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 @math 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 @math 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 more antennas to achieve the same performance as infinite-resolution precoding.
We study low complexity precoding for a downlink massive MIMO multiuser system assuming a base station that employs one-bit digital-to-analog converters (DACs) in order to mitigate power usage. The use of one-bit DACs is equivalent to constraining the transmit signal to be drawn from a QPSK alphabet. While the precoding problem can be formulated using a standard maximum likelihood (ML) encoder, the implementation cost is prohibitive for massive numbers of antennas, even if a sphere encoding approach is used. Instead, we study the performance of a one-bit quantized zero-forcing precoder, and we show that it asymptotically provides the desired downlink vector with low complexity. Simulations show that the quantized ZF precoder can actually outperform the ML encoder for low to moderate signal-to-noise ratios. Massive multiuser (MU) multiple-input multiple-output (MIMO) is foreseen to be one of the key technologies in fifth-generation wireless communication systems. In this paper, we investigate the problem of downlink precoding for a narrowband massive MU-MIMO system with low-resolution digital-to-analog converters (DACs) at the base station (BS). We analyze the performance of linear precoders, such as maximal-ratio transmission and zero-forcing, subject to coarse quantization. Using Bussgang’s theorem, we derive a closed-form approximation on the rate achievable under such coarse quantization. Our results reveal that the performance attainable with infinite-resolution DACs can be approached using DACs having only 3–4 bits of resolution, depending on the number of BS antennas and the number of user equipments (UEs). For the case of 1-bit DACs, we also propose novel nonlinear precoding algorithms that significantly outperform linear precoders at the cost of an increased computational complexity. Specifically, we show that nonlinear precoding incurs only a 3 dB penalty compared with the infinite-resolution case for an uncoded bit-error rate of 10−3, in a system with 128 BS antennas that uses 1-bit DACs and serves 16 single-antenna UEs. In contrast, the penalty for linear precoders is about 8 dB.