A wireless sensor network with single-antenna sensors on the transmitter side and an access point (AP) equipped with multiple antennas on the receiver side is considered. In order to reduce the number of outages resulting from the noise amplification by the linear reconstruction within the successive interference cancellation (SIC) procedure, the AP is given the possibility to request retransmissions of signals from selected sensors in a subsequent time slot (TS). In case retransmissions are needed also in the subsequent time slot, the AP postpones the signal detection until all requested signals have been retransmitted making the signal detection a recursive procedure. The number of sensors required to retransmit depends on the order of the processed sensor signals within the SIC procedure. We propose an optimal algorithm based on a QR-decomposition and a depth-first search through all possible decoding orders, which finds the decoding order necessitating a minimum number of retransmissions suitable for zero-forcing (ZF) and minimum mean square error (MMSE) linear reconstruction approaches. Since the computational complexity of the optimal algorithm is high, different suboptimal algorithms with lower computational complexity are proposed for the case of ZFSIC and MMSE-SIC, respectively. The recursive nature of the retransmission procedure may lead to an unlimited detection delay, because the linear reconstruction followed by SIC starts only when no sensor needs a retransmission from the previous TS. By reducing the number of transmitting sensors for a fixed number of receiving antennas the receive diversity of the AP can be exploited, which leads to less retransmissions. Therefore, we propose an optimal transmit policy, which selects the best set of sensors to maximize the system throughput. This optimal transmit policy is found by means of a Markov decision process in combination with dynamic programming.