  Orthogonal frequency division multiplexing with index modulation (OFDM-IM) is
a novel scheme where the information bits are conveyed through the subcarrier
activation pattern (SAP) and the symbols on the active subcarriers.
Unfortunately, OFDM-IM inherits the high peak-to-average power ratio (PAPR)
problem from the classical OFDM. The OFDMIM signal with high PAPR induces
in-band distortion and out-of-band radiation when it passes through high power
amplifier (HPA). There are attempts to reduce PAPR by adding dither signals in
the idle subcarriers, where the dither signals can have various amplitude
constraints according to the characteristic of the corresponding OFDM-IM
subblock. But, there is no result for the specific amplitude constraint for the
dither signals over a Rayleigh fading channel. In this letter, based on
pairwise error probability (PEP) analysis, a specific constraint for the dither
signals is derived over a Rayleigh fading channel.
