Source-linked AI summary
Channel Estimation for RIS Assisted Wireless Communications: Part II -- An Improved Solution Based on Double-Structured Sparsity
Xiuhong Wei, Decai Shen, Linglong Dai
TL;DR
RIS channel estimation has high pilot overhead because passive RIS elements lack signal-processing capability. The paper identifies double-structured sparsity across users and develops DS-OMP to exploit it. Simulations show that the proposed scheme requires less pilot overhead than existing schemes.
Problem
Passive RIS elements lack signal-processing capability, making RIS-assisted channel estimation require high pilot overhead.
Method
The paper reveals common non-zero rows and partially common non-zero columns across users, then jointly estimates their supports with DS-OMP.
Results
The proposed DS-OMP scheme requires lower pilot overhead than existing schemes at the same estimation accuracy.
Takeaways & Limitations
Exploiting double-structured sparsity provides a low-overhead cascaded channel estimation scheme for RIS-assisted wireless communication systems.
Abstract
from arXiv · showhide
Reconfigurable intelligent surface (RIS) can manipulate the wireless communication environment by controlling the coefficients of RIS elements. However, due to the large number of passive RIS elements without signal processing capability, channel estimation in RIS assisted wireless communication system requires high pilot overhead. In the second part of this invited paper, we propose to exploit the double-structured sparsity of the angular cascaded channels among users to reduce the pilot overhead. Specifically, we first reveal the double-structured sparsity, i.e., different angular cascaded channels for different users enjoy the completely common non-zero rows and the partially common non-zero columns. By exploiting this double-structured sparsity, we further propose the double-structured orthogonal matching pursuit (DS-OMP) algorithm, where the completely common non-zero rows and the partially common non-zero columns are jointly estimated for all users. Simulation results show that the pilot overhead required by the proposed scheme is lower than existing schemes.
I. INTRODUCTION
RIS channel estimation has high pilot overhead because many passive RIS elements lack signal-processing capability. This paper addresses the issue by exploiting shared sparsity across users with DS-OMP.
- Passive RIS elements without signal-processing capability make channel estimation require high pilot overhead.
- Angular cascaded-channel sparsity formulates channel estimation as sparse signal recovery solvable by compressive sensing with reduced pilot overhead.
- Different users’ angular cascaded channels share completely common non-zero rows and partially common non-zero columns.
- DS-OMP jointly estimates common row and column supports while individually estimating user-specific column supports.
II. SYSTEM MODEL
The paper introduces the RIS cascaded channel before formulating its estimation problem.
- The section first introduces the cascaded channel in the RIS-assisted communication system and then formulates its estimation problem.
A. Cascaded Channel
The cascaded channel combines the RIS-to-BS channel with each user-to-RIS channel and admits a sparse virtual angular-domain representation under limited scattering.
- The system simultaneously serves K single-antenna users through an M-antenna BS and an N-element RIS.
- For a typical N1 × N2 UPA, the antenna spacing is usually d = λ/2.
- For user k, the cascaded channel is Hk = Gdiag(hr,k), an M × N matrix combining the RIS-to-BS and user-to-RIS channels.
- The virtual angular-domain representation decomposes Hk using unitary dictionary matrices at the BS and RIS.
- Limited scattering around the BS and RIS makes the angular cascaded channel contain only a few non-zero elements.
B. Problem Formulation
The system collects orthogonal RIS-assisted pilot measurements and rewrites cascaded-channel estimation as a compressive-sensing problem, although conventional CS methods still require substantial pilot overhead.
- The direct BS-user channel is assumed known, so estimation focuses on the cascaded channel.
- Orthogonal pilot transmission lets all users send known pilots through the RIS over Q time slots for uplink estimation.
- The RIS reflecting vector contains the coefficients of its N elements for each pilot time slot, while received noise follows a circularly symmetric complex Gaussian model.
- After Q pilot slots, the received vectors form an M × Q overall measurement matrix for each user.
- The resulting formulation is a compressive-sensing model with a Q × N sensing matrix.
- Conventional OMP-based CS estimation can estimate each user’s angular cascaded channel, but its pilot overhead remains high for the required accuracy.
III. JOINT CHANNEL ESTIMATION FOR RIS ASSISTED WIRELESS COMMUNICATION SYSTEMS
This section exploits double-structured sparsity to reduce pilot overhead through joint support estimation and analyzes the proposed scheme’s computational complexity.
- The section reveals double-structured sparsity and proposes DS-OMP to reduce pilot overhead.It also analyzes the computational complexity of the proposed scheme.
A. Double-Structured Sparsity of Angular Cascaded Channels
Angular cascaded channels are sparse and exhibit common structure across users: completely common non-zero rows and partially common non-zero columns.
- Each angular cascaded channel has LG non-zero rows, each containing Lr,k non-zero columns, so LGLr,k is usually much smaller than MN.This establishes element-level sparsity in the angular domain.
- Row-structured sparsity: Different users’ angular cascaded channels share completely common non-zero rows because their RIS-to-base-station channel is common.The row support is common across all users.
- Partially column-structured sparsity: Within each common non-zero row, users share Lc common non-zero columns due to partially shared scattering paths between the RIS and users.The shared column support is partial rather than identical across all channel entries.
- The common row support and partially common column support can be exploited to jointly estimate cascaded channels for different users.Joint estimation is intended to improve channel estimation accuracy.
B. Proposed DS-OMP Based Cascaded Channel Estimation
DS-OMP integrates double-structured sparsity into OMP through three support-detection stages, followed by least-squares estimation and transformation back to spatial channels.
- DS-OMP detects angular-channel supports in three stages: common rows, partially common columns, and user-specific columns.The stages jointly estimate shared supports before estimating individual supports.
- After support detection, least squares estimates the angular cascaded matrices, which are transformed into spatial cascaded channels.The spatial-domain estimates are obtained for all users.
- Stage 1: Estimating the completely common row support: Stage 1 jointly estimates the completely common row support across users using received-pilot column powers.The largest LG entries of the accumulated power vector are selected as the estimated row support.
- Stage 2: Estimating the partially common column supports: Stage 2 estimates each row’s partially common column support by aggregating column selections across users and retaining Lc most frequent indexes.OMP correlations and least-squares residual updates produce per-user candidate supports before aggregation.
- Stage 3: Estimating the individual column supports: Stage 3 estimates the remaining Lr,k − Lc user-specific column supports for every common row and user.It follows the same correlation, least-squares, and residual-update procedure used for partial common supports.
- If users share no common RIS-side scatterers, the method reduces to row-structured sparsity and omits Stage 2.DS-OMP remains applicable in this setting.
C. Computational Complexity Analysis
The DS-OMP algorithm’s complexity is analyzed across three support-detection stages, with total cost combining Stage 1 column-power calculations and subsequent OMP-based support estimation.
- Stage 1: Stage 1 has computational complexity O(KMQ) for calculating the power of M columns across K users.The columns are taken from matrices of size Q × M.
- Stage 2: Stage 2 has overall complexity O(LGKNQL3 r,k) across LG iterations, matching the complexity of OMP for each non-zero row and user.The per-row, per-user cost is O(NQL3 r,k).
- Overall complexity: The proposed DS-OMP complexity is the sum of O(KMQ), O(LGKNQL3 r,k), and O(LGKNQ(Lr,k − Lc)3).This total reflects the three support-detection stages.
- Stage 3: The subsequent stage has overall complexity O(LGKNQ(Lr,k − Lc)3) for estimating supports outside the common paths.Its per-iteration cost depends on the user-specific paths not included among the Lc common paths.
IV. SIMULATION RESULTS
Simulations compare NMSE against pilot overhead Q under specified RIS, channel, distance, and SNR settings. DS-OMP requires fewer pilots for equal estimation accuracy, and its performance improves as common paths increase.
- Simulation settings: The simulation uses M = 64 BS antennas, N = 256 RIS elements, and K = 16 users, with LG = 5 and Lr,k = 8 for every user.All spatial angles lie on quantized grids.
- Comparison: The proposed DS-OMP scheme is compared with conventional CS and row-structured sparsity schemes using NMSE versus pilot-transmission time slots Q.The comparison evaluates estimation accuracy as pilot overhead changes.
- Results: For the same estimation accuracy, DS-OMP requires lower pilot overhead than both existing schemes.This is the principal performance comparison reported for Fig. 2.
- Results: When Lc = 0, DS-OMP and the row-structured scheme have the same NMSE; increasing Lc improves DS-OMP toward perfect-support performance.Here Lc denotes the number of common paths between the RIS and users.
V. CONCLUSIONS
The paper develops a low-overhead RIS cascaded-channel estimation scheme by exploiting double-structured sparsity and DS-OMP. Simulations report lower pilot overhead than existing algorithms, while future work targets continuous channel angles.
- Conclusion: The paper analyzes double-structured sparsity in angular cascaded channels among users.This structure underpins the proposed estimation scheme.
- Conclusion: It proposes DS-OMP to reduce pilot overhead in RIS-assisted wireless communication systems.The algorithm is based on the identified channel structure.
- Conclusion: Simulation results show that DS-OMP requires lower pilot overhead than existing algorithms.The conclusion reports this comparison as the main empirical outcome.
- Future work: Future work will apply double-structured sparsity to super-resolution channel estimation with continuous channel angles.The proposed extension addresses the fact that channel angles are continuous in practice.