The problem is that when the modulated bits arrive at the Rx after being acted upon by the wireless channel , they are spread out all over that $N$-dimensional space because the signal at each Rx antenna contains the contributions from all the Tx antennas, thus providing us with a mixture (i.e., summation) of all the transmissions. Since the signals from all Tx antennas arrive at each Rx antenna, the main task of the detection algorithms here is to free each modulated bit sent by one Tx antenna from the interference of the other modulated bits sent by rest of the Tx antennas. We earlier assumed that the number of Tx antennas $N_T$ is the same as the number of Rx antennas $N_R$ and each Tx antenna is transmitting an independent modulation symbol $s_i$.