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On the Impact of Hardware Impairments on Massive MIMO
Ulf Gustavsson, Cesar Sanchéz-Perez, Thomas Eriksson, Fredrik Athley, Giuseppe Durisi, Per Landin, Katharina Hausmair, Christian Fager, Lars Svensson
TL;DR
The paper examines how hardware impairments affect massive MU-MIMO, where large arrays require inexpensive, power-efficient hardware. It uses statistical and deterministic models and reports findings on coupling, low-resolution DACs, and dithering.
Problem
Massive MU-MIMO’s projected efficiency and capacity gains rely on large arrays, but the required inexpensive, power-efficient hardware may introduce impairments that affect system performance.
Source: §I · p. 1Method
The paper studies power-amplifier distortion and DAC quantization noise in a single-cell, multiuser system using stochastic and deterministic hardware models.
Source: §I · p. 1, C. Deterministic Behavioral Models · p. 2Results
Simulations characterize mutual-coupling distortion’s dependence on channel correlation, while low-resolution DACs maintain low EVM and controlled emissions, and null-space dithering improves per-user link quality with fewer DAC bits.
Source: §VI · p. 7Takeaways & Limitations
The results suggest stochastic models remain useful for massive MU-MIMO analysis and that hardware requirements can be relaxed in these systems.
Source: §VI · p. 7The study examines a single-cell scenario with multiple users.
Source: §I · p. 1
Abstract
from arXiv · showhide
Massive multi-user (MU) multiple-input multiple-output (MIMO) systems are one possible key technology for next generation wireless communication systems. Claims have been made that massive MU-MIMO will increase both the radiated energy efficiency as well as the sum-rate capacity by orders of magnitude, because of the high transmit directivity. However, due to the very large number of transceivers needed at each base-station (BS), a successful implementation of massive MU-MIMO will be contingent on of the availability of very cheap, compact and power-efficient radio and digital-processing hardware. This may in turn impair the quality of the modulated radio frequency (RF) signal due to an increased amount of power-amplifier distortion, phase-noise, and quantization noise. In this paper, we examine the effects of hardware impairments on a massive MU-MIMO single-cell system by means of theory and simulation. The simulations are performed using simplified, well-established statistical hardware impairment models as well as more sophisticated and realistic models based upon measurements and electromagnetic antenna array simulations.
I. INTRODUCTION
The introduction weighs massive MU-MIMO’s projected capacity and efficiency gains against the hardware demands of large arrays. It motivates examining power-amplifier distortion and DAC quantization noise in a single-cell, multiuser system.
I. INTRODUCTION
- Massive MU-MIMO has been claimed to increase radiated power efficiency by thousands and multiply sum-rate capacity tens of times through spatial focusing and user separation.These gains are presented as claims based mainly on theoretical analysis,.Source: §I · p. 1
- Common stochastic impairment models assume transmit waveforms and impairments are uncorrelated, although power-amplifier distortion, phase noise, and quantization noise depend strongly on the waveform.This motivates more refined analyses.Source: §I · p. 1
- Standard compensation methods such as digital predistortion, and phase-noise estimation may be too complex for massive arrays.The introduction also identifies antenna-port mutual coupling as a source of added power-amplifier distortion.Source: §I · p. 1
- Although output power per antenna falls as antenna count rises, baseband and converter power grows linearly with array size, while fewer converter bits increase quantization noise.Lower digital resolution can reduce converter power consumption according to Walden’s figure of merit.Source: §I · p. 1
- The paper examines power-amplifier distortion and DAC quantization noise at a massive MU-MIMO base station in a single-cell, multiuser scenario under different channel conditions.The introduction identifies these as two key impairments for study.Source: §I · p. 1
II. HARDWARE IMPAIRMENT MODELS
The paper reviews stochastic impairment models and presents deterministic behavioral models for comparative simulations. The additive stochastic model is analytically tractable, but its accuracy is questionable when impairments depend on signal amplitude.
II. HARDWARE IMPAIRMENT MODELS
- The paper reviews stochastic impairment models and presents a more accurate deterministic model for comparative simulations.The deterministic model is used in Section IV.Source: §II · p. 2
A. Additive Stochastic Impairment Models
- The additive stochastic model treats residual impairments after compensation as additive Gaussian noise, with impairment covariance proportional to the diagonal of the transmit-signal covariance matrix.Its normalization constant ensures the nonlinearities add no energy, as dictated by the Manley-Rowe relation.Source: A. Additive Stochastic Impairment Models · p. 2
- Because this model depends on the transmit signal only through its covariance, it is analytically tractable but may be inaccurate for amplitude-dependent hardware impairments.This motivates the multiplicative stochastic models.Source: A. Additive Stochastic Impairment Models · p. 2
B. Multiplicative Stochastic Impairment Models
The multiplicative stochastic approach models hardware errors as amplitude and phase variations, making the error amplitude-dependent. The paper notes that this better reflects some impairments, while quantization noise remains additive and signal-dependent.
B. Multiplicative Stochastic Impairment Models
- The multiplicative stochastic approach represents impairments as amplitude and phase errors, yielding an amplitude-dependent error term.The model includes a normalization constant to preserve energy.Source: B. Multiplicative Stochastic… · p. 2
- This approach appears more suitable than the additive model for power-amplifier distortion and phase noise because both are amplitude-dependent.Source: B. Multiplicative Stochastic… · p. 2
- Data-converter quantization noise is additive and strongly signal-dependent, unlike the amplitude-dependent error term modeled by the multiplicative approach.Source: B. Multiplicative Stochastic… · p. 2
- Both stochastic modeling approaches are simplified and may not fully capture hardware-impairment effects, motivating more refined deterministic behavioral models.Source: B. Multiplicative Stochastic… · p. 2
C. Deterministic Behavioral Models
The deterministic behavioral models cover power amplifiers, antenna arrays, and data converters, supporting impairment simulations and checks of stochastic-model accuracy. The power-amplifier and antenna-array modeling accounts for coupling effects that conventional PA models miss.
C. Deterministic Behavioral Models
- The deterministic behavioral models cover power amplifiers, antenna arrays, and data converters to simulate impairment impacts and assess stochastic-model accuracy.Source: C. Deterministic Behavioral Models · p. 2
1) The Power Amplifier and Antenna Array Models:
- Conventional Volterra-series and memory-polynomial PA models describe 50 Ω RF amplifiers but do not capture mismatch or mutual coupling.Source: 1) The Power Amplifier and Antenna… · p. 2
- The paper uses a dual-input PA model combining the input with a coupled signal from other antennas, a strategy verified by wideband load-pull measurements.The array far field is formed by superposing element patterns; the antenna model uses HFSS-generated S-parameters to represent coupling across array configurations.Source: 1) The Power Amplifier and Antenna… · pp. 2–3
2) Data Converter Models:
The section specifies the converter and simulation assumptions, then defines received EVM and unwanted space-frequency emissions as performance metrics.
2) Data Converter Models:
- Data converters use uniform quantization with ideal timing, a predefined bit depth and dynamic range, hardlimiting above that range, and Cartesian quantization for complex signals.Source: 2) Data Converter Models · p. 3
III. SIMULATION SETUP AND PERFORMANCE METRICS
- Simulations use single-carrier QAM with spatial multiplexing and oversampled complex baseband to analyze nonlinear PA distortion.Source: §III · p. 3
A. Error Vector Magnitude
- Average user received EVM is a comprehensive metric because it accounts for noise, distortion, and interference while removing constant gain and phase errors.Source: A. Error Vector Magnitude · p. 3, §III · p. 3
B. A Metric for Unwanted Spatial Emissions
- Adjacent space-frequency leakage ratio (ASLR) integrates transmitted far-field power over space and frequency around the intended user, with bandwidth and angle bounds defining the regions.Source: B. A Metric for Unwanted Spatial… · p. 3
C. The Channel Model
The Rice channel model represents mixtures of line-of-sight and rich scattering. Its κ-factor and user placement allow the simulations to vary channel correlation.
C. The Channel Model
- The Rice model can represent mixtures ranging from line-of-sight to rich scattering through its κ-factor.Source: C. The Channel Model · p. 3
- The IID channel component is uncorrelated, while the LOS vectors are derived from user placement relative to the base station.Source: C. The Channel Model · p. 3
- Increasing κ and placing users closer together increases channel-vector correlation.Source: C. The Channel Model · p. 3
D. The Pre-coding Scheme
The simulations use RZF precoding with perfect channel and SNR knowledge. The coupling-related EVM impact depends on channel correlation and antenna spacing, and weakens in Rayleigh channels for sufficiently large arrays.
D. The Pre-coding Scheme
- All simulations use RZF precoding and assume perfect base-station knowledge of the channel matrix and SNR.Source: D. The Pre-coding Scheme · p. 4
A. Amplifier Distortion and Mutual Coupling
- The analysis uses a memoryless PA model; as M grows, the residual distortion term tends to zero if its correlation with the channel coefficient vanishes, while the leading coefficient is independent of M.Source: A. Amplifier Distortion and Mutual… · p. 4
- With κ = 100 and closely spaced users, decreasing antenna spacing increases coupling and sharply raises average received EVM, while array size has little impact at larger spacings.Source: Figure 1 · p. 4, A. Amplifier Distortion and Mutual… · p. 4
- For a 64-element array, reducing κ from 100 to 1 decreases EVM sensitivity to increased mutual coupling as channel correlation falls.Source: Figure 2 · p. 4, A. Amplifier Distortion and Mutual… · p. 4
- In a Rayleigh channel (κ = 0), average received EVM appears invariant to mutual coupling for a sufficiently large number of antenna elements.Source: Figure 3 · p. 5, A. Amplifier Distortion and Mutual… · p. 5
B. DAC Resolution
The section examines how DAC resolution affects received EVM and unwanted emissions. It identifies a scenario-dependent resolution threshold beyond which extra bits do not lower average received EVM.
B. DAC Resolution
- Lower-resolution DACs may reduce converter power consumption, while massive MIMO's degrees of freedom may help overcome the loss in resolution.Source: B. DAC Resolution · p. 5
- The study considers 2–8 bits per DAC and transmit chain, and evaluates average received EVM across array sizes M ∈ [25, 225].Source: B. DAC Resolution · p. 5
- Beyond a threshold, adding DAC resolution does not lower average received EVM; the threshold is expected to depend on the scenario, including LOS/NLOS conditions and SNR.Source: B. DAC Resolution · p. 5
C. A Novel Approach to Dithering in MIMO Systems
Independent dithers average out through the channel as the array grows, while null-space projection can enforce zero received dithering for any array size under perfect BS channel knowledge.
C. A Novel Approach to Dithering in MIMO Systems
- Independent uniform dithers cancel as M grows large over an IID Rayleigh channel, with Hε → 0 as M → ∞.Fig. 5 presents the convergence rates of Hε and HP⊥.Source: C. A Novel Approach to Dithering in… · p. 5, Figure 5 · p. 5
- Fig. 4 plots average received EVM against array size M and transmitter DAC bits, using DAC models only.Source: Figure 4 · p. 5
- Projecting the dithering vector onto the channel null-space is the proposed way to enforce Hε = 0 even for small arrays.The simulation averages each point over 200 independent channel realizations.Source: C. A Novel Approach to Dithering in… · p. 5
- Null-space projection guarantees Hε = 0 for any M when the BS has perfect channel knowledge.The projected dithering results are shown alongside DAC-resolution EVM results in Fig. 6.Source: C. A Novel Approach to Dithering in… · p. 5
D. Unwanted Emissions
The unwanted-emission simulations show a DAC-resolution threshold, and the stochastic models closely reproduce deterministic-model EVM scaling across the tested channel conditions.
D. Unwanted Emissions
- A DAC-resolution threshold appears in unwanted emissions for both an ideal DAC-only BS and a BS also modeling PAs and array coupling.Fig. 7 compares unwanted emissions versus per-antenna DAC resolution for these two BS configurations.Source: D. Unwanted Emissions · p. 5, Figure 7 · p. 6
- Fig. 6 presents average received EVM across LOS/IID mixtures without dithering or NSPD, using DAC models only.Source: Figure 6 · p. 6
V. COMPARING MODELING APPROACHES - STOCHASTIC VERSUS DETERMINISTIC MODELS
- The statistical-model parameters were fitted to the deterministic behavioral model at M = 4, with array spacing set to d = 0.5λ.Source: §V · p. 6
- Additive and multiplicative statistical models fit the deterministic model well and yield very similar EVM scaling with array size across channel conditions.Fig. 8 compares the models for IID Rayleigh (κ = 0) and LOS (κ = 100) channels, averaging each point over 200 channel realizations.Source: §V · p. 6, Figure 8 · p. 6
A. A Note On Stochastic Modeling and Power Normalization
Power normalization changes the SNR scaling predicted by stochastic impairment models, although EVM is insensitive to normalization. The conclusion reports low-resolution DACs can preserve low EVM and controlled emissions, and that stochastic models remain useful.
A. A Note On Stochastic Modeling and Power Normalization
- EVM is insensitive to power normalization, but stochastic models require normalization to avoid adding power and behaving nonphysically.Source: A. A Note On Stochastic Modeling and… · p. 6
- With normalization, SNR converges to a finite impairment-dependent value for both stochastic models; without it, additive-model SNR scales linearly with M.The paper attributes the convergence to lost power that does not vanish as M grows.Source: A. A Note On Stochastic Modeling and… · p. 6, Figure 9 · p. 7
VI. CONCLUSION
- The results point toward lower per-PA sensitivity over Rayleigh channels because coupled and transmitted signals are weakly correlated.Source: §VI · p. 7
- Low-resolution DACs decrease overall power consumption while maintaining low average received EVM and controlled unwanted emissions.Source: §VI · p. 7
- The proposed null-space dithering design aims to improve per-user link quality while reducing transmitter DAC bits.Source: §VI · p. 7
- The results suggest state-of-the-art stochastic models are useful tools for massive MU-MIMO analysis and support relaxing stringent hardware requirements.Source: §VI · p. 7