[{/**"_id": 0,*/"name":"shoe","payments":[{"type":"a","amount":10},{"type":"b","amount":15},{"type":"a","amount":15},]},{/**"_id": 0,*/"name":"shirt","payments":[{"type":"a","amount":5},{"type":"b","amount":20},]}]

db.collection.aggregate([{$group:{_id:null,amountSum:{$sum:{$reduce:{input:"$payments",initialValue:0,in:{$sum:["$$value","$$this.amount"]}}}}}}])