Recibo un archivo xml como este.

<radio>
  <channel id="Opus">
    <display-name>Opus</display-name>
    <icon src="" />
  </channel>
  <channel id="Klasika">
    <display-name>Klasika</display-name>
    <icon src="" />
  </channel>
  <channel id="LR">
    <display-name>LR</display-name>
    <icon src="" />
  </channel>
  <programme channel="Opus" start="20130203060000" stop="20130203110000" duration="050000">
    <title lang="lt">OPUS muzika.</title>
    <desc lang="lt">OPUS muzika.</desc>
    <category lang="lt">muzikos laidos</category>
    <date>2013.02.03</date>
  </programme>
  <programme channel="Opus" start="20130203110000" stop="20130203150000" duration="040000">
    <title lang="lt">Vėlyvi pusryčiai su OPUS.</title>
    <desc lang="lt">Vėlyvi pusryčiai su OPUS.</desc>
    <category lang="lt">muzikos laidos</category>
    <date>2013.02.03</date>
  </programme>
</radio>

con muchos casos deprograma ycanal. Intento deserializarlo en este objeto c # pero obtengo un nulo en lugar de un objeto:

[XmlRoot("radio")]
public sealed class radio
{
    [XmlRoot("channel")]
    public sealed class channel
    {
        [XmlAttribute("id")]
        public string id { get; set; }

        [XmlElement("display-name")]
        public string displayName { get; set; }

        [XmlElement("icon")]
        public string icon { get; set; }

        public channel()
        {    
        }
    }

    [XmlRoot("programme")]
    public sealed class programme
    {
        [XmlAttribute("channel")]
        public string channel { get; set; }

        [XmlAttribute("start")]
        public string start { get; set; }

        [XmlAttribute("stop")]
        public string stop { get; set; }

        [XmlAttribute("duration")]
        public string duration { get; set; }

        [XmlElement("title")]
        public string title { get; set; }

        [XmlElement("desc")]
        public string desc { get; set; }

        [XmlElement("category")]
        public string category { get; set; }

        [XmlElement("date")]
        public string date { get; set; }

        public programme()
        {
        }
    }

    [XmlArray]
    public channel[] channels { get; set; }

    [XmlArray]
    public programme[] programmes { get; set; }

    public radio()
    {
        channels = null;
        programmes = null;
    }

    public static radio FromXmlString(string xmlString)
    {
        var reader = new StringReader(xmlString);
        var serializer = new XmlSerializer(typeof(radio));
        var instance = (radio)serializer.Deserialize(reader);

        return instance;
    }
}

¿Qué estoy haciendo mal y cuál sería la clase de objeto xml adecuada?