  Massive deployment of low data rate Internet of things and ehealth devices
prompts us to develop more practical precoding and user selection techniques
that comply with these requirements. Moreover, it is known that when the data
is real-valued and the observation is complex-valued, widely linear (WL)
estimation can be employed in lieu of linear estimation to improve the
performance. With these motivations, in this paper, we study the transmit
precoding (beamforming) in multiuser multiple-input single-output
communications systems assuming the transmit signal is one-dimensionally
modulated and widely linear estimation is performed at the receivers.
Closed-form solutions for widely linear maximum ratio transmission (MRT), WL
zero-forcing (ZF), WL minimum mean square error (MMSE), and WL maximum signal
to leakage and noise ratio (MSLNR) precoding are obtained. It is shown that
widely linear processing can potentially double the number of simultaneous
users compared to the linear processing of one-dimensionally modulated signals.
Furthermore, to deal with the increasing number of communications devices a
user selection algorithm compatible with widely linear processing of
one-dimensionally modulated signals is proposed. The proposed user selection
algorithm can double the number of simultaneously selected users compared to
conventional user selection methods.
