For a constant added noise density at high signal-to-noise ratios and for the same error rate, three-phase PSK requires about 0.75 dB less energy per bit than two-phase or four-phase PSK. However, at very low signal-to-noise ratios, three-phase PSK requires about 0.74 dB more energy per bit of channel capacity than two-phase or four-phase PSK.
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John R. Pierce (1980) studied this question.
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