• The Journal of Korean Institute of Communications and Information Sciences
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• v.31 no.9C
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• pp.831-839
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• 2006

In this paper, we present an exact and general expression involving two-dimensional Gaussian Q-functions for the bit error rate (BER) of hierarchical MPSK with I/Q phase and amplitude imbalances over an additive white Gaussian noise (AWGN) channel. First we derive a BER expression for the k-th bit of hierarchical 4, 8, 16-PSK signal constellations when Gray code bit mapping is employed. Then, from the derived k-th bit BER expression, we present the exact and general average BER expression for hierarchical MPSK with I/Q phase and amplitude imbalances. This result can readily be applied to numerical evaluation for various cases of practical interest in an I/Q unbalanced hierarchical MPSK system, because the one- and two-dimensional Gaussian Q-functions can be easily and directly computed usinB commonly available mathematical software tools.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.20 no.4
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• pp.375-380
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• 2009

Bit error rate(BER) performance of each bit for hierarchical M-ary phase shift keying(H-MPSK) modulation scheme is changed according to the phase parameters. Thus, a method to find the phase parameters appropriate to the requests of the system is needed. In this paper, we propose a method to obtain the phase parameters from an approximate approach of BER for H-MPSK and verify a validity of the proposed method through the previously provided expression for analyzing an exact error probability of H-MPSK.