  A multi-antenna, greedy, iterative, and quantized (MAGIQ) precoding algorithm
is proposed for downlink channels. MAGIQ allows a straightforward integration
with orthogonal frequency-division multiplexing (OFDM). MAGIQ is compared to
three existing algorithms in terms of information rates and complexity:
quantized linear precoding (QLP), SQUID, and an ADMM-based algorithm. The
information rate is measured by using a lower bound for finite modulation sets,
and the complexity is measured by the number of multiplications and
comparisons. MAGIQ and ADMM achieve similar information rates with similar
complexity for Rayleigh flat-fading channels and one-bit quantization per real
dimension, and they outperform QLP and SQUID for higher order modulation.
