Adaptive Unconstrained MQAM

• Adaptive unconstrained MQAM is a modulation scheme that flexibly varies constellation cardinality, geometry, and bit mapping to maximize spectral efficiency and energy savings under dynamic channel conditions.
• It employs both analytic and data-driven methods—including neural autoencoders and water-filling power allocation—to optimize key performance metrics while meeting BER and power constraints.
• The approach extends to diverse applications such as coherent fiber communications, wireless MIMO, and FSO links, enhancing multiuser performance and overcoming the limitations of conventional adaptive MQAM.

Adaptive unconstrained M-ary quadrature amplitude modulation (MQAM) refers to families of transmission schemes in which the constellation cardinality, geometry, bit-mapping, and modulation labels are flexibly varied to optimize spectral efficiency, reliability, energy efficiency, or multiuser utility, under time-varying channel and system constraints. Unlike conventional adaptive MQAM, which is typically restricted to a finite set of standard rectangular constellations and fixed bit mappings (usually Gray mapping), unconstrained adaptive MQAM includes both geometric and algebraic degrees of freedom, and may even realize continuous or nonuniform constellation distributions. Recent research demonstrates that such unconstrained adaptivity, especially when enabled by data-driven or optimization-based frameworks, unlocks significant shaping gains and adaptivity not attainable with classical approaches. Adaptive unconstrained MQAM finds application across coherent fiber communications, terrestrial wireless/stationary MIMO, FSO (free-space optical) links, and multi-access networks.

1. Theoretical Foundations and Channel Models

In adaptive unconstrained MQAM, the essential problem is to maximize a chosen performance objective—such as average spectral efficiency (ASE), achievable information rate (AIR), energy efficiency, or sum-rate—subject to channel constraints (fading/shadowing statistics, SNR, turbulence, pointing errors), system constraints (long-term/instantaneous power, target BER, FEC code rate), and implementation complexity.

• In FSO links under Gamma–Gamma turbulence and pointing error, adaptive unconstrained MQAM achieves the channel capacity subject to a BER constraint and average power budget by dynamically tailoring both the constellation order $M$ and power allocation function $P(I)$ as a function of fading-affected irradiance $I$ (Verma et al., 27 Nov 2025).
• In nonlinear optical fiber channels, the use of geometric and labeling-unconstrained MQAM provides reach and shaping gains by mitigating memoryless nonlinear impairments and optimizing net generalized mutual information (GMI) at each SNR (Jovanovic et al., 2022).
• For indoor WLAN environments with composite fading+shadowing (JFTS model), unconstrained rate and power adaptation over a set of MQAM modes yields maximal $\eta$ under BER and energy constraints (Dey et al., 2017).
• In multiuser MISO downlink systems, adaptive MQAM with symbol-level precoding leverages per-user modulation order and beamforming to maximize goodput or minimize energy consumption under instantaneous constraints (Alodeh et al., 2016).

Each of these channel models involves analytically precise formulation of fading distributions and power allocation policies. In FSO scenarios, for example, the Gamma–Gamma PDF for irradiance is combined with pointing-error statistics, and the optimal power/rate law is derived via water-filling in the $I$ domain (Verma et al., 27 Nov 2025).

2. Design and Optimization Techniques

Adaptive unconstrained MQAM schemes encompass a range of algorithmic solutions, from direct analytic optimization to neural network–based autoencoders.

• Optimal continuous-rate/power adaptation: Theoretically, with perfect CSI, the continuous optimum for constellation size and power as a function of the current SNR $\gamma$ is $M^*(\gamma) = 1 + \mathcal K\,\gamma$ (where $\mathcal K$ is a BER-dependent constant), and the water-filling power allocation $P(\gamma)$ achieves the spectral efficiency limit, with the cutoff chosen by the average power constraint (Verma et al., 27 Nov 2025).
• Finite-mode adaptive MQAM: In practical systems, only a countable set of QAM modes are feasible. The optimal continuous adaptation is discretized by partitioning the SNR space into intervals $[\gamma_{i-1},\gamma_i)$, with $M_i$ chosen accordingly, and corresponding power levels set to just meet the target BER (Verma et al., 27 Nov 2025, Dey et al., 2017).
• Autoencoder-based geometric shaping: A neural autoencoder framework jointly learns both an unconstrained constellation geometry and bit labeling. The encoder maps $m$-bit input words to $\mathbb{R}^2$ constellation points via a parameterized function, and the decoder recovers bit LLRs. The end-to-end loss is bitwise cross-entropy, equivalent to maximizing GMI. No grid or symmetry constraints are imposed; points and mapping are optimized end-to-end (Jovanovic et al., 2022).
• Per-symbol symbol-level precoding: In MISO downlink, the CIPM-AM approach solves for, on each symbol vector, the minimum transmit vector that drives all user symbols into correct MQAM decision regions, using QCQP or SDP relaxations. Modulation order and SNR target are matched to instantaneous goodput requirements (Alodeh et al., 2016).
• Unconstrained composite-constellation multi-access: For non-orthogonal multiple-access (NOMA) scenarios, phase, power, and modulation allocation over the user set are optimized to maximize the minimum composite constellation distance, using either offline lookup or grid search (Shakya et al., 16 Feb 2024).

In all cases, the key parameter to be optimized is either a mapping between instantaneous SNR and MQAM order (possibly with power), or an end-to-end mapping from coded bits to transmitted shapes and decoding regions under error/throughput constraints.

3. Achievable Rate, Power, and Spectral Efficiency

The performance of adaptive unconstrained MQAM is quantified through several metrics:

• Average Spectral Efficiency ($\eta$): For both continuous and finite-constellation adaptivity, the average rate is $\eta = \mathrm{E}[\log_2 M(\gamma)]$, optimized through analytical integration over the SNR/Irradiance PDF (Verma et al., 27 Nov 2025, Dey et al., 2017). In FSO, with six square MQAM constellations, the gap to the unconstrained limit is at most $0.12$ bits/s/Hz across 0–30 dB (Verma et al., 27 Nov 2025).
• Shaping Gain: Unconstrained geometric AEs yield SNR gains (in dB) necessary to reach a fixed net GMI versus uniform QAM. In fiber systems, a full single-span benefit (up to 300 km) is realized over BICM with Gray mapping (Jovanovic et al., 2022).
• Energy Efficiency: For symbol-level precoded downlink, adaptive MQAM provides $2.2$ dB transmit-power reduction and increased energy efficiency over conventional user-level beamforming under similar throughput (Alodeh et al., 2016).
• Sum-rate and Error-Rate in NOMA: Unified composite constellations using adaptive phase, modulation, and power in multiuser systems exhibit 1–2 dB SNR advantage and avoid error floors characteristic of conventional NOMA (Shakya et al., 16 Feb 2024).

A representative table from (Dey et al., 2017):

TBER	Rate Adaptation Only	Power Adaptation Only	Joint Rate+Power (I-BER)	Joint Rate+Power (A-BER)
$10^{-3}$	3.75	3.40	3.92	3.50
$10^{-6}$	4.10	3.60	4.32	3.85

(at $\bar\gamma = 20$ dB, spectral efficiency $\eta$ in bits/s/Hz, JFTS channel).

4. Bit Mapping, Labeling, and Fine-grained Rate Adaptation

Unconstrained adaptive MQAM is characterized not just by flexible constellation orders, but also by the way it handles bit-to-symbol assignments:

• Autoencoder-based label optimization: The bit labeling is optimized jointly with geometry such that, at each SNR, unreliable bit positions (those with low GMI) can be declared “dummy” (non-informative), yielding fine-grained net rate control and, in effect, allowing any net rate between $m R_{\rm FEC}$ and 0 (where $m$ is bits/symbol and $R_{\rm FEC}$ the code rate). Many-to-one mapping (MOM) can merge several bit patterns to the same physical point, further enhancing robustness to channel degradation (Jovanovic et al., 2022).
• SNR-thresholds for mode switching: In practical finite-constellation schemes, the SNR thresholds $\gamma_i = (M_i-1)/\mathcal K$ are determined such that the fixed BER is maintained in each region. This enables system operation at arbitrary points along the spectral efficiency–reliability tradeoff (Verma et al., 27 Nov 2025, Dey et al., 2017).
• Dynamic adaptation: In fading or time-varying channels, adaptation logic can use pilot-aided SNR or channel state feedback (quantized to a few bits) to trigger instantaneous switching or merging of MQAM modes with negligible control overhead (Verma et al., 27 Nov 2025, Jovanovic et al., 2022).

5. Multiuser, Multi-access, and Precoding Contexts

The scope of adaptive unconstrained MQAM extends to multiuser and non-orthogonal access environments:

• Adaptive Constellation Multiple Access (ACMA): In ACMA for beyond 5G systems, the base station computes per-user phase offsets, constellation order, and power allocation to maximize the minimum Euclidean distance of the unified composite constellation. This makes the system fully agnostic to specific user modulations or power splits, and provides robustness with minimal online complexity (Shakya et al., 16 Feb 2024).
• Symbol-level MISO Precoding: Joint design of precoder weights and per-user adaptive MQAM order under per-symbol and per-user SNR/goodput constraints allows for each user's modulation to be selected precisely to match channel conditions, all subject to minimum transmit power QCQP (Alodeh et al., 2016).

A plausible implication is that unconstrained MQAM, when co-designed with multiuser detection and precoding, can enable unprecedented flexibility in multi-access scheduling, user separation, and throughput scaling in dense, high-throughput scenarios.

6. Implementation Complexity and Practicality

The feasibility of adaptive unconstrained MQAM depends on implementation complexity:

• In FSO, operation over six QAM constellations suffices to achieve within $0.10$–$0.12$ b/s/Hz of the unconstrained spectral efficiency limit. Only matching power levels and lookup-based mode selection are required at the transmitter; the receiver only performs MQAM soft demodulation for these constellations (Verma et al., 27 Nov 2025).
• Autoencoder-based shaping is compatible with conventional hardware, requiring only offline training; at runtime, standard LLR demapping and FEC decoding suffice (Jovanovic et al., 2022).
• Multiuser beamforming and symbol-level precoding-based adaptive MQAM can be solved efficiently for moderate user/set sizes and are suitable for parallelization in cloud-RAN or BS-level acceleration (Alodeh et al., 2016).
• Multi-access composite constellation design admits offline optimization and lookup for small user and constellation count, with on-the-fly adaptation based on channel-quality indicators (Shakya et al., 16 Feb 2024).

The minimal run-time and signaling overheads make unconstrained adaptive MQAM realizable within contemporary communication systems across fiber, wireless, and optical domains.

7. Perspectives and Ongoing Challenges

Adaptive unconstrained MQAM as realized through both analytic and data-driven means now offers near-capacity performance in a wide range of fading, shadowing, nonlinear, and multiuser regimes. Practical limitations remain in scenarios with highly dynamic mobility, stringent fairness/latency constraints, or where joint adaptation across users and layers is required. Ongoing work includes deeper integration with higher-layer scheduling, robustness to estimation error in CSI/SNR, and the co-design of FEC and HARQ protocols matched to the fine-grained adaptation enabled by these frameworks.

References:

• "Maximum Spectral Efficiency With Adaptive MQAM Transmissions Over Terrestrial Coherent FSO Links" (Verma et al., 27 Nov 2025)
• "Rate Adaptive Autoencoder-based Geometric Constellation Shaping" (Jovanovic et al., 2022)
• "Adaptive Constellation Multiple Access for Beyond 5G Wireless Systems" (Shakya et al., 16 Feb 2024)
• "Symbol-Level Multiuser MISO Precoding for Multi-level Adaptive Modulation" (Alodeh et al., 2016)
• "Adaptive M-QAM for Indoor Wireless Environments : Rate & Power Adaptation" (Dey et al., 2017)