javascript - fetch data in meteor based on sub element -

i have issue regarding publishing collection. have model of each document in collection.

{     "_id" : "8swmmomhtredndqtn",     "persons" : [          {             "userid" : "29pr753gmydxqzzo6",             "lastreadtime":""         },          {             "userid" : "gwkbykiqsfzdctwkz",             "lastreadtime":""         }     ] } 

now want publish document persons.userid have current user id

here publish code

meteor.publish("chatrooms", function(){    return userdata.find({persons:{$elemmatch:{userid:this.userid}}}); }); 

but is nothing

i had try below code

meteor.publish("chatrooms", function(){    return userdata.find({"persons.userid":this.userid}); }); 

but getting result data 0

how can publish way?