As the powerful cloud-computing infrastructures become more and more popular, the potential of their applications for dealing with the challenges emerging in cognitive radio networks (CRNs) is under scientific investigation. By making use of the parallel computing capacity of the cloud, we propose innovative parallel QR-factorization algorithms to establish an adaptive transmitter system by dynamically selecting the antennae. Our proposed parallel algorithms can efficiently calculate a tight (achievable) lower-bound of the free distance, which determines the error probability of the symbol detection at the receiver. In this paper, we devise a new parallel QR-based antenna selection scheme in the transmitter to maximize the above-stated lower-bound for achieving the nearly optimal symbol detection at the receiver. Monte Carlo simulation results demonstrate that our proposed parallel method leads to a better bit-error-rate (BER) performance than the conventional singular-value-decomposition (SVD) based scheme. The time complexity analysis is also presented for our proposed parallel algorithms.