Beamforming with Joint Phase and Time Array: System Design, Prototyping and Performance

Ahmad AlAmmouri; Gary Xu; Jianhua Mo; Jianzhong (Charlie) Zhan; Shenggang Dong; Won-Suk Choi; Younghan Nam

REVIEW 3 major objections 5 minor 17 references

Beamforming with Joint Phase and Time Array: System Design, Prototyping and Performance

T0 review · 3 major / 5 minor · reviewed 2026-08-09 · deepseek-v4-flash

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Pith's one-line read This paper claims that adding true-time-delay elements to an analog beamformer lets a single RF chain create frequency-dependent beams, so one mmWave base station can serve multiple users in different directions simultaneously; a 28 GHz…

desk verdict The prototype is a 16-channel IF-delay beamformer, not the single-RF-chain JPTA the abstract promises; treat the headline claim as unproven, though the beamforming concept and simulations have merit. read the letter →

arxiv 2502.00139 v1 pith:JL4RBBHW submitted 2025-01-31 cs.IT eess.SPmath.IT

Jianhua Mo , Ahmad AlAmmouri , Shenggang Dong , Younghan Nam , Won-Suk Choi , Gary Xu , Jianzhong (Charlie) Zhan This is my paper · ORCID

classification cs.ITeess.SPmath.IT

keywords jointphase-timearraytruetimedelaymmWavebeamforminganalogfrequencydivisionmultiplexingmulti-userMIMO28GHzprototype6Gradiofrontend

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper argues that a millimeter-wave base station can multiplex several users in different directions using a single radio-frequency chain, by replacing ordinary phase-shifter beamforming with a joint phase-time array (JPTA). Each antenna branch of a JPTA adds a programmable true-time-delay element next to a phase shifter, so the array's beam direction varies with frequency. That frequency dependence lets the base station split its bandwidth among users located in different angles, which a conventional analog beamformer cannot do. The paper backs the idea with a 28 GHz prototype that receives four simultaneous user signals with one chain, and with system simulations that put the cell-edge uplink throughput of a JPTA system N times above a phased-array baseline and extend coverage by roughly a factor of two. A sympathetic reader would care because this gain comes without extra power-hungry RF chains, the main cost of hybrid and digital beamforming.

What carries the argument

The central object is the joint phase-time array (JPTA): an antenna array in which each element is preceded by a programmable true-time-delay element and a phase shifter, all fed by one RF chain. The delay unit contributes a phase $2\pi f_k \tau_m$ that depends linearly on sub-carrier frequency $f_k$, so the composite weight $p_k$ can be a different steering vector on every sub-carrier. The paper uses two beam designs: Type-1, where the band is split and each subband points at a discrete direction, solved by the optimization in equation (4) using the algorithm of [6] or the single-shot method of [12]; and Type-2, where a closed-form delay profile $\tau_m = (m-1)/W \sin(\Delta\theta/2)$ produces a continuous 'rainbow' sweep across an angular range. This frequency-to-angle mapping is what lets one chain schedule different users on different resource blocks, and it is also what demands high-resolution delay elements with a wide delay range.

What would settle it

Run the same uplink simulation with a standardized proportional-fair or max-throughput scheduler that does not reserve a minimum of four resource blocks per user per slot, and compare the cell-edge throughput ratio between JPTA and phased array; if the ratio falls materially below the number of multiplexed users, the claimed N-fold cell-edge gain and the $N^{1/3}$ coverage ratio are artifacts of the paper's allocation rule rather than properties of the hardware.

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Extended reading notes

Core claim

The central claim is that the extra degree of freedom introduced by time delays turns an otherwise frequency-flat analog beam into a frequency-dependent one, and that this is enough to make a single RF chain serve multiple users in separate directions by frequency-division multiplexing. The paper derives the array response as $p_k = \frac{1}{\sqrt M}[e^{j\phi_1+2\pi f_k\tau_1}, \dots, e^{j\phi_M+2\pi f_k\tau_M}]^T$, where the phase-shifter terms $\phi_m$ set a common angle and the delay terms $\tau_m$ make the beam sweep with frequency. With two beam classes, discrete-angle (Type-1) and rainbow (Type-2), it designs the delays by optimizing the fit between the achieved and desired steering vectors. The demonstration at 28 GHz with a 400 MHz band assigns 100 MHz to each of four UEs and reports EVM values 0.5–3 dB worse than single-beam analog reception, matching the predicted beamforming-gain loss. The system-level simulation then reports that at the cell edge a JPTA user gets $N$ times the throughput of a phased-array user because it transmits every slot with its share of resource blocks, while the phased-array user transmits only once per $N$ slots, and the coverage distance grows by $N^{1/3}$ for path-loss exponent 3.

Load-bearing premise

The headline coverage and throughput numbers rest on a scheduling rule in which every JPTA user receives at least four resource blocks in every uplink slot, while a phased-array user on the same cell edge gets four blocks only once per sweep round, together with a fixed path-loss exponent of 3.

Editorial extensions

If this is right

A JPTA base station can schedule users in different directions in the same time slot by assigning them non-overlapping subbands, eliminating the analog-beamforming constraint of one beam per slot.
At cell edge, where users are limited to the lowest modulation and a minimum of four resource blocks, per-user throughput becomes $N$ times the phased-array baseline because JPTA users transmit every slot instead of once per $N$ slots.
With path-loss exponent 3, uplink throughput coverage distance extends by the cube root of the number of multiplexed users, about $2\times$ for $N=8$ users.
The maximum delay a JPTA codebook needs grows with the angular spread and number of users (2.5 ns for 2 users up to 35 ns for 16 users in the paper's examples), so the required delay range is a concrete design parameter.
As the number of scheduled users grows, the Type-1 discrete-angle beam converges to the Type-2 rainbow beam, so the same hardware can serve both scheduled multi-user traffic and fast beam sweeping.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the scheduler does not guarantee every user a minimum number of resource blocks in every slot, the N-fold cell-edge ratio and the $N^{1/3}$ coverage ratio are upper bounds rather than typical gains; a proportional-fair scheduler that lets best-effort users burst could shrink the gap between JPTA and PAA.
The 1–3 dB per-beam gain loss is incurred because each subband steers the full array with a compromised weight; the paper notes this loss becomes less critical with larger arrays, so the architecture's advantage should improve as antenna panels scale up.
The same frequency-to-angle mapping could be used in reverse at the UE side: a JPTA receiver could distinguish multiple simultaneous transmitters by their subband, which suggests extensions to uplink multi-user detection without extra chains beyond what the paper demonstrates.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

You should know two things about this paper. First, the physical prototype does not demonstrate what the abstract says. The gNB receiver uses 16 RF chains, each with its own mixer downconverting to 0.5 GHz IF; the delays are applied at IF and then combined. That is a multi-chain IF beamformer, not the single-TRX architecture of Fig. 1. So the claim 'a single TRX RF chain can serve four users in four different directions' is unsupported by the experiment. The delays are also not the 'newly developed delay elements' in the RF path. This is a real discrepancy, not a nitpick.

Second, the system-level simulation results are largely built into the scheduling model. At the cell edge, every JPTA user gets a minimum of 4 RBs in every slot, while a PAA user gets 4 RBs only once per N slots. That allocation rule, combined with the path-loss exponent, directly forces the N-fold throughput gain and the N^(1/3) coverage ratio. The paper is honest about this—it says the gain increases to N×100% at the cell edge—but it means the 830% gain and 100% coverage extension are consequences of the model, not independent findings.

What the paper does well: it gives a clear description of JPTA beam design, shows Type-1 and Type-2 beams with concrete delay/phase solutions, and includes a real testbed with measured EVM. The measured EVM degradation of 0.5–3 dB roughly matches the predicted beamforming-gain loss, which is a useful sanity check. The simulation study for 2, 4, 8, and 16 UEs is also a reasonable extension of prior work, even if the architecture and coverage analysis came from the authors' earlier papers.

Soft spots beyond the headline mismatch: the prototype used only 8 of 16 receive channels, a 1.2 m link, and backed-off TX power, with no repeated trials or error bars. That is acceptable for a feasibility demo but not for a quantitative claim. Also, the paper does not provide code or data, so the simulations are not independently checkable.

Who is this for? Reading-group material for people working on TTD/mmWave front-ends, and a signal to the authors that the prototype write-up needs to be aligned with what was actually built. I would send it to peer review—the mismatch can be fixed by rewriting the abstract and clarifying the prototype architecture—but in its current form the central claim should not be accepted. I would not cite it for the single-RF-chain feasibility; I might cite it for the measured IF-delay beamforming results if I worked in that niche.

Referee Report

3 major / 5 minor

Summary. The paper proposes joint phase-time arrays (JPTA), an analog beamforming architecture in which each antenna branch contains a tunable time-delay element and a phase shifter, all sharing a single RF chain. The authors describe Type-1 (discrete multi-beam) and Type-2 (rainbow) beam designs, report a 28 GHz prototype with 16 receive channels and IF delay lines that serves four UEs in four directions with measured EVM degradation of 0.5–3 dB, and present system-level simulations using a large-scale-fading-only model. The simulations claim that JPTA extends uplink throughput coverage by 100% and gives up to 830% throughput gain over phased-array beamforming at cell edge. The abstract states that the prototype demonstrates that a single TRX RF chain can serve four users in four different directions in the mmWave band.

Significance. If the single-chain JPTA claim is correct, the architecture is an attractive low-cost alternative to multi-RF-chain hybrid beamforming, and the system-level gains would be relevant for 6G mmWave design. The paper has strengths: a physical prototype with measured EVM results, no parameters fitted to the measurements, and explicit statement of simulation assumptions. The measured 0.5–3 dB EVM degradation matching the predicted 1–3 dB beamforming-gain loss is a useful checkpoint. However, the prototype does not implement the single-TRX architecture claimed in the abstract, and the headline simulation gains are largely forced by the scheduling model rather than by the JPTA beamforming itself. The paper is therefore a useful progress report, but its central demonstration claim needs either stronger evidence or careful reformulation.

major comments (3)

[Section III] The prototype described on the gNB RX side does not implement the single-TRX JPTA architecture of Fig. 1 and Eq. (1). The text states that 16 RF channels are integrated onboard, each connected to a 1x4 patch antenna and down-converted to 0.5 GHz IF through its own mixer, and that the IF signals are delayed by 16 delay lines separately and then combined. This is a multi-chain beamformer with per-element downconversion and IF-domain delays, not a single RF chain with RF true-time-delay elements preceding one TRX. Consequently, the abstract's claim that the prototype demonstrates 'a single TRX RF chain can serve four users in four different directions' is unsupported by the described experiment. The authors should either revise the architecture claim to describe an IF-delay multi-chain beamformer that validates the frequency-dependent multi-beam concept, or they must show a single-TRX RF-delay implementation with measured results.
[Section IV-B] The headline throughput and coverage gains in Fig. 9 are largely a direct consequence of the resource-allocation rule rather than a property of JPTA beamforming. In the cell-edge regime the text states that both schemes operate at MCS 0 with 4 RBs, but PAA users transmit only once every NUE slots while JPTA users transmit in every slot. This allocation structure forces the NUE-fold throughput ratio and, with path-loss exponent beta=3, the coverage ratio NUE^(1/3) (e.g., 2 for 8 UEs). The authors acknowledge the scheduling premise in words, but the abstract and conclusion present the 100% coverage increase and 830% gain as JPTA system-level benefits without this qualification. The paper should state clearly that these numbers are upper bounds under an idealized scheduler that guarantees every user 4 RBs in every slot, and should show how the gains depend on the scheduler, the minimum-RB constraint, and the path-loss exponent.
[Section IV-A] The simulation results in Fig. 9 are deterministic: only one ring of UEs is active at a time, only large-scale fading is included, and no repeated trials or error bars are reported. Since the central quantitative claims are 100% coverage extension and 830% throughput gain, the absence of any statistical variation or sensitivity analysis makes it difficult to assess whether those numbers are robust. The authors should add sensitivity studies for the path-loss exponent beta, the UE angular distribution, and the scheduling parameters, or at least provide confidence intervals from multiple UE drops.

minor comments (5)

[Section III and Figures 3–5] The three figures showing the setup and measured EVM results are all referenced as 'Fig. III' in the text, which appears to be a LaTeX placeholder error; the figure numbers need to be corrected.
[Eq. (1) and Section IV] Equation (1) defines the downlink transmitted signal, while the prototype and simulation are for uplink reception. The authors should clarify whether the same JPTA model applies to uplink combining and, if so, state the reciprocity or transpose relationship explicitly.
[Section II-C] The claim that emulating Type-1 JPTA beam patterns requires at least as many TRXs as subbands is stated without a proof or a precise reference. A short derivation or a citation to a specific equation in [4] would make the comparison with hybrid precoding easier to verify.
[Section IV-B] The sentence 'having N1 UL time slots with N2/k RBs ... is always superior to having N1/k UL time slots with N2 RBs' uses undefined variables N1, N2, and k. These should be defined, and the statement should be stated as an inequality with the appropriate SNR model, since it underlies the claimed gain.
[Conclusion] There is a capitalization typo in the final paragraph: 'Therefore, We believe' should be 'Therefore, we believe'. Also, the axes labels in Fig. 7 appear to show 'Frequency (Hz) 108' with a missing superscript, and the angle axis label is unclear; the figure should be reformatted for readability.

Circularity Check

1 steps flagged · score 4.0 of 10

System-level benefits are forced by the simulation's RB-allocation rule; the headline gains reduce to the model's scheduling assumptions rather than to an independent derivation.

self definitional [Section IV-A/IV-B, scheduling model and Fig. 9 discussion]
"For JPTA, each UE is allocated 1/NUE of the total RBs, but all UEs can transmit in every uplink slot. ... each UE can only transmit every NUE time slots. ... each UE in JPTA can transmit on every UL time slot, resulting in JPTA achieving a throughput that is NUE times higher than that of PAA. ... In summary, JPTA does not yield any throughput enhancement at short distances, while the gain increases to NUE × 100% at the cell edge."

The 'system-level benefits' in the abstract (extending uplink throughput coverage by 100%; 830% throughput gain at 1500 m) are not measured or independently derived. The simulation defines JPTA scheduling as 1/NUE RBs every slot and PAA as all RBs once per NUE slots; at the cell edge both are pinned to MCS 0 with 4 RBs, so T_JPTA = NUE x T_PAA exactly by construction. The coverage ratio N^(1/3) follows from the same allocation rule combined with the chosen path-loss exponent beta=3. The headline gain is therefore the resource-allocation input restated, not a consequence of the JPTA beam equations or a fitted parameter.

full rationale

The physical prototype is a real measurement and provides some independent grounding for frequency-dependent multi-beam operation, and no parameters are fitted to data. However, the headline system-level numbers (830% cell-edge throughput gain, 100% coverage extension) are not independent predictions: the simulation grants JPTA 1/NUE of the RBs in every slot while PAA users wait NUE slots, and at the cell edge both are fixed at 4 RBs and MCS 0, so the NUE-fold gain is an algebraic identity of the simulation setup. The N^(1/3) coverage ratio is likewise set by choosing beta=3. This is a modeling premise rather than an empirical result, and it accounts for most of the claimed benefit. Separately, the prototype section appears to undercut the abstract's 'single TRX RF chain' claim: the gNB uses 16 RF channels, each downconverted by a mixer (ADMV1018) before 16 separate IF delay lines are combined, which is a multi-chain IF-delay beamformer rather than the single-TRX architecture in Fig. 1. That is an evidence mismatch, not a circular derivation, so it does not raise the circularity score further, but it should be counted as a correctness risk. The paper's internal arithmetic is otherwise transparent and stated as such.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The physical feasibility claim rests mainly on the prototype measurement, but the system-level benefits rest on a chain of modeling choices: deterministic large-scale fading, non-overlapping resource blocks, a scheduling floor of 4 RBs per user per slot, and beam-design algorithms taken from the authors' prior papers. No free physical parameters are fitted to data; the listed parameters are hand-chosen simulation and hardware settings that directly shape the reported gains. No new physical entities are postulated.

free parameters (5)

Path-loss exponent beta = 3
Set as default in Table I and used in Eq. (7); the coverage-extension ratio N^(1/beta) depends directly on it, and the paper notes beta=2 would give larger gains.
Minimum RBs per UE = 4
Scheduling floor in Section IV-B; at cell edge both PAA and JPTA use 4 RBs, which is what produces the N-fold JPTA throughput gain.
TTD delay stepsize = 2.5 ns
Table I hardware parameter; constrains the achievable Type-1 codebook beams and the maximum delay range.
BS peak beam gain = 28 dB
Table I simulation parameter; the 1-3 dB JPTA gain loss is relative to this 28 dB peak.
BS noise figure = 5 dB
Table I simulation parameter; affects absolute SNR and therefore the cell-edge distances at which the gains appear.

assumptions (6)

domain assumption Type-1 codebook optimization (Eq. 4) is solvable by algorithms in [6] or [12] with at most 1-3 dB beamforming gain loss.
Invoked in Sections II-B and III to generate beams; no derivation or codebook details are provided in this paper.
domain assumption UEs are assigned non-overlapping RBs, so there is no inter-user interference.
Stated in Section IV-B; ideal OFDM orthogonality is assumed, with no leakage from imperfect beams or synchronization.
domain assumption The channel is characterized by large-scale fading only (Eq. 7), with no shadowing or small-scale fading.
Section IV-A; UEs are placed on a ring at fixed angles and only one ring is active at a time, so the results are deterministic.
domain assumption Each JPTA UE receives 1/N of the RBs in every uplink slot, while PAA users get all RBs in one of every N slots.
Section IV-B; the N-fold cell-edge gain follows from this allocation rule, not from measured channel behavior.
domain assumption EESM-to-BLER mapping follows the approach in [7].
Section IV-A; the throughput computation is inherited from a self-cited earlier paper.
domain assumption The minimum number of TRXs to emulate JPTA patterns scales with the number of subbands (Type-1) and linearly with antenna count and angular range (Type-2).
Section II-C asserts this without derivation, citing [4]; it is used to claim the cost advantage over hybrid beamforming.

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Cite this review

Pith. "Pith review of Beamforming with Joint Phase and Time Array: System Design, Prototyping and Performance." pith.science (2026). https://pith.science/paper/JL4RBBHW

@misc{pith2026250200139,
  author       = {Pith},
  title        = {Pith review of: Beamforming with Joint Phase and Time Array: System Design, Prototyping and Performance},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JL4RBBHW}},
  note         = {Machine review of arXiv:2502.00139}
}

read the original abstract

Joint phase-time arrays (JPTA) is a new mmWave radio frequency front-end architecture constructed with appending time-delay elements to phase shifters for analog beamforming. JPTA allows the mmWave base station (BS) to form multiple frequency-dependent beams with a single RF chain, exploiting the extra degrees of freedom the time-delay elements offer. Without requiring extra power-hungry RF chains, a BS with JPTA can schedule multiple users in different directions in a frequency-division multiplexing (FDM) manner. A BS with JPTA achieves various advantages over the traditional analog beamforming system. Simulation results show that JPTA can bring significant system-level benefits, e.g., extending uplink throughput coverage by 100%. To realize these system benefits of JPTA, high-resolution delay elements with a wide delay dynamic range are essential. With newly developed delay elements, we demonstrate that a single TRX RF chain can serve four users in four different directions in the mmWave band.

Figures

Figures reproduced from arXiv: 2502.00139 by the authors.

**Figure 2.** A simple illustration of Type-1 and Type-2 JPTA Beams. [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

**Figure 3.** JPTA demonstration setup [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

Figures from the paper (5 more)

**Figure 4.** Figure 4: JPTA off. BS serves 4 users sequentially. This figure shows when a beam steered to UE4. [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]

**Figure 5.** Figure 5: JPTA on. Four UEs are supported simultaneously. [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]

**Figure 6.** Figure 6: An example network deployment, where four UEs are placed on a [PITH_FULL_IMAGE:figures/full_fig_p005_6.png]

**Figure 7.** Figure 7: JPTA Type-2 beam pattern for different numbers of UEs. Across the total 400 MHz bandwidth, JPTA generates multiple beams to serve multiple [PITH_FULL_IMAGE:figures/full_fig_p006_7.png]

**Figure 8.** Figure 8: Delay in (ns) for each delay element needed for JPTA for different [PITH_FULL_IMAGE:figures/full_fig_p006_8.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

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Pith tools

Reviewed August 9, 2026 · model on record in the stance chip above.

[1] [1]

Six key challenges for beam management in 5.5G and 6G systems,

Y . Heng, J. G. Andrews, J. Mo, V . Va, A. Ali, B. L. Ng, and J. C. Zhang, “Six key challenges for beam management in 5.5G and 6G systems,” IEEE Communications Magazine , vol. 59, no. 7, pp. 74–79, 2021

work page 2021

[2] [2]

Spatially sparse precoding in millimeter wave MIMO systems,

O. E. Ayach, S. Rajagopal, S. Abu-Surra, Z. Pi, and R. W. Heath, “Spatially sparse precoding in millimeter wave MIMO systems,” IEEE Transactions on Wireless Communications , vol. 13, no. 3, pp. 1499– 1513, 2014

work page 2014

[3] [3]

MIMO precoding and combining solutions for millimeter-wave systems,

A. Alkhateeb, J. Mo, N. Gonzalez-Prelcic, and R. W. Heath, “MIMO precoding and combining solutions for millimeter-wave systems,” IEEE Communications Magazine , vol. 52, no. 12, pp. 122–131, 2014

work page 2014

[4] [4]

An overview of signal processing techniques for millimeter wave MIMO systems,

R. W. Heath, N. Gonz ´alez-Prelcic, S. Rangan, W. Roh, and A. M. Sayeed, “An overview of signal processing techniques for millimeter wave MIMO systems,” IEEE Journal of Selected Topics in Signal Processing, vol. 10, no. 3, pp. 436–453, April 2016

work page 2016

[5] [5]

Hybrid beamforming for massive MIMO: A survey,

A. F. Molisch, V . V . Ratnam, S. Han, Z. Li, S. L. H. Nguyen, L. Li, and K. Haneda, “Hybrid beamforming for massive MIMO: A survey,” IEEE Communications Magazine , vol. 55, no. 9, pp. 134–141, Sept 2017

work page 2017

[6] [6]

Joint phase-time arrays: A paradigm for frequency-dependent analog beamforming in 6G,

V . V . Ratnam, J. Mo, A. Alammouri, B. L. Ng, J. Zhang, and A. F. Molisch, “Joint phase-time arrays: A paradigm for frequency-dependent analog beamforming in 6G,” IEEE Access , vol. 10, pp. 73 364–73 377, 2022

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Extending uplink coverage of mmwave and terahertz systems through joint phase-time arrays,

A. Alammouri, J. Mo, V . V . Ratnam, B. L. Ng, R. W. Heath, J. Lee, and J. Zhang, “Extending uplink coverage of mmwave and terahertz systems through joint phase-time arrays,” IEEE Access , vol. 10, pp. 88 872–88 884, 2022

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3d beamforming through joint phase-time arrays,

O. Yildiz, A. AlAmmouri, J. Mo, Y . Nam, E. Erkip, Jianzhong, and Zhang, “3d beamforming through joint phase-time arrays,” in IEEE V ehicular Technology Conference(VTC), 2024

work page 2024