SNR penalty of hybrid diversity combining in Rayleigh fading

In hybrid selection/maximal ratio combining the receiver selects the L branches with the largest signal-to-noise ratios from N available diversity branches and performs maximal ratio from N available diversity branches and performs maximal ratio combining. A penalty is incurred with respect to maximal ratio combining which can be defined as the increase in signal-to-noise ratio required for hybrid combining to achieve the same symbol error probability as maximal ratio combining. In this paper, we derive the asymptotic signal-to-noise ratio penalties for small and large values of signal-to-noise ratio for arbitrary signaling constellations in Rayleigh fading. We also present new analytical expressions for the symbol error probabilities of 4-ary orthogonal signaling and 8-ary biorthogonal signaling with hybrid diversity combining in Rayleigh fading.