Modeling and Mitigation of Interference in Multi-Antenna Receivers

Aditya Chopra

September 16, 2011

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about me Member of the Wireless Networking and Communications Group at The University of Texas at Austin since 2006.

Completed projects

Currently active projects

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ADSL testbed (Oil & Gas) 2 x 2 wired multicarrier communications testbed using PXI hardware, x86 processor, real-time operating system and LabVIEW

Spur modeling/mitigation (NI) Detect and classify spurious signals; fixed and floating-point algorithms to mitigate spurs

Interference modeling and mitigation (Intel)

Statistical models of interference; receiver algorithms to mitigate interference; MATLAB toolbox

Impulsive noise mitigation in OFDM (NI)

Non-parametric interference mitigiation for wireless OFDM receivers using PXI hardware, FPGAs, and LabVIEW

Powerline communications (TI, Freescale, SRC)

Modeling and mitigating impulsive noise; building multichannel multicarrier communications testbed using PXI hardware, x86 processor, real-time operating system, LabVIEW

Interference in wireless communication systems is caused by communicating and non-communicating

source emissions

Computational Platform Clocks, amplifiers, co-located transceivers

Wireless systems Nearby wireless users Coexisting protocols

Non-communicating devices Microwave ovens

Powerlines

Introduction | Modeling (CoLo) | Modeling (Dist) | Outage Performance | Receiver Design 3

Interference may severely impair communication performance of wireless systems

802.11g Channel 7 802.11g Channel 1

J. Shi, A. Bettner, G. Chinn, K. Slattery, and X. Dong, “A study of platform EMI from LCD panels - impact on wireless, root causes and mitigation methods,” Proc. IEEE Int. Symp. on EM Compatibility , Aug. 2006.

Introduction | Modeling (CoLo) | Modeling (Dist) | Outage Performance | Receiver Design 4

Interference mitigation has been an active area of research over the past decade

INTERFERENCE MITIGATION STRATEGY

LIMITATIONS

Hardware design

- Receiver shielding Does not mitigate interference from

devices using same spectrum

Network planning

- Resource allocation - Basestation coordination - Partial frequency re-use

Requires user coordination Slow updates

Receiver algorithms

- Interference cancellation - Interference alignment - Statistical interference mitigation

Require user coordination and channel state information

Statistical methods require accurate interference models

Introduction | Modeling (CoLo) | Modeling (Dist) | Outage Performance | Receiver Design 5

I employ a statistical approach to the interference modeling and mitigation problem

Proposed solution

1. Develop a statistical-physical model of interference generation

2. Model statistics of interference in multi-antenna receivers

3. Analyze performance of conventional multi-antenna receivers

4. Develop multi-antenna receiver algorithms using statistical models of interference

Introduction | Modeling (CoLo) | Modeling (Dist) | Outage Performance | Receiver Design 6

A statistical-physical model of interference generation and propagation is proposed

Key Features

– Co-located receiver antennae ( )

– Interferers are common to all antennae ( ) or exclusive to nth antenna ( )

– Interferers are stochastically distributed in space as a 2D Poisson point process with intensity 𝜆0 ( ), or 𝜆𝑛 ( )

– Interferer free guard-zone ( ) of radius 𝛿↑

– Power law propagation and fast fading

Introduction | Modeling (CoLo) | Modeling (Dist) | Outage Performance | Receiver Design 7

𝛿↓

𝑛 1

1

1

1

2

2

2

3 3

3

System model with a 3-antenna receiver in a Poisson field of interferers

𝑛

I derive joint statistics of interference observed by multi-antenna receivers

1. Wireless networks with guard zones

2. Wireless networks without guard zones

Introduction | Modeling (CoLo) | Modeling (Dist) | Outage Performance | Receiver Design 8

Using the system model, I express the sum interference at the nth antenna

𝑌𝑛 = 𝐴𝑖0𝑒𝑗𝜙𝑖0𝐻𝑖0,𝑛𝑒𝑗𝜃𝑖0,𝑛 𝑟𝑖0

−𝛾2

𝑖0∈ 𝒮0

+ 𝐴𝑖𝑛𝑒𝑗𝜙𝑖𝑛𝐻𝑖𝑛 𝑒𝑗𝜃𝑖𝑛,𝑛 𝑟𝑖𝑛

−𝛾2

𝑖𝑛∈ 𝒮𝑛

Next, I derive the statistics of 𝐘 for different network models

COMMON INTERFERERS

INTERFERER EMISSION

FADING CHANNEL

PATHLOSS

EXCLUSIVE INTERFERERS

Introduction | Modeling (CoLo) | Modeling (Dist) | Outage Performance | Receiver Design 9

I derive interference statistics in networks with guard zones as a mix of isotropic and i.i.d. Class A noise

Joint characteristic function

Φ 𝑤 = 𝑒𝐴0𝑒−

𝑤2Ω0

2

× 𝑒𝐴𝑛𝑒−

𝑤2Ω𝑛

2 𝑁

𝑛=1

𝐴𝑛 ∝ 𝜆𝑛𝛿↓2 , Ω𝑛 ∝ 𝐴𝑛𝛿↓

−𝛾

Amplitude distribution of interference

– From common interferers: Isotropic Middleton Class A

– From exclusive interferers: Independent Middleton Class A

Introduction | Modeling (CoLo) | Modeling (Dist) | Outage Performance | Receiver Design 10

Interference statistics in networks without guard zones are a mix of isotropic and i.i.d. alpha stable noise

Joint characteristic function

Φ 𝑤 = 𝑒𝜎0 𝐰 𝛼× 𝑒𝜎𝑛|𝜔𝑛|𝛼

𝑁

𝑛=1

𝛼 =4

𝛾, 𝜎𝑛 ∝ 𝜆𝑛

Amplitude distribution of interference

– From common interferers: Isotropic symmetric alpha stable

– From exclusive interferers: Independent symmetric alpha stable

Introduction | Modeling (CoLo) | Modeling (Dist) | Outage Performance | Receiver Design 11

Simulation results indicate a close match between proposed statistical models and simulated interference

Tail probability of simulated interference in networks with guard zones

Tail probability of simulated interference in networks without guard zones

PARAMETER VALUES

𝛾 4 𝜆0 = 10−3, 𝜆𝑛 = 0

𝛿↓ 1.2 (w/ GZ), 0 (w/out GZ) 𝜆0 = 9.5 × 10−4, 𝜆𝑛 = 5 × 10−5

Introduction | Modeling (CoLo) | Modeling (Dist) | Outage Performance | Receiver Design 12

My framework for multi-antenna interference across co-located antennae results in joint statistics that are

1. Spatially isotropic (common interferers)

2. Spatially independent (exclusive interferers)

3. In a continuum between isotropic and independent (mixture)

for two impulsive distributions

1. Middleton Class A (networks with guard zones)

2. Symmetric alpha stable (networks without guard zones)

Introduction | Modeling (CoLo) | Modeling (Dist) | Outage Performance | Receiver Design 13

In networks without guard zones, I incorporate antenna separation into the system model

Applications

– Cooperative MIMO

– Distributed antenna systems

– Two-hop communication

– Temporal modeling of interference in mobile receivers

Introduction | Modeling (CoLo) | Modeling (Dist) | Outage Performance | Receiver Design

Decentralized network (𝛿↓ = 0) with 2 receive antennae ( ) in a Poisson field of interferers ( )

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𝑑

Interference statistics are derived via the joint characteristic function (Φ) for three scenarios

Co-located antennae (𝑑 = 0) : Φ 𝜔1, 𝜔2 = 𝑒𝜎 𝜔12+𝜔2

2𝛼2

Infinitely distant antennae (𝑑 → ∞) : Φ 𝜔1, 𝜔2 = 𝑒𝜎 𝜔1𝛼+𝜔2

𝛼

Distributed antennae (0 < 𝑑 < ∞ ) :

Φ 𝜔1, 𝜔2 ≈ 𝑒𝜈 𝑑 𝜎 𝜔12+𝜔2

2𝛼2+ 1−𝜈 𝑑 𝜎 𝜔1

𝛼+𝜔2𝛼

I use curve fitting to approximate 𝑣 𝑑 ≈ 𝑒−𝑎𝑑𝛼

Introduction | Modeling (CoLo) | Modeling (Dist) | Outage Performance | Receiver Design 15

I use the proposed framework to evaluate outage performance of conventional multi-antenna receivers

1. Pre-detection diversity combiners

2. Post-detection diversity combiners

Introduction | Modeling (CoLo) | Modeling (Dist) |Outage Performance | Receiver Design 16

Multi-antenna receivers combine antenna outputs either before, or after the decoding block

Pre-detection Combining Post-detection combining

Introduction | Modeling (CoLo) | Modeling (Dist) |Outage Performance | Receiver Design

+

X

𝑤1

X

𝑤𝑁

𝐲 = 𝐡𝑥 + 𝐧 𝐰𝐲

SELE

CT

BES

T

Equal Gain Combiner 𝐰 = 𝟏𝑁

Selection Combiner 𝑤𝑛 = ℐ𝒉𝒏=max{𝐡}

Maximum Ratio Combiner 𝐰 = 𝐡∗

⋮ ⋮

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I derive theoretical outage probability expressions for pre- and post-detection diversity combiners

RECEIVER

ALGORITHM

OUTAGE PROBABILITY ℙ 𝑆𝐼𝑅 < 𝜃

Equal Gain Combining

𝐶0𝜃𝛼2 𝜆0 + 𝜆𝑒𝑁

1−𝛼2

Maximum Ratio Combining

C0𝜃𝛼

2𝔼 h 𝛼

𝛼

h 2𝛼 +

1

h 22𝛼

Selection Combining 𝐶0𝜃

𝛼2 −1 𝑛+1

𝑁

𝑛=1

𝐶𝑛𝑁

𝑛!

Post Detection Combining 𝐶0 −1 𝑚+1 𝐶𝑚

𝑚 + 1 + 2/𝛾!

𝑚 − 1! sin2𝜋𝛾

𝑛

𝑁

𝑚=1

𝜃𝛼2 + 𝐶0

𝜋2

𝛾 sin2𝜋𝛾

𝑁 𝜃𝑁𝛼2

Introduction | Modeling (CoLo) | Modeling (Dist) |Outage Performance | Receiver Design 18

Expr match simulated outage Sim

Next, I design robust receivers using interference statistics

Introduction | Modeling (CoLo) | Modeling (Dist) |Outage Performance | Receiver Design 19

Only common interferers 5% exclusive interferers Only exclusive interferers

Using my knowledge of interference statistics, I design algorithms which outperform conventional receivers

1. Improved pre-detection diversity combiners

2. Improved antenna selection in cooperative reception

Introduction | Modeling (CoLo) | Modeling (Dist) | Outage Performance | Receiver Design 20

I propose two diversity combining algorithms that are robust to impulsive interference

‘Deviation’ in an antenna output 𝑦𝑛 is defined as

Δ𝑛 = 𝑦𝑛 − median{ 𝐲 }

Proposed diversity combiners

1. Hard-limiting combiner

𝑤𝑛 = 𝟏Δ𝑛<𝑇ℎ𝑛∗

2. Soft-limiting combiner

𝑤𝑛 = 𝑒−𝐴Δ𝑛ℎ𝑛∗

Introduction | Modeling (CoLo) | Modeling (Dist) | Outage Performance | Receiver Design 21

0 1 2 3 4

0

1

Ante

nna

Weig

ht

(w)

Deviation (

Hard Limiting (T=1)

Soft Limiting (A=1)

My proposed diversity combiners exhibit better outage performance compared to conventional combiners

Introduction | Modeling (CoLo) | Modeling (Dist) | Outage Performance | Receiver Design 22

PARAMETER VALUES

Pathloss coeff. (𝛾) 4

Guard- zone radius (𝛿↓) 0

Common interferer density(𝜆0) 0.0095

Excl. intfr. density(𝜆𝑛) 0.0005

HL combiner parameter (𝑇) 1

SL combiner parameter (𝐴) 2

In conclusion, the contributions of my dissertation are

1. A framework for modeling multi-antenna interference

– Interference statistics are mix of isotropic and independent

2. Statistical modeling of multi-antenna interference – Co-located antennae in networks without guard zones

– Two geographically separate antennae in networks with guard zones

3. Outage performance analysis of conventional receivers in networks without guard zones

4. Design of receiver algorithms with improved performance in impulsive interference

23

thank you

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Interference statistics are derived via the joint characteristic function (Φ) for three scenarios of antenna separation

log {Φ 𝜔1, 𝜔2 }

= 𝜆 1 − 1

1 + 𝑎 𝜔12 𝒓

−𝜸+ 𝑎 𝜔2

2 𝒓 − 𝒅−𝜸 𝑑𝒓

ℛ2

• 𝑑 = 0: Φ 𝜔1, 𝜔2 = 𝑒𝜎 𝜔12+𝜔2

2𝛼2

• 𝑑 → ∞: Φ 𝜔1, 𝜔2 = 𝑒𝜎 𝜔1𝛼+𝜔2

𝛼

• 0 < 𝑑 < ∞ :

Φ 𝜔1, 𝜔2 = 𝑒𝜈 𝑑 𝜎 𝜔12+𝜔2

2𝛼2+ 1−𝜈 𝑑 𝜎 𝜔1

𝛼+𝜔2𝛼

Introduction | Modeling (CoLo) | Modeling (Dist) | Outage Performance | Receiver Design 25

Intuitively, interference statistics lie in a continuum between isotropic and independent

𝑑 = 0

𝑑 = ∞

0 < 𝑑 < ∞

26

A framework of common/exclusive interferers unifies interference models in co-located/distributed antennae

Next, I use this framework to analyze communication performance of multi-

antenna receivers

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Common Interferers Exclusive Interferers