Exact BER computation of generalized hierarchical PSK constellations

Hierarchical constellations offer a different degree of protection to the transmitted messages according to their relative importance. As such they found interesting application in digital video broadcasting systems as well as wireless multimedia services. Although a great deal of attention has been devoted in the literature to the study of the bit error rate (BER) performance of uniform phase shift keyed (PSK) constellations, very few results were published on the BER performance of hierarchical PSK constellations. We obtain exact and generic expressions in M for the BER of the generalized hierarchical M-PSK constellations over additive white Gaussian noise (AWGN) and fading channels. For the AWGN case, these expressions are in the form of a weighted sum of Pawula (1982) F-functions and are solely dependent on the constellation size M, the carrier-to-noise ratio, and a constellation parameter which controls the relative message importance. Because of their generic nature, these new expressions readily allow numerical evaluation for various cases of practical interest.