Technology Category
Search and Optimization: Mixed Discrete/Continuous SearchConstraint Satisfaction and Optimization: Other Foundations of Constraint SatisfactionPlanning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
How Many Simultaneous Beamformers are Needed for Integrated Sensing and Communications?
🤖 AI Summary
This work investigates the minimum number of downlink beamformers required to achieve joint optimal sensing and communication performance in Integrated Sensing and Communication (ISAC) systems. Specifically, we consider a base station simultaneously serving $K$ users and estimating $L$ sensing parameters. We derive the first theoretical lower bound on the number of jointly designed beamformers, revealing that—when interference cannot be fully eliminated—the required beam count may be strictly less than the sum of individual communication and sensing requirements. Our analysis leverages linear beamforming design, Cramér–Rao bound modeling for parameter estimation, SINR characterization, and quadratic optimization. We establish an upper bound on the requisite number of beams: either $K + sqrt{L(L+1)/2}$ or $sqrt{K^2 + L(L+1)/2}$, with exact characterization achieved for the single-target sensing case. The core contribution is a fundamental theoretical lower bound quantifying the intrinsic coupling between sensing and communication beam resources, thereby significantly reducing the resource overhead compared to conventional decoupled designs.
Technology Category
Application Category
📝 Abstract
Consider a downlink integrated sensing and communications (ISAC) system in which a base station employs linear beamforming to communicate to $K$ users, while simultaneously uses sensing beams to perform a sensing task of estimating $L$ real parameters. How many beamformers are needed to achieve the best performance for both sensing and communications? This paper establishes bounds on the minimum number of downlink beamformers, in which sensing performance is measured in terms of the Cramér-Rao bound for parameter estimation and communications performance is measured in terms of the signal-to-interference-and-noise ratios. We show that an ISAC system requires at most $K + sqrt{frac{L(L+1)}{2}}$ beamformers if the remote users have the ability to cancel the interference caused by the sensing beams. If cancelling interference due to the sensing beams is not possible, the bound becomes $sqrt{K^2 + frac{L(L+1)}{2}}$. Interestingly, in the latter case, the bound on the number of beamformers is less than the sum of the bounds for each task individually. These results can be extended to sensing tasks for which the performance is measured as a function of $d$ quadratic terms in the beamformers. In this case, the bound becomes $K + sqrt{d}$ and $sqrt{K^2 + d}$, respectively. Specifically, for estimating complex path losses and angles-of-arrival of $N_ ext{tr}$ targets while communicating to $K$ users, the bound on the minimum number of beamformers scales linearly in $K$ and in $N_ ext{tr}$, assuming interference from sensing can be cancelled. When interference cancellation is not possible, the following exact characterization for the case of $N_ ext{tr} = 1$ can be obtained: when $K=0$ or $1$, two beamformers should be used; when $K ge 2$, exactly $K$ beamformers should be used, i.e., communication beamformers alone are already sufficient.
Problem
Research questions and friction points this paper is trying to address.
Determine minimum beamformers for ISAC performance
Bound beamformers for sensing and communication tasks
Analyze beamformer scaling with interference cancellation
Innovation
Methods, ideas, or system contributions that make the work stand out.
Uses linear beamforming for ISAC systems
Bounds beamformers by Cramér-Rao and SINR
Scales beamformers with K and N_tr
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