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Enhancements to the Generalized Sidelobe Canceller for Audio Beamforming in an Immersive Environment

Phil Townsend

MSEE Candidate

University of Kentucky

Overview1) 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

– 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

y [ n]=W optT [ n] X [n ]

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 ChartNormal 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

w3dB= x3dB2 y3dB2

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):

msee defense

industrial outreach

statistical amplitude

difference perfect bm

r model sound propagation

audio beamforming

traditional blocking

blocking matrix thats

lower branch bm tracks

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