3D Beamforming Through Joint Phase-Time Arrays

TL;DR

This work tackles the challenge of high-latency, frequency-flat beamforming in mmWave systems by developing a 3D frequency-dependent beamforming framework using a joint phase-time array (JPTA). It provides both analytical (joint and separated) and iterative (greedy and gradient-descent) methods to configure per-antenna delays and phases so that the average per-user beam gain across allocated subcarriers is maximized. The key findings show that joint optimization generally yields higher gains than separated, with the gradient-descent approach offering the most robust and fastest convergence, outperforming the state-of-the-art 2D extension across diverse bandwidth allocations. Practically, this enables simultaneous multi-user scheduling in rich 3D directions, reducing beam search latency and expanding coverage for mmWave networks, while highlighting ongoing tradeoffs in aperture size and delay-element costs.

Abstract

High-frequency wideband cellular communications over mmWave and sub-THz offer the opportunity for high data rates. However, it also presents high path loss, resulting in limited coverage. High-gain beamforming from the antenna array is essential to mitigate the coverage limitations. The conventional phased antenna arrays (PAA) cause high scheduling latency owing to analog beam constraints, i.e., only one frequency-flat beam is generated. Recently introduced joint phase-time array (JPTA) architecture, which utilizes both true-time-delay (TTD) units and phase shifters (PSs), alleviates analog beam constraints by creating multiple frequency-dependent beams for scheduling multiple users at different directions in a frequency-division manner. One class of previous studies offered solutions with ``rainbow" beams, which tend to allocate a small bandwidth per beam direction. Another class focused on uniform linear array (ULA) antenna architecture, whose frequency-dependent beams were designed along a single axis of either azimuth or elevation direction. This paper presents a novel 3D beamforming design that maximizes beamforming gain toward desired azimuth and elevation directions and across sub-bands partitioned according to scheduled users' bandwidth requirements. We provide analytical solutions and iterative algorithms to design the PSs and TTD units for a desired subband beam pattern. Through simulations of the beamforming gain, we observe that our proposed solutions outperform the state-of-the-art solutions reported elsewhere.

Figures (7)

• Figure 1: Demonstration of a joint phase-time array and the joint and separated beam design approaches.
• Figure 2: Performance comparison of joint and separated analytical derivations by using LS or infinity norm definition with a) various BW allocation scenarios and b) an unequal BW allocation for $N_u=5$ and $\bm\alpha = [0.3, 0.2, 0.15, 0.1, 0.25 ]$.
• Figure 3: Illustration of the maximum beamforming gain in azimuth and elevation domain for a) separated LS, and b) joint LS when $N_u=5$ with equal BW allocation.
• Figure 4: Beamforming gain of joint LS across an azimuth vs frequency domains when $\theta_{\rm el} = 105^\circ$. User 3 is located at $(\theta_{\rm az}, \theta_{\rm el}) = (0^\circ,105^\circ)$, and assigned the frequency band $[-9.5, 9.5)$ MHz.
• Figure 5: Performance comparison of greedy and gradient descent algorithms using joint and separated optimization with a) an equal BW allocation for $N_u=4$ users, and b) various BW allocation scenarios for $N_u=2$ users. Greedy and gradient descent algorithms yield similar performance.