MongoDB - aggregation performance tuning - mongodb

Question

One of my aggregation pipelines is running rather slow.
About the collection
The collection is named as Document and each document can belong to multiple campaigns and be in one of the five statues, 'a' to 'e'. A small portion of documents may belong to no documents and its campaigns field is set to null.
Sample document:
{_id:id, campaigns:['c1', 'c2], status:'a', ...other fields...}
Some collection stats
Number of documents: 2 million only :(
Size: 2GB
Average document size: 980 bytes.
Storage Size: 780MB
Total index size: 134MB
Number of indexes: 12
Number of fields in document: 30-40, may have array or objects.
About the Query
The query is targeting to count the number of documents per campaign per status if its status is in ['a', 'b', 'c']
[
{$match:{campaigns:{$ne:null}, status:{$in:['a','b','c']}}},
{$unwind:'$campaigns'},
{$group:{_id:{campaign:'$campaigns', status:'$status'}, total:{$sum:1}}}
]
It's expected that the aggregation is going to hit almost the whole collection.
When without index the aggregation is taking around 8 seconds to complete.
I tried to create an index on
{campaings:1, status:1}
Explaining plan shows that the index was scanned but the aggregation took near 11 seconds to complete.
Question
The index consists all fields required by the aggregation to do the counting. Should the aggregation not hit the index only? The index is only 10MB in size. How could it be slower? If not index, any other recommendation to tune the query?
Winning plan shows:
{
"stage" : "FETCH",
"filter" : {"$not" : {"campaigns" : {"$eq" : null}}},
"inputStage" : {
"stage" : "IXSCAN",
"keyPattern" : {"campaigns" : 1.0,"status" : 1.0},
"indexName" : "campaigns_1_status_1",
"isMultiKey" : true,
"isUnique" : false,
"isSparse" : false,
"isPartial" : false,
"indexVersion" : 1,
"direction" : "forward",
"indexBounds" : {
"campaigns" : ["[MinKey, null)", "(null, MaxKey]"],
"status" : [ "[\"a\", \"a\"]", "[\"b\", \"b\"]", "[\"c\", \"c\"]"]
}
}
}
If no index, winning plan:
{
"stage" : "COLLSCAN",
"filter" : {
"$and":[
{"status": {"$in": ["a", "b", "c"]}},
{"$not" : {"campaigns": {"$eq" : null}}}
]
},
direction" : "forward"
}
Update
As requested by #Kevin, here're some details about other all indexes, size in MB.
"indexSizes" : {
"_id_" : 32,
"team_1" : 8, //Single value field of ObjectId
"created_time_1" : 16, //Document publish time in source system.
"parent_1" : 2, //_id of parent document.
"by.id_1" : 13, //_id of author from a different collection.
"feedids_1" : 8, //Array, _id of ETL jobs contributing to sync of this doc.
"init_-1" : 2, //Initial load time of the doc.
"campaigns_1" : 10, //Array, _id of campaigns
"last_fetch_-1" : 13, //Last sync time of the doc.
"categories_1" : 8, //Array, _id of document categories.
"status_1" : 8, //Status
"campaigns_1_status_1" : 10 //Combined index of campaign _id and status.
},

Answer 1

After reading the docs from MongoDB, I found this:
The inequality operator $ne is not very selective since it often matches a large portion of the index. As a result, in many cases, a $ne query with an index may perform no better than a $ne query that must scan all documents in a collection. See also Query Selectivity.
Looking at a few different articles using the $type operator might solve the problem.
Could you use this query:
db.data.aggregate([
{$match:{campaigns:{$type:2},status:{$in:["a","b","c"]}}},
{$unwind:'$campaigns'},
{$group:{_id:{campaign:'$campaigns', status:'$status'}, total:{$sum:1}}}])