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.
Most of the existing literatures on one-bit beamforming focuses on the uplink scenario in which the BS is equipped with one-bit analog-to-digital converters (ADCs). The performance analyses of such systems for narrowband channels are provided in @cite_41 @cite_23 @cite_26 @cite_37 while those for wideband channels are presented in @cite_11 @cite_33 .
@cite_37 @cite_26 @cite_33 @cite_41 @cite_23 @cite_11
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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. We study downlink beamforming in a single-cell network with a multi-antenna base station (BS) serving cache-enabled users. For a given common rate of the files in the system, we first formulate the minimum transmit power with beamforming at the BS as a non-convex optimization problem. This corresponds to a multiple multicast problem, to which a stationary solution can be efficiently obtained through successive convex approximation (SCA). It is observed that the complexity of the problem grows exponentially with the number of subfiles delivered to each user in each time slot, which itself grows exponentially with the number of users in the system. Therefore, we introduce a low-complexity alternative through time-sharing that limits the number of subfiles that can be received by a user in each time slot. It is shown through numerical simulations that, the reduced-complexity beamforming scheme has minimal performance gap compared to transmitting all the subfiles jointly, and outperforms the state-of-the-art low-complexity scheme at all SNR and rate values with sufficient spatial degrees of freedom, and in the high SNR high rate regime when the number of spatial degrees of freedom is limited. With bandwidths on the order of a gigahertz in emerging wireless systems, high-resolution analog-to-digital convertors (ADCs) become a power consumption bottleneck. One solution is to employ low resolution one-bit ADCs. In this paper, we analyze the flat fading multiple-input multiple-output (MIMO) channel with one-bit ADCs. Channel state information is assumed to be known at both the transmitter and receiver. For the multiple-input single-output channel, we derive the exact channel capacity. For the single-input multiple-output and MIMO channel, the capacity at infinite signal-to-noise ratio (SNR) is found. We also derive upper bound at finite SNR, which is tight when the channel has full row rank. In addition, we propose an efficient method to design the input symbols to approach the capacity achieving solution. We incorporate millimeter wave channel characteristics and find the bounds on the infinite SNR capacity. The results show how the number of paths and number of receive antennas impact the capacity. Analog-to-digital converters (ADCs) stand for a significant part of the total power consumption in a massive multiple-input multiple-output (MIMO) base station. One-bit ADCs are one way to reduce power consumption. This paper presents an analysis of the spectral efficiency of single-carrier and orthogonal-frequency-division-multiplexing (OFDM) transmission in massive MIMO systems that use one-bit ADCs. A closed-form achievable rate, i.e., a lower bound on capacity, is derived for a wideband system with a large number of channel taps that employ low-complexity linear channel estimation and symbol detection. Quantization results in two types of error in the symbol detection. The circularly symmetric error becomes Gaussian in massive MIMO and vanishes as the number of antennas grows. The amplitude distortion, which severely degrades the performance of OFDM, is caused by variations between symbol durations in received interference energy. As the number of channel taps grows, the amplitude distortion vanishes and OFDM has the same performance as single-carrier transmission. A main conclusion of this paper is that wideband massive MIMO systems work well with one-bit ADCs.