Including product categories (product_cat taxonomy) title and description in search query

Found out my solution by filtering the search query. Hope that helps:

function new_search_join( $join ) {
    global $wpdb;

    if ( is_search() ) {
        $join .= "
        INNER JOIN {$wpdb->term_relationships} ON {$wpdb->posts}.ID = {$wpdb->term_relationships}.object_id
        INNER JOIN {$wpdb->term_taxonomy} ON {$wpdb->term_taxonomy}.term_taxonomy_id = {$wpdb->term_relationships}.term_taxonomy_id
        INNER JOIN {$wpdb->terms} ON {$wpdb->terms}.term_id = {$wpdb->term_taxonomy}.term_id";
    }

    return $join;
}
add_filter('posts_join', 'new_search_join' );


function new_search_where( $where ) {
    global $pagenow, $wpdb;

    if ( is_search()) {


        $where = preg_replace(
            "/\(\s*".$wpdb->posts.".post_title\s+LIKE\s*(\'[^\']+\')\s*\)/",
            "
              (".$wpdb->posts.".post_title LIKE $1)
              OR
              (".$wpdb->posts.".post_content LIKE $1)
              OR
              (".$wpdb->terms.".name LIKE $1)
              OR
              (".$wpdb->term_taxonomy.".description LIKE $1)
            ", $where );

    }

    return $where;
}
add_filter( 'posts_where', 'new_search_where' );

/**  Prevent duplicates  */
function new_search_distinct( $where ) {
    global $wpdb;

    if ( is_search() ) {
        return "DISTINCT";
    }

    return $where;
}
add_filter( 'posts_distinct', 'new_search_distinct' );