300 400 2 4 6 8 10 12

R∞ = 15.75 bits/s/Hz RZF BF

Number of antennas N Average rate per UT (bits/s/Hz)

No Correlation Physical Model Simulations

P = N/2, α = 1/ρ, Fj = 0

Jakob Hoydis (Sup´ elec) Massive MIMO: How many antennas do we need? 24 / 30

slide-77
SLIDE 77

Conclusions (II) - Downlink

For finite N, RZF is largely superior to BF: A matrix inversion can reduce the number of antennas by one order of magnitude!

Jakob Hoydis (Sup´ elec) Massive MIMO: How many antennas do we need? 25 / 30

slide-78
SLIDE 78

Conclusions (II) - Downlink

For finite N, RZF is largely superior to BF: A matrix inversion can reduce the number of antennas by one order of magnitude! Whether or not massive MIMO will show its theoretical gains in practice depends on the validity of our channel models.

Jakob Hoydis (Sup´ elec) Massive MIMO: How many antennas do we need? 25 / 30

slide-79
SLIDE 79

Conclusions (II) - Downlink

For finite N, RZF is largely superior to BF: A matrix inversion can reduce the number of antennas by one order of magnitude! Whether or not massive MIMO will show its theoretical gains in practice depends on the validity of our channel models. Reducing signal processing complexity by adding more antennas seems a bad idea.

Jakob Hoydis (Sup´ elec) Massive MIMO: How many antennas do we need? 25 / 30

slide-80
SLIDE 80

Conclusions (II) - Downlink

For finite N, RZF is largely superior to BF: A matrix inversion can reduce the number of antennas by one order of magnitude! Whether or not massive MIMO will show its theoretical gains in practice depends on the validity of our channel models. Reducing signal processing complexity by adding more antennas seems a bad idea. Many antennas at the BS require TDD (FDD: overhead scales linearly with N)

Jakob Hoydis (Sup´ elec) Massive MIMO: How many antennas do we need? 25 / 30

slide-81
SLIDE 81

Conclusions (II) - Downlink

For finite N, RZF is largely superior to BF: A matrix inversion can reduce the number of antennas by one order of magnitude! Whether or not massive MIMO will show its theoretical gains in practice depends on the validity of our channel models. Reducing signal processing complexity by adding more antennas seems a bad idea. Many antennas at the BS require TDD (FDD: overhead scales linearly with N) Related work: Overview paper: Rusek, et al., “Scaling up MIMO: Opportunities and Challenges with Very Large Arrays”, IEEE Signal Processing Magazine, to appear. http://liu.diva-portal.org/smash/record.jsf?pid=diva2:450781 Constant-envelope precoding: S. Mohammed, E. Larsson, “Single-User Beamforming in Large-Scale MISO Systems with Per-Antenna Constant-Envelope Constraints: The Doughnut Channel”, http://arxiv.org/abs/1111.3752v1 Network MIMO TDD systems: Huh, Caire, et al., “Achieving “Massive MIMO” Spectral Efficiency with a Not-so-Large Number of Antennas”, http://arxiv.org/abs/1107.3862

Jakob Hoydis (Sup´ elec) Massive MIMO: How many antennas do we need? 25 / 30

slide-82
SLIDE 82

Related publications

◮ T. L. Marzetta

Noncooperative cellular wireless with unlimited numbers of base station antennas IEEE Trans. Wireless Commun., vol. 9, no. 11, pp. 3590–3600, Nov. 2010.

◮ H. Q. Ngo, E. G. Larsson, T. L. Marzetta

Analysis of the pilot contamination effect in very large multicell multiuser MIMO systems for physical channel models

  • Proc. IEEE SPAWC’11, Prague, Czech Repulic, May 2011.

◮ H. Q. Ngo, E. G. Larsson, T. L. Marzetta

Uplink power efficiency of multiuser MIMO with very large antenna arrays Allerton Conference, Urbana-Champaing, Illinois, US, Sep. 2011.

◮ J. Hoydis, S. ten Brink, M. Debbah

Massive MIMO: How many antennas do we need? Allerton Conference, Urbana-Champaing, Illinois, US, Sep. 2011, [Online] http://arxiv.org/abs/1107.1709.

◮ J. Hoydis, S. ten Brink, M. Debbah

Comparison of linear precoding schemes for downlink Massive MIMO ICC’12, submitted, 2010.

Jakob Hoydis (Sup´ elec) Massive MIMO: How many antennas do we need? 29 / 30

slide-83
SLIDE 83

A two-tier network architecture

Massive MIMO base stations (BS) overlaid with many small cells (SCs) BSs ensure coverage and serve highly mobile UEs SCs drive the capacity (hot spots, indoor coverage)

Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 3 / 23

slide-84
SLIDE 84

A two-tier network architecture

Massive MIMO base stations (BS) overlaid with many small cells (SCs) BSs ensure coverage and serve highly mobile UEs SCs drive the capacity (hot spots, indoor coverage) Intra- and inter-tier interference is the main performance bottleneck.

Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 3 / 23

slide-85
SLIDE 85

A two-tier network architecture

Massive MIMO base stations (BS) overlaid with many small cells (SCs) BSs ensure coverage and serve highly mobile UEs SCs drive the capacity (hot spots, indoor coverage) Intra- and inter-tier interference is the main performance bottleneck. There are many excess antennas in the network which should be exploited!

Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 3 / 23

slide-86
SLIDE 86

The essential role of TDD

A network-wide synchronized TDD protocol and the resulting channel reciprocity have the following advantages: The downlink channels can be estimated from uplink pilots. → Necessary for massive MIMO Channel reciprocity holds for the desired and the interfering channels. → Knowledge about the interfering channels can be acquired for free. TDD enables the use of excess antennas to reduce intra-/inter-tier interference.

Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 4 / 23

slide-87
SLIDE 87

An idea from cognitive radio

1

The secondary BS listens to the transmission from the primary UE: y = hx + n

2

...and computes the covariance matrix of the received signal: E

  • yyH

= hhH + SNR−1I

Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 5 / 23

slide-88
SLIDE 88

An idea from cognitive radio

3

With the knowledge of the SNR, the secondary BS designs a precoder w which is

  • rthogonal to the sub-space spanned by hhH.

Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 6 / 23

slide-89
SLIDE 89

An idea from cognitive radio

3

With the knowledge of the SNR, the secondary BS designs a precoder w which is

  • rthogonal to the sub-space spanned by hhH.

4

The interference to the primary UE can be entirely eliminated without explicit knowledge of h.

Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 6 / 23

slide-90
SLIDE 90

Translating this idea to HetNets

Every device estimates its received interference covariance matrix and precodes (partially)

  • rthogonally to the dominating interference subspace.

Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 7 / 23

slide-91
SLIDE 91

Translating this idea to HetNets

Every device estimates its received interference covariance matrix and precodes (partially)

  • rthogonally to the dominating interference subspace.

Advantages

Reduces interference towards the directions from which most interference is received. No feedback or data exchange between the devices is needed. Every device relies only on locally available information. The scheme is fully distributed and, thus, scalable.

Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 7 / 23

slide-92
SLIDE 92

About the literature

Cognitive radio

◮ R. Zhang, F. Gao, and Y. C. Liang, “Cognitive Beamforming Made Practical: Effective

Interference Channel and Learning-Throughput Tradeoff,” IEEE Trans. Commun., 2010.

◮ F. Gao, R. Zhang, Y.-C. Liang, X. Wang, “Design of Learning-Based MIMO Cognitive

Radio Systems,” IEEE Trans. Veh. Tech., 2010.

◮ H. Yi, “Nullspace-Based Secondary Joint Transceiver Scheme for Cognitive Radio

MIMO Networks Using Second-Order Statistics,” ICC, 2010.

TDD Cellular systems

◮ S. Lei and S. Roy, “Downlink multicell MIMO-OFDM: an architecture for next

generation wireless networks,” WCNC, 2005.

◮ B. O. Lee, H. W. Je, I. Sohn, O. S. Shin, and K. B. Lee, “Interference-aware

Decentralized Precoding for Multicell MIMO TDD Systems,” Globecom. 2008.

Blind nullspace learning

◮ Y. Noam and A. J. Goldsmith, “Exploiting spatial degrees of freedom in MIMO

cognitive radio systems,” ICC, 2012.

and many more...

Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 8 / 23

slide-93
SLIDE 93

System model and signaling

Each BS has N antennas and serves K single-antenna MUEs. S SCs per BS with F antennas serving 1 single-antenna SUE each The BSs and SCs have perfect CSI for the UEs they want to serve. Every device knows perfectly its interference covariance matrix and the noise power. Linear MMSE detection at all devices

Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 9 / 23

slide-94
SLIDE 94

System model and signaling

Each BS has N antennas and serves K single-antenna MUEs. S SCs per BS with F antennas serving 1 single-antenna SUE each The BSs and SCs have perfect CSI for the UEs they want to serve. Every device knows perfectly its interference covariance matrix and the noise power. Linear MMSE detection at all devices The BSs and SCs use precoding vectors of the structure: w ∼

  • PHHH + κQ + σ2I

−1 h

◮ h channel vector to the targeted UE ◮ H channel matrix to other UEs in the same cell ◮ P, σ2: transmit and noise powers ◮ Q interference covariance matrix ◮ κ: regularization parameter (α for BSs, β for SCs)

About the regularization parameters

For α, β = 0, the BSs and SCs transmit as if they were in an isolated cell, i.e., MMSE precoding (BSs) and maximum-ratio transmissions (SCs). By increasing α, β, the precoding vectors become increasingly orthogonal to the interference subspace.

Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 9 / 23

slide-95
SLIDE 95

Comparison of duplexing schemes and co-channel deployment

time frequency

SC UL SC DL BS DL BS UL

FDD TDD

SC DL BS DL SC UL BS UL

time frequency co-channel TDD

SC DL BS DL SC UL BS UL

time frequency co-channel reverse TDD

SC UL BS DL SC DL BS UL

time frequency

FDD: Channel reciprocity does not hold TDD: Only intra-tier interference can be reduced co-channel (reverse) TDD: Inter and intra-tier interference can be reduced

Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 10 / 23

slide-96
SLIDE 96

TDD versus reverse TDD (RTDD)

Order of UL/DL periods decides which devices interfere with each other. The BS-SC channels change very slowly. Thus, the estimation of the covariance matrix becomes easier for RTDD.

Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 11 / 23

slide-97
SLIDE 97

Numerical results

1000 m 111 m SC SUE MUE BS 40 m

3 × 3 grid of BSs with wrap around S = 81 SCs per cells on a regular grid K = 20 MUEs randomly distributed 1 SUE per SC randomly distributed on a disc around each SC 3GPP channel model with path loss, shadowing and fast fading, N/LOS links TX powers: 46 dBm (BS), 24 dBm (SC), 23 dBm (MUE/SUE) 20 MHz bandwidth @ 2 GHz No user scheduling, power control Averages over channel realizations and UE locations TDD UL/DL cycles of equal length

Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 12 / 23

slide-98
SLIDE 98

Downlink spectral area efficiency regions

20 40 60 80 100 200 300 400 Macro DL area spectral efficiency

  • b/s/Hz/km2

SC DL area spectral efficiency

  • b/s/Hz/km2

FDD (N = 20, F = 1)

Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 13 / 23

slide-99
SLIDE 99

Downlink spectral area efficiency regions

20 40 60 80 100 200 300 400 FDD region

more antennas N = 20 → 100 F = 1 → 4

Macro DL area spectral efficiency

  • b/s/Hz/km2

SC DL area spectral efficiency

  • b/s/Hz/km2

FDD (N = 20, F = 1) FDD/TDD (N = 100, F = 4)

Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 13 / 23

slide-100
SLIDE 100

Downlink spectral area efficiency regions

20 40 60 80 100 200 300 400 FDD region TDD region

less intra-tier interf. α = 0 → 1 more antennas N = 20 → 100 F = 1 → 4 β = 0 → 1

Macro DL area spectral efficiency

  • b/s/Hz/km2

SC DL area spectral efficiency

  • b/s/Hz/km2

FDD (N = 20, F = 1) FDD/TDD (N = 100, F = 4) TDD (N = 100, F = 4, α = 1, β = 1)

Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 13 / 23

slide-101
SLIDE 101

Downlink spectral area efficiency regions

20 40 60 80 100 200 300 400 FDD region TDD region

less intra-tier interf. α = 0 → 1 more antennas N = 20 → 100 F = 1 → 4 β = 0 → 1

Macro DL area spectral efficiency

  • b/s/Hz/km2

SC DL area spectral efficiency

  • b/s/Hz/km2

FDD (N = 20, F = 1) FDD/TDD (N = 100, F = 4) TDD (N = 100, F = 4, α = 1, β = 1)

Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 13 / 23

slide-102
SLIDE 102

Downlink spectral area efficiency regions

20 40 60 80 100 200 300 400 α FDD region TDD region

less intra-tier interf. α = 0 → 1 more antennas N = 20 → 100 F = 1 → 4 β = 0 → 1

Macro DL area spectral efficiency

  • b/s/Hz/km2

SC DL area spectral efficiency

  • b/s/Hz/km2

FDD (N = 20, F = 1) FDD/TDD (N = 100, F = 4) TDD (N = 100, F = 4, α = 1, β = 1)

Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 13 / 23

slide-103
SLIDE 103

Downlink spectral area efficiency regions

20 40 60 80 100 200 300 400 β α FDD region TDD region

less intra-tier interf. α = 0 → 1 more antennas N = 20 → 100 F = 1 → 4 β = 0 → 1

Macro DL area spectral efficiency

  • b/s/Hz/km2

SC DL area spectral efficiency

  • b/s/Hz/km2

FDD (N = 20, F = 1) FDD/TDD (N = 100, F = 4) TDD (N = 100, F = 4, α = 1, β = 1)

Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 13 / 23

slide-104
SLIDE 104

Downlink spectral area efficiency regions

20 40 60 80 100 200 300 400 β α FDD region TDD region CoTDD region

less intra-tier interf. α = 0 → 1 more antennas N = 20 → 100 F = 1 → 4 β = 0 → 1

Macro DL area spectral efficiency

  • b/s/Hz/km2

SC DL area spectral efficiency

  • b/s/Hz/km2

FDD (N = 20, F = 1) FDD/TDD (N = 100, F = 4) TDD (N = 100, F = 4, α = 1, β = 1)

Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 13 / 23

slide-105
SLIDE 105

Downlink spectral area efficiency regions

20 40 60 80 100 200 300 400 β α FDD region TDD region CoTDD region

less intra-tier interf. α = 0 → 1 more antennas N = 20 → 100 F = 1 → 4 β = 0 → 1

Macro DL area spectral efficiency

  • b/s/Hz/km2

SC DL area spectral efficiency

  • b/s/Hz/km2

FDD (N = 20, F = 1) FDD/TDD (N = 100, F = 4) TDD (N = 100, F = 4, α = 1, β = 1)

Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 13 / 23

slide-106
SLIDE 106

Downlink spectral area efficiency regions

20 40 60 80 100 200 300 400 β α α FDD region TDD region CoTDD region

less intra-tier interf. α = 0 → 1 more antennas N = 20 → 100 F = 1 → 4 β = 0 → 1

Macro DL area spectral efficiency

  • b/s/Hz/km2

SC DL area spectral efficiency

  • b/s/Hz/km2

FDD (N = 20, F = 1) FDD/TDD (N = 100, F = 4) TDD (N = 100, F = 4, α = 1, β = 1)

Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 13 / 23

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Downlink spectral area efficiency regions

20 40 60 80 100 200 300 400 β α β α FDD region TDD region CoTDD region

less intra-tier interf. α = 0 → 1 more antennas N = 20 → 100 F = 1 → 4 β = 0 → 1

Macro DL area spectral efficiency

  • b/s/Hz/km2

SC DL area spectral efficiency

  • b/s/Hz/km2

FDD (N = 20, F = 1) FDD/TDD (N = 100, F = 4) TDD (N = 100, F = 4, α = 1, β = 1)

Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 13 / 23

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Downlink spectral area efficiency regions

20 40 60 80 100 200 300 400 β α β α FDD region TDD region CoTDD region

less intra-tier interf. α = 0 → 1 more antennas N = 20 → 100 F = 1 → 4 β = 0 → 1

CoRTDD region Macro DL area spectral efficiency

  • b/s/Hz/km2

SC DL area spectral efficiency

  • b/s/Hz/km2

FDD (N = 20, F = 1) FDD/TDD (N = 100, F = 4) TDD (N = 100, F = 4, α = 1, β = 1)

Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 13 / 23

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SLIDE 109

Downlink SINR distribution

−20 −10 10 20 30 40 0.2 0.4 0.6 0.8 1

SINR (dB) Pr (SINR ≤ x)

MUE SUE α β

TDD Downlink SINR:

MUE SUE α = 0 α = 1 β = 0 β = 1 Mean 13.11 24.13 23.9 33.78 95% 40.38 48.47 40 42.87 50% 11.58 22.01 24.65 34.35 5% −8.48 7.86 6.02 22.62

−20 −10 10 20 30 40 0.2 0.4 0.6 0.8 1

SINR (dB) Pr (SINR ≤ x)

MUE SUE α,β α,β

Co-channel TDD Downlink SINR:

MUE SUE α, β = 0 α, β = 1 α, β = 0 α, β = 1 Mean −6.29 9.52 14.33 25.45 95% 20.45 35.95 29.88 35.01 50% −8.06 6.44 15.49 26.05 5% −26.64 −6.82 −6.51 13.6

Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 14 / 23

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SLIDE 110

Uplink spectral area efficiency regions

20 40 60 80 100 200 300 400 α

more antennas N = 20 → 100 F = 1 → 4

Macro UL sum-rate

  • b/s/Hz/km2

Small cell UL sum-rate

  • b/s/Hz/km2

FDD/TDD (N = 20, F = 1) FDD/TDD (N = 100, F = 4) co-channel TDD co-channel reverse TDD

Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 15 / 23

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Observations

With the proposed precoding scheme, a TDD co-channel deployment of BSs and SCs leads to the highest area spectral efficiency (α = β = 1, 20 MHz BW): DL UL Area throughput 7.63 Gb/s/km2 8.93 Gb/s/km2 Rate per MUE 38.2 Mb/s 25.4 Mb/s Rate per SUE 84.8 Mb/s 104 Mb/s Even a few “excess” antennas at the SCs lead to significant gains. As the scheme is fully distributed and requires no data exchange between the devices, the rates can be simply increased by adding more antennas to the BSs/SCs

  • r increasing the SC-density.

Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 16 / 23

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Discussion

Channel reciprocity requires:

◮ Hardware calibration ◮ Scheduling of UEs on the same resource blocks in subsequent UL/DL cycles

The network-wide TDD protocol requires tight synchronization of all devices:

◮ GPS (outdoor) ◮ NTP/PTP (indoor) ◮ BS reference signals

Channel estimation will suffer from interference and pilot contamination. Covariance matrix estimation becomes difficult for large N. We have considered a worst-case outdoor deployment scenario with fixed cell association, no power control or scheduling. Location-dependent user scheduling and interference-temperature power control could further enhance the performance.

Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 17 / 23

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Massive MIMO for wireless backhaul

small cell w i r e l e s s b a c k h a u l wireless data wired backhaul user equipment massive MIMO base station Core network

The unrestrained SC-deployment “where needed” rather than “where possible” requires a high-capacity and easily accessible backhaul network. Already for most WiFi deployments, the backhaul capacity (10–100 Mbit/s) and not the air interface (54–600 Mbit/s) is the bottleneck. Why not provide wireless backhaul with massive MIMO?3

  • 3T. L. Marzetta and H. Yang, “Dedicated LSAS for metro-cell wireless backhaul - Part I: Downlink,” Bell Laboratories, Alcatel-Lucent,
  • Tech. Rep., Dec. 2012.

Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 18 / 23

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Massive MIMO for wireless backhaul: Advantages

No standardization or backward-compatibility required BS-SC channels change very slowly over time:

◮ Complex transmission/detection schemes (e.g., CoMP) can be easily implemented. ◮ Even FDD might be possible due to reduced CSI overhead.

Provide backhaul where needed:

◮ Adapt backhaul capacity to the load (support highly variable traffic) ◮ Statistical multiplexing opportunity to avoid over-provisioning of backhaul ◮ Enable user-centric small-cell clustering for virtual MIMO

SCs require only a power connection to be operational Line-of-sight not necessary if operated at low frequencies

Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 19 / 23

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Massive MIMO for wireless backhaul: Is it feasible?

How many antennas are needed to satisfy the desired backhaul rates with a given transmit power budget? Assumptions: Every BS knows the channels to all SCs. The BSs can exchange some control information. Full user data sharing between the BSs is not possible. Single-antenna SCs, BSs with N antennas TDD operation on a separate band (2/3 DL, 1/3 UL) Same modeling assumptions as before Find the smallest N such that the power minimization problem with target SINR constraints for the multi-cell multi-antenna wireless system is feasible.4,5

  • 4H. Dahrouj and W. Yu, “Coordinated beamforming for the multicell multi-antenna wireless system,” IEEE Trans. Wireless Commun.,
  • vol. 9, no. 5, pp. 1748–1759, May 2010.
  • 5S. Lakshminarayana, J. Hoydis, M. Debbah, and M. Assaad, “Asymptotic analysis of distributed multi-cell beamforming, in IEEE

International Symposium in Personal Indoor and Mobile Radio Communications (PIMRC), Istanbul, Turkey, Sep. 2010, pp. 2105–2110. Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 20 / 23

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Massive MIMO for wireless backhaul: Numerical results

20 40 60 80 100 100 200 300 400 500

Downlink backhaul rate (Mbit/s) Required # of BS-antennas

S = 81 S = 40 S = 20

10 20 30 40 50

Uplink backhaul rate (Mbit/s) Average minimum number of required BS-antennas N to serve S ∈ {20, 40, 81} randomly chosen SCs with the same target backhaul rate.

Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 21 / 23

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Summary

Massive MIMO and SCs have distinct advantages which complement each other:

◮ Massive MIMO for coverage and mobility support ◮ SCs for capacity and indoor coverage

TDD and the resulting channel reciprocity allow every device to fully exploit its available degrees of freedom for intra-/inter-tier interference mitigation. A TDD co-channel deployment of massive MIMO BSs and SCs can achieve a very attractive rate region. Massive MIMO BSs can provide wireless backhaul to a large number of SCs. The slowly time-varying nature of the BS-SC channels might allow for complex precoding and detection schemes.

For more details:

  • J. Hoydis, K. Hosseini, S. ten Brink, and M. Debbah, “Making Smart Use of Excess Antennas:

Massive MIMO, Small Cells, and TDD,” Bell Labs Technical Journal, vol. 18, no. 2, Sep. 2013.

Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 22 / 23

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Thank you!

Jakob Hoydis (Bell Labs) Massive MIMO, Small Cells, and TDD CTW 2013 23 / 23

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Thank you!

Jakob Hoydis (Sup´ elec) Massive MIMO: How many antennas do we need? 30 / 30