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In this paper, the statistics of quadratic forms in normal random variables (RVs) are studied and their impact on performance analysis of wireless communication systems is explored. First, a chi-squared series expansion is adopted to represent the probability density function of a quadratic form in normal RVs and novel series truncation error bounds are derived, which are much tighter compared to already known ones. Secondly, it is theoretically shown that when an orthogonal space time block coding (OSTBC) transmission scheme is used, the signal to noise ratio (SNR) at the receiver under various fading conditions can be expressed as a quadratic form in normal RVs. Capitalizing on these results, a thorough error probability and capacity analysis is presented for the performance of OSTBC systems over Nakagami-q (Hoyt) fading channels. For all error probability and capacity performance criteria considered, simple, closed-form truncation error bounds expressions are derived, which avoid the use of infinite sums and complicated functions. The proposed theoretical analysis is validated through extensive Monte Carlo simulations.