Pilot-Based Estimation Scheme

• Pilot-based estimation schemes are protocols that use embedded reference signals to probe and accurately derive channel state information in wireless systems.
• They balance trade-offs among estimation accuracy, spectral efficiency, and computational complexity through strategies such as orthogonal, superimposed, and index-modulated pilots.
• These methods are pivotal in applications like MIMO, OFDM, and RIS-assisted IoT, enhancing throughput and robustness in diverse and high-mobility environments.

A pilot-based estimation scheme refers to any channel estimation protocol in which known reference signals ("pilots") are embedded into the transmitted sequence to facilitate the estimation of channel parameters at the receiver. Such techniques are fundamental to modern digital communication systems, wireless networking, MIMO and OFDM architectures, and emerging paradigms including RIS-aided IoT, high-mobility OFDM, and ISAC. Pilot-based schemes vary widely in their design: they may employ dedicated resource elements (orthogonal or embedded pilots), overlay pilots directly on data (superimposed pilots), or exploit implicit pilot patterns to carry additional side information or adapt to sparsity and spatial non-stationarity. The core goal is to balance estimation accuracy, spectral efficiency, complexity, robustness, and system constraints.

1. Fundamental Principles and Taxonomy

Pilot-based estimation leverages the transmission of known sequences to probe the channel response, allowing the receiver to derive channel state information (CSI) required for coherent detection or advanced equalization. There are several principal paradigms:

• Orthogonal or Embedded Pilots: Pilots are placed on dedicated time-frequency or spatial resources, known to both transmitter and receiver, ensuring interference-free estimation but incurring overhead (e.g., comb, block, and diamond patterns in OFDM) (Walk et al., 2015, Soltani et al., 2020).
• Superimposed Pilots (SIP): Pilots are linearly combined with data symbols, improving spectral efficiency by eliminating resource overhead, but introducing pilot-data interference that complicates estimation (Qing et al., 2022, Li et al., 14 Jul 2025, Kanazawa et al., 27 Jan 2025).
• Phaseless and Index-Modulated Pilots: Pilot amplitude (but not phase) is known, or the pilot location itself is modulated, enabling embedding of side information or boosting spectral efficiency (Walk et al., 2015, Keykhosravi et al., 26 Feb 2024).
• Spatial/Grouped Pilots: In systems with spatial non-stationarity (e.g., XL-MIMO), user grouping and resource-sharing exploit spatial decoupling for pilot reuse (Zhang et al., 11 Dec 2025).

The design of pilot patterns, assignment strategies, and power allocation is closely tied to the channel model (stationary, doubly-selective, sparse, or massive MIMO) and system constraints (latency, covertness, energy, and hardware).

2. Signal Models and Pilot Design Strategies

Orthogonal, Embedded, and Phaseless Pilot Assignment

• OFDM: Pilots are allocated on selected subcarriers; the receiver performs LS or MMSE estimation on these tones, interpolating across unpiloted subcarriers (Walk et al., 2015, Soltani et al., 2020).
• Phaseless Pilots: Only amplitudes are fixed; phases are "freed" for data purposes. Two-symbol combinations and phase retrieval techniques reconstruct the impulse response from magnitude-only measurements (Walk et al., 2015). This approach can enhance spectral efficiency and flexibility.

Superimposed Pilots

• Spectral Efficiency Trade-off: A known sequence $p[n]$ is superimposed on data $s[n]$, with power split governed by a fraction $\lambda$; at the receiver, the signal is $y[n] = h(n; \theta)[s[n] + \alpha p[n]] + w[n]$ with $\alpha = \sqrt{\lambda/(1-\lambda)}$ (Qing et al., 2022, Li et al., 14 Jul 2025).
• RIS-aided Uplink: For RIS-assisted IoT, superimposed pilots enable estimation of the composite channel $h(n; \theta)$, combining direct and RIS-reflected paths, without sacrificing bandwidth or energy. Channel estimation exploits both conventional LS on pilots and lightweight neural network refinement (Qing et al., 2022).
• MIMO-OFDM and OTFS: Superimposed pilots facilitate high-rate operation in doubly-selective channels. Multiple spatially and temporally multiplexed SPs allow for iterative interference cancellation, leveraging soft decoder feedback (Kanazawa et al., 27 Jan 2025, Li et al., 14 Jul 2025).

Index-Modulated and Adaptive Pilots

• Index Modulation (IM): The placement (timing) of pilot sequences is itself modulated, carrying additional bits and improving spectral efficiency. In FTN signaling for HF, pilot blocks' positions modulate $N_b$ extra bits (Keykhosravi et al., 26 Feb 2024).
• Adaptive and Learned Patterns: Data-driven or GMM-based pilot assignment adapts to the underlying channel statistics, either via deep learning for both pilot and estimator design (Chun et al., 2018, Mashhadi et al., 2020, Soltani et al., 2020) or via mixture models and feedback in FDD-MIMO (Turan et al., 26 Mar 2024, Turan et al., 7 Aug 2024).

3. Channel Estimation Algorithms and Architectures

Classical Linear Estimation

• LS and MMSE: For known pilot positions, LS and LMMSE estimators are canonical, forming the basis for many advanced approaches. LMMSE performance is dependent on second-order statistics, which may be unavailable or computationally intensive (Walk et al., 2015, Mashhadi et al., 2020).
• CRLB and Optimal Power Allocation: Cramér–Rao bound analysis motivates pilot power allocation schemes, e.g., closed-form PCRB-optimal pilot allocation for multi-user OTFS (Nie et al., 2023).

Data-Driven and Hybrid Learning Approaches

• NN-based Refinement: Lightweight (shallow) NNs can be used to "denoise" LS estimates (CE-Net) and to perform symbol fusion and detection (FUS-Net) in RIS-assisted and MIMO-OFDM systems. Shallow networks (2–3 hidden layers) have low computational/processing cost and require fewer training samples (Qing et al., 2022).
• Deep Joint Pilot and Estimator Learning: In multiuser MIMO, two-layer NNs serve as pilot designers and deep NNs serve as channel estimators, trained end-to-end with MSE loss; successive interference cancellation is embedded (Chun et al., 2018).
• Convolutional and Attention NNs: In massive MIMO and OFDM, architectures combine convolutional layers and non-local attention to exploit spatial and spectral correlations, further refined by pilot pruning methods to reduce overhead (Mashhadi et al., 2020).
• Iterative and Model-based Learning: In superimposed pilot receivers, iterative channel estimation and detection is enhanced by VMP (variational inference), and deep CNNs with attention, for robust performance in nonstationary and high-mobility scenarios (Li et al., 14 Jul 2025).

Compressed Sensing and Position-Based Estimation

• Position-Adaptive Pilots: Channel sparsity due to high mobility or large arrays can be exploited by compressed sensing methods, with pilot design (location and amplitude) tailored to minimize coherence in the effective dictionary (Ren et al., 2020).
• Clustered Sparsity and MRF Models: In XL-MIMO, pilots are grouped and allocated based on users’ spatial non-stationarity, and turbo Bayesian inference with 2D MRF priors is used for channel recovery (Zhang et al., 11 Dec 2025).

4. Performance Metrics and Practical Results

The evaluation of pilot-based schemes focuses on:

• Accuracy: Normalized mean square error (NMSE) for channel estimation and bit error rate (BER) for detection. For RIS-IoT with superimposed pilots, CE-Net achieves NMSE $\approx 10^{-2}$, outperforming MMSE-CE and LS-CE for a wide range of pilot/data power splits (Qing et al., 2022).
• Complexity: Measured in FLOPs, memory, and processing delay. NN-based schemes can reduce computation versus cubic-complexity MMSE; e.g., CE-Net+FUS-Net: $O(N^2)$ vs. MMSE: $O(N^3)$ (Qing et al., 2022, Mashhadi et al., 2020).
• Overhead and Throughput: Superimposed, index-modulated, or phaseless pilots enhance net spectral efficiency, particularly when pilot phases or positions are used for added data (Walk et al., 2015, Keykhosravi et al., 26 Feb 2024). In coded OTFS, multiple SPs with iterative cancellation enable throughput gains of $50$–$60\%$ over embedded pilots (Kanazawa et al., 27 Jan 2025).
• Adaptivity and Scalability: Learning-based pilot assignment adapts to channel, SNR, and user count without retraining (Turan et al., 26 Mar 2024, Turan et al., 7 Aug 2024). Fully distributed pilot selection algorithms minimize contamination at scale with negligible coordination (Khan et al., 15 Oct 2025).

5. Advanced Pilot Assignment and Optimization

• Graph and Clustering-Based Pilot Sharing: For distributed or cell-free massive MIMO, pilot contamination is mitigated via clustering (e.g., K-means), graph coloring with swap-matching, and prioritized resource allocation, minimizing sum CRB or estimation error across the network (critical for ISAC and cooperative systems) (Peng et al., 29 May 2024, Khan et al., 15 Oct 2025).
• Spatial Orthogonality and User Grouping in XL-MIMO: Pilot overhead is minimized while supporting more users by exploiting users' distinct visibility regions, frequency-division multiplexing among groups, and cyclic codes for intra-group orthogonality. Turbo Bayesian inference with clustered support models yields superior channel estimation even with one OFDM symbol for many users (Zhang et al., 11 Dec 2025).

6. Application Domains and Extensions

Pilot-based estimation schemes are ubiquitous and have been extensively tailored for specialized domains:

• RIS-Assisted IoT: Superimposed pilots with neural refinement efficiently resolve composite channels in RIS-augmented systems (Qing et al., 2022).
• OTFS and High-Mobility Channels: Embedded, superimposed, and IM-based pilots, with support for iterative interference cancellation and robust power allocation (Keykhosravi et al., 26 Feb 2024, Kanazawa et al., 27 Jan 2025, Nie et al., 2023).
• Covert and Secure Communications: Pilot allocation is jointly optimized with power and code design to maximize intended SNR while satisfying covertness constraints, using MMSE-based methods grounded in detection theory (Xu et al., 2019).
• Optical Networks: Joint two-dimensional pilot distribution optimization for phase estimation over multi-channel optical fibers achieves >90% MSE reduction and boosts achievable information rate (Alfredsson et al., 2020).
• Backscatter and Passive IoT: One-shot time-spread pilots with orthogonal sequence design achieve Cramer-Rao optimality and >10 dB power savings (Rezaei et al., 2023).

7. Current Challenges and Emerging Directions

Despite the advances, key challenges persist:

• Pilot Contamination and Reuse: Addressed via spatial/user grouping, adaptive pilot selection, and distributed prioritization (Khan et al., 15 Oct 2025, Zhang et al., 11 Dec 2025).
• Pilot Overhead Reduction: Sparse, superimposed, or learning-pruned pilot strategies maintain estimation accuracy at minimized resource expense (Mashhadi et al., 2020).
• Robustness to Hardware and Channel Non-Idealities: Methods such as VMP/VMP-L and data-driven CNNs adapt to time-varying and mismatched channel statistics, as needed for massive MIMO and high-mobility (Li et al., 14 Jul 2025).
• Joint Optimization with Data Detection and Resource Allocation: Integration of channel estimation, symbol detection, and pilot resource management is performed via iterative deep learning architectures and model-based inference (Qing et al., 2022, Kanazawa et al., 27 Jan 2025).

• Superimposed Pilot-based Channel Estimation for RIS-Assisted IoT Systems Using Lightweight Networks (Qing et al., 2022)
• OFDM Channel Estimation via Phase Retrieval (Walk et al., 2015)
• IM-based Pilot-assisted Channel Estimation for FTN Signaling HF Communications (Keykhosravi et al., 26 Feb 2024)
• Deep Learning Based Joint Pilot Design and Channel Estimation for Multiuser MIMO Channels (Chun et al., 2018)
• Channel-Adaptive Pilot Design for FDD-MIMO Systems Utilizing Gaussian Mixture Models (Turan et al., 26 Mar 2024)
• Pruning the Pilots: Deep Learning-Based Pilot Design and Channel Estimation for MIMO-OFDM Systems (Mashhadi et al., 2020)
• Pilot Distributions for Joint-Channel Carrier-Phase Estimation in Multichannel Optical Communications (Alfredsson et al., 2020)
• A Versatile Pilot Design Scheme for FDD Systems Utilizing Gaussian Mixture Models (Turan et al., 7 Aug 2024)
• Learning-Aided Iterative Receiver for Superimposed Pilots: Design and Experimental Evaluation (Li et al., 14 Jul 2025)
• Position Based Compressed Channel Estimation and Pilot Design for High Mobility OFDM Systems (Ren et al., 2020)
• Pilot-Based Channel Estimation Design in Covert Wireless Communication (Xu et al., 2019)
• Improving Channel Estimation Performance for Uplink OTFS Transmissions: Pilot Design based on A Posteriori Cramer-Rao Bound (Nie et al., 2023)
• Low-Complexity Joint Channel Estimation and List Decoding of Short Codes (Coşkun et al., 2019)
• Time-Spread Pilot-Based Channel Estimation for Backscatter Networks (Rezaei et al., 2023)
• Novel Synchronization Scheme for Cooperative ISAC Systems (Peng et al., 29 May 2024)
• Scalable Pilot Assignment for Distributed Massive MIMO using Channel Estimation Error (Khan et al., 15 Oct 2025)
• Superimposed Pilot-Based OTFS -- Will it Work? (Kanazawa et al., 27 Jan 2025)
• Channel Estimation By Transmitting Pilots From Reconfigurable Intelligent Surface (Zhu et al., 2023)
• Pilot Pattern Design for Deep Learning-Based Channel Estimation in OFDM Systems (Soltani et al., 2020)
• A Novel Pilot Scheme for Uplink Channel Estimation for Sub-array Structured ELAA in XL-MIMO systems (Zhang et al., 11 Dec 2025)