Transcript Massive MIMO Systems with Hardware

Massive MIMO Systems with
Hardware-Constrained
Base Stations
Emil Björnson‡*,
Michail Matthaiou‡§, and Mérouane Debbah‡
‡Alcatel-Lucent
*Dept.
§ECIT,
2014-05-07
Chair on Flexible Radio, Supélec, France
Signal Processing, KTH, and Linköping University, Sweden
Queen’s University Belfast, U.K., and S2, Chalmers, Sweden
Massive MIMO Systems with Hardware-Constrained Base Stations, E. Björnson (Supélec, KTH)
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A Conjecture for Massive MIMO
”Massive MIMO can be built with inexpensive, low-power
components.”
“Massive MIMO reduces the constraints on accuracy and
linearity of each individual amplifier and RF chain.”
[5] “Massive MIMO for next generation wireless systems,”
by E. G. Larsson, O. Edfors, F. Tufvesson and T. L. Marzetta,
in IEEE Communications Magazine, 2014.
Is this true?
There are some indicative results in the literature [9]-[11]
In this paper we provide a more comprehensive answer!
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Introduction
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Introduction: Massive MIMO
• Multi-Cell Multiple-Input Multiple-Output (MIMO)
-
Cellular system with 𝐿 cells
Base stations (BSs) with 𝑁 antennas
𝐾 single-antenna users per cell
Share a flat-fading subcarrier
Beamforming: Spatially directed
transmission/reception
Massive MIMO
Large arrays: e.g., 𝑁 = 200
Very narrow beamforming
Often: 𝑁 ≫ 𝐾 (not necessary!)
Little interference leakage
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What is New with Massive MIMO?
• Many Antenna Elements?
- We already have many antennas!
- LTE-A: 𝑁 = 3 ∙ 4 ∙ 20 = 240
- But only 12-24 antenna ports!
• MIMO with Many Antenna Ports
- Duplicate hardware components
3 sectors, 4 vertical arrays/sector,
20 antennas/array
Image source: gigaom.com
On Each Uplink Receiver Chain
Different Filters
Low-Noise Amplifier (LNA)
Mixer, Local Oscillator (LO)
Analog-to-Digital Converter (ADC)
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Hardware-Constrained Base Stations
• Can We Afford 𝑁 High-Quality Components?
- Does the hardware cost 𝑁 times more?
- Can we get away with cheaper components?
- How does cheaper hardware affect massive MIMO?
Partial
answer
given in
this paper
• Real Hardware is Imperfect (Non-Ideal)
- Less Expensive = More imperfect
Noise
amplification
Modeling of
Imperfections
Essential to understand
the impact of lowquality components!
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Massive MIMO Systems with Hardware-Constrained Base Stations, E. Björnson (Supélec, KTH)
Phase noise
Quantization
noise
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System Model
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Basic Assumptions
• Channel Assumptions
- Channels from cell 𝑙 to cell 𝑗:
- Rayleigh fading:
• Block Fading
- Fixed realizations for 𝑇 channel uses (coherence block)
• Uplink Signals
- From UE 𝑘, cell 𝑙: 𝑥𝑙𝑘 (𝑡) with power
- Used for both pilot and data
- Signals from cell 𝑙:
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Conventional and New Uplink Model
• Received in Cell 𝑗:
Channels from
UEs in cell 𝑙
• New Generalized Model:
Thermal noise
(variance 𝜎 2 )
Signal from
UEs in cell 𝑙
Receiver Noise
Phase Drift
Rotates phases by Wiener process:
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Distortion Noise
Proportional to received signal:
Massive MIMO Systems with Hardware-Constrained Base Stations, E. Björnson (Supélec, KTH)
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Characterization: Hardware Imperfections
• Model has 3 Parameters: 𝛿, κ, ξ
- Ideal hardware: 𝛿 = κ = ξ = 0
• Phase Drifts
- 𝛿 = Variance of innovations
- Source: Phase noise in oscillator
Main Question
How do 𝛿, κ, ξ
affect the
performance in
massive MIMO?
• Distortion Noise
- κ = Error vector magnitude (EVM)
- Ratio between distortion and signal magnitudes
- Source: Quantization noise (with automatic gain control)
• Receiver Noise
- ξ = Noise amplification factor
- Source: Amplification of thermal noise
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Overview of Analytic Contributions
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Channel Estimator and Predictor
• Effective Channel:
- Time-varying: Channel fixed but phase drifts
- Distortion noise correlated with channels
Need new
estimator/
predictor
• Pilot Sequence: User 𝑘 in cell 𝑗:
Theorem 1
Linear minimum mean squared error (LMMSE) estimate of 𝐡𝑗𝑙𝑘 (𝑡):
Error covariance:
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Achievable User Rates
• New Lower Bound on Rate at UE 𝑘 in cell 𝑗:
- Time-varying receive combining: 𝐯𝑗𝑘 (𝑡)
- Signal-to-interference-and-noise ratio (SINR):
Signal Power
Inter-User Interference
Distortion Noise
Receiver Noise
Theorem 2
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Closed form expressions for all expectations for
(maximum ratio combining (MRC))
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Asymptotic Limit and Scaling Law
• What Happens to User Rates as 𝑁 → ∞?
- Distortion noise and receiver noise vanish!
- Phase drifts remain: Reduce signal and interference power
Corollary 1 (Rates with MRC)
Inner product of pilot sequences
Corollary 2 (Scaling Law on Hardware Imperfections)
Substitute
If exponents τ1 , τ2 , τ3 are selected as
then the SINRs stay non-zero as 𝑁 → ∞
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Interpretation of Scaling Law
• Hardware can be Gradually Degraded as 𝑁 → ∞
- May use hardware components of lower quality!
- Increase Distortion/Receiver Noise Variances (κ2 , ξ) as 𝑁
- Example: 0.25 ∙ log 2 (𝑁) fewer quantization bits (in ADC)
5 log10 (𝑁) higher noise figure (in LNA)
Additive
distortions
- Increase Phase Drift Variance as
Multiplicative
distortions
1
log 𝑒 (𝑁)
𝛿0 (𝑇−𝐵)
- Example: Increase phase noise variance 𝛿 or handle larger 𝑇
Corollary 2 (Scaling Law on Hardware Imperfections)
Substitute
If exponents τ1 , τ2 , τ3 are selected as
then the SINRs stay non-zero as 𝑁 → ∞
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Numerical Example
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Simulation Scenario
• Main Characteristics
- 𝐾 = 8, uniform UE distribution in 8 virtual sectors (> 35 m)
- Typical 3GPP pathloss model
Assumptions
Pilot sequences:
𝐵=8
Coherence block:
𝑇 = 500
Number of antennas:
0 ≤ 𝑁 ≤ 500
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Area Sum Rates
• Three Cases
- Ideal Hardware
- Fixed imperfect hardware:
- Variable Imperfect hardware: As in Corollary 2
Observations
Manageable impact if
scaling law is fulfilled
Otherwise: Drastic reduction
MMSE Receiver
Higher performance
Suffers more from
imperfections
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Conclusions
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Conclusions
• Massive MIMO with Hardware Imperfections at BSs
• Result: Massive MIMO is Resilient to Such Imperfections
- Distortion noise and amplified receiver noise vanish as 𝑁 → ∞
- Phase drifts remains but do not get worse
• Scaling Law for Hardware Imperfections
- Distortion/receiver noise variance can increase as
- Phase drift variance increase as log 𝑁
𝑁
Important Conclusions for Massive MIMO
Conjecture from [5] is true!
Can be deployed with inexpensive and imperfect hardware!
Hardware cost increases slower than linear!
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Thank You for Listening!
Questions?
Also check out:
E. Björnson, M. Matthaiou, M. Debbah,
“Circuit-Aware Design of Energy-Efficient Massive MIMO Systems,”
Proceedings of ISCCSP, Athens, Greece, May 2014.
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