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On the Spectral Efficiency of Massive MIMO Systems with Low-Resolution ADCs
Jiayi Zhang, Linglong Dai, Shengyang Sun, Zhaocheng Wang
TL;DR
Massive MIMO’s high-resolution ADCs create substantial power-consumption costs, motivating low-resolution ADCs for uplink operation over Rician fading channels. Using AQNM and MRC, the paper derives SE expressions for perfect and imperfect CSI and analyzes how resolution, the Rician K-factor, and antenna count affect SE. The results indicate that low-resolution ADCs can still provide satisfying SE, including fairly good performance with 2-bit ADCs when the Rician K-factor is small.
Problem
High-speed, high-resolution ADCs impose heavy power-consumption costs, while prior low-resolution-ADC analyses largely assumed Rayleigh fading and one-bit resolution rather than Rician channels.
Method
The paper models quantization with AQNM and derives uplink SE expressions for MRC receivers under perfect and imperfect CSI in Rician fading channels.
Results
The derived expressions characterize SE dependence on ADC resolution, Rician K-factor, and base-station antenna count for both perfect and imperfect CSI.
Takeaways & Limitations
Massive MIMO can achieve fairly good performance with 2-bit-resolution ADCs when the Rician K-factor is small.
Abstract
from arXiv · showhide
The low-resolution analog-to-digital convertor (ADC) is a promising solution to significantly reduce the power consumption of radio frequency circuits in massive multiple-input multiple-output (MIMO) systems. In this letter, we investigate the uplink spectral efficiency (SE) of massive MIMO systems with low-resolution ADCs over Rician fading channels, where both perfect and imperfect channel state information are considered. By modeling the quantization noise of low-resolution ADCs as an additive quantization noise, we derive tractable and exact approximation expressions of the uplink SE of massive MIMO with the typical maximal-ratio combining (MRC) receivers. We also analyze the impact of the ADC resolution, the Rician $K$-factor, and the number of antennas on the uplink SE. Our derived results reveal that the use of low-cost and low-resolution ADCs can still achieve satisfying SE in massive MIMO systems.
I. INTRODUCTION
Massive MIMO improves spectral efficiency but its many high-speed, high-resolution ADCs impose substantial power costs. The paper therefore studies low-resolution ADCs for uplink massive MIMO over Rician fading channels.
- Motivation: ADC power consumption scales exponentially with resolution and linearly with sampling rate, making high-speed, high-resolution converters costly in massive MIMO.A typical flash ADC with b-bit resolution and sampling frequency fs performs fs2^b conversion steps per second.
- Motivation: Low-resolution ADCs, typically using 1–3 bits, are proposed as an alternative to reduce power consumption, although prior work studied limited channel and resolution settings.Earlier studies primarily considered Rayleigh fading channels and one-bit resolution.
- Research gap: Rayleigh fading is inadequate for line-of-sight-dominated propagation, motivating analysis under the more suitable Rician fading model.The prior literature cited in the paper focused on Rayleigh fading, while practical LoS-dominated scenarios can be better represented by Rician fading.
- Contributions: The paper derives uplink SE expressions for low-resolution ADCs with perfect and imperfect CSI and examines ADC resolution, Rician K-factor, antenna count, and power scaling.The analysis uses the additive quantization noise model and includes exact limits and approximations.
II. SYSTEM MODEL
The system comprises N single-antenna users communicating with an M-antenna base station, with channels modeled by large-scale fading and Rician small-scale fading. Low-resolution ADCs are represented through an additive quantization-noise model.
- System configuration: N single-antenna users simultaneously transmit to an M-antenna base station over shared time-frequency resources.The uplink received vector has dimension M × 1.
- Channel model: The channel matrix is G = HD1/2, where D models geometric attenuation and shadow fading and H contains line-of-sight and scattered components.The deterministic component H̄ represents LoS signals, while Hω represents Rayleigh-distributed scattered signals.
- Channel model: The Rician channel model uses user arrival angles and a diagonal matrix Ω whose elements are the users’ Rician K-factors.The steering expression depends on wavelength and antenna interelement spacing through k = 2πd/λ.
- ADC model: AQNM approximates quantization error through a linear gain, with κ = 1−ρ, and models the resulting quantization noise covariance.The parameter ρ represents the proportionality between quantizer input variance and quantization-error variance.
- ADC model: The quantization-noise covariance analysis treats G as a fixed channel realization.This assumption is stated when forming the covariance matrix of the quantization noise.
III. UPLINK SPECTRAL EFFICIENCY
The paper derives uplink SE for MRC receivers under perfect and imperfect CSI. The imperfect-CSI analysis uses pilot transmission and MMSE channel estimation, while the perfect-CSI case directly uses the channel matrix.
- Receiver model: MRC is used because it performs fairly well for massive MIMO systems.The receiver matrices are A = G for perfect CSI and  = Ĝ for imperfect CSI.
- Perfect CSI: Under perfect CSI, the receiver multiplies the quantized received vector by AH to obtain the MRC output and derive each user’s SE.The derivation separately expresses the nth-user output and its interference-plus-noise variance.
- Imperfect CSI: Under imperfect CSI, transmission uses a coherence interval T with τ pilot symbols, pilot power pp ≜ τpu, and an MMSE estimate Ĝ of G.The channel-estimation error Ξ = Ĝ−G is assumed independent of Ĝ.
- Imperfect CSI: The imperfect-CSI analysis derives the nth user’s uplink SE using the estimated channel and channel-estimation error statistics.The resulting SE expression is presented after specifying the variance of the estimation error.
A. Perfect CSI
For perfect CSI, Lemma 1 gives an approximated uplink SE for MRC receivers in Rician fading with low-resolution ADCs. The analysis identifies how ADC resolution, the Rician K-factor, and antenna count affect SE, including power-scaling behavior.
- Perfect-CSI SE expression: Lemma 1 gives the approximated SE of the nth user for massive-MIMO MRC with low-resolution ADCs, Rician fading, and perfect CSI.The result is derived from the SE expression by evaluating its expectations and substituting the resulting covariance term.
- Perfect-CSI SE expression: Mixed-ADC architecture can estimate channels antenna-by-antenna in a round-robin manner, omitting low-resolution ADC effects during channel estimation.
- Parameter effects: The general SE result reveals the effects of ADC resolution, the Rician K-factor, and the number of BS antennas, with SE increasing as resolution bits increase.
- Parameter effects: For infinite precision, the expression coincides with the ideal-ADC result; setting Kn = Ki = 0 reduces it to the Rayleigh-fading case.
- Power scaling: Under transmit-power scaling proportional to 1/M, the SE retains a non-zero constant coefficient κ and improves with larger κ, corresponding to more quantization bits.
B. Imperfect CSI
For imperfect CSI, the paper derives an approximated uplink SE expression for MRC receivers and analyzes its dependence on ADC resolution, Rician K-factor, and antenna scaling.
- B. Imperfect CSI: Lemma 2 gives the approximated uplink SE for massive MIMO with low-resolution ADCs, MRC receivers, and imperfect CSI.The derivation uses channel estimates and their estimation errors.
- B. Imperfect CSI: The imperfect-CSI result reduces to the full-resolution result when ρ = 0.This establishes consistency with the corresponding ideal-ADC expression.
- B. Imperfect CSI: The asymptotic interference-plus-noise term depends on both the Rician K-factor and the transmit-power scaling exponent α.For Kn = 0 and α = 1/2, the relevant expression tends to a constant.
- B. Imperfect CSI: The derived expressions reduce to previously known infinite-resolution results for the relevant asymptotic cases.This comparison is stated for expressions (24) and (25).
- B. Imperfect CSI: Increasing κ, which corresponds to higher ADC resolution, monotonically increases the uplink SE.For very strong LoS components, the imperfect-CSI result converges to the perfect-CSI limit.
IV. NUMERICAL RESULTS
Numerical results validate the analytical expressions and examine how ADC resolution, Rician fading, antenna count, and transmit-power scaling affect uplink SE.
- IV. NUMERICAL RESULTS: The analytical SE approximation closely matches simulations across the considered numbers of BS antennas and ADC resolutions.Figure 1 compares simulated and analytical SEs for K = 10 dB and N = 10.
- IV. NUMERICAL RESULTS: With 2-bit ADCs, the SE nearly approaches the ideal-ADC performance.The comparison considers b = 1, 2, and ∞.
- IV. NUMERICAL RESULTS: For fixed pu, SE grows without bound as M increases, whereas variable-pu curves eventually saturate.This behavior is reported in the antenna-scaling comparison.
- IV. NUMERICAL RESULTS: For fixed pu, low-resolution ADC rate loss increases with the Rician K-factor relative to ideal ADCs.Figure 2 uses normalized ideal-ADC SE as the benchmark.
- IV. NUMERICAL RESULTS: For fixed pu, the rate loss is much larger than for variable pu, making SE more vulnerable to larger Rician K-factors.For variable pu with M →∞, SE approaches a fixed value.
V. CONCLUSIONS
The paper derives large-antenna limits and approximations for perfect and imperfect CSI, showing how key system parameters affect uplink SE and identifying favorable 2-bit performance at small Rician K-factors.
- V. CONCLUSIONS: The derived uplink SE limits for perfect and imperfect CSI converge to the same constant as M →∞.The expressions characterize dependence on ADC resolution, Rician K-factor, and BS antenna count.
- V. CONCLUSIONS: Massive MIMO can achieve fairly good performance with 2-bit ADCs when the Rician K-factor is small.This is the paper’s stated practical conclusion.