electromagnetism - EM wave generation from different frames of reference

Take 2 observers and a charged particle,

Observer S is stationary to the particle and sees the electric field and no magnetic field as he is stationary to the particle.

Observer A decides to accelerate and decelerate over and over back and forth in front of the particle.

From A's frame of reference, it can be said, by the equivalence principal, that the particle is accelerating and decelerating in A's frame of reference and therefor should emit a EM wave.

So A sees a Em wave come off the particle.

But wait, S does not see any such thing, other than A moving back and forth...

What am I missing?? Thanks! Eric