Integrating Sensing, Computing, and Communication in 6G Wireless Networks: Design and Optimization (2207.03634v1)

Abstract: The roll-out of various emerging wireless services has triggered the need for the sixth-generation (6G) wireless networks to provide functions of target sensing, intelligent computing and information communication over the same radio spectrum. In this paper, we provide a unified framework integrating sensing, computing, and communication to optimize limited system resource for 6G wireless networks. In particular, two typical joint beamforming design algorithms are derived based on multi-objective optimization problems (MOOP) with the goals of the weighted overall performance maximization and the total transmit power minimization, respectively. Extensive simulation results validate the effectiveness of the proposed algorithms. Moreover, the impacts of key system parameters are revealed to provide useful insights for the design of integrated sensing, computing, and communication (ISCC).

• The paper introduces a unified framework for integrating sensing, computing, and communication in 6G networks, enabling joint beamforming optimization.
• It employs alternating optimization algorithms to iteratively optimize receive and transmit beams, reducing MSE and enhancing SINR performance.
• Simulation results demonstrate fast convergence and significant improvements over baseline methods in sensing accuracy, computing reliability, and power efficiency.

This paper addresses the growing need for integrated sensing, computing, and communication (ISCC) functionalities in future sixth-generation (6G) wireless networks, which are required to support emerging services like autonomous vehicles, holographic communication, and extended reality. Unlike current 5G systems where these functions are largely separate, 6G envisions a unified architecture to improve the utilization of limited spectrum and power resources. The authors propose a general framework for ISCC involving a multi-antenna base station (BS) and multiple multi-antenna sensors.

The system model considers a BS equipped with $N$ antennas and $K$ multi-function sensors each with $M$ antennas, where $KM \leq N$. Each sensor transmits a superposition of sensing, computing, and communication signals. Sensing signals are used to estimate reflection coefficients of $I$ targets in a defined range of interest (ROI), which may also contain $O$ clutters acting as interference. Computing signals facilitate federated learning (FL) by enabling the BS to aggregate local model parameters from sensors (Over-the-Air FL). Communication signals carry data to be decoded at the BS. The paper models the cascaded channels for sensing (sensor-target-BS path) and direct channels for computing and communication (sensor-BS path). Noise is modeled as AWGN.

The performance of each function is quantified by specific metrics:

• Sensing: The accuracy of estimating target reflection coefficients is measured by the Mean Squared Error (MSE) between the estimated and actual coefficients ($\text{MSE}_{i}^{\text{sens}}$ for target $i$). This MSE is influenced by interference from other sensing signals, clutter reflections, computing signals, communication signals, and noise.
• Computing: The distortion in aggregating local model parameters for FL is measured by the MSE between the estimated aggregated signal at the BS and the desired global model signal ($\text{MSE}_{l}^{\text{comp}}$ for the $l$-th model parameter). This MSE is also affected by cross-interference from other computing signals, sensing signals (including clutter reflections), communication signals, and noise.
• Communication: The quality of data transmission is measured by the Signal-to-Interference-plus-Noise Ratio (SINR) for each communication stream ($\Gamma_{k,j}$ for the $j$-th stream from sensor $k$). The SINR is influenced by desired signal strength, interference from other communication streams, and cross-interference from sensing (including clutter) and computing signals, as well as noise.

The paper highlights that these three performance metrics are interdependent and potentially competitive for system resources, necessitating a joint optimization approach for transmit beamforming vectors at the sensors and receive beamforming vectors at the BS.

Two typical multi-objective optimization problems (MOOPs) are formulated to capture different system priorities:

1. Weighted Overall Performance Maximization (WOPM): This problem minimizes a weighted sum of normalized performance metrics (normalized MSEs for sensing and computing, and normalized log-MSE for communication, which is equivalent to maximizing weighted sum-rate) subject to individual sensor transmit power constraints. The weights ($\alpha_1, \alpha_2, \alpha_3$) represent the priorities assigned to sensing, computing, and communication, respectively, summing to 1.
2. Total Transmit Power Minimization (TTPM): This problem minimizes the sum of transmit powers across all sensors subject to minimum quality of service (QoS) requirements for each function (maximum tolerable MSEs for sensing and computing, and minimum required SINRs for communication).

Since both MOOPs are non-convex due to the coupling of transmit and receive beamforming variables, the authors propose alternating optimization (AO) algorithms to find sub-optimal solutions.

WOPM Algorithm (Algorithm 1):

The AO algorithm iterates between optimizing receive beams, weight variables (for communication's weighted MSE formulation), and transmit beams.

• Receive Beam Optimization: By fixing transmit beams and weights, the problem decomposes. Applying KKT conditions yields optimal receive beamforming vectors (MMSE receivers) for sensing ($\mathbf{v}_i$), computing ($\mathbf{z}_l$), and communication ($\mathbf{u}_{k,j}$), expressed as closed-form solutions involving channel matrices and transmit beamforming vectors.
• Weight Variable Optimization: Fixing transmit and receive beams, the optimal weights for the weighted communication MSE are found in closed-form using the first-order derivative of the objective.
• Transmit Beam Optimization: Fixing receive beams and weights, the problem becomes a convex quadratic constrained quadratic programming (QCQP) problem. This subproblem is solved using an interior-point method (IPM), specifically the barrier method combined with Newton's method, which iteratively updates the transmit beams ($$\mathbf{a}_{k,i}, \mathbf{b}_{k,l}, \mathbf{c}_{k,j}$$) based on gradients and Hessians derived from the objective function and power constraints.

TTPM Algorithm (Algorithm 2):

The AO algorithm iterates between optimizing receive beams and transmit beams.

• Receive Beam Optimization: MMSE receivers derived in the WOPM algorithm are also used here when transmit beams are fixed.
• Transmit Beam Optimization: Fixing receive beams, the problem remains non-convex due to the SINR constraints. The authors transform the SINR constraint into an inequality involving trace and auxiliary variables $$\mathbf{C}_{k,j} = \mathbf{c}_{k,j}\mathbf{c}_{k,j}^H$$. The rank-one constraint $\text{Rank}(\mathbf{C}_{k,j})=1$ is then relaxed using semi-definite relaxation (SDR), resulting in a semi-definite programming (SDP) problem that can be solved using standard convex optimization solvers like CVX. A theorem is proven demonstrating that the optimal solution of the relaxed SDP is indeed rank-one for the communication matrices $\mathbf{C}_{k,j}$, allowing the recovery of the optimal transmit communication beams $\mathbf{c}_{k,j}$ via eigenvalue decomposition (EVD).

Convergence and Complexity:

Both algorithms are shown to be convergent based on the monotonic non-increasing nature of their respective objective functions and lower bounds on performance/power, leveraging the Monotone Bounded Convergence theorem. The per-iteration computational complexity for both algorithms stems primarily from solving the transmit beamforming subproblems (QCQP for WOPM, SDP for TTPM). The complexity analysis is presented, showing that the runtime is polynomial in the problem size (number of antennas, sensors, targets, etc.) and logarithmic in the desired precision, making them computationally feasible, particularly Algorithm 1.

Simulation Results:

Extensive simulations validate the effectiveness and reveal key insights:

• Both algorithms demonstrate fast convergence within a few iterations.
• For WOPM, varying the priority weights allows trading off performance among sensing, computing, and communication. Higher sensor transmit SNR and increasing the number of sensors and BS antennas generally improve overall performance.
• Comparisons show that the proposed WOPM algorithm outperforms baseline methods (fixed-MMSE, MFBF, ZFBF) in achieving better sensing accuracy, computing accuracy, and communication rate simultaneously.
• For TTPM, loosening the QoS requirements for sensing, computing, or communication reduces the total transmit power consumption.
• Increasing the number of clutters significantly increases the required total transmit power to meet QoS constraints, while increasing the number of BS antennas helps reduce power consumption by exploiting array gains.
• The proposed TTPM algorithm achieves lower total transmit power compared to baseline methods for given QoS requirements, demonstrating its power efficiency, especially under stringent communication demands.

In conclusion, the paper provides a unified framework and practical beamforming design algorithms for integrating sensing, computing, and communication in 6G wireless networks. The results highlight the trade-offs involved and the benefits of optimizing transmit and receive beamforming jointly, demonstrating the feasibility and performance gains of ISCC in future wireless systems. The authors also point out that deep integration and cross-layer optimization across sensing, computing, and communication are necessary to meet the ultra-high performance requirements of future applications.