  This study focuses on (traditional and unsourced) multiple-access
communication over a single transmit and multiple ($M$) receive antennas. We
assume full or partial channel state information (CSI) at the receiver. It is
known that to fully achieve the fundamental limits (even asymptotically) the
decoder needs to jointly estimate all user codewords, doing which directly is
computationally infeasible. We propose a low-complexity solution, termed coded
orthogonal modulation multiple-access (COMMA), in which users first encode
their messages via a long (multi-user interference aware) outer code operating
over a $q$-ary alphabet. These symbols are modulated onto $q$ orthogonal
waveforms. At the decoder a multiple-measurement vector approximate message
passing (MMV-AMP) algorithm estimates several candidates (out of $q$) for each
user, with the remaining uncertainty resolved by the single-user outer
decoders. Numerically, we show that COMMA outperforms a standard solution based
on linear multiuser detection (MUD) with Gaussian signaling. Theoretically, we
derive bounds and scaling laws for $M$, the number of users $K_a$, SNR, and
$q$, allowing to quantify the trade-off between receive antennas and spectral
efficiency. The orthogonal signaling scheme is applicable to unsourced random
access and, with chirp sequences as basis, allows for low-complexity fast
Fourier transform (FFT) based receivers that are resilient to frequency and
timing offsets.
