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Beamfocusing Beyond the Near Field: Frequency Diverse Arrays for OFDM-ISAC Systems

Arda Akyazi et al. · arxiv_cs

arXiv CS · Papers

distributed-systems internet networking protocols

Traditional phased arrays (PAs) achieve near-field (NF) beamfocusing through spherical wavefront curvature, but lose this range selectivity in the far field (FF). Frequency diverse arrays (FDAs) instead introduce frequency offsets across antenna elements. These offsets synthesize a range-dependent b

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Beamfocusing Beyond the Near Field: Frequency Diverse Arrays for OFDM-ISAC Systems

arXiv:2610.41415v1 [cs.NI] 30 Oct 2026

Arda Akyazi⋆, Ahmed Hussain⋆, Asmaa Abdallah, Ahmed M. Eltawil, and Abdulkadir Celik

Unlike the PAs, the frequency diverse array (FDA) provides range selectivity even in the FF [3] by employing small frequency shifts across its antenna elements. Originally proposed for radar [4], the FDA has been extensively developed for range-dependent clutter suppression [5] and secure physicallayer transmission [6]. Moreover, FDAs differ from frequencyscanning arrays, which achieve beam steering through timevarying frequencies applied uniformly across all spatial channels. Architecturally, a PA requires a single local oscillator (LO) to provide the same carrier frequency to all elements, whereas an FDA requires additional mixer circuitry to transmit signals with different carrier frequencies. In a fully digital architecture, these offsets can be generated directly in the digital baseband without requiring separate analog circuitry. Gigantic PAs exploit wavefront curvature in the NF to enable distance-domain multiplexing. In contrast, FDAs achieve beamfocusing in the FF by exploiting frequency offsets rather than relying on large antenna apertures. Although FDAs have been investigated for sensing and secure communications, their potential for spatial multiplexing remains largely unexplored. This motivates a uniﬁed comparison of PAs and FDAs across both the NF and FF. In this position paper, we ﬁrst contrast their underlying beamfocusing mechanisms and examine the range–angle coupling and periodicities of the FDA beam pattern. We then investigate FDA–orthogonal frequency-division multiplexing (OFDM) architectures and their trade-offs in I NTRODUCTION orthogonality, array gain, and bandwidth utilization, and disEAMFORMING with traditional phased arrays (PAs) has cuss how FDA range selectivity complements waveform-based long been the cornerstone of directional wireless trans- sensing in integrated sensing and communication (ISAC). mission that relies on plane-wave propagation to steer energy Finally, we compare beamwidth, beamdepth, and single-user toward a speciﬁc angular direction. However, as physical aper- effective degrees of freedom (EDoF), and evaluate multiuser tures enlarge from massive to gigantic arrays, and operating sum-rates while accounting for the bandwidth consumed by frequencies extend into the millimeter wave (mmWave) and frequency offsets. This comparison identiﬁes the conditions terahertz (THz) bands, the Rayleigh distance can span hun- under which FDAs offer a net multiplexing gain and highlights dreds of meters. Consequently, communication may transition future research directions in practical architectures, receiver to radiating near-ﬁeld (NF), wherein the incident wavefront processing, resource allocation, and physical-layer security. is spherical rather than planar [1]. By matching the quadratic FDA F UNDAMENTALS phase curvature across the aperture, the PA concentrates energy at a speciﬁc location in the NF region. This fundamental Two Ways to Focus a Beam shift from angular beamsteering to beamfocusing endows the Two ways of beamfocusing are contrasted side by side in array with a ﬁnite beamdepth, thereby enabling a new multiFig. 1(a) and (b).1 An NF-PA leverages the array aperture to plexing dimension such as location division multiple access focus a beam. Its elements radiate at the same carrier frequency (LDMA) [2]. However, the distance-dependent beamfocusing fc but with a progressive quadratic phase shift, causing the with a PA relies on wavefront curvature and is therefore signals from different elements to interfere constructively at conﬁned to the NF, limiting its ability to provide distancea prescribed focal point within the NF region. The resulting domain discrimination in the far-ﬁeld (FF).

Abstract—Traditional phased arrays (PAs) achieve near-ﬁeld (NF) beamfocusing through spherical wavefront curvature, but lose this range selectivity in the far ﬁeld (FF). Frequency diverse arrays (FDAs) instead introduce frequency offsets across antenna elements. These offsets synthesize a range-dependent beam whose beamdepth is governed by the aggregate frequency-offset span rather than the physical aperture, thereby extending ﬁnite beamdepth into the FF. Although FDAs have been extensively studied for radar, their broader potential for wireless communications remains largely unexplored. Accordingly, this article examines how this capability can support wireless communications and integrated sensing and communication (ISAC). We compare PA and FDA focusing mechanisms, explain FDA coupling and periodicities, and assess coexistence with orthogonal frequencydivision multiplexing (OFDM). Integer-multiple offsets preserve alignment with the OFDM subcarrier grid and avoid offsetinduced intercarrier interference under ideal synchronization, but require suitable symbol mapping and receiver processing. We also distinguish FDA beamdepth from waveform-based radar range resolution and discuss their complementary roles in sensing. For the conﬁgurations studied, FDAs offer no additional singleuser spatial degrees of freedom. Interestingly, their principal beneﬁt is multiuser separation through location division multiple access (LDMA). Numerical case studies under an idealized FDA channel model show that FDA-LDMA achieves higher sum-rates than PA-based schemes for users with small angular separation in the FF, even after accounting for the bandwidth reserved for frequency offsets.

⋆ Arda Akyazi and Ahmed Hussain contributed equally.

1We kindly refer readers to https://akadircelik.com/demos/fda-ofdm-isac/ for an interactive and accessible version of the ﬁgures.

Antenna Power M−1 2 Ampliﬁer Spherical wavefronts

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(BS) where its elements are indexed as m = 0, · · · , M − 1. The m-th antenna element transmits at an offset frequency fm = fc + ∆ fm . The frequency offset ∆ fm is a design parameter of FDA. For a standard linear FDA, ∆ fm = m∆ f . A singleantenna user equipment (UE) is located at range R and angle θ relative to array broadside. Under a narrowband Fresnel approximation, the received phase contribution from element m is given by [8] φm ≈ 2π ∆ fm t − | {z}

− M−1 2

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where t denotes time and xm is the element position relative to the array center. Setting ∆ fm = 0 leaves only the beamsteering f0 and curvature terms and reduces the FDA to a conventional PA. In the NF, wavefront curvature enables beamfocusing, fm RF chain whereas in the FF, the curvature vanishes, leaving only angular f M−1 − 2 beamsteering. RF chain c/∆ f Figure 2 illustrates the coupling and periodicities produced 0.886c beamdepth = M∆ f by the ﬁrst three terms of the phase equation above. The example uses a 128-element ULA operating at fc = 28 GHz R0 R0 + c/∆ f R and focused at (R0 , θ0 ) = (1000 m, 0◦ ) with the linear proﬁle ∆ fm = m∆ f and ∆ f = 60 kHz. Fig. 1: Architecture and focusing mechanism. (a) PA transmitter focuses by a) Range–Angle Coupling: In case of standard linear matching wavefront curvature, (b) FDA transmitter focuses by aligning carrier phases on a planar wavefront. FDA, the beamfocusing and the beamsteering terms are both linear in the element index. Consequently, an inﬁnite number of range and angle combinations produce the same phase beam has a ﬁnite beamdepth that can be approximated as signature across the array. The maximum gain is therefore 7λ (R0 /D)2 [7], where λ is the wavelength, R0 is the focal distributed along the S-shaped range–angle ridge in Fig. 2(a), distance, and D is the maximum physical dimension of the ar- rather than conﬁned to a unique point. ray, such as the diagonal of a planar array. As R0 increases, the b) Range Periodicity: As the observation range changes, wavefront curvature across a ﬁxed aperture becomes weaker the beamfocusing term causes the element contributions to and the beamdepth broadens. Effective beamfocusing with a move out of phase and subsequently realign. Complete rePA is therefore conﬁned to a fraction of the Rayleigh distance, alignment occurs whenever the range changes by c/∆ f , so and extending the focusing range requires a larger aperture. the entire range–angle ridge repeats after this interval. For An FDA, by contrast, creates range selectivity through the parameters above, the period is c/∆ f = 5000 m. Thus, frequency-dependent phase accumulation rather than wave- the ridge passing through (1000 m, 0◦ ) has a replica passing front curvature. In a standard FDA, adjacent antenna elements through (6000 m, 0◦ ), producing the two S-shaped maximumtransmit at frequencies separated by a ﬁxed increment ∆ f , gain loci in Fig. 2(b). introducing a range-dependent phase difference across the c) Time Periodicity: The ﬁrst term m∆ f t evolves linarray. By appropriately conﬁguring the initial phases, the early with time and an element-dependent phase-rotation signals from all elements can be aligned at a desired focal rate proportional to m. Unlike the stochastic time variation range, resulting in constructive interference. Away from this caused by fading or physical Doppler, this programmed phase range, the accumulated phase differences cause the signals evolution causes the beampattern to periodically auto-scan to become progressively misaligned, reducing the coherent across the range domain. At a ﬁxed angle, the maximum-gain array gain. Because this frequency-dependent phase term does ridge moves outward at the speed of light and repeats every not rely on wavefront curvature, it provides range selectivity 1/∆ f = 16.67 µ s, producing the recurring trajectories shown in both the NF and the FF, irrespective of the Rayleigh in Fig. 2(c). boundary. In the FF, where curvature-based focusing vanishes, These replicas differ from PA grating lobes. Grating lobes the FDA maintains a beamdepth of 0.886c/(M∆ f ), governed arise from spatial undersampling, typically when the element by the aggregate frequency-offset span rather than by the spacing exceeds half a wavelength. FDA periodicity instead physical aperture D. The range focus is periodic, however, and arises from the frequency-offset proﬁle and therefore persists equivalent focal ranges recur at intervals of c/∆ f . even with half-wavelength spacing. RF chain

Periodicities and Coupling To expose the resulting periodicities and coupling, consider an M-element uniform linear array (ULA) at the base station

Mitigating Coupling and Periodicities The effects shown in Fig. 2 lead to distinct communication impairments. The range–angle ridge illuminates unintended

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Fig. 2: FDA beampattern top row, standard offsets: (a) range–angle at t = 0, (b) range–angle at t = 0 with a larger range span, (c) range–time at θ = 0◦ ; Bottom row: (d) range–angle for the random-permutation design; (e) gain versus range across the mainlobe at ∆ f and 10∆ f ; (f) the same cut over the full span.

locations, range replicas introduce spatial ambiguity, and temporal scanning produces intra-symbol channel variation. Each therefore requires a distinct mitigation strategy.

c) Time Variance: The scan observed in Fig. 2(c) cannot be eliminated by attempting to synthesize a strictly timeinvariant physical FDA beampattern [9]. In radar, its impact a) Range–Angle Coupling: A localized focal spot can be on time on target can be mitigated through wideband pulsesynthesized using nonuniform frequency-offset proﬁles, such compression waveforms, such as linear frequency-modulated as logarithmic assignments, but arbitrary frequency values chirps [10]. In communications, a more useful remedy is to generally do not lie on the discrete OFDM subcarrier grid. constrain the frequency offset to an integer multiple of the A practical alternative is to use linear frequency offsets that OFDM subcarrier spacing. The receive fast Fourier transform align with OFDM grid but randomly permute them across the (FFT), evaluated over the useful symbol duration Tu = 1/δ f , array [3]. The permutation disrupts the element-wise linear then spans an integer number of offset cycles and orthogonally progression responsible for the ridge (range-angle coupling) separates the shifted components. Under ideal synchronization, while preserving grid-aligned frequencies. It consequently this avoids offset-induced intercarrier interference (ICI) and transforms Fig. 2(a) into the localized spot in Fig. 2(d). makes the post-demodulation channel on each subcarrier timeBecause the span of frequency offsets remains unchanged, the invariant, even though the physical beampattern continues to FF beamdepth, governed by M∆ f , is also preserved, as shown scan. The next section develops this FDA–OFDM integration in detail. in Fig. 2(e). b) Range Replicas: The periodicity in range can be removed by using a nonuniform frequency-offset proﬁle. For linear frequency offset proﬁles, range replicas can instead be placed outside the coverage region by selecting ∆ f ≤ c/Rmax , where Rmax is the maximum operating range of the BS. Figure 2(f) shows the resulting trade-off. Increasing the increment from 60 to 600 kHz narrows the range response by a factor of ten, but also reduces the replica spacing from 5000 to 500 m. Thus, a larger offset span improves range resolution at the cost of a smaller ambiguity-free range.

C OEXISTENCE OF FDA AND OFDM Since OFDM underpins contemporary wireless systems, compatibility with this waveform is essential to the practical adoption of FDAs. Understanding how antenna-level frequency offsets interact with the OFDM subcarrier grid is therefore crucial to assessing whether FDA range selectivity can be exploited while preserving reliable data transmission.

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Fig. 3: FDA-OFDM architectures with frequency offsets applied across the antenna elements. sn denotes the data symbol on baseband subcarrier n and bin k denotes the receive FFT bin.

FDA–OFDM Architectures

contributions can combine coherently at each shared frequency, restoring array gain without frequency-offset beating between the co-frequency copies. In the FF, this coherent combination provides angular steering as in a PA; it does not retain the FDA range discrimination associated with combining different carrier frequencies. The repeated blocks also consume spectral resources that could otherwise carry new data.

An OFDM receiver uses an FFT to separate signals on equally spaced subcarriers. Each receive bin corresponds to one frequency on this grid, whose spacing is denoted by δ f . Applying a frequency offset at an antenna shifts its entire subcarrier grid. The four panels of Fig. 3 illustrate how different subcarrier assignments and frequency offset proﬁles affect orthogonality, array gain, and bandwidth use. d) Integer Offsets: Each antenna shifts its subcarrier grid a) Subcarrier Partitioned: Each antenna transmits a by an integer number of spacings. For example, Fig. 3(d) distinct subset of subcarriers as shown in Fig. 3(a), where uses ∆ f = 2δ f for shifting successive antenna spectra by the three antennas occupy separate frequency blocks, so each two bins. The tones remain aligned with the receive grid, receive bin contains a symbol from only one antenna. This preserving orthogonality and avoiding offset-induced ICI unavoids overlap between antennas, but each symbol is trans- der ideal synchronization. Unlike panel (c), however, the mitted by a single element and therefore receives no coherent highlighted bin contains different symbols: s4 , s2 , and s0 . transmit array gain. For physical-layer security, the subcarrier- Thus, frequency alignment alone does not separate all antenna to-antenna assignment can be changed from symbol to symbol contributions; the symbol mapping, precoding, and receiver while compensating the transmit phases toward the intended processing must account for their overlap. Copies of the same receiver. This preserves the desired symbol constellations in symbol occupy different frequencies and retain the frequencythat direction while introducing varying phase distortions at dependent propagation phases that can be used for rangeeavesdroppers in other directions, making their data recovery selective transmission. This architecture therefore provides the more difﬁcult [11]. basis for the FDA-LDMA comparison developed in the next b) Conventional (full overlap): All antennas transmit the section. Integer offsets preserve compatibility with the OFDM same OFDM waveform with small frequency offsets, as shown grid, but introduce two practical costs: in Fig. 3(b). When an offset is a fraction of the subcarrier spacing, the shifted tones no longer align with the receiver grid. • Data Bandwidth Contraction: For a ﬁxed total bandwidth Their energy leaks into neighboring FFT bins, which results B, the offset span Bs = (M − 1)∆ f leaves B − Bs for the in offset-induced ICI. As a result, conventional per-subcarrier common data waveform. Larger offsets improve range equalization cannot directly accommodate the resulting intraselectivity but reduce the bandwidth available for data symbol variation. transmission. c) Partial Overlap: Repeating data blocks across fre• Edge Subcarrier Gain-Loss: Fewer antennas contribute to quency allows copies of the same symbols from different the outermost receive bins, as indicated by the elements antennas to overlap on selected subcarriers [12]. In the highper bin counts in Fig. 3(d). These edge bins therefore lighted block of Fig. 3(c), all three antennas contribute the cannot provide the same array gain as bins shared by all same two symbols with different precoding weights. These antennas.

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Fig. 4: Focal geometry and the spatial degrees of freedom: (a) beamdepth and the OFDM range resolution (left) and beamwidth (right) vs. focus distance, (b) the spectra vs. singular value index at four link distances, (c) the EDoF vs. link distance.

FDA–OFDM for ISAC Originally introduced for radar sensing [4], FDAs are also relevant to future wireless networks that are expected to offer ISAC. The central question is therefore how FDA range selectivity can complement OFDM waveform-based sensing while preserving data transmission. a) OFDM Radar Fundamentals: In monostatic sensing, where the transceivers are co-located, the receiver processes echoes using the known transmitted data. The phase progression across subcarriers reveals the round-trip propagation delay and hence the target range. On the other hand, the phase evolution across successive symbols reveals Doppler and thus radial velocity. For conventional radar processing over a contiguous bandwidth B, the nominal range resolution is c/(2B) [13], independent of the target distance. Since the offset span Bs is smaller than B, the radar range resolution remains below the beamdepths of both the PA and FDA across the focal distances considered in Fig. 4(a). In contrast, the subcarrier spacing sets the delay-ambiguity interval: using every subcarrier on the uniform grid gives an unambiguous range interval of c/(2δ f ). These quantities answer different questions: bandwidth determines how closely spaced targets can be distinguished, whereas subcarrier spacing determines when delay signatures repeat. Conventional FFT-based radar processing also requires the echo delay to ﬁt within the cyclic preﬁx (CP), measured relative to the receiver’s timing reference, to avoid intersymbol interference (ISI). A CP sufﬁcient for the communication channel’s multipath delay spread may therefore be insufﬁcient for the desired sensing range. Note that this is a processing constraint, not a fundamental range-ambiguity limit. Meanwhile, choosing δ f large compared with the expected Doppler shift reduces Doppler-induced ICI. With an unchanged CP and one Doppler sample per symbol, increasing δ f shortens the symbol interval and expands the unambiguous velocity interval, but reduces the unambiguous range. Finer velocity resolution instead requires a longer coherent observation. b) Complementary FDA Range Selectivity: Since OFDM radar separates echoes by propagation delay, an FDA addi-

tionally makes the array response range dependent through its antenna-level frequency offsets. Its transmit beamdepth describes spatial selectivity at a given time and angle, rather than the separation between two delay-resolved radar targets. The two measures should therefore not be equated. When Bs is much smaller than the processed waveform bandwidth, waveform-based ranging can distinguish targets lying within the same broader FDA range-selective region. A similar distinction applies to NF-PA beamdepth [13]; there is no universal resolution ordering independent of bandwidth, aperture, and focal range. With suitable waveform separation and joint range–angle processing, the range-dependent FDA response can help discriminate a target from clutter at other ranges, including clutter arriving from the same direction [8]. This beneﬁt depends on the offset proﬁle and receiver design, as range dependence alone does not guarantee clutter suppression or remove the periodic ambiguities discussed earlier. For communication, the same spatial selectivity supports the LDMA operation examined next. F ROM R ANGE S ELECTIVITY TO S PATIAL M ULTIPLEXING Having established how FDAs can coexist with OFDM, we now examine when their range selectivity translates into communication gains. Two distinct questions arise: can it support additional independent data streams within a single point-to-point link, and can it help separate multiple users that are close in angle but differ in range? Single-User MIMO Spatial degrees of freedom (DoF) represent the number of independent subchannels that can support parallel communication modes and, hence, multiple data streams. They are quantiﬁed by the singular values of the multiple-input multiple-output (MIMO) channel. For this comparison, modes with singular values above a prescribed threshold are counted toward the EDoF.

From an electromagnetic perspective, the EDoF represents where R denotes the radial distance and ∆θ is the angular the number of distinct transmit beams that can be spatially beamwidth in radians. Thus, for a ﬁxed angular beamwidth, the resolved by the receive aperture along a given spatial dimen- physical beamwidth decreases at near ranges. Consequently, sion, such as angle or distance. Accordingly, angular-domain a sector can accommodate more resolvable beams at shorter and distance-domain multiplexing are fundamentally related to ranges, enabling the NF to multiplex more UEs simultanethe beamwidth and beamdepth, respectively. ously. a) Angular Domain Multiplexing: Since beamwidth is The system bandwidth B is also the data bandwidth for determined solely by the aperture length in wavelengths, the PA. However, the FDA sacriﬁces Bs = (M − 1)∆ f for the PA and FDA exhibit almost identical beamwidths. As beamfocusing and is thereby left with a data bandwidth of demonstrated in Fig. 4(a) for a 128-element ULA operating B − Bs (Section: Coexistence of FDA and OFDM). That is, at 28 GHz, both arrays have the same beamwidth for a given Bs is the beamfocusing cost and has a direct impact on the aperture. In the FF, this results in an identical and constant achievable rate of the FDA, which is studied in the case study angular EDoF under line-of-sight (LoS) conditions. As the below. UE moves closer to the array and enters the NF, however, the same angular beamwidth corresponds to a narrower physical Case Study footprint. Together with the spatial variation introduced by This case study compares the EDoF and spatial multiplexing spherical wavefronts, this enables ﬁner spatial resolution and, consequently, a substantial increase in the angular EDoF in capabilities of the PA and the FDA. For the single-user case in Fig. 4, the BS is equipped with a 128-element ULA, while the NF. b) Distance Domain Multiplexing: In the FF, the the UE employs a 64-element ULA. The OFDM paramebeamdepth of an FDA is determined by the frequency off- ters are: S = 1920 subcarriers, δ f = 60 kHz, B ≈ 115 MHz, sets. In the NF, however, its beamdepth is governed jointly ∆ f = 60 kHz (Bs ≈ 7.6 MHz) with randomly permuted offsets. by the aperture-dependent and frequency-offset-dependent For the multiuser case demonstrated in Fig. 5, the same BS beamdepths. At short focal distances, wavefront curvature serves K = 4 single-antenna UEs at high signal-to-noise ratio dominates the range selectivity, making the FDA beamdepth (SNR) with minimum mean-squared error (MMSE) precoding. nearly identical to that of a conventional PA up to approxi- The presented results are obtained by averaging over 3000 mately 6 m, well within the effective beamfocusing Rayleigh Monte Carlo trials. distance (EBRD). As the focal distance increases beyond a) Single-User: The multiplexing capability of the singlethe EBRD, the FDA beamdepth approaches 0.886c/(M∆ f ), user case is characterized by the singular values of the channel whereas the PA beamdepth becomes unbounded [Fig. 4(a)]. matrix. The normalized singular values σi of H are plotted The EBRD deﬁnes the maximum focal distance at which a at different distances in Fig. 4(b), wherein the normalized PA can maintain ﬁnite beamdepth in the NF [7]. However, singular values above a threshold (σi > 0.9) represent the exploiting distance-domain EDoF in either the NF or FF EDoF. As the UE moves away from the BS, the EDoF count requires the receive aperture to be oriented along the radial decreases and ultimately becomes one at about 10 m, which is direction. Moreover, beamdepth is generally much larger than close to the EBRD boundary. Next, the EDoF count is plotted beamwidth when measured in physical distance [7], implying against the link distance in Fig. 4(c), where it can be observed that resolving multiple distance-domain beams requires an that the PA’s and FDA’s EDoF numbers are equal to each other impractically large receive aperture. Hence, practical array both in the FF and in the NF, which supports the claims made dimensions cannot resolve multiple distance beams, and the in the Single-User MIMO subsection. distance-domain EDoF remains limited to one in the FF. b) Multiuser MIMO: The multiplexing capability of the multiuser case is measured by the sum-rates. In Fig. 5, the Multiuser Multiplexing total sum-rates are compared for SDMA and LDMA [2], State-of-the-art communication systems employing PAs in [3] with PA and FDA. Following [3], we evaluate FDAthe FF exploit spatial division multiple access (SDMA) to LDMA with an idealized narrowband channel model. This separate UEs based on their angular direction. However, UEs model assumes that each UE keeps the BS timing instead at similar angles experience interference and cannot be simul- of synchronizing to its received signal, that the CP covers taneously served through SDMA. In contrast, the spherical the propagation delay, and that the frequency-shifted copies wavefronts in the NF enable beamfocusing in the joint angle- of each symbol combine coherently across FFT bins. For distance domain. This allows a PA to employ LDMA by benchmarking purposes, we also introduce the “No Overhead” simultaneously serving UEs located at the same angle but case, where we hypothetically assume that bandwidth spread different distances. The LDMA capability of a PA, however, is cost Bs is free. In this way, we aim to show performance limited to the EBRD of the NF, beyond which the beamdepth degradation caused by the bandwidth used for beamfocusing. Fig. 5(a) presents the sum-rate as a function of distance becomes unbounded. An FDA can overcome this limitation by enabling distance-domain multiplexing in the FF, owing to its for UEs uniformly distributed over the angular range θ ∈ [−1◦ , +1◦ ]. At short distances, PA-LDMA achieves a higher ﬁnite beamdepth, as discussed earlier. The reduced propagation distance in the NF also improves sum-rate because the PA provides a ﬁnite beamdepth that angular spatial multiplexing for both PAs and FDAs. Speciﬁ- reduces inter-user correlation without requiring additional cally, the physical beamwidth is approximately given by R∆θ , bandwidth. Beyond the EBRD, however, the PA loses its

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Fig. 5: Total downlink sum-rate for SDMA, PA-LDMA, FDA-LDMA and the “No Overhead” ceiling. (a) Versus UE distance, with user ranges drawn from a window spanning ±4 m about each distance and a sector half-angle of 1◦ . (b),(c) Versus sector half-angle, with ranges drawn from [3.5, 11.5] m in the NF and [86, 351] m in the FF.

ability to provide a ﬁnite beamdepth and its performance approaches that of SDMA. In contrast, FDA-LDMA maintains a ﬁnite beamdepth even in the FF. As a result, FDA achieves a higher sum-rate in the FF. In Fig. 5(b) and (c), we evaluate the sum-rate as a function of the angular spread. In Fig. 5(b), the UEs are restricted to the NF region, with user distances uniformly distributed over R ∈ [3.5, 11.5] m. In contrast, Fig. 5(c) considers UEs located in the FF region, with distances distributed over R ∈ [86, 351] m. As shown in Fig. 5(b), operating below the EBRD allows the PA to generate a beamdepth comparable to that of the FDA without incurring additional bandwidth overhead. Consequently, the PA yields higher sum-rates than the FDA across the entire simulated angular sweep. Conversely, Fig. 5(c) demonstrates that the PA loses its range selectivity in the FF, resulting in performance equivalent to standard SDMA. At very small angular spreads, where the UEs must be distinguished primarily in the range domain, the PA sum-rate falls to 0.2 Gbit/s. In contrast, FDA-LDMA achieves 2.3 Gbit/s by leveraging its frequency offsets. As the angular spread increases, the performance gap between the PA and FDA narrows because the PA increasingly exploits angular-domain multiplexing. Ultimately, in this conﬁguration, the FDA achieves higher sum-rates for angular half-spreads below ≈ 8◦ , which corresponds to a total sector angle of ≈ 16◦ . Beyond this angular threshold, the UEs are sufﬁciently separated in the angular domain, and the bandwidth overhead of the FDA leads to lower sum-rates compared to the PA.

multiuser separation: FDA-LDMA improves the FF sum-rate in narrow angular sectors under the idealized channel model, while the offset-bandwidth cost favors the PA in the NF and wider sectors. Translating this beneﬁt into practical systems motivates the following research directions. Hybrid Architectures and Hardware Impairments Hybrid architectures offer a route to lower hardware cost and power consumption. In a hybrid FDA, frequency offsets can be applied at the radio frequency (RF)-chain level, such that all antenna elements within a subarray share a common frequency offset. This reduces the number of independently controlled frequency offsets, but its impact on beamdepth, range replicas, and focal-point localization remains to be characterized. Moreover, phase noise and frequency errors can perturb the frequency-dependent phase proﬁle, potentially shifting or broadening the focal region and thereby motivating dedicated calibration methods for FDAs. FDA-Enabled ISAC

An FDA embeds range information into its transmit steering vector, thereby enabling a single waveform transmission to simultaneously support LDMA and distance-dependent sensing. Within the ISAC framework, the applied frequency offsets dictate both the communication bandwidth overhead and the sensing beamdepth. Consequently, jointly optimizing these offsets with standard OFDM parameters remains a critical, unresolved challenge. In this context, index modulation that conveys additional data bits through the dynamic selection of C ONCLUSION AND F UTURE D IRECTIONS active frequency offsets offers a promising strategy to mitigate This article compared PAs and FDAs in terms of beamfo- this bandwidth overhead and elevate overall spectral efﬁciency cusing, OFDM compatibility, and spatial multiplexing across [14]. Furthermore, fusing traditional OFDM radar range esthe NF and FF. The PA has a ﬁnite beamdepth limited to timation with the spatial selectivity of the FDA presents a the EBRD, whereas the FDA extends beamfocusing into the promising mechanism to resolve the spatial ambiguities introFF at the cost of additional bandwidth. For the conﬁgurations duced by periodic range replicas [15]. Finally, extending these studied, both arrays offer approximately the same beamwidth stationary designs to accommodate mobile UEs and dynamic and single-user EDoF. The main FDA beneﬁt is instead targets, where the deterministic per-element phase drift heavily

couples with the physical Doppler shifts, represents a complex but essential frontier for future research. Frequency Offset and Waveform Design

[7] A. Hussain et al., “Analyzing URA geometry for enhanced near-ﬁeld beamfocusing and spatial degrees of freedom,” IEEE Trans. Commun., vol. 74, pp. 8008–8024, 2026. [8] B. Huang et al., “Frequency diverse arrays: Fundamentals, key insights, and future directions,” 2026. [9] K. Chen et al., “Accurate models of time-invariant beampatterns for frequency diverse arrays,” IEEE Trans. Antennas Propag., vol. 67, no. 5, pp. 3022–3029, 2019. [10] M. Zubair et al., “Frequency diverse array radar: New results and discrete Fourier transform based beampattern,” IEEE Trans. Signal Process., vol. 68, pp. 2670–2681, 2020. [11] Y. Ding et al., “Frequency diverse array OFDM transmitter for secure wireless communication,” Electron. Lett., vol. 51, no. 17, pp. 1374–1376, 2015. [12] M. Wachowiak et al., “Frequency diverse array OFDM transmit system with partial overlap in frequency,” in Proc. IEEE Int. Symp. Joint Commun. & Sens. (JC&S), 2026, pp. 1–6. [13] A. Hussain et al., “Near-ﬁeld ISAC: Synergy of dual-purpose codebooks and space-time adaptive processing,” IEEE Wireless Commun., vol. 32, no. 4, pp. 64–70, 2025. [14] J. Jian et al., “FDA-MIMO-based integrated sensing and communication system with frequency offsets permutation index modulation,” IEEE Trans. Commun., vol. 72, no. 11, pp. 6707–6721, 2024. [15] W. Chen et al., “FDA-based integrated sensing and multi-mode communication waveform design and receiver processing algorithm,” IEEE Trans. Wireless Commun., vol. 25, pp. 22 782–22 799, 2026.

The achievable sum-rate in FDA-LDMA systems does not scale monotonically with the bandwidth allocated to the array’s frequency shifts. The optimal allocation is highly dependent on the spatial distribution and the total number of UEs. Because the relative penalty of the FDA frequency overhead diminishes as the total system bandwidth grows, adaptive bandwidth allocation emerges as an effective strategy to dynamically balance the superior distance-domain user separation of the FDA with the high raw data throughput of the PA. Looking forward, extending this multiplexing paradigm to planar arrays will require synthesizing multidimensional frequencyoffset proﬁles capable of forming highly localized focal spots across range, azimuth, and elevation, while strictly adhering to the discrete OFDM subcarrier grid [8]. Finally, developing novel waveforms and symbol-to-antenna mapping schemes that mitigate edge-subcarrier gain losses, repurpose the offset bandwidth for active data transmission, and accommodate non- Arda Akyazi is currently an undergraduate student at the integer frequency offsets remain promising avenues for future Middle East Technical University, Ankara, Türkiye. research. Ahmed Hussain is currently a Ph.D. student at King Abdullah University of Science and Technology. Physical-Layer Security

Frequency-to-antenna assignments offer security design opAsmaa Abdallah received a Ph.D. in electrical engineering portunities in FDA–OFDM. Permuting grid-aligned offsets from the American University of Beirut, Beirut, Lebanon, in reshapes off-target responses without increasing the offset 2020. She is currently a research scientist at KAUST. span. Joint permutation, precoding, and artiﬁcial-noise design may improve secrecy rates or artiﬁcial-noise jamming Ahmed M. Eltawil received a Ph.D. degree in electrical efﬁciency. Updating permutations may also hinder intercep- engineering from the University of California, Los Angeles, tion, but this uncertainty-based beneﬁt can disappear if the CA, USA, in 2003. He is currently a full professor at KAUST. eavesdropper learns the mapping or effective channel. Secrecycapacity claims must therefore distinguish physical-channel ad- Abdulkadir Celik received a Ph.D. in double majors of vantages from mapping uncertainty. Neither permutation alone electrical engineering and computer engineering from Iowa nor a ﬁxed-time beampattern establishes secrecy. Permuting State University, Ames, IA, USA, in 2016. He is currently an unchanged occupied frequencies also provides no inherent associate professor at the University of Southampton. protection against wideband jamming. Future work should compare known, partially known, and unknown permutations using the complete received waveform, accounting for channel estimation, adversary capability, and coordination overhead. R EFERENCES [1] A. Abdallah et al., “Exploring frontiers of polar-domain codebooks for near-ﬁeld channel estimation and beam training: A comprehensive analysis, case studies, and implications for 6G,” IEEE Signal Process. Mag., vol. 42, no. 1, pp. 45–59, 2025. [2] Z. Wu and L. Dai, “Multiple access for near-ﬁeld communications: SDMA or LDMA?” IEEE J. Sel. Areas Commun., vol. 41, no. 6, pp. 1918–1935, 2023. [3] H. Liu et al., “Distance-angle joint multiple access for far-ﬁeld MIMOOFDM via frequency diverse array,” in Proc. IEEE Int. Conf. Commun. Workshops (ICC Workshops), 2025, pp. 1001–1006. [4] P. Antonik et al., “Frequency diverse array radars,” in Proc. IEEE Conf. Radar, 2006. [5] Q. Kan et al., “Range-ambiguous clutter suppression for space–air bistatic radar based on FDA-MIMO,” IEEE Trans. Aerosp. Electron. Syst., vol. 62, pp. 7731–7746, 2026. [6] J. Jian et al., “Physical layer security for frequency diverse array-based dual-hop spatial modulation,” IEEE Trans. Wireless Commun., vol. 22, no. 11, pp. 7565–7579, 2023.

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