up to $1$ dB better BER performance than SMX–ML decoder.'
author:
- 'Abdelhamid Younis, Sinan Sinanović, Marco Di Renzo, Raed Mesleh and Harald Haas [^1] [^2] [^3] [^4] [^5] [^6] [^7]'
title: |
    Generalised Sphere Decoding for\
    Spatial Modulation
---

Multiple–input–multiple–output (MIMO) systems, spatial modulation (SM), spatial multiplexing (SMX), sphere decoding (SD), large scale MIMO.

Introduction {#sec1}
============

–input multiple–output (MIMO) systems offer a significant increase in spectral efficiency in comparison to single antenna systems [@t9902]. An example is Spatial Multiplexing (SMX) [@f9601], which transmits simultaneously over all the transmit antennas. This method achieves a spectral efficiency that increases linearly with the number of transmit antennas. However, these systems cannot cope with the exponential increase of wireless data traffic, and a larger number of transmit antennas (large scale MIMO) should be used [@hbd1101]. Large scale MIMO studied in [@mzcr0901; @cv0901; @mcs0801], offers higher data rates and better bit error rate (BER) performance. However, this comes at the expense of an increase in:

1.  Computational complexity: A SMX maximum likelihood (ML) optimum receiver searches across all possible combinations, and tries to resolve the inter–channel interference (ICI) caused by transmitting from all antennas simultaneously, on the same frequency. Sphere decoder (SD) was 