What you could use is some sound proof windows if all else fails and you do not wish to move. These sound proof windows really do work. I live in Taipei and had sound proof windows installed. The amount of sound that is reduced is amazing but be prepared to spend some money on these windows. With proper windows the speaker can be right outside of the window and you won't hear jack****.. The windows that they use in the UAE are of very poor quality. They are practically paper thin with nearly zero sound insulation so the sound from the outside goes right into your house and bedroom or where ever you are in the house. If you are half deaf,don't mind any noise,or if you are religious and love the sound of the Imam doing prayer calls 5 times a day then these poor windows are of no concern but if you like being in your home and being isolated from all the outside sounds then you need properly built windows which are soundproof.
I doubt complaining to the local authorities will get you any where. They will see this as an foreign expat complaining who is not used to living in an Islamic nation. Arabs in general are not very quiet people. If you want to live in peace next to quiet people you could consider Japan. The Japanese are very quiet and respect the privacy of others. Arabs in general don't care much about others (Not all but generally speaking that is..)