Broadband multi-beam lens-assisted mmID enabling multi-gigabit backscatter data rates for next-generation wireless networks

Domain: biology
Published: 2026-03-10
Editorial outcome: minor_revision

Abstract
The growth of next-generation Internet-of-Things (IoT) and digital-twin systems has created wireless environments where identification must sustain fiber-level data rates with low latency while operating at minimal energy cost and maintaining robust angular coverage. Conventional backscatter at microwave frequencies remains limited to megabit rates, and most millimeter-wave demonstrations operate with limited coverage. This work presents a lens-assisted millimeter-wave identification (mmID) system that unites multi-gigabit connectivity with wide solid-angle coverage. The design integrates a cross-polarized broadband antenna array with a dielectric lens, enabling multi-beam operation with angle-dependent modulation across ±55◦ and a peak differential radar cross section of −13.4dBsm. Demonstrated backscatter performance includes 4Gbps 32-QAM at 5m with an energy cost of 0.08pJbit−1 and 1Gbps operation over 20m. Link-budget analysis projects 1Gbps backscatter ranges up to 2.6km under the 75dBm EIRP permitted in 5G millimeter-wave systems, establishing an energy-efficient pathway for high-capacity, long-range wireless identification.

Introduction
The growth of Internet of Things (IoT) infrastructures, together with the deployment of 5G networks, is expected to interconnect tens of billions of devices in the coming decade [1]. Projections estimate nearly 43 billion IoT connections by 2030, with cellular IoT alone exceeding 7 billion [2]. These large-scale networks form the basis for city-scale digital twins, enabling distributed sensing for environmental monitoring, traffic coordination, and asset tracking at fine resolution [3, 4, 5]. A central challenge in such systems is achieving communication that is simultaneously high-throughput and energy-efficient, as conventional approaches struggle to scale with increasing device density and data demands. Wired solutions such as fiber or Ethernet provide gigabit data rates but lack scalability and flexibility for dense, distributed deployments. Running cables to tens of billions of nodes across cities, factories, and logistics hubs incurs prohibitive installation and maintenance costs while restricting device mobility. Active radios incur significant energy overhead due to oscillators and mixers, typically consuming hundreds of picojoules to nanojoules per bit, which is incompatible with sustainable, large-scale IoT.

Shifting to backscatter communication substantially reduces energy consumption by eliminating active RF components, but existing implementations at sub-GHz and microwave frequencies remain constrained to kilobit–megabit data rates due to limited bandwidth and low-order modulation schemes [6, 7, 8, 9, 10, 11]. These constraints limit the applicability of conventional backscatter for emerging IoT and digital-twin platforms that demand both high data throughput and scalable deployment. Millimeter-wave (mmWave) frequencies offer a promising pathway to overcome these limitations. Large spectral allocations in the 24–30GHz 5G bands enable gigabit-level data rates, while high equivalent isotropic radiated power (EIRP), up to 75dBm, allows concentrated energy delivery over extended ranges [12, 13]. The growing deployment of mmWave base stations in commercial 5G networks highlights the availability of this infrastructure for backscatter-based systems. Short wavelengths at mmWave frequencies also support compact, high-gain antennas suitable for small-form-factor tags, with beamforming and steering enabling spatial selectivity. Prior demonstrations have shown that mmWave backscatter can achieve multi-gigabit throughput with extremely low energy per bit [14, 15]. However, these systems are typically constrained to highly directional operation, limiting connectivity across wide angular ranges.

To improve angular coverage and effective gain, lens-based and retro-directive architectures have been explored. Rotman lenses and Van Atta arrays reshape incoming wavefronts to enhance range and angular performance, enabling wide-angle backscatter with increased realized gain [16, 17, 18, 19, 20, 21, 22]. Three-dimensional mmWave lenses further extend this concept by providing coverage across both azimuth and elevation planes [23, 24, 25, 26, 27, 28]. Despite these advances, reported systems remain largely limited to sub-gigabit data rates, as their antennas and semi-passive front-ends lack the bandwidth required to exploit the multi-gigahertz spectrum available at mmWave frequencies. As a result, existing approaches do not simultaneously achieve gigabit-level throughput, wide angular acceptance, and ultra low energy operation.

In this work, a broadband millimeter-wave identification (mmID) system is presented that combines multi-gigabit backscatter communication with wide solid-angle coverage at ultra low energy per bit. The proposed architecture, as seen in Fig. 1, integrates a cross-polarized broadband antenna array with a dielectric lens to enable multi-beam operation and angle-dependent modulation while maintaining a compact and scalable form factor. By unifying broadband mmWave backscatter with lens-enabled angular robustness, this system addresses the fundamental trade-offs between data rate, coverage, and energy efficiency that have limited prior backscatter platforms, establishing a practical foundation for high-capacity identification in future IoT, digital-twin, and Industry 4.0 environments.

Results
Broadband Cross-Polarized Antenna and Modulator Front-End

At the core of the mmID is a broadband, cross-polarized antenna designed to operate across the full 26–30GHz band. A broadband element is essential to sustain gigabit-level backscatter, since narrowband operation would constrain throughput and increase distortion under high-order modulation. Cross-polarization is critical at mmWave, as a co-polarized backscatter would be masked by strong Tx–Rx coupling from the reader. Using orthogonal feeds enforces polarization separation between the incident and re-radiated waves, thereby suppressing interference and enhancing the effective signal-to-noise ratio (SNR) [18, 29]. Thus, to meet these requirements, a single-layer capacitively-coupled patch antenna was implemented, as shown in Fig. 2(a). Capacitive edge coupling excites multiple resonances that broaden the impedance bandwidth, while the matching stub in the feed network compensates the mismatch of the coupled feed, improving return loss and yielding a flatter impedance profile across the operating band. Two orthogonal ports provide cross polarizations, ensuring efficient capture and re-radiation regardless of the polarization of the incident wave. The antenna was designed in CST Microwave Studio and fabricated on Rogers 3003 (ε = 3.00, tanδ = 0.0013), with thickness of 0.254mm. The measured and simulated results are shown in Fig. 2(b), confirming broadband impedance matching and cross-polarized performance, with S remaining below −10dB across the 26–30GHz range.

To generate the subcarrier required for load modulation, the antenna is interfaced with a compact FET-based modulation network. By toggling the antenna impedance with a low-frequency bias, the circuit shifts the backscattered signal away from the carrier, suppressing direct leakage and enabling recovery of high-rate modulated backscatter. The backscatter modulator comprises a GaAs pHEMT CE3520K3 from California Eastern Laboratories integrated with radial stubs and a parallel stub connection, dimensioned to switch the electrical length between λ/4 and λ/2, as shown in Fig. 2(c) [30]. In the unbiased state with V equal to zero, the conducting channel sets the stub to act as a λ/4 open at the junction, which enables transmission and suppresses reflection. When V is driven negative toward threshold, the channel is cut off and the stub instead behaves as a λ/2 short at the junction, which redirects the incident wave back toward the port. Additionally, λ/4 stubs are placed at the source terminals to act as radial-stub-based RF chokes, which isolate the RF path while still enabling baseband biasing between the gate and drain of the FET. Through this combination of wireless mixing and RF choking, the circuit provides the necessary amplitude contrast for subcarrier generation while keeping the layout compact and ultra low in power consumption [17, 23, 29].

The backscatter modulator was designed in Keysight Advanced Design System and fabricated on the same Rogers 3003 substrate as the broadband antenna. The measured and simulated results are shown in Fig. 2(d), where the reflection response is plotted as V is swept from 0V to −0.75V in −0.25V steps. At zero bias, the device resides in its strong-reflection state with S near −20dB. As V is driven more negative, the device transitions into its weak-reflection state with S improving to about −2dB. The corresponding modulation factor is given by
|∆Γ|=|Γ −Γ |, (1)
biased unbiased
where Γ corresponds to the zero-bias reflection state and Γ corresponds to the maximum applied bias, −0.75V. Under these conditions, |∆Γ| reaches a maximum of 0.71 at 27GHz, with values above 0.65 maintained across the 26GHz–29GHz band. This ensures that the front-end bandwidth is not limited by the modulator. Instead, the overall system response is governed by the broadband antenna aperture, which later combines with the lens to enable multi-gigabit communication. When integrated with the broadband cross-polarized antenna, the FET-based backscatter modulator forms the complete pixel backscatter element, capable of enabling gigabit-level data rates, as demonstrated in Fig. 2(e). In the resulting pixel architecture, the antenna operates in a cross-polarized configuration because the two orthogonal feeding edges of the capacitive-coupled patch are tied together through a λ/2 microstrip transmission line, ensuring that the combined feed excites the patch in the orthogonal polarization of the incident wave. The FET-based modulation network is placed directly along this unified feed line so that the antenna and modulator function as a single coupled structure rather than as independent components. As a result, the applied bias sets whether the pixel resides in a strong-reflection state or a weak-reflection state. In the strong-reflection state, the pixel sends data by reradiating in the orthogonal polarization of the received wave, while in the weak-reflection state this cross-polarized reradiation is greatly reduced and no data is sent. This design provides the high-contrast binary backscatter response required for reliable multi-gigabit mmID operation.

Dielectric Lens-Enabled mmWave Focalization for High-Rate Backscatter Systems

Gigabit backscatter at mmWave frequencies requires an antenna module that delivers both high gain and wide angular coverage. A dielectric lens provides an efficient solution, acting as a passive focusing element that concentrates incident energy onto the pixel [23, 24, 27, 31, 32, 33, 34]. Much like optical lenses that extend the field of view in imaging systems, the curved dielectric geometry focuses signals arriving from both boresight and oblique angles, thereby enhancing directivity with minimal loss compared to active beam-steering networks [35]. Material selection is critical since dielectric losses in backscatter systems penalize both the forward and return paths. Polytetrafluoroethylene (PTFE) (ε = 2.10, tanδ = 0.001) was chosen as the lens material, since its exceptionally low loss enables focusing without degradation, which preserves long-range detectability.

The geometry of the lens is governed by its focal length, surface curvature, and the lateral dimension W, defined as the physical width of the planned mmID board. To ensure wide angular coverage while preserving a compact form factor, a target angular field of view (AFOV) of at least 110◦ was set. The angular field of view (AFOV) is given by
AFOV = 2arctan(W/2F). (2)
With W set to 78mm, the board length establishes the span of the device and directly sets the achievable AFOV. At this stage, W provides the lateral constraint that ties the lens geometry to the system form factor. In the complete design, the mmID board will later integrate a pixel array to extend angular coverage and enable multi-beam operation, but for the lens synthesis it simply acts as the boundary condition linking board size to focal length. Based on this geometry, the focal length was chosen as 25mm to realize the target AFOV, providing a balance between compact lens depth and wide angular range.

Ray-tracing simulations in Optometrika at 28GHz were used to refine the lens geometry and confirm stable focusing across different angles. A sweep of the front and rear surface radii identified optimal values of 80mm and −80mm, as shown in Fig. 3(a) and (b). Here, ray trajectories are illustrated for the optimized lens for incident angles of 0◦ and 55◦, both of which converge at the focal plane, confirming consistent focalization for on-axis and off-axis excitation. To further validate stability, a ray-bundle analysis was performed at 28GHz. As illustrated in Fig. 3(c), the plot shows the bundle spread as a function of focal length, with the minimum occurring at the previously calculated value of 25mm, confirming consistent focusing for both boresight and 55◦ incidence.

To further optimize the design for higher peak realized gain and wider 3dB angular coverage, the optimized lens was modeled in CST Microwave Studio and a diameter sweep from 55mm to 90mm in 2mm increments was performed. The results are shown in Fig. 3(d). Increasing the aperture size enhanced the realized gain, but the improvement diminished at larger diameters due to focal mismatch between the central and edge regions. A diameter of 74mm provided the best balance, achieving up to 21dBi of realized gain while preserving the 110◦ angular coverage. This size ensures efficient capture of both boresight and off-axis rays without enlarging the overall form factor. Broadband performance was then evaluated from 24GHz to 32GHz in 1GHz steps, with the results plotted in Fig. 3(e). Sustaining gigabit-level backscatter requires stable behavior across wide bandwidths, since narrowband responses would limit throughput under higher-order modulation. The lens maintained realized gain above 20dBi and angular coverage greater than 110◦ throughout 26GHz to 29GHz, confirming robust broadband performance. By combining compact geometry, optimized surface curvature, low-loss material properties, and broad operational bandwidth, the PTFE bi-convex lens achieves the gain and angular robustness required for gigabit-level backscatter operation.

Pixel-Array Implementation for Wide-Angle Backscatter

To extend the single pixel design into a practical mmID with wide angular coverage, a 25-element broadband cross-polarized pixel array was implemented, arranged in three concentric rings with a central element, as shown in Fig. 4(a). The rings have diameters of 26mm, 52mm, and 78mm, each populated by eight evenly spaced elements. This geometry maximizes use of the aperture while preserving symmetry, which supports uniform angular coverage across both azimuth and elevation planes [23, 24, 27, 31]. An inter-element spacing of 13mm was selected as the minimum distance that suppresses coupling while still leaving room for bias routing on the top side of the board, avoiding extra layers or via transitions. Each ring of elements is biased together, with the center pixel grouped with the innermost ring, resulting in three independent bias groups. Three southwest connectors are mounted at the edge of the board and connected to the three groups to provide external bias access.

These groups map naturally to different angular sectors. Each pixel element exhibits a 3dB beamwidth of about 18◦, and when combined across the concentric rings and the focusing of the lens, the structure achieves continuous 3dB angular coverage from boresight to ±55◦, corresponding to a solid angle of 2.68sr. The physical dimensions of the optimized dielectric lens are shown in Fig. 4(b). By assigning separate bias signals to each group, the system enables angle-dependent modulation in which each sector of the array can operate with its own modulation state. This effectively creates spatial channels that can be selected electronically, without the complexity of mechanical steering or active beamforming. This design offers two key advantages. It allows multiple readers positioned at different angles to interrogate the tag without interfering with one another, since each angular sector can be assigned a distinct modulation state. It also provides flexibility to adapt the link: higher-order modulation can be applied along boresight where SNR is strongest, while simpler schemes are reserved for wider angles with reduced link margin. In both cases, the per-ring biasing ensures that modulation is only applied to illuminated sectors, improving efficiency and maintaining robust performance across the full angular range.

Angular Coverage Characterization and Differential RCS Analysis of the Lens-Integrated mmID

To evaluate the radiation performance of the lens-integrated pixel array, a single row of the capacitive-coupled cross-polarized antennas was fabricated and positioned at the focal plane of the dielectric lens, located 25mm from the aperture, as shown in Fig. 5(a). Each element in the row was connected directly to one port of the vector network analyzer in turn, while a 20dBi A-INFO LB-180400-20-C-KF horn antenna driven from the other port served as the transmitter inside the anechoic chamber. The array–lens structure was rotated from –70◦ to +70◦ in 1◦ steps, and the angular response of each element was recorded across the sweep. At each rotation angle, the realized gain of the individual elements was measured at 26, 27, 28, and 29GHz, with the corresponding radiation patterns shown in Fig. 5(b)–(e). The measurements exhibit strong agreement with simulations, confirming broadband stability across the band, with the lens-integrated array sustaining a 3dB angular coverage of approximately ±55◦ and achieving peak realized gains of 20.1dBi, 20.7dBi, 20.4dBi, and 20.3dBi at the four test frequencies.

After angular response characterization, the full mmID design was fabricated and tested for detectability, as shown in Fig. 6(a). The prototype was assembled with the dielectric lens and evaluated inside an anechoic chamber using two horn antennas: a 20dBi A-INFO LB-180400-20-C-KF serving as the transmitter and an identical horn in cross-polarization serving as the receiver. The mmID was rotated from ±70◦ in 1◦ steps. To assess detectability, the differential radar cross section (RCS) was extracted, capturing the contrast between the biased and unbiased states and directly reflecting the strength of the modulated backscatter relative to the static reflection. The differential RCS was then determined using
∆σ = (λ2G^2 |Γ −Γ |^2) / 4π, (3)
RCS mmID A B
where λ is the free-space wavelength, G is the realized gain of the mmID, and Γ and Γ represent the reflection coefficients in the two states. A 12 inch diameter metal sphere served as a calibration reference to normalize the mmID's response. The measured and simulated differential RCS responses are plotted in Fig. 6(b), showing strong agreement across horizontal, vertical, and −45◦ cuts. The prototype achieved a peak differential RCS of −13.4dBsm while maintaining a −10dB angular coverage of nearly ±55◦, corresponding to a solid angular coverage of 2.68sr. To confirm stability across frequency, additional azimuth-plane measurements were performed at 26 to 29GHz in 1GHz steps. As shown in Fig. 6(c), simulation and measurement results remain consistent across the band, with the angular coverage and differential RCS preserved throughout. Together, the wide spherical angular coverage and broadband differential RCS highlight the effectiveness of the lens-integrated pixel array in delivering robust multi-beam interrogation to enable backscatter systems capable of sustaining gigabit data rates at long ranges.

Backscatter Link Budget and Read Range Analysis

With the angular coverage and differential RCS characterized, a link budget analysis was carried out to evaluate the achievable read range of the lens-integrated mmID. Two interrogation scenarios were considered: first, using a proof-of-concept (PoC) reader operating at an EIRP of 35dBm, and second, utilizing the maximum allowed EIRP of 75dBm in the 5G/mmWave bands. In both cases, the mmID was evaluated at boresight and at an incidence angle of 55◦, corresponding to the angular limits of the measured coverage. These scenarios capture both the current hardware limits of the PoC reader, further explained below, and the upper bounds of regulatory-compliant transmission. Importantly, the analysis focuses on the maximum range at which a 1Gbps backscatter link can be sustained. First, the incident power on the mmID as a function of distance is given by
P_I = P_Tx + G_Tx + G_mmID + 10n_fo log_10(λ_fo / 4πR), (4)
where P_Tx is the transmitted power, G_Tx is the transmit antenna gain, G_mmID is the realized receive gain of the lens-integrated mmID, n_fo is the path loss exponent at the operating frequency f_o, λ_fo is the corresponding wavelength, and R is the range between reader and tag. The resulting curves for both EIRP levels are plotted in Fig. 6(d), illustrating the lens-enhanced impinging power onto the mmID as a function of distance.

The backscattered return was then calculated using the differential RCS previously characterized yielding
P_Rx,Reader = G_Rx + ∆σ_RCS(θ,ϕ) + 10n_fo log_10(λ_fo / 4πR) + G_LNA, (5)
where G_Rx is the receive antenna gain, ∆σ_RCS is the differential RCS as a function of azimuth θ and elevation ϕ, and G_LNA is the gain of the low-noise amplifier. This expression accounts for both the forward and return propagation paths and directly links the measured detectability of the mmID to the received power at the reader. As the mmID re-radiates the incident signal through the same lens-integrated aperture that receives it, the forward-path coupling is already incorporated into the differential RCS term described earlier. As a result, the formulation does not include an additional P_Rx,tag term, since the differential RCS already encompasses the complete receive–reradiate coupling of the mmID and naturally accounts for the forward-path interaction within ∆σ_RCS. The reader’s detection threshold was determined by the limits of the spectrum analyzer, with the resolution bandwidth RBW determining the effective noise bandwidth of the measurement. Accordingly, the minimum detectable signal at the analyzer input can be expressed as
S_Rx,det = −174 + G_LNA + NF_Rx + 10log_10(RBW) + L_Rx + 20log_10(EVM), (6)
where G_LNA is the gain of the LNA, NF_Rx is the noise figure of the receive chain, RBW is the analyzer resolution bandwidth in Hz, L_Rx represents cable losses, and the last term represents the minimum SNR required to sustain low-BER 1Gbps backscatter. Here, EVM denotes the error vector magnitude of the recovered constellation, which quantifies the deviation of measured symbols from their ideal positions. Because this expression characterizes the detection threshold of the LNA–analyzer measurement chain, rather than the intrinsic sensitivity of a communication receiver, inclusion of RBW and LNA gain is appropriate and reflects the practical noise limitations of the measurement setup.

Since 32-QAM was the highest-order modulation experimentally demonstrated in this work, as will be presented in the upcoming section, it was chosen to determine the required SNR margin. In uncoded operation, BER values at or below 10−6 are generally regarded as sufficient for reliable demodulation, while in coded systems pre-forward error correction (FEC) thresholds as high as 10−4 to 10−5 are routinely adopted in practice [36, 37]. For the measurement system, the noise floor was approximately −90dBm, and achieving BER < 10−6 with 32-QAM requires a minimum SNR of about 16.5dB, corresponding to an effective detection threshold of −73.5dBm.

The projected received power at the reader is shown in Fig. 6(e). Under the current PoC conditions at an EIRP of 35dBm, the estimated maximum interrogation ranges were 100m at boresight and 60m at 55◦. With the same detection threshold but an increased transmit power of 75dBm EIRP, the ranges extend to 2.6km at boresight and 1.2km at 55◦. These results confirm that the lens-enabled mmID supports both ultra-long-range detection and high-rate gigabit-level operation, while maintaining robust performance across wide angular coverage.

Experimental Setup and Demonstration of Angle-Selective Gigabit Data Rate Backscatter

To evaluate the performance of the lens-integrated mmID under modulated backscatter operation, a CW testbed was assembled, as illustrated in Fig. 7. A Keysight 836640L Signal Generator produced a continuous-wave tone at 27GHz, which was split by a PS2-53-450/15S power divider to provide a common local oscillator (LO) reference for both the transmit and receive chains. In the transmit path, the divided signal was amplified by a 16dBm power amplifier and radiated through a 20dBi A-INFO LB-180400-20-C-KF horn antenna. In parallel, a vector signal generator (VSG) provided the modulation bias waveforms to the three Southwest connectors of the mmID, driving each antenna group with a swing from 0V to -0.75V to produce modulated backscatter. The re-radiated signal was captured by a second 20dBi horn antenna in cross-polarization, minimizing direct leakage from the transmitter and isolating the weaker backscattered response. The received waveform was amplified by a 43dB RLNA26G40B low-noise amplifier, downconverted using an ZMIQ-653H-E+ IQ mixer driven by the LO reference, and digitized on a Tektronix DPTO70000SX oscilloscope for real-time constellation and spectrum analysis. A complete illustration of the modulation and demodulation sequence, including baseband formation, FET-based mixing, and baseband demodulation, is provided in Supplementary Note 1.

To benchmark the proposed system, three different modulation formats were applied to the three rings of pixel elements on the mmID: 32-QAM on the center and inner ring, 16-QAM on the middle ring, and 8-PSK on the outer ring. The signals were generated at a symbol rate of 800Msym/sec, centered on a 2GHz intermediate frequency (IF) subcarrier. Here, the IF denotes an offset carrier frequency used to shift the modulation away from the continuous-wave tone, simplifying separation of the backscattered signal from leakage at the reader and improving detection robustness. Each waveform was pulse-shaped with a square-root raised cosine (SRRC) filter with roll-off factor α=0.25, confining the occupied spectrum and minimizing inter-symbol interference for efficient high-rate operation [14, 38]. The occupied bandwidth of the modulated waveform is given by
B_occ = (1+α)·R_S, (7)
where B_occ is the occupied bandwidth, R_S is the symbol period, and α is the roll-off factor. For a symbol rate of R_S = 800Msym/sec and α = 0.25, the occupied bandwidth evaluates to B_occ = 1GHz. The corresponding bit rates, R_b are calculated as
R_b = R_S · log_2(M), (8)
where M denotes the number of constellation points, modulation order, in the chosen scheme. This results in 4.0Gbps for 32-QAM, 3.2Gbps for 16-QAM, and 2.4Gbps for 8-PSK. A time-domain validation of the SRRC-shaped modulation chain is provided in Supplementary Note 2, confirming that the backscattered signal preserves the applied SRRC amplitude envelope.

The backscattered spectra and corresponding demodulated constellations for each modulation are shown in Fig. 8. The error vector magnitude (EVM), defined as the root-mean-square (RMS) difference between the measured constellation points and their ideal locations, was used to evaluate modulation accuracy, and the corresponding bit error rate (BER) was estimated from EVM using standard analytical mappings [39]. For square M-QAM,
BER ≈ (4/log_2(M)) · (1 - 1/√M) · Q(√(3 log_2(M) / (M-1)) · (1/EVM)), (9)
and for M-PSK,
BER ≈ Q(sin(π/M) / EVM), (10)
For 32-QAM, the measured EVM was 7.1%, corresponding to a BER of 2×10−6. In the case of 16-QAM, the results showed an EVM of 6.3% and a BER of 4.8×10−13. With 8-PSK, the system exhibited an EVM of 5.6%, giving a BER of 1.2×10−8. Across all cases, low BER was achieved for reliable demodulation, demonstrating that the mmID achieves gigabit-level backscatter across its wide angular coverage. These results confirm that high-order modulations can be successfully recovered across the pixel array. In addition to demonstrating reliable gigabit demodulation, the system achieves ultra-low switching energy, quantified as the energy per bit. The total consumed power is expressed as
P_tot = I_gs V_gs + 0.5 C_gs V_gs^2 f_max, (11)
where I_gs is the gate–source leakage current of the FET, V_gs is the applied bias voltage, C_gs is the gate–source capacitance of the FET, and f_max is the maximum frequency component of the modulation. The corresponding energy per bit can then be expressed as
E_b = P_tot / R_b. (12)
Although the modulation bias is distributed across all 25 pixel elements, only one illuminated element contributes to the backscattered signal at a given moment. The switching energy is therefore referenced to a single FET, since only one element is effectively active in the communication link at a time. The estimated energy per bit was 0.08pJ/bit for 32-QAM operating at 4.0Gbps, 0.10pJ/bit for 16-QAM at 3.2Gbps, and 0.13pJ/bit for 8-PSK at 2.4Gbps. These results demonstrate that the lens-integrated mmID achieves reliable wide-angle gigabit backscatter, with both low BER and ultra low energy per bit sustained across higher-order modulation formats.

Demonstration of Long-Range Gbps Backscatter Across Boresight and Off-Axis Incidence

The final characterization of the mmID focused on its ability to sustain gigabit backscatter communication over extended distances and wide angular coverage. In this measurement, the device was operated at a data rate of 1Gbps, driven by a 500Msym/sec QPSK waveform shaped with the same SRRC filter with α=0.25 at an IF of 2GHz. This signal was applied uniformly to all three southwest connectors of the mmID. The tag was placed at boresight and ranged from 2m to 20m in 2m increments.

Fig. 9(a) shows the received power as a function of distance, together with the theoretical fit for a two-way backscatter link. Path-loss exponents for indoor office environments are typically reported in the range of 1.4–2.0 [16, 21, 40]. In the case of backscatter, the signal undergoes a two-way propagation, resulting in an effective exponent of approximately 3.2. The measured data follow this R−3.2 trend closely, confirming the expected propagation behavior. For this measurement, while the system noise floor is −90dBm, at least a 10.5dB margin above the noise floor is required to maintain BER < 10−6, giving an effective sensitivity of −79.5dBm. Across the 2–20 m link, the received SNR remained above this threshold, ensuring reliable gigabit operation. The demodulated constellations at 2m and 20m are shown in Fig. 9(b) and (c), with EVM values of 1.3% and 13.4%, corresponding to BERs of below 10−18 for both. Even at 20m, the signal remains resolvable, although with increased distortion compared to short ranges. To benchmark performance, the energy-per-bit was recalculated for this configuration and yielded 0.2pJ/bit, which is higher than the earlier cases due to the increased modulation order, but remains very low for gigabit-level operation. The same measurement procedure was repeated at an incidence angle of 55◦, representing the outer limit of the mmID’s coverage. The received power versus distance is shown in Fig. 9(d), together with the same R−3.2 fit, again showing good agreement with the measured data. At 2m and 20m, the demodulated constellations are shown in Fig. 9(e) and Fig. 9(f). The corresponding EVM values are 5.6% and 27.2%, which translate to BERs of 1.1×10−19 and 1.02×10−7, respectively. As expected, performance declines compared to boresight, but the system still maintains 1Gbps operation with BER below 10−6 throughout the 20m link. These results confirm the robustness of the mmID across both boresight and wide-angle incidence, demonstrating gigabit backscatter operation consistent with theoretical two-way path-loss behavior.

Table 1 highlights that the proposed mmID outperforms prior high–data rate backscatter systems in maximum data rate, interrogation range and energy efficiency. Early sub-GHz and 2.45GHz implementations [6, 38, 41, 42] demonstrated data rates below 1Gbps, with ranges typically under 5m and energy costs on the order of several to tens of pJbit−1. More recent mmWave demonstrations at 24GHz and 28GHz [14, 15] have reached data rates at or above 1Gbps, but either incurred energy costs in the multi-nanojoule range or were limited to sub-5m distances. In contrast, this work achieves sustained 1Gbps backscatter over 20m and extends to 4Gbps over 5m, while maintaining an energy consumption of only 0.08pJbit−1. These results make this the first mmWave backscatter platform to simultaneously combine gigabit-level throughput, long-range operation, ultra-low energy consumption per bit, and wide angular coverage.

Methods
Design and Simulation

All electromagnetic simulations were carried out using CST Microwave Studio and Keysight ADS. The cross-polarized capacitive-coupled patch antenna was modeled in CST using the time-domain solver, with open (add space) boundary conditions on all sides and discrete wave ports defined at the orthogonal microstrip feeds. The substrate was set to Rogers 3003 (ε = 3.00, tanδ = 0.0013) with a thickness of 0.254mm, matching the fabricated design. Simulations were performed across the 24GHz to 32GHz band to extract S-parameters, radiation patterns, and polarization isolation.

For the lens analysis, a broadband dielectric structure was modeled in CST using PTFE (ε = 2.10, tanδ = 0.001). The lens geometry was set to the fabricated design, with a focal length of 25mm. Plane-wave excitation was applied at boresight and at off-axis incidence up to 55◦, while additional simulations were performed by exciting the patch antenna through its feed to confirm that the combined structure preserved retrodirective behavior. Parametric sweeps of lens diameter and curvature were carried out, and far-field monitors were used to evaluate angular gain shaping and coverage across the 24GHz to 32GHz band, ensuring retrodirective response across the full angular range. Circuit-level simulations of the FET-based modulator were carried out in Keysight ADS using the Modelithics nonlinear model for the CEL3520K3 transistor. Harmonic-balance simulations were performed with bias voltage swept from 0V to −0.75V to capture both the on and off states. S-parameters were extracted in each state, and matching stubs and transmission-line sections were tuned within ADS using the Modelithics parameters to maximize the difference in transmission response, thereby improving modulation depth and optimizing the mixing performance of the FET across the 24GHz to 32GHz band.

Signal Model of the Continuous-Wave Backscatter Testbed

The continuous-wave (CW) carrier generated by the reader is expressed as
x_TX(t) = A_TX cos(2πf_c t + θ_TX(t)), (13)
where x_TX(t) is the transmitted signal, A_TX is the carrier amplitude, f_c is the carrier frequency in Hz, and θ_TX(t) represents the phase noise of the source. At the mmID, the applied bias waveform drives the on-board FETs, resulting in the modulated backscatter
x_BS(t) = A_BS m(t) cos(2π(f_c + f_IF)t + θ_TX(t) + ϕ_c), (14)
where x_BS(t) is the reradiated backscatter signal, A_BS is the backscattered amplitude, m(t) denotes the baseband modulation waveform applied through the bias line, f_IF is the chosen intermediate frequency offset, θ_TX(t) is the transmit phase, and ϕ_c = −2πf_c Rc−1 represents the one-way propagation phase delay over range R. After free-space propagation, the received signal at the reader can be expressed as
x_RX(t) = A_BS m(t) cos(2π(f_c + f_IF)t + θ_TX(t) + 2ϕ_c), (15)
where R is the distance between reader and tag and n is the path-loss exponent of the propagation channel. The total round-trip propagation phase is 2ϕ_c = −4πf_c Rc−1. Finally, IQ downconversion produces the complex baseband signal
x_IQ(t) = 0.5 A_BS m(t) [cos(θ_TX(t) + ϕ_c) + jsin(θ_TX(t) + 2ϕ_c)], (16)
where x_IQ(t) contains the in-phase (I) and quadrature (Q) components of the modulated backscatter.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This work presents an interesting mmWave backscatter system, which achieves a data rate of 1Gbps at a distance of 20m. This communication distance is much better than those in the reference [14,15]. It seems to me that the major difference is in the dielectric len. [14,15] used antenna array, and this work uses a dielectric len to focus the receive signal onto one antenn element. I am not sure why the dielectric len could bring such a significant improvement on the communication distance and energy efficiency. Could the authors provide a convincing explanation? How about a two-dimensional phased array is used, instead of the dielectric len.", "reviewer_2": "In this paper, a low power consumption and high data rate backscatter Tag is designed and measured. Here are my comments:\n1.Overall, the paper lacks a detailed discussion of the design principles for key components, such as the patch antenna with FET. The authors should provide more details on the design of the patch antenna with FET.\n2.The paper mentions using a dual-polarized antenna element. However, based on the description, I do not believe this element qualifies as \"dual-polarized.\" A dual-polarized antenna in a communication system must have two independent feed ports, capable of simultaneously radiating and receiving two orthogonal polarization waves, with each polarization carrying independent or identical information. A key metric of dual-polarized antenna is polarization isolation. If the antenna element mentioned in this paper is truly dual-polarized, what is its polarization isolation metric? The authors should provide simulation or test results.\nFrom the information provided, the element uses two orthogonal microstrip lines to excite the patch via edge coupling, generating two orthogonally polarized linear radiations. However, these two microstrip lines are connected together.\nConsequently, these two orthogonal linear polarizations will combine (based on their relative amplitude and phase) into a single linear polarization at an arbitrary angle, or even a circular polarization.\n3.In Fig. 2(c) and Fig. 2(e), the orientation of the FET CE3520K3 is different. That is, the circuit connected to the FET's gate (pin 4, marked with a dot) is different in the two figures. The authors should check this. From the text, V_GD should be a negative value, but in the legend of Fig. 2(d), V_GD is positive. Please ensure the description is consistent.\n4.The FET CE3520K3 is referred to as a \"switch\" in the paper, which I believe is inappropriate. Unlike a switch that only toggles between two or several discrete states, the FET in this paper is modulated by a continuous modulation signal , acting as a mixer. Therefore, calling it a \"switch\" is incorrect.\n5. On page 3, it is mentioned that the substrate used in the antenna simulation is Rogers 4350B, whereas the substrate used in the FET simulation is Rogers 3003. Please explain why these two circuits were simulated using different substrate.\n6.As shown in Fig. 6(d), when the Reader's transmitted EIRP is 35 dBm, the incident power at the Tag 10 meters away is approximately -20dBm. However, according to Equation (4), the free-space path loss at 27 GHz over 10 meters should be approximately 81 dB. This would imply an incident power at the Tag of approximately -46 dBm. Please explain this discrepancy.\n7.In Equation (5), a term Prx,tag appears to be missing. Please check the equation and the corresponding calculations.\n8.The calculation of receiver sensitivity in Equation (6) is incorrect. First, the thermal noise floor should be calculated based on the received signal's bandwidth, not the spectrum analyzer's RBW (Resolution Bandwidth). Second, receiver sensitivity is determined by the receiver's Noise Figure (NF), signal bandwidth, and the required SNR, not by the limitations of the spectrum analyzer as mentioned. Moreover, the gain of the Reader's LNA should not be included in the sensitivity calculation. According to Equation (6), a higher LNA gain would incorrectly lead to a worse (higher) receiver sensitivity. Please review this equation carefully. By the same logic, the LNA gain should likely be excluded from Equation (5) as well.\n9.In the experimental results of Fig. 8, it can be seen from Fig. 8(b) and Fig. 8(c) that the received signal power is greater than the received signal power in Fig. 8(a). Additionally, based on the received signal power, the SNR in Fig. 8(b) and Fig. 8(c) should be able to support higher-order modulation, yet low-order modulation was used. Please explain the reasons for this.\n10.From Fig. 2(d), it can be seen that the relationship between the amplitude of the modulation signal and the amplitude of the reflected signal is not necessarily linear. For example, at 29 GHz (the center frequency of the reflected signal), the amplitude of the modulation voltage varies, but the amplitude of the reflected signal changes very little. This would cause a large discrepancy between the reflected signal's constellation diagram and an ideal one. In severe cases, calibration would be needed before use (refer to the constellation diagram in reference [6]). Please explain how, given the test results in Fig. 2(d), the received signal constellation diagram appears normal. Was some form of amplitude calibration technique used?\n11.It is known that for a non-linear device like an FET, the non-linear effect will produce mixing when two signals are applied. Therefore, the Tag described in the paper will radiate not only the upper sideband (USB) signal centered at 29 GHz but also a lower sideband (LSB) signal centered at 25 GHz and other intermodulation signals. The paper does not include a spectrum measurement of the reflected signal before the demodulator. Please provide test results for the Tag's spurious emissions. If this LSB signal and other spurious signals exist, the application scenarios for this device will be severely limited, unless the authors can provide evidence that these emissions meet the requirements of regulatory authorities."}, "author_response": "The authors thank the reviewer for the comment. The extended communication distance demonstrated in this work is enabled in large part by the low-loss PTFE dielectric lens, which passively concentrates the incident mmWave energy onto the pixel element. As described in the manuscript, the curved PTFE geometry focuses signals arriving from both boresight and oblique angles, similar to an optical lens, and provides enhanced directivity with minimal insertion loss. The extremely low-loss PTFE material (ε = 2.10, r tanδ = 0.001) preserves signal strength across both the forward and return paths, and this directly strengthens the backscattered signal. However, the lens is only one part of the system. The long-range and high-throughput performance also relies on the broadband patch antenna and the high-speed FET-based modulator that are integrated within each pixel. The broadband antenna provides efficient reception and reradiation across the operating band, and the FET modulator enables clean mixing that supports high-order constellations and high data rates. The combination of these three elements, namely the dielectric lens, the broadband antenna, and the high-speed modulator, enables the gigabit- class backscatter operation presented in this work.\nThe array-based tags in references [14] and [15] use smaller antenna structures with lower gain and narrower angular response, which limits the power delivered to the tag and reduces the effective reradiated cross-section. This results in lower capabilities in terms of maximum data rates and higher order modulation schemes. Because backscatter systems experience free-space attenuation on both the incoming and outgoing paths, even a moderate increase in passive gain leads to a significant improvement in achievable range.\nRegarding the possibility of replacing the dielectric lens with a two-dimensional phased array, such an approach would require phase shifters, RF routing, and control circuitry, which introduce loss, increase cost, and consume power. One of the central goals of the proposed mmID is to remain semi-passive, ultra-low-power, and cost-efficient, making phased-array beamforming incompatible with the intended design constraints. The dielectric lens provides the required directivity and angular coverage with zero power consumption, and it works together with the broadband antenna and high-speed modulator to achieve the reported communication distance and efficiency.\nOverall, the dielectric lens offers an efficient, low-loss, and power-free mechanism for enhancing both the incident signal on the mmID and the strength of the reradiated backscatter, which directly supports the extended communication distance and improved energy efficiency demonstrated in this work. This focusing enhancement works together with the broadband antenna element and the high-speed FET modulator, which provide effective reception, and enables the long-range and high-rate mmWave backscatter performance achieved in the measurements. An additional section has been added to the Discussion section of the paper and can also be found below:\nIn this work, the authors present a broadband, lens-enabled mmWave identification (mmID) platform that unifies multi-gigabit throughput with wide solid-angle coverage and record-low energy-per-bit consumption. The system integrates a pixelated array of cross-polarized capacitive-coupled patch antennas with a broadband dielectric lens to realize multi-beam operation and angle-dependent modulation. Measurements confirm a peak differential RCS of −13.4 dBsm across ±55°, corresponding to a solid-angle coverage of 2.68 sr. The prototype achieved 4 Gbps using 32-QAM modulation at a distance of 5 m, and sustained 1 Gbps QPSK across 20 m at both boresight (0°) and off-axis (55°), with an energy cost of only 0.08 pJ/bit. Link budget analysis further projects 1 Gbps communication up to 100 m with the current reader, and up to 2.6 km under 75 dBm EIRP, underscoring the scalability of the approach. A key contributor to this long-range performance is the PTFE dielectric lens, which passively concentrates incident mmWave energy onto the pixel element in a manner analogous to an optical lens. The curved PTFE geometry maintains stable focusing for both boresight and oblique angles, and its very low dielectric loss preserves signal strength along both the forward and return paths. This passive gain improves the effective differential RCS without consuming power or adding RF complexity, enabling high-rate backscatter over extended distances while remaining fully compatible with ultra-low-power, semi-passive mmID operation.\n\n1. Overall, the paper lacks a detailed discussion of the design principles for key components, such as the patch antenna with FET. The authors should provide more details on the design of the patch antenna with FET.\nThe authors thank the reviewer for the comment. More information on the integration of the FET-based modulator with the patch antenna has been added to the end of the section titled “Broadband Cross-Polarized Antenna and Modulator Front-End” and can also be found below:\n“When integrated with the broadband cross-polarized antenna, the FET-based backscatter modulator forms the complete ‘pixel’ backscatter element, capable of enabling gigabit- level data rates, as demonstrated in Fig. 2(e). In the resulting pixel architecture, the antenna operates in a cross-polarized configuration because the two orthogonal feeding edges of the capacitive-coupled patch are tied together through a λ /2 microstrip transmission line, ensuring that the combined feed excites the patch in the orthogonal polarization of the incident wave. The FET-based modulation network is placed directly along this unified feed line so that the antenna and modulator function as a single coupled structure rather than as independent components. As a result, the applied bias sets whether the pixel resides in a strong-reflection state or a weak-reflection state. In the strong-reflection state, the pixel sends data by reradiating in the orthogonal polarization of the received wave, while in the weak-reflection state this cross-polarized reradiation is greatly reduced and no data is sent. This design provides the high-contrast binary backscatter response required for reliable multi-gigabit mmID operation.”\n2. The paper mentions using a dual-polarized antenna element. However, based on the description, I do not believe this element qualifies as \"dual-polarized.\" A dual-polarized antenna in a communication system must have two independent feed ports, capable of simultaneously radiating and receiving two orthogonal polarization waves, with each polarization carrying independent or identical information. A key metric of dual-polarized antenna is polarization isolation. If the antenna element mentioned in this paper is truly dual-polarized, what is its polarization isolation metric? The authors should provide simulation or test results. From the information provided, the element uses two orthogonal microstrip lines to excite the patch via edge coupling, generating two orthogonally polarized linear radiations. However, these two microstrip lines are connected together. Consequently, these two orthogonal linear polarizations will combine (based on their relative amplitude and phase) into a single linear polarization at an arbitrary angle, or even a circular polarization.\nThe authors thank the reviewer for the comment and agree with the observation. The antenna elements are not used as true dual-polarized radiators in this design. Each antenna has two orthogonal feeding edges, but these edges are connected through the matching microstrip sections and operate together as a single path. Because of this, the structure does not provide two independent polarization channels. The manuscript has been updated to remove the term “dual-polarized” and refer to the antenna element simply as a cross-polarized patch used for the backscatter mmID. Additionally, the cross polarization is explained with more details in the response to Question 1.\n3. In Fig. 2(c) and Fig. 2(e), the orientation of the FET CE3520K3 is different. That is, the circuit connected to the FET's gate (pin 4, marked with a dot) is different in the two figures. The authors should check this. From the text, V_GD should be a negative value, but in the legend of Fig. 2(d), V_GD is positive. Please ensure the description is consistent.\nThe authors thank the reviewer for the comment. The FET figure has been changed in Fig. 2(e) to its correct layout. Additionally, V should be listed as a negative value. The GD caption for Fig. 2(d) has been changed to match this. The updated figure can be found below:\nW C6 Gc Ls (a) (b) RR 12 C6 RR 3 RR 2 12 (c) (d) (e)\n4. The FET CE3520K3 is referred to as a \"switch\" in the paper, which I believe is inappropriate. Unlike a switch that only toggles between two or several discrete states, the FET in this paper is modulated by a continuous modulation signal , acting as a mixer. Therefore, calling it a \"switch\" is incorrect.\nThe authors thank the reviewer for the comment and agree with the clarification. While the CE3520K3 behaves like a switch in our cross-polarized backscatter configuration, since the modulation either passes through or is suppressed depending on the FET bias, it is technically not an ideal RF switch. It is a FET whose gate-controlled impedance creates the mixing behavior observed in the measured results. To avoid any confusion, the manuscript has been revised to refer to the device simply as a FET based backscatter modulator, and the prior references of “switch” has been removed.\n5. On page 3, it is mentioned that the substrate used in the antenna simulation is Rogers 4350B, whereas the substrate used in the FET simulation is Rogers 3003. Please explain why these two circuits were simulated using different substrate.\nThe authors thank the reviewer for the comment. A typo was made when listing the substrate used for the antenna. The correct substrate used for the entire mmID was Rogers 3003, and the antenna substrate has been updated in the text and can be found below:\n“The antenna was designed in CST Microwave Studio and fabricated on Rogers 3003(ε r = 3.00, tan δ = 0.0013), with thickness of 0.254 mm.”\nR 2 6C R 3 R 2\n6. As shown in Fig. 6(d), when the Reader's transmitted EIRP is 35 dBm, the incident power at the Tag 10 meters away is approximately -20dBm. However, according to Equation (4), the free-space path loss at 27 GHz over 10 meters should be approximately 81 dB. This would imply an incident power at the Tag of approximately -46 dBm. Please explain this discrepancy.\nThe authors thank the reviewer for the comment. The forward-path incident-power curve in Fig. 6(d) was originally generated using the free-space expression in Equation (4), but the lens-enhanced receive gain of the mmID was unintentionally omitted. As the reviewer correctly noted, Equation (4) gives an isotropic received power of approximately –46 dBm at 10 meters, while the dielectric lens provides roughly 20 dBi of realized receive gain, resulting in the –25 dBm level shown in the figure. To address this, the forward-path equation has been updated to explicitly include the lens-integrated gain term, and the accompanying text has been revised to clarify that Fig. 6(d) plots the lens-enhanced incident power. The updated equation and revised paragraph can also be found below:\nFirst, the incident power on the mmID as a function of distance is given by:\n𝛌 𝑷 = 𝑷 +𝑮 +𝑮 +𝟏𝟎𝒏 𝐥𝐨𝐠 , 𝒇𝒐 1 𝑹𝒙,𝒕𝒂𝒈 𝑻𝒙 𝑻𝒙 𝒎𝒎𝑰𝑫 𝒇𝒐 𝟏𝟎 𝟒𝛑𝑹\nwhere P is the transmitted power, G is the transmit antenna gain, G is the Tx Tx mmID realized receive gain of the lens-integrated mmID, n is the path loss exponent at the fo operating frequency f , λ is the corresponding wavelength, and R is the range between o fo reader and tag. The resulting curves for both EIRP levels are plotted in Fig. 6(c), illustrating the lens-enhanced impinging power onto the mmID as a function of distance.\n7. In Equation (5), a term P appears to be missing. Please check the equation and Rx,tag the corresponding calculations.\nThe authors thank the reviewer for the comment. In a backscatter link, the receive power at the reader is governed by the two-way radar equation, where the forward-path power incident on the tag and the re-radiated power from the tag are combined through the radar cross section. For this reason, the intermediate term P does not explicitly Rx,tag appear in Equation (5). Instead, the forward-path power is already embedded within the differential radar cross section through Equation (3), repeated here for clarity:\n𝝀𝟐𝑮𝟐 |𝚪 −𝚪 |𝟐 𝒎𝒎𝑰𝑫 𝑨 𝑩 𝚫𝝈 = 𝑹𝑪𝑺 𝟒𝝅\nBecause the mmID is a passive scatterer, the same physical aperture (lens + antenna) is used for receiving and re-radiating. As a result, the effective scattering strength is proportional to P , which inherently incorporates:\nRx,tag\n• the receive-side gain of the lens-integrated mmID (forward-path enhancement),\n• the modulation contrast introduced by the modulator network (through |𝚪 − 𝑨 𝚪 |𝟐 ) 𝑩\n• the re-radiation gain of the mmID (backward-path enhancement).\nThus, 𝚫𝝈 already captures the complete effect of the power delivered to the pixel, and RCS inserting an explicit term would double-count the forward-path contribution. To ensure clarity, the manuscript has been updated to explain that Equation (5) uses the differential RCS, which intrinsically contains both forward and return propagation effects, and can be found below:\nThe backscattered return was then calculated using the differential RCS previously characterized, yielding:\n𝜆 𝑃 = 𝐺 +Δ𝜎 (𝜃,𝜙)+10𝑛 log ( 𝑓𝑜 )+𝐺 𝑅𝑥,𝑅𝑒𝑎𝑑𝑒𝑟 𝑅𝑥 𝑅𝐶𝑆 𝑓𝑜 10 4𝜋𝑅 𝐿𝑁𝐴\nwhere G is the receive antenna gain, Δ𝜎 is the differential RCS as a function of Rx 𝑅𝐶𝑆 azimuth 𝜃 and elevation 𝜙, and G is the gain of the low-noise amplifier. This LNA expression accounts for both the forward and return propagation paths and directly links the measured detectability of the mmID to the received power at the reader. As the mmID re-radiates the incident signal through the same lens-integrated aperture that receives it, the forward-path coupling is already incorporated into the differential RCS term described earlier. As a result, the formulation does not include an additional 𝑷 term, since the 𝐑𝐱,𝐭𝐚𝐠 differential RCS already encompasses the complete receive–reradiate coupling of the mmID and naturally accounts for the forward-path interaction within 𝚫𝝈 .\n𝐑𝐂𝐒\n8. The calculation of receiver sensitivity in Equation (6) is incorrect. First, the thermal noise floor should be calculated based on the received signal's bandwidth, not the spectrum analyzer's RBW (Resolution Bandwidth). Second, receiver sensitivity is determined by the receiver's Noise Figure (NF), signal bandwidth, and the required SNR, not by the limitations of the spectrum analyzer as mentioned. Moreover, the gain of the Reader's LNA should not be included in the sensitivity calculation. According to Equation (6), a higher LNA gain would incorrectly lead to a worse (higher) receiver sensitivity. Please review this equation carefully. By the same logic, the LNA gain should likely be excluded from Equation (5) as well.\nThe authors thank the reviewer for the comment. The reviewer is correct that a true receiver sensitivity should be defined from the signal bandwidth, receiver noise figure, and required SNR, and is not determined by the spectrum analyzer’s RBW or by the gain of the external LNA. To avoid confusion, the authors have clarified that Equation (6) does not represent the intrinsic sensitivity of a communication receiver. Instead, it describes the minimum detectable backscatter level of the measurement chain used in the experiments, which consists of the reader’s LNA, cabling, and the spectrum analyzer operating with a fixed RBW. Because this expression is referenced to the analyzer input, the inclusion of RBW and LNA gain is appropriate for characterizing the measurement detection threshold, rather than a receiver sensitivity. The text has been updated to reflect this distinction, and the terminology in the manuscript has been revised accordingly, which can also be found below:\nThe reader’s detection threshold was determined by the limits of the spectrum analyzer, with the resolution bandwidth (RBW) setting the effective noise bandwidth of the measurement. Accordingly, the minimum detectable signal at the analyzer input is given by:\n𝑺 = −𝟏𝟕𝟒+𝑮 +𝑵𝑭 +𝟏𝟎𝐥𝐨𝐠 (𝑹𝑩𝑾)+𝑳 +𝟐𝟎𝐥𝐨𝐠 (EVM) 𝑹𝒙,𝒅𝒆𝒕 𝑳𝑵𝑨 𝟏𝟎 𝑹𝒙 𝟏𝟎\nwhere 𝑮 is the gain of the LNA, 𝑵𝑭 is the noise figure of the receive chain, 𝑹𝑩𝑾 is 𝑳𝑵𝑨 the analyzer resolution bandwidth in hertz, 𝑳 represents cable losses, and the last term 𝑹𝒙 reflects the minimum SNR required to sustain low-BER 1 Gbps backscatter. Here, EVM denotes the error vector magnitude of the recovered constellation, which quantifies the deviation of measured symbols from their ideal positions. Because this expression characterizes the detection threshold of the LNA–analyzer measurement chain rather than the intrinsic sensitivity of a communication receiver, inclusion of RBW and LNA gain is appropriate and reflects the practical noise limitations of the measurement setup.\nSince 32-QAM was the highest-order modulation experimentally demonstrated in this work, as detailed in the following section, it was used to determine the required SNR margin. In uncoded operation, BER values at or below 𝟏𝟎−𝟔 are generally regarded as sufficient for reliable demodulation, while in coded systems pre-FEC BER thresholds as high as 𝟏𝟎−𝟒 to 𝟏𝟎−𝟓 are routinely adopted in practice. For the measurement system, the noise floor was approximately −90 dBm, and achieving BER < 𝟏𝟎−𝟔 with 32-QAM requires a minimum SNR of about 16.5 dB, corresponding to an effective detection threshold of −73.5 dBm.\nThe projected received power at the reader is shown in Fig. 6(e). Under the current proof-of-concept conditions at an EIRP of 35 dBm, the estimated maximum interrogation ranges were 100 m at boresight and 60 m at 55°. With the same detection threshold but an increased transmit power of 75 dBm EIRP, the ranges extend to 2.6 km at boresight and 1.2 km at 55°. These results confirm that the lens-enabled mmID supports both ultra-long-range detection and high-rate gigabit-level operation while maintaining robust performance across wide angular coverage.\n9. In the experimental results of Fig. 8, it can be seen from Fig. 8(b) and Fig. 8(c) that the received signal power is greater than the received signal power in Fig. 8(a). Additionally, based on the received signal power, the SNR in Fig. 8(b) and Fig. 8(c) should be able to support higher-order modulation, yet low-order modulation was used. Please explain the reasons for this.\nThe authors thank the reviewer for the comment. The purpose of Fig. 8 was to demonstrate that different digital modulation formats can be applied to different rings of the mmID, rather than to show the maximum achievable modulation order. Although the received power in Figs. 8(b) and 8(c) is higher than in Fig. 8(a), the highest-order modulation that could be generated and processed in the measurement setup was limited by the capabilities of the waveform generator. The vector singal generator used in this work only supported a maximum symbol rate of 800 Msym/s, with 32-QAM being the highest-order constellation it could produce. As a result, lower-order modulations were used in Figs. 8(b) and 8(c) simply to illustrate the mmID’s ability to accommodate different modulation formats across rings, not because of any limitation in the mmID hardware. The mmID itself can support higher-order modulation, but Fig. 8 was designed to highlight modulation flexibility rather than to maximize modulation order.\n10. From Fig. 2(d), it can be seen that the relationship between the amplitude of the modulation signal and the amplitude of the reflected signal is not necessarily linear. For example, at 29 GHz (the center frequency of the reflected signal), the amplitude of the modulation voltage varies, but the amplitude of the reflected signal changes very little. This would cause a large discrepancy between the reflected signal's constellation diagram and an ideal one. In severe cases, calibration would be needed before use (refer to the constellation diagram in reference [6]). Please explain how, given the test results in Fig. 2(d), the received signal constellation diagram appears normal. Was some form of amplitude calibration technique used?\nThe authors thank the reviewer for the comment. We appreciate the concern regarding the nonlinear behavior shown in Fig. 2(d). In the proposed system, the tag does not perform analog RF amplitude modulation at the sideband frequencies. Instead, modulation is produced through reflection-based mixing of the 27 GHz continuous wave (CW) with a 2 GHz subcarrier applied to the FET gate. The pixel antenna is implemented in a cross-polarized configuration in which the FET is placed between the two orthogonal polarization paths of the capacitive-coupled patch; as a result, a change in the FET’s reflection state determines whether energy is reradiated into the orthogonal polarization that the reader receives. When the FET state is static, almost no energy couples into the receive polarization; when the FET state switches, the time-varying reflection coefficient generates the cross-polar component that carries the backscatter signal. The modulation depth is set by the reflection-coefficient contrast at the carrier frequency, 𝚫𝚪 = |𝚪 − 𝚪 | 𝟏 𝟎 and Fig. 2(d) shows that even moderate gate voltages such as -0.25 V provide sufficient contrast at 27 GHz to generate the strong mixing products observed at 25 GHz and 29 GHz. The small-signal behavior at 29 GHz therefore does not dictate constellation quality; the QAM waveform is recovered through coherent demodulation of the 2 GHz IF, consistent with the expected behavior of a nonlinear reflection mixer.\nTo further address the reviewer’s point, we have added time-domain measurements showing the applied and received waveforms, which can be found below. In these measurements, the tag is driven with a 32-QAM waveform shaped by a square-root raised-cosine filter, roll-off = 0.25, and upconverted to a 2 GHz subcarrier. The backscatter is measured at very low received power and therefore exhibits visible noise, however its envelope still follows the SRRC-shaped gate excitation, confirming that the reflection-coefficient variation at 27 GHz is sufficient, even at intermediate bias levels such as -0.25 V, to generate stable sidebands and undistorted constellations. These results have been added to the Supplementary Note 2 to directly illustrate the reflection-mixing process.\n0 0.02 0.04 0.06 0.08 0.1 0.12 Time (7s) Supplementary Figure 3: Measured Time-domain signals used to verify reflection-based mixing: (a) Digitally generated 32−QAM symbol sequence from the vector signal generator (VSG). (b) SRRC-shaped 2 GHz subcarrier waveform applied to the FET gate with roll-off factor α = 0.25. (c) Measured backscatter signal from the mmID demonstrating that its amplitude envelope follows the SRRC-shaped gate excitation. )Vm( egatloV 0 0.02 0.04 0.06 0.08 0.1 0.12 Time (7s) 1.5 1 0.5 0 -0.5 -1 -1.5 )V( egatloV 0 0.02 0.04 0.06 0.08 0.1 0.12 Time (7s) 0.8 0.6 0.4 0.2 0 )V( egatloV 0.8 0.6 0.4 0.2 0\n11.It is known that for a non-linear device like an FET, the non-linear effect will produce mixing when two signals are applied. Therefore, the Tag described in the paper will radiate not only the upper sideband (USB) signal centered at 29 GHz but also a lower sideband (LSB) signal centered at 25 GHz and other intermodulation signals. The paper does not include a spectrum measurement of the reflected signal before the demodulator. Please provide test results for the Tag's spurious emissions. If this LSB signal and other spurious signals exist, the application scenarios for this device will be severely limited, unless the authors can provide evidence that these emissions meet the requirements of regulatory authorities.\nThe authors thank the reviewer for the comment. We agree that the nonlinear behavior of the FET modulator can generate both an upper and a lower sideband as well as higher order mixing products. In the original submission, we focused on the desired upper sideband used for demodulation and did not include a wideband spectrum measurement. To address this, we have performed an additional measurement using a 2-GHz ASK excitation and captured the reflected signal before any down-conversion. The resulting spectrum has been added to the supplementary information and can be found below. From this measurement, the dominant component is clearly the upper sideband at 29 GHz. The corresponding lower sideband near 25 GHz is present but appears close to the noise floor. This is due to the lower sideband falls outside the high-gain region of this receive chain and therefore appears significantly attenuated. Additionally, all higher order mixing products and harmonics are also at or near noise floor levels. These observations indicate that unwanted emissions produced by the modulation process are strongly suppressed by the combined frequency response of the tag and the receive chain.\nThe current system is a laboratory proof-of-concept operating at modest power levels, and a full regulatory certification analysis is beyond the scope of this work. However, the measured spectrum demonstrates that spurious emissions are significantly attenuated, in addition to the lower sideband, and do not affect the operation of the mmID in the scenarios evaluated in this paper. An additional section has been added to the paper under Supplementary Note #1, including the backscatter signal modelling and the additional measurement showing the spectrum demonstrating suppressed lower sideband and dominant upper sideband.\n19 21 23 25 27 29 31 33 35 Frequency (GHz) Supplementary Figure 2: Measured RF Spectrum of the mmWave Backscatter Signal Showing the Dominant Upper Sideband and Suppressed Lower Sideband. )Bd( edutingaM 0 -20 -40 -60 -80 -100 -120"}, {"round": 2, "reviewer_comments": {"reviewer_1": "I have no more comment.", "reviewer_2": "The authors have already answered my questions, and the article has been revised accordingly. I have no further questions."}, "author_response": ""}]

Decision letter