One-Bit Precoding and Constellation Range Design for Massive MIMO with QAM Signaling
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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 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 SER with low-resolution DAC precoding is first derived. The derived expression suggests that the performance degradation of 1-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 1-bit symbol-level precoding is that of the infinite-resolution precoding with per-symbol power constraint, but reduced by a factor of √(2/π) or about 0.8. The corresponding minimum distance reduction translates to about 2dB gap between the performance of 1-bit precoding and infinite-resolution precoding. This paper further proposes a low-complexity two-step heuristic algorithm for one-bit precoder design. Finally, the proposed QAM constellation range and precoder design are generalized to the multi-user downlink. We propose to scale the constellation range for infinite-resolution zero-forcing (ZF) precoding with per-symbol power constraint by the same factor of √(2/π) for one-bit ZF precoding. The proposed 1-bit precoding scheme is shown to be within 2dB of infinite-resolution ZF precoding. In term of number of antennas, 1-bit precoding requires about 50 infinite-resolution precoding.
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