Bit Error Rate (BER)

Besides the above information-theoretical point of view on hierarchical modulation, it is also interesting to understand hierarchical modulation from a practical signal-processing perspective. At this time, the performance of hierarchical modulation will be evaluated through an actual implementation, where demodulation error is one of the major concerns. In general, it is difficult to give a simple closed-form BER or symbol-error rate (SER) expression for hierarchical signal constellation, which also depends on receiver design and bits-to-symbol mapping. The BER of square-shaped MQAM constellation and a hierarchical QAM constellation for maximum likelihood (ML) demodulator can be computed by using recursive algorithms [8]. For a simple QPSK modulation, it is known that the BER is

Pe,QPSK (γ) = Q γ 2 , (8)

where Q(x) = 12 erfc√x2 denotes the Q-function.