SVG Animation on a ring outside of an icon

I am trying to animate the outer ring of an SVG. Since it's not filled circle, I can't change the element and spell it out with cx and cy and then change it via the animateTransform in the code. What I' trying to do is make the outer ring "pulse" by going from 100% down to 80% then back up to 100%. I can make the entire SVG animate changing the scale="1 1" to scale=".8 .8" but that scales the whole SVG and from the upper left corner. Any thoughts on how to animate just the outer ring? I generate my SVG using Illustrator which doesn't make clean SVG. Any help is much appreciated.

    <?xml version="1.0" encoding="utf-8"?>
<!-- Generator: Adobe Illustrator 18.1.1, SVG Export Plug-In . SVG Version: 6.00 Build 0)  -->
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN" "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
<svg version="1.1" id="Layer_1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" x="0px" y="0px"
     viewBox="0 0 50 50" enable-background="new 0 0 50 50" xml:space="preserve">
<g>
    <g>
        <path fill="#00AEEF" d="M4.5,25.1c0-1.9,0.3-3.7,0.7-5.4c0.5-1.7,1.2-3.4,2.1-4.9s2-2.9,3.2-4.2s2.6-2.3,4.2-3.2
            c1.5-0.9,3.2-1.6,4.9-2.1c1.8-0.5,3.6-0.8,5.4-0.8c1.9,0,3.7,0.2,5.4,0.7c1.8,0.6,3.4,1.3,4.9,2.2s2.9,2,4.2,3.2
            c1.3,1.3,2.3,2.6,3.2,4.2c0.9,1.5,1.6,3.1,2.1,4.9c0.5,1.7,0.7,3.5,0.7,5.4s-0.2,3.7-0.7,5.4c-0.5,1.7-1.2,3.4-2.1,4.9
            c-0.9,1.5-2,2.9-3.2,4.2c-1.3,1.2-2.7,2.2-4.2,3.1s-3.2,1.6-4.9,2.1c-1.7,0.5-3.5,0.7-5.4,0.7s-3.7-0.2-5.4-0.7
            c-1.7-0.5-3.4-1.2-4.9-2.1c-1.5-0.9-2.9-2-4.2-3.2c-1.2-1.3-2.3-2.6-3.2-4.1s-1.6-3.1-2.1-4.9C4.8,28.7,4.5,26.9,4.5,25.1z
             M6.4,25c0,1.7,0.2,3.3,0.7,4.9C7.5,31.5,8.2,33,9,34.3c0.8,1.4,1.8,2.6,2.9,3.8c1.1,1.1,2.4,2.1,3.8,2.9c1.4,0.8,2.9,1.4,4.4,1.9
            c1.6,0.4,3.2,0.7,4.9,0.7c1.7,0,3.3-0.2,4.9-0.7c1.6-0.4,3.1-1.1,4.4-1.9c1.4-0.8,2.6-1.8,3.8-2.9c1.1-1.1,2.1-2.4,2.9-3.8
            c0.8-1.4,1.4-2.9,1.9-4.4c0.5-1.6,0.7-3.2,0.7-4.9c0-1.7-0.2-3.3-0.7-4.9S41.8,17,41,15.7c-0.8-1.4-1.8-2.6-2.9-3.8
            C37,10.8,35.7,9.8,34.3,9s-2.9-1.4-4.4-1.9c-1.6-0.5-3.2-0.7-4.9-0.7c-2.5,0-4.9,0.5-7.2,1.5s-4.2,2.3-5.9,4c-1.7,1.7-3,3.7-4,5.9
            C6.9,20.1,6.4,22.5,6.4,25z"/>
    </g>
    <path id="pattern_3_" fill="#00AEEF" d="M15,35h10v-1.4H15V35z M16.4,15H15v10h1.4V15z M15,31.4h10V30H15V31.4z M15,27.9h10v-1.4
        H15V27.9z M23.6,15h-1.4v10h1.4V15z M20,15h-1.4v10H20V15z M25,15v1.4h10V15H25z M25,20h10v-1.4H25V20z M25,23.6h10v-1.4H25V23.6z
         M30,35h1.4V25H30V35z M33.6,35H35V25h-1.4V35z M26.4,35h1.4V25h-1.4V35z"/>
</g>
</svg>

Solution

The simplest solution would be to convert your outer circle back to a thick line. The equivalent circle would be:

<circle cx="25" cy="25" r="19.5" stroke-width="2" fill="none" stroke="#00AEEF"/>

Then you can just animate the radius.

<circle cx="25" cy="25" r="19.5" stroke-width="2" fill="none" stroke="#00AEEF">
    <animate attributeName="r" values="19.5; 15.6; 19.5" dur="1s" repeatCount="indefinite"/>
</circle>

The final working demo is as follows:

<svg version="1.1" id="Layer_1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" x="0px" y="0px"
     viewBox="0 0 50 50" enable-background="new 0 0 50 50" xml:space="preserve">
<g>
    <g>
        <circle cx="25" cy="25" r="19.5" stroke-width="2" fill="none" stroke="#00AEEF">
            <animate attributeName="r" values="19.5; 15.6; 19.5" dur="1s" repeatCount="indefinite"/>
        </circle>
    </g>
    <path id="pattern_3_" fill="#00AEEF" d="M15,35h10v-1.4H15V35z M16.4,15H15v10h1.4V15z M15,31.4h10V30H15V31.4z M15,27.9h10v-1.4
        H15V27.9z M23.6,15h-1.4v10h1.4V15z M20,15h-1.4v10H20V15z M25,15v1.4h10V15H25z M25,20h10v-1.4H25V20z M25,23.6h10v-1.4H25V23.6z
         M30,35h1.4V25H30V35z M33.6,35H35V25h-1.4V35z M26.4,35h1.4V25h-1.4V35z"/>
</g>
</svg>