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Transmit laser selection (TLS) diversity scheme has been proposed recently for free-space optical communication systems and its bit error rate (BER) performance has been investigated over K-distributed turbulence channels based on lengthy simulations. Moreover, for a limiting case of strong turbulence conditions that have been modelled by negative exponential distribution, a closed-form expression for the average BER has been presented in the open technical literature. In this study, first a novel approximate analytical expression is derived for the probability density function (PDF) of the resulting channel irradiance corresponding to a TLS diversity scheme over the K channel. The approximated PDF accurately estimates the statistics of the channel irradiance over a wide range of channel conditions. Then, based on the derived PDF, an analytical closed-form expression is presented for the average BER, which can be used to estimates the BER of the system very accurately over K-distributed turbulence channels without resorting to lengthy simulations. Additionally, based on the derived analytical results, the effect of using laser pulse shape with increased peak-to-average optical power ratio on the system performance is investigated. Numerical results are further demonstrated to confirm the analytical results.