One-Bit Precoding and Constellation Range Design for Massive MIMO With QAM Signaling

The use of low-resolution digital-to-analog converters (DACs) for transmit precoding provides crucial energy efficiency advantage for massive multiple-input multiple-output (MIMO) implementation. This paper formulates a quadrature amplitude modulation (QAM) constellation range and a one-bit symbol-level precoding design problem for minimizing the average symbol error rate (SER) in downlink massive MIMO transmission. A tight upper bound for the SER with low-resolution DAC precoding is first derived. The derived expression suggests that the performance degradation of one-bit precoding can be interpreted as a decrease in the effective minimum distance of the QAM constellation. Using the obtained SER expression, we propose a QAM constellation range design for the single-user case. It is shown that in the massive MIMO limit, a reasonable choice for constellation range with one-bit precoding is that of the infinite-resolution precoding with per-symbol power constraint, but reduced by a factor of $\sqrt{2/\pi }$ or about 0.8. The corresponding minimum distance reduction translates to about a 2 dB gap between the performance of one-bit precoding and infinite-resolution precoding. This paper further proposes a low-complexity heuristic algorithm for the one-bit precoder design. Finally, the proposed QAM constellation range and precoder design are generalized to the multiuser downlink. We propose to scale the constellation range for the infinite-resolution zero-forcing (ZF) precoding with per-symbol power constraint by the same factor of $\sqrt{2/\pi }$ for one-bit precoding. The proposed one-bit precoding scheme is shown to be within 2 dB of infinite-resolution ZF. In term of number of antennas, one-bit precoding requires about 50% more antennas to achieve the same performance as infinite-resolution precoding.