Fog　computing　paradigm　extends　computing,　communication,　storage,　and　network　resources　to　the　network＇s　edge.　As　the　fog　layer　is　located　between　cloud　and　end-users,　it　can　provide　more　convenience　and　timely　services　to　end-users.　However,　in　fog　computing　(FC),　attackers　can　behave　as　real　fog　nodes　or　end-users　to　provide　malicious　services　in　the　network.　The　attacker　acts　as　an　impersonator　to　impersonate　other　legitimate　users.　Therefore,　in　this　work,　we　present　a　detection　technique　to　secure　the　FC　environment.　First,　we　model　a　physical　layer　key　generation　based　on　wireless　channel　characteristics.　To　generate　the　secret　keys　between　the　legitimate　users　and　avoid　impersonators,　we　then　consider　a　Double　Sarsa　technique　to　identify　the　impersonators　at　the　receiver　end.　We　compare　our　proposed　Double　Sarsa　technique　with　the　other　two　methods　to　validate　our　work,　i.e.,　Sarsa　and　Q-learning.　The　simulation　results　demonstrate　that　the　method　based　on　Double　Sarsa　outperforms　Sarsa　and　Q-learning　approaches　in　terms　of　false　alarm　rate　(FAR),　miss　detection　rate　(MDR),　and　average　error　rate　(AER).