in [@yrmh1101] can still be used for the case of $(2N_r-1)\geq N_t>N_r$, where SM–Tx is referred to as enhanced Tx–SD (E–Tx–SD). Moreover, in [@rh1201_gen; @rh1201a] a detector for the case of $N_t>N_r$ referred to as generalised Tx–SD (G–Tx–SD) is proposed. By using the division algorithm the G–Tx–SD technique: 1) Divides the set of possible antennas to a number of subsets. 2) Performs E–Tx–SD over each subset. 3) Takes the minimum solution of all the sets. However, in this paper we propose a simple solution, in which all that is needed is to set a constant $\varphi$ to $0$ for $N_t\leq N_r$ and $\varphi=\sigma_n^2$ for $N_t>N_r$, where $\sigma_n^2$ is the noise variance. In [@rh1201_gen; @rh1201a], the normalised expected number of nodes visited by the SM–Tx algorithm is used to compare its complexity with the complexity of the SM–ML algorithm. This does not take into account pre–computations needed by SM–Tx. In this paper, when comparing the complexity of SM–Tx with the complexity of SM–ML and SM–Rx, we take into account the pre–computations needed by the SM–Tx. We show that because of those pre–computations, the SM–Tx technique is not always the best solution, where in some cases it is even more complex than 