Remove element from dom tree xml php

I have a xml file with many elements, I am looking to remove certain elements based on their indexes.

Sample XML:

<songs>
   <song>
      <title>A</title>
      <artist>AA</artist>
   </song>
</song>

PHP Code I have so far:

<?php
$index = $_GET['song'];

$doc = new DOMDocument();
$doc->load("songs.xml");
$songs = $doc->getElementsByTagName("song");

foreach($songs as $song) {
    if(in_array( $song[$index], $songs)){
          unset($song);
    }
}
$doc->save("songlist.xml");
?>

But I get this error from this code:

Fatal error: Cannot use object of type DOMElement as array

Any help at all is appricated in this issue, thank you.