The authors investigate linear transceiver design in uplink (UL) coordinated multipoint transmission and reception (CoMP) multiple-input multiple-output (MIMO) systems with joint detections. A two-stage design algorithm is proposed by exploiting the technique of interference alignment, optimising the structure of the effective channel and employing power loading, with the goal to achieve high throughput and convergence performance. In contrast to conventional CoMP transceiver design, which is investigated under a predefined number of data streams transmitted by each user, the authors further investigate the selection of the number of data streams, called the configuration selection, and propose a corresponding low-complexity algorithm. By combining the proposed linear transceiver algorithm and low-complexity configuration selection algorithm, this work presents a new practical framework for linear transceiver design in UL CoMP MIMO systems. The simulation results confirm that the proposed algorithms achieve higher sum-rate performance than prior linear transceivers used in UL CoMP MIMO systems. Furthermore, the proposed transceiver offers comparable performance to existing IA-aided transceivers with significantly faster convergence.