SM–ML. The performance of both SDs is closely tied to the choice of the initial radius. The chosen radius should be large enough for the sphere to contain the solution. On the one hand, the larger the radius is, the larger the search space, which increases the complexity. On the other hand, a small radius may cause the algorithm to fail in finding a point inside the sphere.

In this paper, a careful study of the performance of these two detectors is provided, along with an accurate comparison of their computational complexity. Numerical results show that with no loss in the BER performance, the proposed solutions provide a substantial reduction in computational complexity with respect to the SM–ML decoder. We also derive a closed form expression for the BER performance of SM–SD and show that the initial radius can be chosen such that SM–SD gives an optimum performance. Furthermore, it is shown that SM–Rx is less complex than SM–Tx for lower spectral efficiencies, while SM–Tx is the best solution for higher spectral efficiencies. Finally, using numerical results we show that SM–SD offers a significant reduction and nearly the same performance when compared to SMX with ML decoder or SD.

The 