detector is especially suitable when the number of receive–antennas is very large. This technique reduces the size of the search space related to the multiple antennas at the receiver (we denote this search space as “receive search space”). It will be shown later that there is no loss in either the diversity order or the coding gain, *i.e.* the BER is very close to that of the ML detector. However, the main limitation is that it does not reduce the search space related to the number of possible transmitted points (we denote this as “transmit search space”). This limitation prevents the detector from achieving a significant reduction in computational complexity when high data rates are required.

The second SD, which is called Transmit–centric (SM–Tx) was first presented in [@yrmh1101]. It aims at reducing the transmit search space by limiting the number of possible spatial and constellation points. The SM–Tx algorithm avoids an exhaustive search by examining only those points that lie inside a sphere with a given radius. However, SM–Tx is limited to the overdetermined MIMO setup $\left(N_t\leq N_r\right)$, where $N_t$ and $N_r$ are the number of transit and receiver antennas respectively. In [@rh1201_gen; @rh1201a], it is shown that SM–Tx 