Throughput Analysis for Near-Field Mobile Communications: Beamfocusing or Caustic Beamforming?

Abstract: The migration to the Terahertz (THz) band and the deployment of extremely large antenna arrays (ELAAs) are transitioning wireless communications into the radiative near-field regime, fundamentally evolving conventional angular beam steering to beamfocusing (BF). However, the combination of the extremely narrow beamwidth and the mobility of the users necessitates frequent beamfocusing reconfigurations, incurring a significant switching overhead that degrades the system achievable throughput. In this regard, caustic beamforming (CB) is a promising alternative based on the synthesis of a continuous curved beam, which eliminates the need for beam tracking at the expense of a distributed beamforming gain. By leveraging the Airy beam as a canonical model, this paper develops an analytical framework to compare the throughputs achieved by CB and BF. Our main results include closed-form throughput expressions for both beamforming strategies and a performance boundary for paradigm selection. First, we derive the BF throughput by modeling a defocusing penalty induced by continuous user movement. The optimal beam dwell time that maximizes the throughput is analytically determined, and the impact of user speed and switching overhead on the throughput is quantified. For the CB scheme, we demonstrate that its throughput is determined by the signal-to-noise ratio (SNR) and the geometry of the trajectory of the user, yet invariant to the user speed. Finally, we analytically establish a threshold for the switching overhead to define the crossover point of the achievable throughput of both beamformers. Crucially, this threshold asymptotically vanishes at extremely high frequencies, positioning the continuous CB scheme as the preferred beam design paradigm for high-mobility THz communications.

• The paper establishes closed-form throughput analysis comparing beamfocusing (BF) and caustic beamforming (CB) in near-field mobile communications.
• It reveals a trade-off between high instantaneous gain from BF and continuous temporal support of CB, with switching overhead critically affecting performance.
• Numerical evaluations confirm the analytical expressions, providing practical guidelines for optimal beamforming design in 6G/THz networks.

Throughput Analysis for Near-Field Mobile Communications: Comparing Beamfocusing and Caustic Beamforming

Introduction and Motivation

The advent of THz band communications and the proliferation of Extremely Large Antenna Arrays (ELAAs) are transitioning wireless systems into the near-field radiative regime, calling for new beamforming paradigms. In this context, precise spatial focusing (beamfocusing, BF) becomes possible, but mobility and the resultant ultra-narrow beamwidth necessitate frequent retargeting, incurring significant switching overhead and throughput degradation. Caustic Beamforming (CB), inspired by optical caustics (specifically Airy beams), offers continuous trajectory illumination by constructing a curved, self-bending intensity pattern. This eliminates overhead but spatially distributes the transmit power, reducing peak gain.

The paper establishes a rigorous analytical comparison between these paradigms for a mobile user traversing a parabolic trajectory, developing closed-form throughput expressions for both BF and CB and deriving the performance boundary in terms of switching overhead.

Figure 1: A schematic comparison of dynamic BF and static CB. The left side visualizes BF with discrete beam focusing along anchor points, while the right depicts a CB trajectory with continuous beam intensity enveloping the user path.

System Model and Beamforming Strategies

The considered setup involves a BS equipped with an $M$-element ULA on the $y$-axis, serving a mobile user moving at velocity $V$ on a 2D parabolic trajectory. The near-field regime imposes a spherical wavefront model; thus, both spatial and distance domains become degrees of freedom when designing beamformers. The BF paradigm maintains temporal reconfigurability by focusing at discretized anchor points along the user's path, requiring periodic beam updates incurring switching overhead $\tau_s$. In contrast, CB constructs a static, continuous beam along the entire trajectory through a one-time phase configuration, nullifying switching overhead but sacrificing concentrated gain.

The core distinction is thus a spatiotemporal trade-off: high instantaneous gain but temporal inefficiency (BF), versus continuous temporal support but reduced spatial gain (CB).

Closed-Form Throughput Analysis

Beamfocusing (BF) Throughput

The analysis models the BF process as $N$ sequential intervals of active communication ($T_c$) plus overhead ($\tau_s$). The SNR varies unimodally within each interval due to misalignment from user movement. The closed-form throughput, incorporating a cubic penalty arising from spatial mismatch, is:

$$R_{\mathrm{BF}} \approx \frac{R_0 T_c - C_{\mathrm{p}}\alpha_{\mathrm{geo}} V^2 T_c^3}{T_c + \tau_s}$$

where $R_0$ is the anchor-point-optimal rate, $C_{\mathrm{p}}$ is a penalty coefficient determined by mobility, and $y$0 encodes the effects of trajectory geometry and aperture.

Numerical evaluation in the paper confirms the tightness of this formulation compared to exact simulation.

Figure 2: BF throughput as a function of reference SNR at different aperture sizes; theoretical and simulation results are indistinguishable, showing the validity of the analytic expression.

A critical insight is that the optimal dwell time $y$1 balances spatial defocusing (growing cubically with $y$2) against the overhead penalty (imposed by $y$3). This internal minimum is given by solving a cubic stationary equation in $y$4.

Figure 3: Achievable BF throughput as a function of dwell time $y$5, highlighting the unimodal behavior and illustrating the spatial-temporal trade-off.

Caustic Beamforming (CB) Throughput

CB employs an Airy beam phase distribution to synthesize a continuous, curved intensity envelope along the trajectory. Through a stationary phase approximation and paraxial simplification, the CB SNR at each spatial point is determined, leading to the closed-form throughput:

$y$6

where the auxiliary parameter $y$7 and $y$8 define the covered segment. This CB throughput is notably independent of the user speed—the time-agnostic continuous illumination is a fundamental differentiator.

Figure 4: Geometric illustration of the CB configuration, showing the trajectory, beam tangency, and aperture relationship.

Figure 5: CB throughput versus reference SNR, again verifying analytical and numerical agreement.

Throughput Boundary and Switching Overhead Threshold

The explicit closed-form expressions allow the derivation of a critical switching overhead threshold $y$9 at which CB and BF attain identical throughput:

$V$0

If the system's actual switching overhead exceeds this threshold, CB is guaranteed superior. Detailed analysis uncovers:

• For increasing $V$1, the threshold is unimodal: a specific $V$2 maximizes the tolerable overhead.
• As the carrier frequency grows (i.e., $V$3), the switching overhead threshold asymptotically vanishes, as ultra-narrow beamwidths force tiny dwell times, making periodic BF unviable.

  Figure 6: Throughput comparison versus switching overhead $V$4, with crossover points tightly matching theoretical thresholds.

  

  Figure 7: The switching overhead threshold $V$5 as a function of carrier frequency, demonstrating rapid decay towards zero at THz frequencies.

Practical and Theoretical Implications

The results highlight critical guidelines for next-generation near-field wireless systems:

• BF remains advantageous only when switching overhead is minimal and carrier frequencies are moderate. In high-mobility or very high-frequency regimes (THz), CB becomes categorically preferable.
• The expressions offer system designers a formulaic means to select optimal dwell times (for BF) and to judge, given system hardware and user trajectory, which beamforming paradigm is throughput optimal.

On a theoretical level, the analysis clarifies the precise impact of user mobility, switching protocol, and geometry on achievable rates—a significant step beyond previous feasibility or simulation-based explorations of Airy/caustic beams for wireless.

Future Directions

Future research includes:

• Extending analysis to more complex, non-parabolic user trajectories and environments with blockages; e.g., incorporating NLOS and multi-path effects.
• Integrating machine learning or adaptive trajectory planning for fully beam-management-free near-field systems.
• Evaluating trade-offs in multi-user or multi-beam contexts, investigating CB's potential in spatial multiplexing and robustness.

Conclusion

This work delivers a rigorous, quantitative framework for selecting between beamfocusing and caustic beamforming in the near-field, high-frequency, mobile setting. By providing closed-form throughput expressions and highlighting fundamental trade-offs dictated by hardware and trajectory, it positions caustic (Airy) beamforming as the inevitable choice in ultra-high-frequency, high-mobility conditions where switching overheads are non-negligible. This paradigm shift carries profound implications for the architecture of future 6G/THz networks and beam management protocols.

Reference: "Throughput Analysis for Near-Field Mobile Communications: Beamfocusing or Caustic Beamforming?" (2606.09652)