Substitute Suitable RNAV system for Inop Radar on approach “requiring” Radar
Since "radar" means "ATC radar", I'm not sure how a pilot could substitute anything for it. The issue isn't that the pilot needs radar to navigate the approach; it's that's ATC needs radar in order to allow the approach in the first place.

Per this answer, ATC can only clear aircraft for an RNAV approach without an IAF if radar monitoring is available. I don't think we've found out why that's the case, but it's what the ATC orders say (4-8-1(h)). Since the approach above has no IAF, that means ATC can only clear you for it if they have radar monitoring.

4-8-1(g) also instructs controllers not to let pilots choose their approach if there's no radar available:


  g. Where instrument approaches require radar monitoring and radar
  services are not available, do not use the phraseology “cleared
  approach,” which allows the pilot his/her choice of instrument
  approaches.


In other words, ATC has to make sure that they clear pilots for approaches only if their own requirements are met.

But as it happens, ATC does have a possible substitution for radar. The ATC orders 5-5-4 say:


  The use of ADS-B only information may be used to support all radar
  requirements associated with any published instrument procedure that
  is annotated “Radar Required”.


I assume that means that - at least theoretically - if ATC lost radar but could still receive ADS-B, they could clear you for the approach. But that would be ATC substituting equipment, not the pilot :-)