An Optimization-Based User Scheduling Framework for Multiuser MIMO Systems

Resource allocation is a key factor in multiuser (MU) multiple-input multiple-output (MIMO) wireless systems to provide high quality of service to all user equipments (UEs). In congested scenarios, UE scheduling enables UEs to be distributed over time, frequency, or space in order to mitigate inter-UE interference. Many existing UE scheduling methods rely on greedy algorithms, which fail at treating the resource-allocation problem globally. In this work, we propose a UE scheduling framework for MU-MIMO wireless systems that approximately solves a nonconvex optimization problem that treats scheduling globally. Our UE scheduling framework determines subsets of UEs that should transmit simultaneously in a given resource slot and is flexible in the sense that it (i) supports a variety of objective functions (e.g., post-equalization mean squared error, capacity, and achievable sum rate) and (ii) enables precise control over the minimum and maximum number of resources the UEs should occupy. We demonstrate the efficacy of our UE scheduling framework for millimeter-wave massive MU-MIMO and sub-6-GHz cell-free massive MU-MIMO systems, and we show that it outperforms existing scheduling algorithms while approaching the performance of an exhaustive search.

💡 Research Summary

This paper addresses the fundamental problem of user equipment (UE) scheduling in multi‑user (MU) massive MIMO systems, including both millimeter‑wave (mmWave) and sub‑6 GHz cell‑free deployments. The authors argue that most existing scheduling solutions rely on greedy heuristics that select users one at a time, which prevents a global view of resource allocation and makes it difficult to enforce practical constraints such as minimum and maximum numbers of users per time slot or minimum and maximum numbers of slots per user.

To overcome these limitations, the authors formulate UE scheduling as a binary matrix optimization problem: a matrix C∈{0,1}^{U×T} indicates whether user u is active in time slot t. The objective is to minimize a generic cost function F(C) subject to two families of linear inequality constraints. The first family (C_U) enforces that each time slot contains at least U_min and at most U_max active users. The second family (C_T) forces each user to occupy at least T_min and at most T_max slots. This formulation is combinatorial and NP‑hard in its original discrete form.

The key methodological contribution is a relaxation‑and‑refinement scheme. The binary matrix is first relaxed to a continuous matrix in the unit hypercube. The resulting non‑convex but smooth problem is tackled with Forward‑Backward Splitting (FBS), a proximal‑gradient method well suited for problems that consist of a differentiable term (the objective) plus a simple convex constraint set. The authors provide explicit gradients for three representative objective functions: (i) post‑LMMSE mean‑squared error (MSE), (ii) channel capacity (log₂det(I+SNR·HHᴴ)), and (iii) sum of achievable rates based on the post‑LMMSE equalizer.

A central technical challenge is the proximal step, which requires projecting a point onto the intersection of two simplexes defined by the inequality constraints. The authors derive the Karush‑Kuhn‑Tucker (KKT) conditions for this projection and propose an efficient algorithm that computes the orthogonal projection in closed form. After a fixed number of FBS iterations, a quantization routine converts the continuous solution back to a binary matrix while guaranteeing that all constraints remain satisfied.

The paper validates the framework through extensive simulations. For the mmWave scenario, channel vectors are generated with a commercial 2‑ray ray‑tracing tool and denoised using the BEACHS algorithm; for the sub‑6 GHz cell‑free case, standard least‑squares channel estimation is employed. In both settings, the authors consider U=32 users, T=2–4 slots, and a range of SNR values. Performance metrics include uncoded bit‑error rate (BER), hard‑output mutual information (HMI), per‑user MSE, and per‑user achievable rate.

Results show that the proposed optimization‑based scheduler consistently outperforms a suite of baseline greedy methods (e.g., semi‑orthogonal user selection, channel‑structure‑based scheduling, chordal distance scheduling, LoFi, LoFi++) across all metrics. The performance gap is typically 10–20 % in terms of rate or BER, and the scheduler’s results lie very close to those obtained by exhaustive search, which enumerates all possible schedules but is computationally infeasible for realistic system sizes. Moreover, the framework respects the prescribed minimum/maximum resource constraints, something many baselines cannot guarantee.

The authors list several contributions: (1) a unified scheduling formulation that accommodates arbitrary differentiable cost functions; (2) detailed derivations of gradients for the three cost functions; (3) a novel KKT‑based projection algorithm for intersecting simplexes; (4) a quantization step that yields feasible binary schedules; (5) extensive performance evaluation in both mmWave massive MIMO and sub‑6 GHz cell‑free massive MIMO, demonstrating superiority over existing methods. The MATLAB implementation will be released on GitHub after review, facilitating reproducibility.

Limitations are acknowledged. The FBS algorithm may converge to local minima because the relaxed problem remains non‑convex. The quantization step, while constraint‑preserving, could introduce sub‑optimality in some edge cases. The current work focuses solely on time‑slot scheduling; extending the approach to joint time‑frequency or UE‑to‑beam association is left for future research. Potential future directions include learning‑based initialization to improve convergence, multi‑objective formulations (e.g., jointly optimizing rate and energy efficiency), and real‑time low‑complexity variants suitable for hardware implementation.

Overall, the paper presents a solid, mathematically rigorous, and practically relevant framework that advances the state of the art in MU‑MIMO scheduling by moving from greedy heuristics to a globally aware, optimization‑driven methodology.