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The authors derive a lower bound on the performance of generalised multilevel quadrature amplitude modulations (M-QAM) in time-discrete multipath Rayleigh fading environments with imperfect channel estimation. The bound can be regarded as an extension of the well-known matched filter bound (MFB), taking into account the impact of imperfect channel knowledge. The analytical expressions derived allow the computation of the bit error rate for the different bit streams that can be mapped simultaneously onto M-QAM symbols using a hierarchical approach when unequal bit error protection is desired.

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Performance bound for generalised multilevel-quadrature amplitude modulations constellations in multipath Rayleigh fading channels with imperfect channel estimation