Fast Maximum Likelihood Detection of the Generalized Spatially Modulated Signals Using Successive Sphere Decoding Algorithms

The generalized spatial modulation (GSM) scheme is used in wireless communication to map each block of data bits to a set of spatially multiplexed (SMX) symbols and an index of transmit antenna combination (TAC) of active antennas. The SMX symbols are then transmitted simultaneously through the multiple active antennas. The detection of the GSM signals at the receiver side needs to recover both the SMX symbols and TAC index. To achieve maximum likelihood detection (MLD) of GSM signals with low complexity, two previous algorithms modify the computationally efficient sphere decoding algorithm (SDA) and needs to discriminate the SMX symbols from the null symbols transmitted by inactive antennas. In this letter, we propose a new successive SDA (SSDA) that employs multiple times of SDA though but does not need to process the null symbols during tree traversals. Particularly, when used together with the radius update and reordering of the multiple SDAs, our SSDA achieves great complexity reduction and is the fastest one among the algorithms that achieve exact MLD of GSM signals.