I have a GRE PSR 500 with a stock antenna and I can hear AWIN on President's Island.
Harbor Town and up towards De Wit Spain airport, up & down Riverside Drive and on Front St., south on I-55 until ya make the turn at the refinery is OK......once ya get in amongst the buildings or head more easterly ya lose any signal ya may have.....
I work on PI and I hear AWIN right until I walk in the door of my building.....all metal structure. I can still get all of Crittenden Co. analog and I can hear Memphis' P25 system just fine.
AWIN is just so weak once ya get east of West Memphis........doesn't make for good inter-operability in my opinion.
I have heard AWIN from NW MS on occasion......last week as I was driving back from Jackson, MS I was catching Troop D (Walnut Corner tower in Phillips Co,) from between Clarksdale & Tutwiler on US 49.......that's the second time I've done that.
I can't say much about DeSoto Co. coverage tho......don't know how far down you'd have to go until ya lose Shell Lake and pick up Walnut Corner.