Large penalty of hybrid diversity with uncoded modulation in slow rayleigh fading

In hybrid selection/maximal ratio combining (H-S/MRC) the receiver selects the L branches with the largest signal-to-noise ratios (SNRs) from N available diversity branches and performs maximal ratio combining (MRC). A penalty is incurred with respect to MRC which can be defined as the increase in SNR required for H-S/MRC to achieve the same symbol error probability as MRC. Recently, this penalty was investigated specifically for two-dimensional modulations. In this paper, we derive the asymptotic SNR penalties in slow Rayleigh fading for small and large values of SNR for general uncoded signaling constellations