Low PAR means less fluctiations in the magnitude of a signal and hence analog signal processing (e.g., power amplifier) is tremendously reduced. For example, constant envelope modulation schemes like BPSK, GMSK can use a switching amplifier which are >90% efficient. The downside is low spectral efficiency.
On the other side, high-order QAM or OFDM have high spectral efficiencies but the PAR becomes very high (up to 12dB for OFDM) and hence power amplifiers only reach 10-20% effiency.
Specieal cases and tricks aside (like Crest Factor Reduction, Digital Predistortion, ...) and leaving SNR out of the picture, is there a first order relationship between spectral efficiency and PAR? Any theoretical bounds?
If not, are there at least published plots that plot spectral efficiency vs PAR for various standards/modulation formats? (I did not find any)