Analytical 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) expressions for the performance of hierarchical quadrature amplitude modulations (M-HQAM) over time-discrete multipath Rayleigh fading environments with diversity. The expressions are valid for multipath environments where different paths and antennas can be correlated. Since hierarchical constellations are usually employed to achieve unequal bit error protection, the MFB expressions are given in terms of the individual bit error rate (BER) for the different bit streams. Although typically the MFB is obtained assuming slow time varying channels, fast varying channels are also considered in this paper.