Stream-Adaptive Quantization and Power Allocation in Fronthaul-Constrained MIMO Systems

Abstract: Many wireless systems divide the baseband processing between two locations, interconnected by a fronthaul. This paper examines the impact of fronthaul quantization on multiple-input multiple-output (MIMO) systems. Starting from a Bussgang-based analysis of quantized single-input single-output (SISO) channels, we extend the framework to MIMO and derive a capacity lower bound under fronthaul quantization, where the receive combining is performed before the quantization. To maximize the sum rate, we propose a joint bit and power allocation (JBP-Alloc) scheme that efficiently distributes fronthaul bits and transmit power across active data streams. Asymptotic analysis shows that uniform bit allocation becomes optimal at high SNR. Numerical results confirm that JBP-Alloc outperforms uniform allocation and quantization-unaware water-filling, and achieves the same performance as Greedy bit allocation but with substantially lower computational complexity.

• The paper introduces the JBP-Alloc algorithm that jointly optimizes quantization bits and power allocation in MIMO systems under fronthaul constraints, significantly improving capacity.
• It employs Bussgang’s theorem and SVD-based spatial decomposition to model quantization effects and transform MIMO channels into parallel SISO streams for tractable resource optimization.
• The study demonstrates that joint resource allocation outperforms traditional water‐filling and uniform bit assignments, promising practical gains for cell‐free massive MIMO deployments.

Stream-Adaptive Quantization and Power Allocation in Fronthaul-Constrained MIMO Systems

Introduction

This paper addresses the problem of fronthaul quantization in MIMO systems, focusing on optimal resource allocation under stringent fronthaul and power constraints. Unlike traditional MIMO analyses that neglect quantization effects between distributed baseband and radio units, the authors construct a formal framework that explicitly models the capacity penalty induced by quantization on fronthaul links. They develop a theoretical analysis from the SISO case, extend it to MIMO channels via SVD-based spatial separation, and provide a capacity lower bound that incorporates both quantization and power allocation. The central contribution is a joint bit and power allocation (JBP-Alloc) algorithm, which optimally distributes quantization bits and transmit power over the active spatial streams. Asymptotic analysis is provided, and numerical results are presented to substantiate the theoretical claims.

Theoretical Framework and Capacity Lower Bounds

SISO and Bussgang-Based Quantization Modeling

The foundation rests on Bussgang’s theorem, providing an elegant decomposition of the quantized channel where the quantizer is modeled via the Lloyd-Max (conditional mean optimal) mapping. The quantized output is split into a linear function of the input and an uncorrelated distortion noise. A lower bound on the mutual information is derived under the assumption that the distortion induced by the quantizer remains uncorrelated with both the channel input and additive noise. The resultant lower bound for SISO channels post-quantization takes the form:

$$I(x;z) \geq \log_2 \left(1 + \frac{(1-\beta)P|h|^2}{\beta P |h|^2 + \sigma^2} \right)$$

where $\beta$ is the quantizer's distortion factor, parameterized by the bit budget and input statistics.

Extension to MIMO via Matrix Decomposition

For MIMO channels, SVD-based diagonalization transforms the system into a set of parallel, independent SISO subchannels, each subject to individual quantization and power allocation. The lower bound for the sum capacity aggregates across these streams with their respective power and bit allocations $(p_i, b_i)$:

$$R\left(\{p_i, b_i\}\right) = \sum_{i=1}^r \log_2 \left(1 + \frac{(1 - \beta_i) p_i s_i^2}{\beta_ip_i s_i^2 + \sigma^2 } \right)$$

This structure accommodates fronthaul quantization noise, enabling downstream optimization of resource allocation.

Joint Bit and Power Allocation: JBP-Alloc Algorithm

The authors formulate the optimization of the stream-wise resource distribution as a constrained maximization of the derived sum-rate lower bound, subject to total fronthaul (bit) and transmit power constraints. The high-rate approximation for $\beta_i$ as a function of quantization bits permits tractable analytic expressions, leading to a closed-form structure for bit allocation:

• For streams with nonzero allocation, the optimal bit assignment exhibits a log-dependence on both the allocated power and channel gain:

$$b_i^\star = \max\left(0, \mu^\star + \log_2(\sqrt{p_i s_i^2})\right)$$

• Power allocation for active streams follows a modified water-filling criterion:

$$p_i = \max\left(0, \lambda' - \frac{\sigma^2}{s_i^2}\right)$$

The resulting JBP-Alloc algorithm searches over the number of active streams, applies bisection for power allocation, and greedily adjusts integer bit allocations to maximize the sum rate without exceeding constraints. Notably, the complexity is reduced to $2r$ bisection searches, a substantial improvement compared to the greedy alternative.

Asymptotic and Numerical Analysis

High-SNR Behavior

At asymptotically high SNR, effects of channel noise become negligible relative to quantization noise, and the optimal bit allocation approaches uniformity across active streams, i.e., $b_i = b_{\text{tot}} / r$. This fundamentally differentiates the regime from classical MIMO, where water-filling is always optimal; here, at high SNR, fairness (in quantization resource allocation) supersedes channel-aware adaptation.

Statistical Evaluation & Comparison

Empirical results demonstrate the superiority of the proposed JBP-Alloc algorithm compared to benchmarks:

• JBP-Alloc consistently matches the sum-rate performance of the computationally expensive Greedy allocation while incurring only a fraction ($b_{\text{tot}}/2$ times) of its complexity.
• For channels with closely grouped singular values (e.g., $\beta$0 Rician fading), uniform bit allocation suffices and matches optimal performance.
• In more skewed channels ($\beta$1), adaptive stream selection and joint allocation show considerable gains, highlighting scenarios where classical water-filling or uniform bit assignments are strictly suboptimal.
• The quantization-unaware water-filling approach can suffer up to 20% sum-rate degradation compared to the proposed method.

These trends are consistent across channel realizations and power/bit regimes.

Implications and Future Work

The findings indicate that when fronthaul quantization is non-negligible, the conventional decoupling of bit and power allocation is fundamentally inadequate. Instead, joint adaptation enables near-information-theoretic achievable rates under practical hardware constraints. Practically, this has implications for cell-free massive MIMO and distributed RAN deployments, where fronthaul bandwidth is a limiting and costly resource.

On a theoretical front, the results motivate further work on hybrid analog-digital quantization strategies, adaptive user scheduling, and cross-layer design where fronthaul allocation is dynamically coordinated with higher-layer resource management. The explicit characterization of the high-SNR regime and bit allocation optimality merits more rigorous analysis in broader scenarios (e.g., non-i.i.d. fading, time-varying channels, multi-user interference).

Conclusion

This study rigorously analyzes and optimizes power and fronthaul quantization resource allocation in SVD-processed MIMO systems. The proposed JBP-Alloc algorithm enables significant capacity improvements with manageable complexity, outperforming both uniform and uncoordinated approaches. The theoretical framework and algorithmic tools presented here provide essential insights for the design of future fronthaul-constrained networks, supporting the evolution toward flexible, high-capacity, and energy-efficient architectures (2604.11471).