Clustering procedure for $N_t \times N_r$ BPSK MIMO systems

The geometrical property indicated in the previous section is not limited to $2 \times 2$ systems. In a general $N_t \times N_r$ BPSK MIMO system with fast time-varying channels, for any cluster following a certain trajectory in time, there is always another cluster following the symmetric trajectory. Combining the data of two such clusters might provide a more robust clustering problem. This observation leads to the following two-phase algorithm: In the first phase, groups of symmetric clusters are detected. One clustering problem needs to be solved here to find $2^{N_t-1}$ clusters. In the second phase, each group of symmetric clusters is separated into two different clusters, representing $N_t$ independent problems.