  Recently, three Sphere Decoding (SD) algorithms were proposed for Spatial
Modulation (SM) scheme which focus on reducing the transmit-, receive-, and
both transmit and receive-search spaces at the receiver and were termed as
Receiver-centric SD (Rx-SD), Transmitter-centric SD (Tx-SD), and Combined SD
(C-SD) detectors, respectively. The Tx-SD detector was proposed for systems
with Nt \leq Nr, where Nt and Nr are the number of transmit and receive
antennas of the system. In this paper, we show that the existing Tx-SD detector
is not limited to systems with Nt \leq Nr but can be used with systems Nr < Nt
\leq 2Nr - 1 as well. We refer to this detector as the Extended Tx-SD (E-Tx-SD)
detector. Further, we propose an E- Tx-SD based detection scheme for SM systems
with arbitrary Nt by exploiting the Inter-Channel Interference (ICI) free
property of the SM systems. We show with our simulation results that the
proposed detectors are ML-optimal and offer significantly reduced complexity.
