Digital and Hybrid Precoding and RF Chain Selection Designs for Energy Efficient Multi-User MIMO-OFDM ISAC Systems

Technical Summary: Digital and Hybrid Precoding and RF Chain Selection Designs for Energy Efficient Multi-User MIMO-OFDM ISAC Systems

Problem Statement
While Integrated Sensing and Communication (ISAC) systems utilizing Multiple-Input Multiple-Output (MIMO) and Orthogonal Frequency Division Multiplexing (OFDM) have gained significant attention, existing research primarily focuses on improving sensing and communication performance metrics. There is a notable gap in addressing Energy Efficiency (EE) for wideband MIMO-OFDM ISAC systems. Specifically, current EE studies largely concentrate on narrowband systems and often overlook the substantial power consumption of Radio-Frequency (RF) circuits. As the number of antennas increases, the energy cost of RF chains becomes critical. The challenge lies in jointly optimizing precoding and RF chain selection (ON/OFF switching) to maximize EE while satisfying stringent sensing performance constraints, a task complicated by the non-convex nature of the problem and the distinct channel fading experienced across different subcarriers in wideband systems.

Methodology
The paper proposes a comprehensive framework for joint precoding and RF chain selection across three antenna architectures: Fully Digital (FD), Fully-Connected (FC) Hybrid, and Partially-Connected (PC) Hybrid.

1. Problem Formulation: The authors formulate an EE maximization problem subject to sensing performance constraints (defined by a lower bound on beam power toward target angles) and total transmit power limits. The objective function involves a fractional ratio of spectral efficiency (SE) to total power consumption, where the latter includes a non-differentiable unit-step function representing RF chain activation.
2. FD Precoding Solution:
   • Approximation: To handle the non-differentiable unit-step function, the authors approximate it using a hyperbolic tangent function, parameterized by a coefficient $\lambda$.
   • Transformation: The fractional objective is transformed into a subtractive form using the Quadratic Transform (QT). The non-convex SE term is addressed via the Weighted Minimum Mean Square Error (WMMSE) method.
   • Iterative Optimization: The resulting problem is solved using Successive Convex Approximation (SCA). An iterative algorithm (Algorithm 1) is proposed where $\lambda$ is gradually increased to tighten the approximation, eventually converging to a 0-1-like solution for RF chain selection.
   • Alternatives: To avoid approximation errors, the paper also proposes brute-force and greedy-based approaches. The brute-force method exhaustively searches all RF chain combinations, while the greedy method iteratively turns off chains if EE improves.
3. Hybrid Precoding (FC and PC) Solution:
   • The approach for hybrid architectures builds upon the FD solution. First, an optimal FD precoder is obtained for a specific number of active RF chains.
   • Matching: The hybrid design is then formulated as a matrix matching problem, minimizing the Frobenius norm distance between the optimal FD precoder and the product of the analog and digital precoders.
   • Decomposition: For both FC and PC architectures, Block Coordinate Descent (BCD) is used to iteratively update the analog and digital precoders. For the PC architecture, the problem is decomposed into independent subproblems for each RF chain subarray.
4. Tradeoff Extension: The framework is extended to provide Spectral Efficiency (SE) vs. Power Consumption tradeoff designs by modifying the objective function to a weighted sum.

Key Contributions

• Novel Investigation: This is the first work to investigate joint precoding and RF chain selection for EE maximization specifically in multi-user MIMO-OFDM ISAC systems, addressing the gap left by existing narrowband-focused studies.
• Algorithmic Framework: The paper proposes efficient iterative algorithms for FD, FC, and PC architectures. The FD approach utilizes QT, WMMSE, and SCA with hyperbolic tangent approximation, while the hybrid approaches utilize a matching-based strategy derived from the FD solution.
• Alternative Designs: The inclusion of brute-force and greedy-based alternatives provides benchmarks for optimality and complexity tradeoffs.
• Theoretical Analysis: The paper provides rigorous convergence and complexity analyses, demonstrating that the proposed iterative approach converges monotonically and offers lower computational complexity compared to exhaustive search methods.

Simulation Results
Extensive simulations were conducted under two setups with varying parameters (e.g., number of antennas, targets, and SNR).

• EE-Sensing Tradeoff: The proposed iterative approach consistently outperforms reference schemes from existing literature (e.g., [14], [23], [30]) in terms of the EE-detection probability tradeoff.
• Performance vs. Complexity: The proposed iterative approach achieves performance very close to the brute-force method (which is optimal but computationally prohibitive) and the greedy method, but with significantly lower runtime.
• RF Chain Adaptation: Results show that the proposed methods effectively adapt the number of active RF chains based on sensing requirements ($P_{th}$). As sensing requirements increase, the algorithms activate more chains; conversely, they deactivate unnecessary chains to save power when requirements are lower.
• Architecture Comparison: In the context of EE, the PC architecture is shown to be more energy-efficient than the FC architecture due to the reduced number of phase shifters, whereas the FC architecture incurs higher power consumption from its dense phase shifter network.

Significance and Claims
The paper claims that its proposed designs fill a critical gap in the ISAC literature by addressing energy efficiency in wideband, multi-user scenarios where both transmit power and hardware circuit power are jointly optimized. The authors assert that their approaches offer a superior balance between EE and sensing performance compared to existing schemes. Furthermore, the ability to dynamically adjust RF chain activation allows the system to operate efficiently under varying sensing constraints, making the proposed designs suitable for next-generation wireless networks where energy sustainability is paramount. The work also provides a pathway for SE-power tradeoff designs, offering flexibility for different network operational modes.