Error Floor Analysis of Signal Space Diversity Schemes Under Erasure Effect in Single Frequency Network

This paper provides numerical results for proving the performance gain afforded by signal space diversity (SSD). First, we derive the exact distribution of Bernoulli-<formula formulatype="inline"><tex Notation="TeX">$\chi^{2}$</tex> </formula> product random variables in order to obtain the average bit error rate (BER). Then, to attain the asymptotic error floor of the average BER, the Chernoff upper bound and the moment generating function of the Bernoulli-<formula formulatype="inline"><tex Notation="TeX">$\chi^{2}$</tex></formula> distribution are adopted. As a consequence, we confirm the accuracy of our analysis by simulations, and prove that BER without SSD converges to <formula formulatype="inline"> <tex Notation="TeX">$p/2$</tex></formula>, whereas when SSD is used, it converges to <formula formulatype="inline"><tex Notation="TeX">$p^{2}/2$</tex> </formula> regardless of the modulation type and order when the erasure probability is equal to <formula formulatype="inline"><tex Notation="TeX">$p$</tex></formula> over both Rayleigh and Rician fading channels.

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