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Performance Analysis of Mixed-ADC Massive MIMO Systems over Rician Fading Channels
Jiayi Zhang, Linglong Dai, Ziyan He, Shi Jin, Xu Li
TL;DR
Massive MIMO deployment is constrained by the hardware cost and power consumption of large antenna arrays and high-resolution ADCs, while low-resolution ADCs create quantization challenges. The paper derives closed-form approximate uplink-rate expressions for mixed-ADC systems over Rician fading with perfect and imperfect CSI. It shows inverse-antenna power scaling, constant rate limits with increasing Rician K-factor, and favorable rate-energy trade-offs versus ideal- and low-resolution architectures.
Problem
Large massive-MIMO arrays and high-resolution ADCs impose high hardware cost and power consumption, while low-resolution ADCs introduce severe quantization distortion and prior analyses largely considered Rayleigh fading.
Method
The paper derives closed-form approximate achievable-rate expressions for mixed-ADC massive MIMO over Rician fading under perfect and imperfect CSI.
Results
For both CSI cases, user transmit power can scale down by 1/M, and achievable-rate limits converge to a constant as the Rician K-factor increases.
Takeaways & Limitations
Mixed-ADC systems can achieve larger sum rate than ideal-ADC systems with similar hardware cost while reducing signal-processing complexity and power consumption.
Abstract
from arXiv · showhide
The practical deployment of massive multiple-input multiple-output (MIMO) in future fifth generation (5G) wireless communication systems is challenging due to its high hardware cost and power consumption. One promising solution to address this challenge is to adopt the low-resolution analog-to-digital converter (ADC) architecture. However, the practical implementation of such architecture is challenging due to the required complex signal processing to compensate the coarse quantization caused by low-resolution ADCs. Therefore, few high-resolution ADCs are reserved in the recently proposed mixed-ADC architecture to enable low-complexity transceiver algorithms. In contrast to previous works over Rayleigh fading channels, we investigate the performance of mixed-ADC massive MIMO systems over the Rician fading channel, which is more general for the 5G scenarios like Internet of Things (IoT). Specially, novel closed-form approximate expressions for the uplink achievable rate are derived for both cases of perfect and imperfect channel state information (CSI). With the increasing Rician $K$-factor, the derived results show that the achievable rate will converge to a fixed value. We also obtain the power-scaling law that the transmit power of each user can be scaled down proportionally to the inverse of the number of base station (BS) antennas for both perfect and imperfect CSI. Moreover, we reveal the trade-off between the achievable rate and energy efficiency with respect to key system parameters including the quantization bits, number of BS antennas, Rician $K$-factor, user transmit power, and CSI quality. Finally, numerical results are provided to show that the mixed-ADC architecture can achieve a better energy-rate trade-off compared with the ideal infinite-resolution and low-resolution ADC architectures.
I. INTRODUCTION
Massive MIMO improves achievable rate and energy efficiency but becomes costly and power-hungry as antenna counts grow. Mixed-ADC designs reduce ADC resolution while retaining RF chains, yet introduce quantization-related challenges; this paper addresses analysis under Rician fading and imperfect CSI.
- Massive MIMO uses many BS antennas to reduce inter-user interference through simple MRC and ZF processing.
- Large antenna arrays make dedicated RF chains difficult to afford because hardware cost and power consumption increase substantially.
- High-resolution ADCs consume substantial power, with consumption scaling roughly linearly with signal bandwidth and exponentially with quantization bits.
- Low-resolution ADCs can reduce hardware demands while keeping RF chains unchanged, but coarse quantization causes capacity loss, pilot overhead, detection error floors, and complex precoder design.
- Mixed-ADC architectures reserve a small number of high-resolution ADCs, supporting reduced-complexity algorithms and potentially affordable channel estimation.
- Rician fading includes line-of-sight propagation and is more general for relevant massive-MIMO scenarios, but it complicates tractable performance analysis and motivates accounting for imperfect CSI.
B. Contributions
The paper analyzes mixed-ADC massive MIMO over Rician fading with perfect and imperfect CSI, deriving rate approximations and studying power, hardware, and energy-efficiency effects. It identifies inverse-antenna power scaling and favorable rate-energy trade-offs relative to ideal-ADC designs.
- The study derives novel closed-form approximate achievable-rate expressions for mixed-ADC massive MIMO under Rician fading.
- The analysis incorporates both perfect and imperfect CSI and examines effects of antennas, transmit power, quantization bits, high-resolution ADCs, and the Rician K-factor.
- 1/M power scaling lets each user's transmit power decrease as BS antennas grow, for both CSI cases when the Rician K-factor is nonzero.
- Achievable-rate limits converge to a constant, while the limits depend on the high-resolution ADC proportion and total ADC counts.
- The paper quantifies rate-energy-efficiency trade-offs, identifies optimal quantization bits and antenna counts, and finds stronger Rician fading and larger transmit power favorable for mixed-ADC operation.
C. Outline
The paper models a mixed-ADC massive MIMO uplink with Rician fading, partitioning BS antennas between high- and low-resolution ADC pairs. It develops the system, channel, signal, and quantization-noise representations used for subsequent rate and energy-efficiency analyses.
- System model: The system is a single-cell uplink with M BS antennas and N≪M single-antenna users.Each user transmits with power p_u, and x is the transmitted signal vector.
- Receiver architecture: The receiver uses M0 high-resolution ADC pairs and M1 low-resolution ADC pairs across M=M0+M1 receive antennas.The high-resolution ADC proportion is defined as κ=M0/M, with M1=M−M0.
- Channel model: The Rician channel combines a deterministic line-of-sight component with a Rayleigh-distributed scattered component.The Rician K-factor is the ratio of deterministic-component power to scattered-component power.
- Signal model: High-resolution and low-resolution ADC branches are represented by channel matrices G0 and G1, respectively, with AWGN on the high-resolution branch.G0 covers M0 antennas and G1 covers M1 antennas; low-resolution outputs include additive quantization noise under the AQNM.
- Quantization model: The low-resolution ADC model uses a linear gain α=1−ρ and additive Gaussian quantization noise, an approximation stated as accurate at low and medium SNRs.The distortion factor ρ depends on the quantization resolution b and is tabulated for different bit values.
III. ACHIEVABLE RATE
This section derives approximate closed-form uplink achievable-rate expressions for mixed-ADC massive MIMO over Rician fading. The analysis covers both perfect and imperfect CSI using an MRC receiver.
- Rate analysis: Approximate closed-form uplink achievable-rate expressions are derived for both perfect and imperfect CSI.The expressions target mixed-ADC massive MIMO systems over Rician fading channels.
- Receiver: MRC is assumed at the BS because it is simple and near optimal when the number of BS antennas becomes large.
A. Perfect CSI
For perfect CSI, the paper derives an approximate Rician-fading uplink rate under MRC and analyzes its dependence on antennas, fading, ADC resolution, and transmit-power scaling. Strong line-of-sight conditions impose a finite rate limit, while 1/M power scaling remains feasible.
- Rate expression: The perfect-CSI achievable rate is given by a closed-form approximation for the nth user under MRC over Rician fading.The derivation uses large-M approximations of the detected signal and interference-plus-noise terms.
- Parameter effects: The achievable rate increases with the number of BS antennas.
- Rician fading: As the Rician K-factor tends to infinity, the achievable rate approaches a constant, revealing a rate limit in strong LoS scenarios.When α=1, the expression reduces to the corresponding unquantized massive MIMO special case.
- Power scaling: With p_u=E_u/M, the uplink rate converges to log2(1+E_uβ_n(ρκ+α)) as M→∞.The exact limit is independent of the Rician K-factor because of channel hardening, while κ and ρ affect the limit.
- ADC resolution: Increasing the high-resolution ADC proportion κ or the low-resolution ADC quantization gain α improves the achievable rate.The rate is monotonic in α, so higher quantization bits improve performance in the low-resolution ADC branch.
B. Imperfect CSI
For imperfect CSI, the paper derives a closed-form approximate rate under MRC and examines estimation error, Rician fading, and power scaling. The approximation becomes more accurate with more antennas and weaker Rician factors, while CSI errors reduce achievable rate.
- Rate expression: A closed-form approximate achievable-rate expression is derived for mixed-ADC massive MIMO with imperfect CSI over Rician fading.The result applies the MRC receiver and is presented for the nth user.
- Approximation accuracy: The imperfect-CSI rate approximation becomes more accurate as the number of antennas increases and the Rician K-factor decreases.
- CSI quality: Channel estimation error has a detrimental effect on the achievable rate.
- Power scaling: With imperfect CSI, the power-scaling law depends on the user's Rician K-factor, while transmit power can be scaled proportionally to 1/M.For Rayleigh fading, the power reduction is limited to the factor stated in the derived result.
- ADC and LoS effects: The imperfect-CSI rate improves monotonically with either the high-resolution ADC proportion κ or the low-resolution ADC gain α.In very strong LoS scenarios, the imperfect-CSI limit converges to the perfect-CSI limit because channel estimation becomes more robust.
IV. NUMERICAL RESULTS
The numerical study evaluates uplink sum achievable rate and energy efficiency under a uniformly distributed user model with specified pathloss, shadowing, and angular assumptions.
- The simulations and analytical results examine uplink sum achievable rate and energy efficiency.
- The pathloss model uses exponent v = 3.8, with large-scale fading β_n = s_n(r_n/r_min)^−v.
- Shadowing is log-normal with standard deviation δ_s = 8 dB, and user angles are uniform over [−π/2, π/2].
A. Achievable rate
The achievable-rate results compare mixed-ADC configurations across transmit power, quantization resolution, antenna count, Rician K-factor, and CSI conditions. Higher high-resolution ADC proportions improve rates, power scaling with antennas is supported, and rates approach a fixed value as K increases.
- Analytical and simulated curves are very tight in all considered cases, confirming the derived results.
- Achievable rate increases with quantization bits and converges to a limited value with high-resolution ADCs.
- For Rayleigh fading, the mixed-ADC architecture reaches the same sum rate with 5 bits, whereas Rician fading with K = 10 requires more quantization bits.
- Higher proportions of high-resolution ADCs improve achievable rate, while ideal ADCs outperform mixed- and low-resolution ADC architectures.
- With pu = Eu/M, curves eventually saturate as M increases, validating user-power scaling as Eu/M for perfect CSI.
- As K →∞, the sum rate approaches a fixed value, and more high-resolution ADCs enhance overall sum-rate performance.
- At low SNR, architectures have similar rates; as transmit power increases, their gaps become larger, with ideal ADCs achieving superior performance.
B. Energy Efficiency
The paper studies energy efficiency using a total-power model and frames mixed-ADC design as a trade-off between achievable rate, hardware cost, and power consumption.
- Unquantized systems outperform mixed-ADCs in sum rate, but require higher hardware cost and power consumption.
- Energy efficiency is studied for mixed-ADC massive MIMO systems over Rician fading channels.
- The total-power model defines energy efficiency using sum rate R, bandwidth W, and total consumed power P_total.
ADC, P L
Energy-efficiency results show that mixed-ADC systems balance rate and power more effectively than ideal high-resolution systems while retaining advantages over pure low-resolution designs. Quantization resolution, antenna count, Rician K-factor, and CSI quality determine the operating trade-offs.
- Mixed-ADC energy efficiency is significantly higher than ideal high-resolution ADCs, while pure low-resolution ADCs achieve the highest energy efficiency.
- Energy efficiency decreases as the high-resolution ADC proportion κ increases, while mixed-ADCs provide higher achievable rate than low-resolution ADCs.
- Partial high-resolution ADCs make channel estimation more tractable and enable relatively high energy efficiency with better achievable rate.
- With around 30 BS antennas, the mixed-ADC architecture achieves optimal energy efficiency for the selected system parameters.
- Energy efficiency rises only to a certain resolution because rate grows sub-linearly with bits while ADC power increases exponentially with b.
- Stronger Rician fading yields a larger operating region, whereas imperfect CSI produces a smaller region whose gap narrows as user transmit power increases from 0 dB to 10 dB.
V. CONCLUSIONS
The paper analyzes mixed-ADC massive MIMO over Rician fading and derives approximate uplink-rate results for perfect and imperfect CSI. It reports favorable rate, power-scaling, and energy-efficiency properties, including convergence as the Rician K-factor grows.
- Closed-form approximate uplink achievable-rate expressions are derived for mixed-ADC massive MIMO over Rician fading with perfect and imperfect CSI.
- With similar hardware cost, mixed-ADC architecture can achieve a larger sum rate than the ideal-ADC architecture.
- User transmit power can be cut down by a factor of 1/M while obtaining a desirable rate in both perfect- and imperfect-CSI cases.
- For both perfect and imperfect CSI, the achievable-rate limit converges to a constant as K →∞.
- The mixed-ADC architecture can provide a large operating region with few high-resolution ADCs and achieve more energy efficiency in stronger LoS scenarios.
- The results are general enough to include previously reported results as special cases, supporting practical massive MIMO with small power consumption.