Matched Filter Bound for M-QAM Hierarchical Constellations with Diversity Reception in Multipath Rayleigh Fading Channels

In this paper we derive matched filter bound (MFB) bit error rate (BER) expressions for the individual bit classes of multilevel hierarchical quadrature amplitude modulations (M-HQAM). The expressions are valid for time-discrete multipath Rayleigh fading environments with diversity where the different paths can be correlated. Though typically MFB are obtained assuming slow-varying channels in this paper we also consider fast varying channels.