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1-Bit Massive MIMO Transmission: Embracing Interference with Symbol-Level Precoding
Ang Li, Christos Masouros, A. Lee Swindlehurst, Wei Yu
TL;DR
Massive MIMO can improve data rates, but fully digital systems carry substantial hardware and power costs, motivating hardware-limited architectures such as low-resolution DACs. This paper surveys CI-based symbol-level precoding for 1-bit massive MIMO, which designs signals using both data symbols and channel information. It describes how making interference constructive can move received signals farther from constellation decision boundaries and improve performance.
Problem
Fully digital massive MIMO has substantial hardware complexity, cost, and power consumption, motivating hardware-efficient architectures; the paper focuses on 1-bit DAC systems.
Source: §I · p. 1Method
The paper surveys CI-based symbol-level precoding that uses data symbols and channel information to design 1-bit transmit signals and make interference constructive.
Source: B. 1-Bit DAC Transmission: The Scope… · p. 3, B. Signal Design · p. 4Results
Constructive interference can move received signals farther from constellation decision boundaries, leading to improved performance.
Source: A. The Concept of Interference… · p. 4Takeaways & Limitations
The overviewed CI-based solutions offer prominent BER gains and illustrate the potential of interference exploitation for energy- and hardware-efficient massive MIMO.
Source: §V · p. 6CI-based hardware-efficient massive MIMO remains an open and ongoing research topic.
Source: §IV · p. 6
Abstract
from arXiv · showhide
The deployment of large-scale antenna arrays for cellular base stations (BSs), termed as `Massive MIMO', has been a key enabler for meeting the ever-increasing capacity requirement for 5G communication systems and beyond. Despite their promising performance, fully-digital massive MIMO systems require a vast amount of hardware components including radio frequency chains, power amplifiers, digital-to-analog converters (DACs), etc., resulting in a huge increase in terms of the total power consumption and hardware costs for cellular BSs. Towards both spectrally-efficient and energy-efficient massive MIMO deployment, a number of hardware limited architectures have been proposed, including hybrid analog-digital structures, constant-envelope transmission, and use of low-resolution DACs. In this paper, we overview the recent interest in improving the error-rate performance of massive MIMO systems deployed with 1-bit DACs through precoding at the symbol level. This line of research goes beyond traditional interference suppression or cancellation techniques by managing interference on a symbol-by-symbol basis. This provides unique opportunities for interference-aware precoding tailored for practical massive MIMO systems. Firstly, we characterize constructive interference (CI) and elaborate on how CI can benefit the 1-bit signal design by exploiting the traditionally undesired multi-user interference as well as the interference from imperfect hardware components. Subsequently, we overview several solutions for 1-bit signal design to illustrate the gains achievable by exploiting CI. Finally, we identify some challenges and future research directions for 1-bit massive MIMO systems that are yet to be explored.
I. INTRODUCTION
Massive MIMO offers data-rate gains through spatial multiplexing, but fully digital deployments require costly, power-intensive hardware. Low-resolution DACs, especially 1-bit DACs, are a hardware-efficient direction that retains massive MIMO’s degrees of freedom while making precoding difficult.
I. INTRODUCTION
- Fully digital massive MIMO requires many RF chains, power amplifiers, and high-resolution DACs, increasing base-station hardware complexity, cost, and power consumption.The power burden is especially significant on the downlink, where power amplifiers and DACs account for much of base-station power dissipation.Source: §I · p. 1
- Low-resolution DACs are being studied for hardware-efficient massive MIMO in both sub-6 GHz and millimeter-wave bands.The paper focuses on this approach among options that also include analog-only, hybrid analog-digital, and constant-envelope transmission.Source: §I · p. 1
- With two DACs per RF chain, 1-bit DACs can reduce hardware cost, complexity, and power while retaining massive MIMO degrees of freedom and enabling constant-envelope outputs.The per-antenna transmit signal must be selected from {±1 ± j}, making 1-bit precoding highly nonconvex.Source: §I · p. 1
A. Classical 1-Bit DAC Transmission: MSE-Based Approaches
Classical 1-bit precoding ranges from low-complexity linear methods to nonlinear symbol-level optimization. The methods trade computational cost against error-rate performance, while constellation range affects the difficulty of 1-bit signal design.
A. Classical 1-Bit DAC Transmission: MSE-Based Approaches
- Linear zero-forcing and MSE-based precoding have the lowest computational complexity, but perform poorly because block-level designs cannot compensate for severe 1-bit signal distortion.These methods use a closed-form precoding matrix over a transmission block with a constant channel.Source: A. Classical 1-Bit DAC Transmission:… · p. 2
- Symbol-level methods use both channel state information and data symbols to design transmitted signals, with approaches including C1PO, C2PO, semidefinite relaxation, sphere decoding, and QAM SER minimization,,.The cited work reports C1PO as superior to 1-bit linear approaches and presents C2PO as a lower-complexity alternative for very large systems.Source: A. Classical 1-Bit DAC Transmission:… · p. 2
- 80% of the infinite-resolution dynamic range at the user side makes 1-bit precoder design considerably easier, allowing heuristic greedy and exhaustive search methods to do well as antenna arrays grow.The 1-bit antenna signals are restricted to {±1 ± j}.Source: A. Classical 1-Bit DAC Transmission:… · p. 2
- Nonlinear 1-bit precoding offers significant error-rate improvements over linear closed-form methods, but requires iterative optimization at the symbol rate.Table I is identified as a summary of representative linear and nonlinear schemes; its caption does not specify individual table entries.Source: A. Classical 1-Bit DAC Transmission:… · p. 2, Table I · p. 3
B. 1-Bit DAC Transmission: The Scope for Interference Exploitation
The section argues that suppressing all interference is not optimal for symbol-level 1-bit precoding. It frames constructive and destructive interference characterization as a basis for CI-based designs tailored to 1-bit massive MIMO.
B. 1-Bit DAC Transmission: The Scope for Interference Exploitation
- At symbol level, MSE-based designs that suppress all interference are no longer optimal because some interference can be beneficial.The paper identifies both multiuser interference and interference introduced by 1-bit quantization as opportunities for exploitation.Source: B. 1-Bit DAC Transmission: The Scope… · p. 3
- The paper overviews CI-based symbol-level precoding for 1-bit massive MIMO, first characterizing CI and then discussing several CI-based 1-bit solutions.Source: B. 1-Bit DAC Transmission: The Scope… · p. 3
II. CI CHARACTERIZATION
This section introduces constructive interference and proceeds to CI signal design for downlink 1-bit massive MIMO.
II. CI CHARACTERIZATION
- The section introduces the concept of constructive interference.Source: §II · p. 3
- The section proceeds from the CI concept to signal design for downlink 1-bit massive MIMO.Source: §II · p. 3
A. The Concept of Interference Exploitation
Constructive interference (CI) pushes received symbols farther from their constellation decision boundaries, improving their separation from decoding thresholds. Symbol-level precoding can shape interference to make it constructive, so minimizing mean-squared error (MSE) is not always the right objective.
A. The Concept of Interference Exploitation
- For QPSK, CI is interference that pushes the received symbol farther from the real and imaginary decision axes; in the BPSK example, ρ < 0 moves the received symbol farther from its decision boundary.With s1 = 1, s2 = −1, and h1 = 1, the received signal is 1 − ρ; when ρ < 0, it exceeds 1.Source: A. The Concept of Interference… · pp. 3–4
- Figure 2 contrasts the CI metric with MSE, which can be suboptimal when interference is shaped to aid decoding rather than suppressed.The paper frames CI in the context of known interference and data available at the base station.Source: A. The Concept of Interference… · pp. 3–4, Figure 2 · p. 4
- Symbol-level precoding controls interfering signals’ magnitude and phase so they can push each user’s received signal into a constructive constellation region.This moves received signals farther from decision boundaries and can improve performance.Source: A. The Concept of Interference… · p. 4
B. Signal Design
CI-based signal design uses symbol-level precoding to push received symbols away from their decision boundaries. It uses modulation-specific constructive regions and exploits both multi-user interference and interference introduced by 1-bit DAC quantization.
B. Signal Design
- CI-based signal design pushes received symbols away from their decision boundaries, increasing received SINR and improving receiver performance.The approach exploits interference rather than suppressing it.Source: B. Signal Design · p. 4
- The constructive region depends on modulation; symbol-level precoding uses data symbols and CSI to make all users’ interfering signals constructive simultaneously.For BPSK, an interfering signal is constructive when its real part has the same sign as the intended signal’s real part.Source: B. Signal Design · p. 4
- In 1-bit precoding, both inherent inter-user interference and artificial interference from coarse DAC quantization can be made constructive.Symbol-level design can use transmit power more judiciously than block-level interference suppression.Source: B. Signal Design · p. 4
III. CI-BASED 1-BIT PRECODING SOLUTIONS
The reviewed CI-based 1-bit precoders include branch-and-bound and zero-power-allocation designs, as well as a linear-programming approach. The 1-bit LP method reports the best BER among the benchmark schemes in its stated massive-MIMO scenario.
III. CI-BASED 1-BIT PRECODING SOLUTIONS
- Other reviewed CI-based designs include an optimal branch-and-bound solution, limited to small MIMO systems by its computational cost, and a zero-power-allocation approach that improves performance in some scenarios.The two formulations coincide with the symbol-scaling formulation in, although CI is not explicitly named in those works.Source: §III · p. 4
A. Linear Programming Based Solution
- ‘1-Bit LP’ exhibits the best BER among the benchmark schemes, with less than 3 dB SNR loss versus unquantized ZF at a 10−5 BER target.Figure 3 compares CI- and MSE-based 1-bit precoding under standard uncorrelated Rayleigh fading; the reported scenario uses K = 8 users and NT = 128 transmit antennas.Source: Figure 3 · p. 5, A. Linear Programming Based Solution · p. 5
- The CI-based 1-bit LP achieves the best BER among benchmarked methods in K=8, NT=128 Rayleigh channels, with under 3 dB SNR loss versus unquantized ZF at BER target 10−5.Source: A. Linear Programming Based Solution · p. 5
B. Symbol Scaling Based Solution
The 1-bit symbol-scaling scheme decomposes data symbols and transmit signals along decision boundaries, then allocates and refines the transmit-signal entries. It offers a favorable performance-complexity tradeoff in the reported comparison.
B. Symbol Scaling Based Solution
- The three-stage 1-bit SS scheme allocates some precoded entries from data symbols and CSI, assigns residual entries using two criteria, then greedily refines signs to improve CI.Its iterative algorithm avoids solving an optimization problem.Source: B. Symbol Scaling Based Solution · p. 5
- At K = 8 users and 10 dB transmit SNR, 1-bit SS requires only 10% of the complexity of existing 1-bit algorithms at the cost of slight BER losses.The comparison varies the number of transmit antennas from 32 to 128.Source: B. Symbol Scaling Based Solution · p. 5
C. P-BB Based Near-Optimal Solution
The partial branch-and-bound method offers near-optimal 1-bit precoding with improved BER over existing designs, while the article identifies DAC-resolution tradeoffs as an open research direction.
C. P-BB Based Near-Optimal Solution
- P-BB yields more than 4 dB SNR gain for 64QAM and 6 dB for 256QAM over existing 1-bit precoding designs.It leaves entries already satisfying the 1-bit constraint unchanged and applies branch-and-bound only to entries that violate it.Source: C. P-BB Based Near-Optimal Solution · p. 5
IV. OPEN CHALLENGES AND FUTURE WORKS
- CI-based hardware-efficient massive MIMO remains an open research topic for 5G and future wireless systems.Source: §IV · p. 6
A. CI Precoding for Different DAC Architectures
- An analytical study is needed to determine DAC bit resolution across low, medium, and high SNR while balancing BER, hardware efficiency, and energy efficiency.The passage notes that using more than one bit per dimension can improve error-rate performance and approach the unquantized case, at increased hardware cost.Source: A. CI Precoding for Different DAC… · p. 6
B. Task-Based Quantization
Task-based quantization tailors quantizer design to downstream processing, while future few-bit-DAC work must account for nonlinear power-amplifier distortion when signals are not constant-envelope.
B. Task-Based Quantization
- Task-based quantization designs for the system’s specific task and considers post-reception signal processing, rather than only accurately representing the underlying signal.The passage relates this approach to CI-based 1-bit precoding and points to its potential for downlink data transmission.Source: B. Task-Based Quantization · p. 6
C. Effect of Nonlinear Power Amplifiers
- Near-saturation nonlinear power-amplifier operation generally works well with constant-envelope transmissions, including CE precoding and 1-bit DACs.Source: C. Effect of Nonlinear Power Amplifiers · p. 6
- With few-bit DACs and non-constant-envelope signals, increased PAPR may cause in-band distortion and out-of-band radiation, motivating joint design of DAC resolution, precoded signals, and peak power.The passage calls for communication models that account for nonlinear-PA signal distortion in future higher-order-DAC work.Source: C. Effect of Nonlinear Power Amplifiers · p. 6
D. Machine Learning Based 1-Bit CI Transmitter
The article describes emerging neural-network approaches to 1-bit precoding that can incorporate channel uncertainty during training. It concludes that CI exploitation offers BER gains, while significant open challenges remain.
D. Machine Learning Based 1-Bit CI Transmitter
- Autoencoder-based neural networks can incorporate channel uncertainty during training and jointly design the encoder, decoder, and constellation for changing channel conditions.The passage describes this data-driven direction as emerging in 1-bit precoding.Source: D. Machine Learning Based 1-Bit CI… · p. 6
V. CONCLUSIONS
- The overviewed CI-based solutions offer prominent BER gains in hardware-constrained massive MIMO, but open challenges remain.The conclusion describes manipulating downlink interference, including interference artificially introduced by 1-bit systems, to benefit system performance.Source: §V · p. 6