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.
The recent contributions of @cite_2 @cite_12 consider designing the constellation range, as well as a non-linear precoder scheme with higher order modulations. The algorithms in @cite_2 @cite_12 , which seek to minimize the mean squared error at the user side, achieve excellent performance within few dB gap to the infinite-resolution precoding benchmarks. However, in the algorithm of @cite_2 @cite_12 , the constellation range is designed for each symbol transmission, which means that the range information needs to be communicated to the receiver as side information on a symbol-by-symbol basis. This is a significant overhead. The recent work @cite_27 extends the algorithm in @cite_12 by considering the constellation range design for @math symbol transmissions in which the channel remains constant. However, the high computational complexity of the algorithm in @cite_27 (which is @math for a system with @math transmit antennas) prohibits its use for the typical massive MIMO systems in which @math and @math are both large.
@cite_27 @cite_12 @cite_2
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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. One-bit quantization at the base-station (BS) of a massive multiple-input multiple-output (MIMO) wireless system enables significant power and cost savings. While the 1-bit uplink (users communicate to BS) has gained significant attention, the downlink (BS transmits to users) is far less studied. In this paper, we propose a novel, computationally-efficient 1-bit beamforming algorithm referred to as POKEMON (short for PrOjected downlinK bEaMfOrmiNg), which—after its convolution with the MIMO channel matrix—minimizes multi-user interference (a.k.a. spatial leakage). Our algorithm builds upon the biconvex relaxation (BCR) framework, which efficiently approximates the optimal 1-bit beamforming problem that is of combinatorial nature. Our simulation results show that POKEMON significantly outperforms linear beamformers followed by 1-bit quantization in terms of error-rate performance and recent non-linear beamformers in terms of complexity.