MSEE Defense

Enhancements to the Generalized Sidelobe Canceller
for Audio Beamforming in an Immersive Environment
Phil Townsend
MSEE Candidate
University of Kentucky

www.vis.uky.edu | Dedicated to Research, Education and Industrial Outreach | 859.257.1257

Overview
1) Introduction
- Adaptive Beamforming and the GSC
2) Amplitude Scaling Improvements
- 1/r Model, Acoustic Physics, Statistical
3) Automatic Target Alignment
- Thresholded Cross Correlation using PHAT-β
4) Array Geometry Analysis
- Volumetric Beamfield Plots
- Monte Carlo Test of Geometric Parameters
5) Final Conclusions and Questions


Part 1: Introduction
• What's beamforming?
• A spatial filter that enhances sound
based on its spatial position through the
coherent processing of signals from
distributed microphones.
– Reduce room noise/effects
– Suppress interfering speakers


Adaptive Beamforming
• Optimization of Generalized Filter
Coefficients
T
y[ n]=W [ n] X [n ] opt
– Often requires minimizing output energy
while keeping target component unchanged
• Estimate statistics on the fly
– Input Correlation Matrix unknown/changing
• Gradient Descent Toward Optimal Taps
– Constrained Lowest Energy Output Forms
Unique Minimum to Bowl-Shaped Surface

Visualization of Gradient Descent

From http://en.wikipedia.org/wiki/Gradient_descent; Image in Public Domain

Generalized Sidelobe Canceller
(GSC)
• Simplifies Frost's constrained adaptation
into two stages
– A fixed, Delay-Sum Beamformer
– A Blocking Matrix that's adaptively filtered
and subtracted.
– Adaptation can be any algorithm; we use
NLMS here
– Simplification comes mostly from enforcing
distortionless response

GSC (con't)
• Upper branch DSB result

• Lower branch BM tracks are

where traditional Blocking Matrix is


GSC (con't)
• Final output is

• Adaption algorithm for each BM track is
(NLMS, much faster than constrained)


Limitations of Current Models and
Methods
• Blocking Matrix Leakage
– Farfield assumption not valid for immsersive
microphone arrays
– Target steering might be incorrect
• Most research limited to equispaced linear arrays
– Hard to construct
– Limited useful frequency range
– Want to explore other geometries and find the best


Part 2: Amplitude Correction
• Nearfield acoustics means target
component has different amplitude in
each microphone
• Propose and test a few models to correct
cancellation
– 1/r Model
– Sound propagation filtering
– Statistical filtering


Simple 1/r Model
• The acoustic wave equation is solved by
a function inversely proportional in r

• so make a BM using that fact (keep
tracks in distance order)


ISO Acoustic Physics Model
• Fluid dynamics can be taken into
account to design a filter based on
distance, temperature, humidity, and
pressure (ISO standard 9613)

• Might allow us to add easily-obtainable
information to enhance beamforming


Statistical Amplitude Scaling
• Lump all corruptive effects together and
minimize energy of difference of tracks

• Carry out as a function of frequency to
get


ISO and Statistical BM's
• ISO Model (Frequency Domain)

• Statistical Scaling (Frequency Domain)


A Perfect Blocking Matrix
• Audio Cage data was collected with
targets and speakers separate, so a
perfect BM can be simulated
• Shows upper bound on possible
improvement


Experimental Evaluation of
Methods
• Set initial intelligibility to around .3
• Beamform for many target and noise
scenarios
• Find mean correlation coefficient of BM
tracks (want as low as possible) and
overall output (want as large as possible)


Results
• Most real methods make little difference
– Statistical scaling a little worse b/c of bad
SNR
– ISO filtering a little better b/c of more info
– 1/r model made no difference
• Perfect BM made slight improvement,
but array geometry was most important!
• Listen to some examples...


Output Correlation Chart


BM Correlation Chart


Part 3: Automatic Steering
• If steering delays aren't right then target
signal leakage occurs and DSB is
weaker.
• Cross correlation is a highly robust
technique for finding similarities between
signals, so use to fine tune delays
• Apply window and correlation strength
thresholds to try to improve performance
in poor SNR environment

GCC and PHAT-β
• Find the cross correlation between tracks

over only a small window of possible movements

and whiten to make the spike stand out


Correlation Coefficient Threshold
• Since environment is noisy and speaker
might go silent, update only if max
correlation is sufficiently strong


Experimental Evaluation
• Same setup as before
– Initial intel ~.3
– Find output correlation with closest mic
• Vary correlation threshold .1 to .9


Results
• Tighter threshold better but updates never help
vs original GSC
– Low threshold: erratic focal point movement
– High threshold: can't recover from bad
updates
– Low SNR makes good estimates very
difficult
• Retrace of lags (multilateration) shows search
window D should be tighter
• Array geometry still more important
• Listen to some more examples...

Output Correlation Chart
Normal GSC Performance for Comparison


Part 4: Array Geometry
• Since array geometry is the most
important factor, we need to find what
the best layouts are and why
• Start by generating beamfields to
visualize array performance and look for
patterns qualitatively
• Then propose parameters and run
computer simulations quantitatively


Volumetric Beamfield Plots
• GSC beamfield changes over time, but
DSB is root of the system and
performance is constant.
• Need to see performance in three
dimensions
• Use layered approach with colors to
indicate intensity and transparency to
see features inside the space


Linear Array
• Generally good performance
– Office too small for sidelobes to appear
• Mainlobe elongated toward array


Perimeter Array
• Also generally good
– Very tight mainlobe
• No height resolution
– Not a problem in an office though
– Motivation for ceiling arrays


Random Arrays
• Performance highly variable
– One best of the lot, one very bad
• Need to find ways to describe and select
best random arrays (coming soon)


A Monte Carlo Experiment for
Analysis of Geometry
• Propose the following parameters for
describing array geometry in 2D and
evaluate array performance for many
randomly-chosen geometries:
– Centroid
• Array center of gravity (mean position)
– Dispersion
• Mic spread (standard deviation of positions)


Parameter Examples


Monte Carlo (con't)
• For a given centroid and dispersion,
evaluate the array based on:
– PSR – Peak to Side lobe Ratio
• Worst-case interference
– MLW – Main Lobe Width
• Tightness of enhancement area
• Redefined in 2D to use x and y 3dB widths

2 2
w3dB=  x  y 3dB 3dB


Monte Carlo Simulation
• Test variation of one parameter while
holding the other constant.
• Generate random positions from an
8x8m square and target a sound source
1m below center
• Choose 120 random geometries for each
run (a “class” of arrays)
• Compare to rectangular array


Layout


Centroid Displacement


Dispersion


Results
• Centroid centered over target always best
– Irregular arrays more robust when centroid
shifts
• Dispersion a classic tradeoff
– Tightly-packed array: tight mainlobe but strong
sidelobes
– Widely-spread array: wide mainlobe but weak
sidelobes


Part 5. Final Conclusions & Future Work
• Statistical methods for improving GSC ineffective
– Low SNR introduces large error
• Introducing separate, concrete info helped
– ISO model gave a tiny improvement
– More accurate target position (laser, SSL) always best
for steering
• Array geometry is most important to improving performance
– Linear array good, but random arrays have potential to
do better
– Found that a ceiling array should be centered over its
intended target, but...
– Open question: how does one describe the best array
for beamforming on human speech?

Special Thanks
• Advisor
– Dr. Kevin Donohue
• Thesis Committee Members
– Dr. Jens Hannemann
– Dr. Samson Cheung
• Everyone at the UK Vis Center


Questions?


Extra Slides


Frost Algorithm
• Solution to the constrained optimization

subject to the constraint (C a selection
matrix)

The constraint vector dictates the sum of
column weights, often F = [1 0 0 0...]
• Solution (P and F constant matrices):


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