Channel Aging in Massive MIMO Systems

• Channel aging in Massive MIMO is a phenomenon where time variations degrade CSI accuracy, impairing beamforming and detection, especially under high mobility.
• It reduces the coherent array gain and spectral efficiency in both uplink and downlink, leading to significant performance loss in fast-changing environments.
• Advanced methods such as online channel prediction, adaptive pilot allocation, and robust precoding can mitigate aging effects, recovering up to 30% of the lost performance.

Channel aging in massive MIMO refers to the phenomenon where time variations in the wireless channel impair the reliability of channel state information (CSI), causing misalignment between the actual channel and the CSI utilized for beamforming or detection. In massive MIMO systems, the issue is especially pronounced due to the large spatial degrees of freedom, the reliance on time-division duplex (TDD) reciprocity, and the prevalence of mobile or high-speed users. The severity of channel aging is governed by the Doppler spread (user mobility), the protocol-induced delays between CSI acquisition and data transmission, phase noise at transceivers, and system-specific factors such as pilot structure, antenna count, and frame formats.

1. Theoretical Models for Channel Aging

Channel aging is conventionally modeled via first-order autoregressive (AR(1)) Gaussian processes, in which the channel vector at time $n$ is

$$\mathbf{h}[n] = \rho\,\mathbf{h}[n-1] + \sqrt{1-\rho^2}\mathbf{w}[n]$$

where $\rho=J_0(2\pi f_D T_s)$ is Jakes' temporal correlation with $f_D$ the Doppler shift and $T_s$ the symbol duration, and $\mathbf{w}[n]\sim\mathcal{CN}(0,\mathbf{R})$ is innovation noise reflecting spatial correlation (Truong et al., 2013, Papazafeiropoulos, 2015). The effective "aging coefficient" $\rho\in(0,1)$ shrinks with increasing $f_D T_s$, representing more rapid channel decorrelation. In joint models that include oscillator phase noise, the coefficient generalizes to

$$\alpha = J_0(2\pi f_D T_s)\cdot e^{-\tfrac{1}{2}(\sigma^2_{UE}+\sigma^2_{BS})}$$

where $\sigma^2$ denotes the phase noise variance per time step (Papazafeiropoulos, 2016).

In multi-antenna distributed (cell-free) systems, the Doppler shift may vary per access point (AP) due to differing geometries and velocities, leading to a matrix of coefficients $\rho_{m,k}$ with independent or correlated distributions (Chopra et al., 2021).

2. Protocol Factors and Manifestations of Channel Aging

The degree and system-level impact of channel aging are shaped by protocol choices:

• TDD Massive MIMO: The base station estimates uplink channels from pilots, then forms downlink precoders by exploiting reciprocity. Delays—either protocol-mandated (as in 3GPP-type UL/DL switching gaps) or inherent to hardware/processing—directly contribute to aging loss since no new pilots are available during data transmission (Li et al., 2022). Aging is aggravated by protocols that require infrequent pilot updates and long payload periods.
• Frame Structure and Pilot Allocation: In classic frame designs, such as "TDD-I" (UL pilots, switch, then DL data), all DL symbols rely on the same initial pilot CSI. In “TDD-II” (UL pilots, then UL and DL phases), DL transmissions after the UL phase experience increased aging.
• Alternative Duplexing: Multicarrier-division duplex (MDD) separates UL and DL subcarriers in frequency, allowing concurrent continuous pilot insertion and DL data—a structure that keeps CSI prediction horizons fixed and enables better tracking (Li et al., 2022).
• Full-Duplex and In-band Full-Duplex (IBFD): True in-band full-duplex suffers from residual self-interference (SI), often limiting the practical benefit of pilot saturation due to digital SI cancellation constraints.
• Processing Latency and Fronthaul: In distributed architectures, aged CSI arises not only from radio propagation but also CPU scheduling, fronthaul delays, and coordination lags (Jiang et al., 2021).

3. System-Level Impact and Rate Degradation

The fundamental effect of channel aging is to reduce the coherent array gain, destructively impact beamforming, and shift the system from being interference-limited (with strong CSIT) to noise/aging-limited (with outdated CSIT).

• Uplink: The post-combining SINR is damped by factors $\rho^2$, so the desirable scaling of SINR with antenna number $M$ (e.g., $\mathcal{O}(M)$ for MRC) is preserved structurally, but at absolute lower gain (Truong et al., 2013, Kong et al., 2015).
• Downlink: Due to the combination of aging and precoder reliance on old CSIT, signal power shrinks as $\rho^4$, interference may even be reduced (since both desired and pilot contamination terms vanish together), but the overall sum rate degrades rapidly for $\rho<1$ (Truong et al., 2013).
• Spectral Efficiency Decay: Quantitative simulation in (Zheng et al., 2020, Chopra et al., 2021, Papazafeiropoulos, 2015) shows that sum-rate per user may halve or worse at normalized Doppler $f_DT_s\approx0.2$. System performance under high mobility (e.g., 100–300 km/h) can collapse to less than 10% of the ideal CSI case if unaddressed.
• Distributed and Cell-Free Scenarios: With spatially varying $\rho_{m,k}$, some APs age more slowly and dominate the MMSE combining weights, marginally mitigating SINR loss; but under uniform aging, cell-free performance can deteriorate below that of cellular MIMO in high mobility regimes (Chopra et al., 2021).
• RIS-Assisted and Hybrid Systems: Channel aging in RIS-enhanced systems impacts both direct and reflected links, generally reducing the effectiveness of beamforming and phase optimization (Qian et al., 4 Jul 2024, Papazafeiropoulos et al., 2022).

4. Mitigation Strategies and Channel Prediction

Multiple methodologies can partially offset channel aging, with distinct trade-offs:

• Online Channel Prediction: Wiener filtering/predictors with order $p$ use recent pilot history or detected data to extrapolate the channel forward. The optimal FIR predictor (time or frequency domain) for massive MIMO is

$$\hat{\mathbf{h}}_{n+1} = \sum_{q=0}^p \mathbf{V}_{q}\,\tilde{\mathbf{y}}[n-q]$$

where stacking benefits from long-term correlation. Prediction increases the “effective” $\rho^2$ by summing over $\rho^{2j}$, mitigating but not eliminating degradation (Truong et al., 2013, Kong et al., 2015, Li et al., 2022). In large systems and moderate Doppler, prediction recovers 15–30% of aging-induced sum-rate loss for realistic prediction orders ($p=15,25$) (Truong et al., 2013).

• Multicarrier Division Duplex (MDD): By continuously injecting pilots over dedicated UL subcarriers throughout the frame (rather than only at the start), MDD architectures nearly flatten the CSI error variance and rate across the frame duration. Decision-directed predictors operating in the frequency domain update the channel estimate using detected UL data; this is especially effective in MDD Type-II frames, providing 10–30% sum-rate gain over standard TDD under high-speed mobility (Li et al., 2022).
• Orthogonal Precoding (OP) and Diversity Exploitation: OP in the time–frequency plane spreads each data symbol across the entire OFDM block, restoring channel hardening even when spatial hardening is lost due to aging. This mechanism leverages time-frequency diversity to reduce BER and maintain link reliability, as demonstrated with up to $\sim$100$\times$ improvement in high-mobility simulations (Zemen et al., 2019).
• Rate-Splitting and Robust Precoding: In cell-free and multi-user scenarios, rate-splitting (RS) decomposes messages into private and common parts, with adjustable power sharing between streams. Bisection-based common stream design robustly maintains spectral efficiency in the face of aging, especially when combined with MMSE or MR precoding for private streams (Zheng et al., 2023). Symbol-level precoding schemes can be directly adapted to the "a posteriori" channel model under aging, and robust formulations for SINR balancing or MMSE can provide significant SINR/SER gains versus naive precoding (Wang et al., 7 Feb 2024).
• Enhanced Pilot Allocation and RIS Phase Optimization: Two-phase MMSE pilot arrangements, especially in RIS-aided scenarios, separate direct and cascaded path estimation, reducing the NMSE in aged CSI. Optimizing RIS reflection phases using projected gradient ascent further compensates for aging losses, with up to 10–15% likely SE improvement in large array/EMI settings (Qian et al., 4 Jul 2024, Papazafeiropoulos et al., 2022).

5. Quantitative Design Trade-Offs

The system-level implications of channel aging are directly tied to operational parameters:

• Frame/Block Length: Longer blocks increase payload efficiency but cause more severe aging, as the prediction horizon from the last pilot increases. There exists a unique block length $L^*$ maximizing area spectral efficiency; $L^*$ scales inversely with user speed and angular spread (for vehicular or non-isotropic scattering scenarios) (Li et al., 2022). Rule-of-thumb: select $\tau_c \lesssim 0.383/(f_DT_s)_{\max}$ to avoid severe aging-induced SE collapse (Zheng et al., 2021).
• Pilot Overhead: Increased pilot frequency enables better prediction but reduces data rates due to overhead. The optimal trade-off depends on user mobility: high-mobility regimes require shorter blocks and more frequent pilot insertion.
• Antenna Scaling: While increasing $M$ (the number of base station antennas) always increases instantaneous array gain, channel aging scales the coherent gain multiplicatively by $\rho^2$ (uplink) or $\rho^4$ (downlink), but the $1/\sqrt{M}$ array power-scaling law remains intact—a main finding of (Kong et al., 2015, Papazafeiropoulos, 2015).
• Power Control and Cooperative Decoding: Fractional power control (FPC) and large-scale fading decoding (LSFD) can partly offset the interference penalty of aged CSI, but as aging dominates (for small $\rho$), the potential benefit vanishes and systems become aging-limited rather than interference-limited. Advanced combining (e.g., MMSE rather than matched filter) yields ~3–5 dB gain under aging (Chopra et al., 2021, Zheng et al., 2020).
• Hardware Budget and Phase Noise: In practical regimes, user mobility (Doppler aging) is much more significant than oscillator phase noise. Phase noise becomes a significant contributor to aging only at extremely low velocities or with poor LOs (Papazafeiropoulos, 2016, Papazafeiropoulos, 2015).

6. Empirical and Comparative Results

Empirical studies across diverse system configurations document key trends:

• Comparative Performance:
  • At moderate normalized Doppler ($f_DT_s\approx 0.1$), TDD sum-rate collapses beyond a few tens of ms under high user speed, while MDD sustains near-constant CSI error variance and frame-averaged rate, even at 200 km/h (Li et al., 2022).
  • CF massive MIMO retains 95%-likely SE above small-cell benchmarks by 2–3$\times$ at low mobility; the gap narrows as aging increases, but CF is more robust due to distributed processing and diversity (Zheng et al., 2021, Zheng et al., 2020).
• Multi-Cell, RIS and mmWave Environments:
  • Channel aging equally impacts the direct and cascaded components in RIS-assisted systems; higher RIS element counts partially recover lost SE only if phases are re-optimized per block (Papazafeiropoulos et al., 2022, Qian et al., 4 Jul 2024).
  • In mmWave, angular-domain channel tracking plus per-path Doppler compensation, implemented as dynamic compressive sensing plus parametric Bayesian inference, can reduce pilot overhead by 70–80% while mitigating aging effects (i.e., tracking dominant fast-varying directions) (Liu et al., 2019).
• DL Prediction and OTFS:
  • OTFS-based systems with basis-expansion + Slepian-sequence predictor (SBEE) fit the temporal evolution of channel taps and extrapolate over long horizons, outperforming Kalman and AR predictors by 8–15 dB in NMSE, achieving 94% of genie-aided SE up to 5 frames ahead (Zhang et al., 2 Jul 2025).
• Deep Reinforcement Learning:
  • Multi-agent deep RL schemes (DDRL, PDRL, CDRL) for beamforming dynamically learn to track temporal correlation in $\rho$, maintaining ~90% of the ideal ZF sum-rate even when feedback is delayed and CSI is aged. Distributed learning achieves best resilience, but at greater complexity (number of DQNs) (Feng et al., 2023).

7. Guidelines and Open Directions

Key technical guidelines and open research challenges outlined in the literature are as follows:

• Keep Doppler $\times$ frame duration moderate—target $f_D T_s \leq 0.1$ to limit aging loss to below 10%; above this, resort to online prediction, increased pilot frequency, or MDD-style frame structures (Truong et al., 2013, Li et al., 2022).
• Adopt robust precoding and channel prediction for interference management—design precoders for "statistical" or "a posteriori" CSI, explicitly accounting for time evolution and spatial correlation under aging (Wang et al., 7 Feb 2024, Zheng et al., 2023).
• Combining and Power Allocation—MMSE combining and two-layer LSFD are recommended under channel aging for CF architectures; naive power increase or added antennas do not materially offset aging-induced loss (Chopra et al., 2021, Tentu et al., 2023).
• RIS-phase and frame-length reoptimization—as large-scale statistics vary with user mobility, control both RIS phases and frame structure adaptively (Papazafeiropoulos et al., 2022, Qian et al., 4 Jul 2024).
• Pilot structure and block-length optimization—fit resource block size empirically to measured angular spreads and user speed; non-isotropic scattering substantially affects optimal parameters (Li et al., 2022).
• Multi-user and network-level scheduling—aging-aware scheduling and beam management remain challenging when users have widely heterogeneous mobilities and channels evolve in correlated ways.
• Hardware and phase-noise constraints—choose high-quality oscillators for ultra-low mobility regimes; phase noise is generally secondary to mobility for channel aging in realistic deployments (Papazafeiropoulos, 2016, Papazafeiropoulos, 2015).
• Algorithmic scalabilty—in large arrays, exploit approximate orthogonality to simplify robust precoder or channel predictor implementations to $\mathcal{O}(K^2 (N+K))$ or lower complexity (Wang et al., 7 Feb 2024).

A persistent challenge is achieving high spectral efficiency and reliability in ultra-high-mobility or latency-constrained scenarios without prohibitive pilot or computational overhead. Integrating advanced channel prediction, adaptive duplexing (e.g., MDD), robust symbol-level or split-stream precoding, and possibly machine-learning-driven adaptation constitutes the current frontier of channel aging mitigation in massive MIMO.