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Acoustic Echo Cancellation (AEC)

This example shows how to apply adaptive filters to acoustic echo cancellation (AEC).

Author(s): Scott C. Douglas

Introduction

Acoustic echo cancellation is important for audio teleconferencing when simultaneous communication (or full-duplex transmission) of speech is necessary. In acoustic echo cancellation, a measured microphone signal $d(n)$ contains two signals:

  • The near-end speech signal $v(n)$

  • The far-end echoed speech signal $\widehat{d}(n)$

The goal is to remove the far-end echoed speech signal from the microphone signal so that only the near-end speech signal is transmitted. This example has some sound clips, so you might want to adjust your computer's volume now.

The Room Impulse Response

You first need to model the acoustics of the loudspeaker-to-microphone signal path where the speakerphone is located. Use a long finite impulse response filter to describe the characteristics of the room. The following code generates a random impulse response that is not unlike what a conference room would exhibit. Assume a system sample rate of 16000 Hz.

fs = 16000;
M = fs/2 + 1;
frameSize = 2048;

[B,A] = cheby2(4,20,[0.1 0.7]);
impulseResponseGenerator = dsp.IIRFilter('Numerator', [zeros(1,6) B], ...
    'Denominator', A);

FVT = fvtool(impulseResponseGenerator);  % Analyze the filter
FVT.Color = [1 1 1];

roomImpulseResponse = impulseResponseGenerator( ...
        (log(0.99*rand(1,M)+0.01).*sign(randn(1,M)).*exp(-0.002*(1:M)))');
roomImpulseResponse = roomImpulseResponse/norm(roomImpulseResponse)*4;
room = dsp.FIRFilter('Numerator', roomImpulseResponse');

fig = figure;
plot(0:1/fs:0.5, roomImpulseResponse);
xlabel('Time (s)');
ylabel('Amplitude');
title('Room Impulse Response');
fig.Color = [1 1 1];

The Near-End Speech Signal

The teleconferencing system's user is typically located near the system's microphone. Here is what a male speech sounds like at the microphone.

load nearspeech

player          = audioDeviceWriter('SupportVariableSizeInput', true, ...
                                    'BufferSize', 512, 'SampleRate', fs);
nearSpeechSrc   = dsp.SignalSource('Signal',v,'SamplesPerFrame',frameSize);
nearSpeechScope = dsp.TimeScope('SampleRate', fs, ...
                    'TimeSpan', 35, 'TimeSpanOverrunAction', 'Scroll', ...
                    'YLimits', [-1.5 1.5], ...
                    'BufferLength', length(v), ...
                    'Title', 'Near-End Speech Signal', ...
                    'ShowGrid', true);

% Stream processing loop
while(~isDone(nearSpeechSrc))
    % Extract the speech samples from the input signal
    nearSpeech = nearSpeechSrc();
    % Send the speech samples to the output audio device
    player(nearSpeech);
    % Plot the signal
    nearSpeechScope(nearSpeech);
end

The Far-End Speech Signal

In a teleconferencing system, a voice travels out the loudspeaker, bounces around in the room, and then is picked up by the system's microphone. Listen to what the speech sounds like if it is picked up at the microphone without the near-end speech present.

load farspeech
farSpeechSrc    = dsp.SignalSource('Signal',x,'SamplesPerFrame',frameSize);
farSpeechSink   = dsp.SignalSink;
farSpeechScope  = dsp.TimeScope('SampleRate', fs, ...
                    'TimeSpan', 35, 'TimeSpanOverrunAction', 'Scroll', ...
                    'YLimits', [-0.5 0.5], ...
                    'BufferLength', length(x), ...
                    'Title', 'Far-End Speech Signal', ...
                    'ShowGrid', true);

% Stream processing loop
while(~isDone(farSpeechSrc))
    % Extract the speech samples from the input signal
    farSpeech = farSpeechSrc();
    % Add the room effect to the far-end speech signal
    farSpeechEcho = room(farSpeech);
    % Send the speech samples to the output audio device
    player(farSpeechEcho);
    % Plot the signal
    farSpeechScope(farSpeech);
    % Log the signal for further processing
    farSpeechSink(farSpeechEcho);
end

The Microphone Signal

The signal at the microphone contains both the near-end speech and the far-end speech that has been echoed throughout the room. The goal of the acoustic echo canceler is to cancel out the far-end speech, such that only the near-end speech is transmitted back to the far-end listener.

reset(nearSpeechSrc);
farSpeechEchoSrc = dsp.SignalSource('Signal', farSpeechSink.Buffer, ...
                    'SamplesPerFrame', frameSize);
micSink         = dsp.SignalSink;
micScope        = dsp.TimeScope('SampleRate', fs,...
                    'TimeSpan', 35, 'TimeSpanOverrunAction', 'Scroll',...
                    'YLimits', [-1 1], ...
                    'BufferLength', length(x), ...
                    'Title', 'Microphone Signal', ...
                    'ShowGrid', true);

% Stream processing loop
while(~isDone(farSpeechEchoSrc))
    % Microphone signal = echoed far-end + near-end + noise
    micSignal = farSpeechEchoSrc() + nearSpeechSrc() + ...
                0.001*randn(frameSize,1);
    % Send the speech samples to the output audio device
    player(micSignal);
    % Plot the signal
    micScope(micSignal);
    % Log the signal
    micSink(micSignal);
end

The Frequency-Domain Adaptive Filter (FDAF)

The algorithm in this example is the Frequency-Domain Adaptive Filter (FDAF). This algorithm is very useful when the impulse response of the system to be identified is long. The FDAF uses a fast convolution technique to compute the output signal and filter updates. This computation executes quickly in MATLAB®. It also has fast convergence performance through frequency-bin step size normalization. Pick some initial parameters for the filter and see how well the far-end speech is cancelled in the error signal.

% Construct the Frequency-Domain Adaptive Filter
echoCanceller    = dsp.FrequencyDomainAdaptiveFilter('Length', 2048, ...
                    'StepSize', 0.025, ...
                    'InitialPower', 0.01, ...
                    'AveragingFactor', 0.98, ...
                    'Method', 'Unconstrained FDAF');

AECScope1   = dsp.TimeScope(4, fs, ...
                'LayoutDimensions', [4,1], ...
                'TimeSpan', 35, 'TimeSpanOverrunAction', 'Scroll', ...
                'BufferLength', length(x));

AECScope1.ActiveDisplay = 1;
AECScope1.ShowGrid      = true;
AECScope1.YLimits       = [-1.5 1.5];
AECScope1.Title         = 'Near-End Speech Signal';

AECScope1.ActiveDisplay = 2;
AECScope1.ShowGrid      = true;
AECScope1.YLimits       = [-1.5 1.5];
AECScope1.Title         = 'Microphone Signal';

AECScope1.ActiveDisplay = 3;
AECScope1.ShowGrid      = true;
AECScope1.YLimits       = [-1.5 1.5];
AECScope1.Title         = 'Output of Acoustic Echo Canceller mu=0.025';

AECScope1.ActiveDisplay = 4;
AECScope1.ShowGrid      = true;
AECScope1.YLimits       = [0 50];
AECScope1.YLabel        = 'ERLE (dB)';
AECScope1.Title         = 'Echo Return Loss Enhancement mu=0.025';

% Near-end speech signal
release(nearSpeechSrc);
nearSpeechSrc.SamplesPerFrame = frameSize;

% Far-end speech signal
release(farSpeechSrc);
farSpeechSrc.SamplesPerFrame = frameSize;

% Far-end speech signal echoed by the room
release(farSpeechEchoSrc);
farSpeechEchoSrc.SamplesPerFrame = frameSize;

Echo Return Loss Enhancement (ERLE)

Since you have access to both the near-end and far-end speech signals, you can compute the echo return loss enhancement (ERLE), which is a smoothed measure of the amount (in dB) that the echo has been attenuated. From the plot, observe that you achieved about a 35 dB ERLE at the end of the convergence period.

diffAverager = dsp.FIRFilter('Numerator', ones(1,1024));
farEchoAverager = clone(diffAverager);
setfilter(FVT,diffAverager);

micSrc = dsp.SignalSource('Signal', micSink.Buffer, ...
    'SamplesPerFrame', frameSize);

% Stream processing loop - adaptive filter step size = 0.025
while(~isDone(nearSpeechSrc))
    nearSpeech = nearSpeechSrc();
    farSpeech = farSpeechSrc();
    farSpeechEcho = farSpeechEchoSrc();
    micSignal = micSrc();
    % Apply FDAF
    [y,e] = echoCanceller(farSpeech, micSignal);
    % Send the speech samples to the output audio device
    player(e);
    % Compute ERLE
    erle = diffAverager((e-nearSpeech).^2)./ farEchoAverager(farSpeechEcho.^2);
    erledB = -10*log10(erle);
    % Plot near-end, far-end, microphone, AEC output and ERLE
    AECScope1(nearSpeech, micSignal, e, erledB);
end

Effects of Different Step Size Values

To get faster convergence, you can try using a larger step size value. However, this increase causes another effect: the adaptive filter is "mis-adjusted" while the near-end speaker is talking. Listen to what happens when you choose a step size that is 60% larger than before.

% Change the step size value in FDAF
reset(echoCanceller);
echoCanceller.StepSize = 0.04;

AECScope2 = clone(AECScope1);
AECScope2.ActiveDisplay = 3;
AECScope2.Title = 'Output of Acoustic Echo Canceller mu=0.04';
AECScope2.ActiveDisplay = 4;
AECScope2.Title = 'Echo Return Loss Enhancement mu=0.04';

reset(nearSpeechSrc);
reset(farSpeechSrc);
reset(farSpeechEchoSrc);
reset(micSrc);
reset(diffAverager);
reset(farEchoAverager);

% Stream processing loop - adaptive filter step size = 0.04
while(~isDone(nearSpeechSrc))
    nearSpeech = nearSpeechSrc();
    farSpeech = farSpeechSrc();
    farSpeechEcho = farSpeechEchoSrc();
    micSignal = micSrc();
    % Apply FDAF
    [y,e] = echoCanceller(farSpeech, micSignal);
    % Send the speech samples to the output audio device
    player(e);
    % Compute ERLE
    erle = diffAverager((e-nearSpeech).^2)./ farEchoAverager(farSpeechEcho.^2);
    erledB = -10*log10(erle);
    % Plot near-end, far-end, microphone, AEC output and ERLE
    AECScope2(nearSpeech, micSignal, e, erledB);
end

Echo Return Loss Enhancement Comparison

With a larger step size, the ERLE performance is not as good due to the misadjustment introduced by the near-end speech. To deal with this performance difficulty, acoustic echo cancellers include a detection scheme to tell when near-end speech is present and lower the step size value over these periods. Without such detection schemes, the performance of the system with the larger step size is not as good as the former, as can be seen from the ERLE plots.

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