RL-Based Beam Weighting Framework

• Reinforcement learning based beam weighting frameworks are advanced optimization strategies that autonomously design beamforming weights while bypassing explicit CSI and enforcing hardware constraints.
• They leverage RL algorithms such as actor–critic, DQN, PPO, and multiagent approaches to effectively navigate complex state-action spaces in mmWave, massive MIMO, and satellite systems.
• Extensive simulations demonstrate rapid convergence near-optimal beamforming gains, improved energy efficiency, and enhanced coverage across diverse wireless scenarios.

A reinforcement learning based beam weighting framework refers to a class of optimization methodologies that utilize RL techniques to autonomously design, adapt, or select transmit/receive beamforming weight vectors in large-array wireless systems, including mmWave/THz MIMO, massive MIMO, ISAC, satellite, and energy beamforming networks. These frameworks directly interact with the environment via signal or power measurements, obviating the need for explicit CSI, and are architected to enforce practical hardware constraints such as constant-modulus, quantized-phase, and limited beam-codebook structures. They leverage advanced RL formulations (actor–critic, value-based, policy-gradient, multiagent), complex state-action spaces, and neural approximators (DQN, PPO, A3C, Wolpertinger-variant architectures), and are validated against conventional beam design and searching methods on standardized datasets or realistic deployments.

1. System and Channel Models

Reinforcement learning based beam weighting frameworks are deployed across a range of wireless scenarios, including fully analog/hybrid mmWave MIMO front-ends with large antenna arrays, ISAC systems, UAV communications, LEO satellite constellations, and RF energy transfer systems. The common baseline is a signal model of the form: $$y = \mathbf{w}^H\mathbf{h} \, x + \mathbf{w}^H\mathbf{n}$$ with $\mathbf{w}$ the beam weight vector and $\mathbf{h}$ a geometric multipath channel, usually expressed as

$$\mathbf{h} = \sum_{\ell=1}^L \alpha_\ell \mathbf{a}(\phi_\ell)$$

where $\mathbf{a}(\phi)$ is the array steering vector accounting for arbitrary array errors or hardware impairments such as per-element position errors and phase mismatches. In beam weighting for satellite positioning, the observable is a function of the user location and beam center, and the system state embeds geometric, link-quality and previous estimation features (Chou et al., 12 Nov 2025). Hardware constraints are imposed at the weight level: constant-modulus ($|w_m|=1/\sqrt{M}$), phase-only ($\theta_m\in\Theta$), and quantization (e.g., $r$-bit entries).

2. RL Problem Formulations

The mapping of beam search and codebook optimization to an MDP is central. The state typically encodes the current beam configuration, recent measurements, environmental features (user positions, buffer states, prior codewords, etc.), or in multi-agent setups, the full summary of global actions and rewards (Bai et al., 2020). The action can be an entire phase vector ($\Theta^M$), a codebook index for each specified beam (Zhang et al., 2021), or power and beamwidth selection (Gao et al., 2020). The reward reflects the dominant design metric, from SNR/beamforming gain (Zhang et al., 2021), data rate, harvested energy, coverage, buffer discharge (Wang et al., 9 May 2025), or estimation error (Chou et al., 12 Nov 2025). Notably, discrete ternary rewards, sum-rates, and penalty-augmented objectives for positioning accuracy are all utilized across frameworks.

The table below summarizes state, action, and reward realizations in representative frameworks:

Reference	State	Action	Reward
(Zhang et al., 2021)	Phase vector $\in\Theta^M$	Next phase vector	Ternary: +1/0/-1 (RSSI gain)
(Zhang et al., 2021)	Phase/codeword vector	Next codeword/phase	Relative gain, ternary
(Praneeth et al., 2021)	UAV loc., past beams	TX/RX beam-pair	+1 if rate≥best-so-far, –1 otherwise
(Wang et al., 9 May 2025)	Buffers, beam powers	λ, codebook index shift	Buffer/throughput based
(Chou et al., 12 Nov 2025)	Geometry+SINR+prior WLS error	Beam weights	–(WLS error)^2 + SINR, entropy terms
(Bai et al., 2020)	Energy/previous codebook indices	Each agent: beam codeword	Total energy, constraint penalties

3. DRL Architectures and Training Algorithms

The curse of dimensionality (action space scaling as $|\Theta|^M$) is addressed using actor–critic (DDPG, Wolpertinger-variant), value-based DQN, policy-gradient (PPO), or multiagent A3C decompositions. Notable developments:

• Wolpertinger-variant actor–critic: The actor network outputs a continuous proto-action, quantized to nearest valid phase or codebook member. The critic evaluates Q(s,a), and target networks with soft updates ensure stability (Zhang et al., 2021, Zhang et al., 2021).
• DQN for codebook/beam-pair optimization: Fully connected networks with one-hot or history-embedded states, two hidden layers (typically 128 units), and linear output per action (Praneeth et al., 2021, Shafin et al., 2019).
• PPO and Policy Gradient: For sequence decision-making, PPO with clipped surrogate objectives and entropy regularization demonstrates efficient convergence in multi-beam, multi-user ISAC scenarios (Wang et al., 9 May 2025).
• Multi-agent A3C: Each transmitter in a distributed energy beamforming setup operates as an independent agent with local policy/value heads; coordination emerges via state-augmentation and intermediate-state rollout, bypassing exponential action explosion (Bai et al., 2020).

All architectures are paired with experience replay, target networks (for stability), stochastic exploration strategies ($\epsilon$-greedy, Ornstein-Uhlenbeck noise), mini-batch updates, and Adam optimization.

4. Hardware Constraint Handling

Beam weighting optimization must comply with the physical constraints imposed by mmWave/THz RF front-ends:

• Constant-modulus: Ensured by parameterizing the beamweight via phase-only vectors, always dividing by $\sqrt{M}$.
• Quantized phases: Actions–either via direct codebook lookup or hard quantization of proto-action outputs–are projected to the nearest quantization grid ($\Theta$).
• Multi-beam superposition and normalization: For scenarios using more than one active beam/precoder per user, weights are normalized ($\ell_1$ or $\ell_2$), and high-correlation duplicates in the action space are pruned (Chou et al., 12 Nov 2025).

These constraints are enforced both by direct construction (state-action mapping) and in the neural pipeline (quantization or soft-proxy layers), ensuring all actions are feasible in hardware (Zhang et al., 2021, Zhang et al., 2021).

5. Performance Evaluation and Comparison

Simulation results on standard datasets (e.g., DeepMIMO O1_60, I1_28B) and scenario-specific platforms demonstrate near-optimality and rapid convergence of RL-based frameworks:

• Beamforming gain: Achieves 90–95% of EGC (equal-gain combining) bounds within $10^4–10^5$ iterations; robust to hardware impairments with <2 dB loss even under significant phase/spacing errors (Zhang et al., 2021, Zhang et al., 2021).
• Convergence speed: Orders-of-magnitude faster than classical beam sweep or bandit algorithms, typically converging in $10^2–10^3$ episodes (Praneeth et al., 2021).
• Coverage and throughput: Self-tuning sectorization (Double-DQN) closes the gap to Oracle (exhaustive) performance for both periodic and Markovian user mobility, eliminating coverage gaps due to static codebooks (Shafin et al., 2019).
• ISAC use cases: PPO-based agents dynamically switch between single high-gain beam and multi-beam refinement modes, maintaining high throughput (>0.80 normalized) under high user mobility, outperforming both periodic sweep and CRLB-based AoD heuristics (Wang et al., 9 May 2025).
• Energy beamforming: A3C based distributed beam selection boosts harvested energy by 40–60% over random codebooks, showing superior convergence and energy fairness (Bai et al., 2020).
• LEO satellite positioning: DQN-WLS hybrid reduces RMSE by 99.3% compared to pure geometry baselines, with real-time inference capability (Chou et al., 12 Nov 2025).
• Joint resource optimization: DRL-based selection of beamwidth and power simultaneously achieves high throughput and low complexity, generalizing well across network sizes and deployment scenarios (Gao et al., 2020).

6. Key Insights, Limitations, and Practical Extensions

RL-based beam weighting frameworks exhibit strong robustness to channel state uncertainty, hardware nonideality, and environment/model mismatches:

• No CSI is required; optimization relies purely on signal/power feedback or sensing echoes.
• Adaptivity to unknown array geometries, mobile user distributions, and environmental nonstationarity is inherent, owing to the closed-loop RL paradigm (Zhang et al., 2021, Zhang et al., 2021).
• Modular architectures decouple the action space, enabling linear or distributed scaling (not exponential) in array size or agent number (Shafin et al., 2019, Bai et al., 2020).

However, several limitations are recognized:

• Current RL-based designs depend on fixed, finite codebooks and quantized phase sets; extension to continuous beam parameterizations necessitates more sophisticated RL (e.g., policy gradient or actor-critic with continuous action support).
• Convergence and optimality may degrade under severe model mismatch (e.g., real-world versus simulated raytracing), indicating the need for online transfer/fine-tuning.
• Empirical reward shaping, state featurization, and quantization hyperparameters strongly influence learning speed and stability.
• In dense, interference-limited deployments, explicit agent coordination (possibly via GNNs or message passing) may improve global joint beamforming, which is only partially addressed in current approaches (Shafin et al., 2019).

A plausible implication is that the synergy of RL with hybrid analog-digital architectures and low-overhead codebook design will be key in realizing adaptive, hardware-efficient, and fully autonomous beam management for 6G and beyond wireless systems (Zhang et al., 2021, Wang et al., 9 May 2025).

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References:

• "Reinforcement Learning for Beam Pattern Design in Millimeter Wave and Massive MIMO Systems" (Zhang et al., 2021)
• "Reinforcement Learning of Beam Codebooks in Millimeter Wave and Terahertz MIMO Systems" (Zhang et al., 2021)
• "DQN-based Beamforming for Uplink mmWave Cellular-Connected UAVs" (Praneeth et al., 2021)
• "Multiagent Reinforcement Learning based Energy Beamforming Control" (Bai et al., 2020)
• "Multi-User Beamforming with Deep Reinforcement Learning in Sensing-Aided Communication" (Wang et al., 9 May 2025)
• "Self-Tuning Sectorization: Deep Reinforcement Learning Meets Broadcast Beam Optimization" (Shafin et al., 2019)
• "Deep Reinforcement Learning for Joint Beamwidth and Power Optimization in mmWave Systems" (Gao et al., 2020)
• "DRL-Based Beam Positioning for LEO Satellite Constellations with Weighted Least Squares" (Chou et al., 12 Nov 2025)