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Uplink Achievable Rate for Massive MIMO with Low-Resolution ADC
Li Fan, Shi Jin, Chao-Kai Wen, Haixia Zhang
TL;DR
The paper addresses uplink-rate analysis for massive MIMO receivers using finite-precision ADCs, whose low resolution reduces achievable rate. It applies AQNM with MRC to derive an approximate rate expression and studies antenna scaling, ADC resolution, and power scaling. The results show that increasing the number of base-station antennas can compensate low-resolution ADC performance loss, supporting economical low-resolution ADCs.
Problem
Massive MIMO’s large antenna arrays increase hardware cost and power consumption, motivating analysis of uplink rates with low-resolution ADCs.
Method
The paper uses AQNM with an MRC receiver and perfect CSI to derive a tight approximate achievable uplink-rate expression.
Results
Increasing the number of base-station antennas can compensate for the performance loss caused by low-resolution ADCs.
Takeaways & Limitations
Low-resolution ADCs, including 1–2-bit ADCs, are supported as a feasible and energy-efficient option for massive MIMO systems.
Abstract
from arXiv · showhide
In this letter, we derive an approximate analytical expression for the uplink achievable rate of a massive multi-input multi-output (MIMO) antenna system when finite precision analog-digital converters (ADCs) and the common maximal ratio combining technique are used at the receivers. To obtain this expression, we treat quantization noise as an additive quantization noise model. Considering the obtained expression, we show that low-resolution ADCs lead to a decrease in the achievable rate but the performance loss can be compensated by increasing the number of receiving antennas. In addition, we investigate the relation between the number of antennas and the ADC resolution, as well as the power-scaling law. These discussions support the feasibility of equipping highly economical ADCs with low resolution in practical massive MIMO systems.
I. INTRODUCTION
Massive MIMO can improve wireless capacity but its many antennas raise hardware cost and power consumption, motivating low-resolution ADCs. The letter uses AQNM with MRC to analyze uplink rate and the roles of antenna count, ADC resolution, and transmit-power scaling.
- Massive MIMO uses hundreds of base-station antennas to serve relatively few users on the same time-frequency channel.
- Low-resolution ADCs are studied because the large antenna count substantially increases hardware cost and power consumption.The considered ADC resolutions can be as low as 1–3 bits.
- AQNM models quantization noise as additive and independent noise, providing a tractable approximation for analyzing quantized systems.The model is approximate but widely used because it facilitates analysis and provides insights.
- The letter analyzes uplink achievable rate with AQNM and an MRC receiver under perfect CSI at the base station.It provides a tight approximate expression valid for an arbitrary number of antennas and examines antenna count, ADC resolution, and power scaling.
II. SYSTEM MODEL
The system models a multi-user uplink with an M-antenna base station, N single-antenna users, fading channels, and AQNM-based quantizer outputs. The model defines channel, noise, quantization, and fading parameters used for the subsequent MRC rate analysis.
- The uplink contains an M-antenna base station serving N single-antenna users over one time-frequency resource.The received signal is represented by an M-dimensional vector.
- The received-signal model uses transmit power p_u, channel matrix G, symbol vector x, and additive Gaussian noise n.G is M × N, x is N × 1, and n follows a circularly symmetric complex Gaussian distribution with identity covariance.
- The channel coefficient g_mn models independent fast fading, geometric attenuation, and log-normal shadow fading.It connects user n to base-station antenna m.
- Each coefficient factors fast fading h_mn and large-scale fading β_n, with β_n constant across the antenna array.
- AQNM represents quantizer outputs using gain α = 1 − ρ and additive Gaussian quantization noise n_q uncorrelated with the received vector.The quantizer input is assumed Gaussian, with b denoting the number of quantization bins.
III. ANALYSIS OF ACHIEVABLE UPLINK RATE
The section derives a tractable approximation for the ergodic uplink rate of an MRC receiver with quantized observations, then analyzes antenna count, ADC resolution, and transmit-power effects.
- Rate approximation: Theorem 1 approximates the nth user's achievable uplink rate for quantized MIMO using MRC and perfect CSI.The derivation models the noise-plus-interference term as additive Gaussian noise and evaluates the required expectations through channel-norm statistics.
- Rate approximation: The approximation incorporates the number of antennas M, quantization effect α, and transmit power p_u in the rate expression.Theorem 1 is stated to reveal how these parameters affect rate performance and to include earlier infinite-precision results as special cases.
- ADC resolution: As b →∞ with fixed p_u and M, the approximation reduces to the previously derived infinite-precision result because quantization error becomes negligible.The quantization effect influences both numerator and denominator, so it cannot be represented only as additional denominator noise.
- Transmit power: As p_u →∞ with fixed b and M, the approximate rate approaches a quantization-bit-dependent constant, so transmit-power increases cannot compensate ADC-induced degradation.The rate also cannot grow without bound because desired signal and multiuser interference powers increase together with p_u.
- Power scaling: With p_u = E_u/M, increasing antenna count permits transmit power to scale as 1/M while maintaining the rate of an SISO system with transmit power αE_u.The result supports power scaling with low-resolution ADCs when the number of antennas grows without limit.
IV. NUMERICAL RESULTS
The simulations validate the rate approximation, examine power scaling with antenna growth, and show that low-resolution ADCs can improve energy efficiency despite lower rates.
- The simulated and analytical uplink achievable rates agree precisely for 1-, 2-, and infinite-bit quantizers.
- With p_u = E_u/M, sum-rate curves eventually saturate as M increases because antenna gains balance reduced transmit power.
- Increasing quantization bits raises sum rate, but the gaps between curves narrow as resolution increases.
- At M = 100, sum rate converges while its growth slows with increasing bits, causing significant energy-efficiency degradation.Energy efficiency is defined as η = BR/P, with P = c_0M2^b + c_1.
V. CONCLUSIONS
The paper derives a tight approximate uplink-rate expression using AQNM to model ADC effects. It concludes that additional BS antennas can compensate for low-resolution ADC performance loss, supporting their feasibility in massive MIMO.
- A tight approximate achievable-uplink-rate expression is derived using AQNM to account for ADC effects.
- Performance loss from low-resolution ADCs can be compensated by increasing the number of BS antennas.