What regulations exist for ATC real time RADAR simulator software?
So according to EASA, it is the AMCs/GM for Regulation 2015/340, Part ATCO.OR (Annex III to Decision 2015/10/R) and specifically in AMC1.ATCO.OR.C015(b)(b) where is specifies 11 criteria regarding STD standards, among them being accuracy of aircraft performance, voice recognition realism, equipment, data displays, etc:


  STD criteria
  
  If  a  synthetic  training  device  (STD)  is  used  for  training, it should
  be approved by the competent authority as part of the course approval process 
  for  any  training  plan.  Training  organisations  should  demonstrate  how  the STD  will  provide  adequate  support  for the  intended training,  in  particular, how  the  STD  will  meet  the  stated  objectives  of  the  practical  training exercises and enable the performance objectives to be assessed to the level determined in the training programme.
  
  This  demonstration  and  the  related  documentation  should  include  the 
  following relevant criteria:
  
  (1) the  general  environment,  which  should  provide  an  environment  in 
  which  STD  exercises  may  be  run  without  undue  interference  from unrelated activities;
  
  (2) the STD layout;
  
  (3) the equipment provided;
  
  (4) the  display  presentation,  functionality,  and  updating  of operational information;
  
  (5) data displays, including strip displays, where appropriate;
  
  (6) coordination facilities;
  
  (7) aircraft   performance   characteristics,   including   the   availability   of manoeuvres,   e.g.   holding   or instrumental landing system   (ILS) operation, required for a particular simulation;
  
  (8) the availability of real-time changes during an exercise;
  
  (9) the  processes  by  which  the  training  organisation can be assured that staff associated with the training conducted with the use of an STD are 
  competent;
  
  (10) the degree of realism of any voice recognition system associated with 
  the STD;
  
  (11) where  a  simulator  is  an  integral  part  of  an  operational  ATC
  system, the  processes  by  which  the  training  organisation  is  assured  that interference  between  the  simulated  and  operational  environments  is prevented.
  
  The  extent  to  which  the  STD  achieves  the above criteria  will  be  used  to determine  the  adequacy  of  the  STD  for  the  proposed  use.  As  a  general principle,  the  greater  the  degree  of  replication  of  the  operational  position being  represented  the  greater  the  use  will  be  possible  for  any  particular training.