Design of RIS-aided mMTC+ Networks for Rate Maximization under the Finite Blocklength Regime with Imperfect Channel Knowledge

Within the context of massive machine-type communications+, reconfigurable intelligent surfaces (RISs) represent a promising technology to boost system performance in scenarios with poor channel conditions. Considering single-antenna sensors transmitting short data packets to a multiple-antenna collector node, we introduce and design an RIS to maximize the weighted sum rate (WSR) of the system working in the finite blocklength regime. Due to the large number of reflecting elements and their passive nature, channel estimation errors may occur. In this letter, we then propose a robust RIS optimization to combat such a detrimental issue. Based on concave bounds and approximations, the nonconvex WSR problem for the RIS response is addressed via successive convex optimization (SCO). Numerical experiments validate the performance and complexity of the SCO solutions.

💡 Research Summary

This paper addresses the design of reconfigurable intelligent surface (RIS)–assisted massive machine‑type communications (mMTC+) networks where a large number of single‑antenna sensors transmit short packets to a multi‑antenna collector node (CN). The authors focus on maximizing the weighted sum‑rate (WSR) under the finite blocklength (FBL) regime, which is essential for ultra‑reliable low‑latency IoT applications where traditional Shannon capacity analysis is no longer accurate. In the FBL regime the achievable rate is approximated by the Shannon capacity minus a penalty term that depends on channel dispersion, blocklength, and target error probability.

Because RIS elements are passive and numerous, acquiring perfect channel state information (CSI) is unrealistic. The paper therefore adopts a Rician fading model for the cascaded RIS‑sensor‑CN channels and explicitly incorporates channel estimation errors through an error‑covariance matrix. Direct sensor‑to‑CN links are assumed negligible, emphasizing the RIS’s role as the sole viable propagation path.

The received signal at the CN is processed with linear spatial filters. To keep the analysis tractable, the authors adopt maximum‑ratio combining (MRC) at the CN, which leads to a signal‑to‑interference‑plus‑noise ratio (SINR) that is a rational function of the RIS reflection vector ψ and the estimated channels. The instantaneous FBL rate for sensor i is expressed as

R_i(ψ) ≈ log₂(1+ρ_i(ψ)) – a_i · √V(ρ_i(ψ))/√n_i,

where a_i captures the target error probability and blocklength. The expectation over channel realizations is approximated via Monte‑Carlo sampling, yielding a stochastic objective that is non‑convex in ψ because both the logarithmic capacity term and the dispersion‑based penalty are non‑concave.

To solve this challenging problem, the authors propose a successive convex optimization (SCO) framework. First, they lift the vector variable ψ to a matrix variable Φ = ψψᴴ, which is Hermitian positive semidefinite with a rank‑one constraint. The rank constraint is relaxed (SDR) and the resulting convex sub‑problems are solved iteratively. At each iteration k, concave lower bounds for the capacity term and convex upper bounds for the dispersion penalty are constructed around the previous point Φ^{(k‑1)} using first‑order Taylor expansions and well‑known inequalities (e.g., log‑linear lower bound and square‑root upper bound).

For the single‑antenna CN case (K = 1) the SINR reduces to a trace expression, and explicit bound formulas (12)–(14) are derived. For the general multi‑antenna CN case (K > 1) the SINR involves quadratic forms and cross‑terms; the authors define auxiliary matrices Ξ_{i,j} and decompose the SINR into signal, noise, estimation‑error, and interference components (15)–(16). Concave lower bounds for the capacity (17)–(18) and convex upper bounds for the dispersion penalty (19)–(21) are then obtained.

Each convex sub‑problem is solved with standard semidefinite programming tools (e.g., CVX). After convergence of the SCO loop, a feasible ψ is recovered from Φ using Gaussian randomization. The authors emphasize that while the final solution is sub‑optimal (due to the rank relaxation and randomization), it is guaranteed to converge to a stationary point of the original problem.

Numerical results explore the impact of the number of RIS elements L and the number of CN antennas K on the WSR. The proposed robust SCO‑based design consistently outperforms a baseline with random phase shifts and also exceeds the performance of earlier work that assumed perfect CSI and a single‑antenna CN. The gains increase with both L and K, confirming the scalability of the approach. Complexity analysis shows that the SDR + SCO pipeline incurs modest computational overhead compared with directly tackling the non‑convex problem, making it attractive for practical deployment.

In summary, the paper makes three key contributions: (1) it integrates finite‑blocklength rate modeling into RIS‑assisted mMTC+ system design; (2) it develops a robust optimization framework that explicitly accounts for imperfect CSI; and (3) it extends the design from single‑antenna to multi‑antenna collectors using successive convex approximation and semidefinite relaxation. The work provides a solid theoretical foundation and practical algorithmic tools for future RIS‑enhanced ultra‑reliable low‑latency IoT networks, and suggests future directions such as hardware impairments, dynamic two‑timescale RIS updates, and low‑complexity stochastic optimization.