Integrated Data and Energy Multicast (IDEM)

• Integrated Data and Energy Multicast (IDEM) is a communication paradigm that simultaneously transmits common data and RF energy to multiple receivers while meeting QoS, energy-harvesting, and security constraints.
• Research in IDEM employs joint optimization techniques over beamforming, scheduling, and modulation to balance trade-offs between data rates, energy delivery, and secrecy, adapting to various system architectures.
• Recent studies of IDEM span from information-theoretic formulations to near-field holographic designs, offering practical insights for scalable IoT scheduling, efficient power allocation, and enhanced interference management.

Searching arXiv for recent and foundational papers on Integrated Data and Energy Multicast (IDEM). Integrated Data and Energy Multicast (IDEM) denotes a class of communication systems in which a transmitter simultaneously delivers multicast data and radio-frequency energy to multiple receivers using a common physical-layer transmission, while satisfying information-decoding, energy-harvesting, and often security or efficiency constraints. Across the literature, the term covers several technically distinct formulations: secure layered multicast with wireless information and power transfer (Ng et al., 2013), information-theoretic multicast under received-energy constraints (Wu et al., 2018), hybrid multicast–unicast SWIPT architectures in millimeter-wave and cell-free massive MIMO systems (Hao et al., 2020, Tan et al., 2020), integrated-receiver IoT scheduling with modulation control (Kim et al., 2023), and near-field holographic beamforming for data–energy multicast (Huang et al., 2024, Huang et al., 7 Jul 2025). The common structure is a joint optimization over signaling, beamforming, scheduling, receiver operation, or aperture control so that data users achieve rate or SINR targets while energy users or all receivers satisfy minimum harvested-energy requirements.

1. Foundational formulations and scope

IDEM appears in two principal senses in the cited literature. In an information-theoretic sense, it is the problem of sending the same message using the same physical-layer signal to multiple receivers over distinct, independent channels, while simultaneously delivering guaranteed received energy to each receiver (Wu et al., 2018). In a beamforming and system-design sense, it refers to downlink architectures in which a transmitter jointly designs spatial transmission to satisfy multicast QoS and wireless power transfer constraints, possibly together with secrecy, SWIPT receiver operation, or hybrid multicast–unicast coexistence (Ng et al., 2013, Hao et al., 2020, Tan et al., 2020, Huang et al., 7 Jul 2025).

The compound-channel formulation in "Multicasting Energy and Information Simultaneously" characterizes IDEM through the multicast capacity-energy function

$$C(\mathbf{B}) = \max_{P_X: E[b_m(Y_m)] \ge B_m, \forall m} \min_{m} I(X; Y_m),$$

with the operational capacity equal to the information-theoretic characterization, $C_O(\mathbf{B}) = C(\mathbf{B})$ (Wu et al., 2018). For discrete memoryless channels, the paper shows single-letterization, $C_n(\mathbf{B}) = n C_1(\mathbf{B})$, so the common-message IDEM limit is governed by the weakest information channel under the feasible input distributions induced by the energy constraints (Wu et al., 2018). This formulation isolates the two fundamental bottlenecks: the tightest energy requirement across receivers and the weakest information channel.

A more engineering-oriented lineage begins with secure layered multicast beamforming for simultaneous information and power transfer. "Secure Layered Transmission in Multicast Systems with Wireless Information and Power Transfer" studies downlink multicast transmit beamforming for secure layered transmission systems with wireless simultaneous information and power transfer, with multicast video receivers, idle energy-harvesting receivers, and passive eavesdroppers (Ng et al., 2013). In that setting, IDEM is instantiated through layered video coding, artificial noise, energy harvesting constraints, and secrecy constraints on eavesdropper SINR. This work establishes a template that later reappears in SWIPT and holographic formulations: common or layered data streams, auxiliary energy-bearing components, and constrained optimization over power allocation or beamforming.

A plausible implication is that IDEM is not a single protocol but a design paradigm spanning information theory, PHY-layer beamforming, receiver architecture, and network control. The exact meaning of “multicast” also varies: in some works it means a common stream to all intended data users (Wu et al., 2018, Huang et al., 7 Jul 2025); in others it coexists with unicast layers or task-specific multicast groups (Hao et al., 2020, Tan et al., 2020, Kim et al., 2023).

2. Core system models

The secure layered multicast model in (Ng et al., 2013) considers a downlink transmitter with $N_T$ transmit antennas, single-antenna multicast video receivers indexed by $k \in \{1,\ldots,K\}$, idle receivers that harvest energy, and passive eavesdroppers indexed by $j \in \{1,\ldots,J\}$. Active receivers are partitioned into premium subscribers, which require QoS for all layers, and basic subscribers, which require QoS only for the base layer. Video is encoded into $L$ layers via superposition coding, and receivers use successive interference cancellation. The transmit signal is

$$\mathbf{x} = \sum_{i=1}^L \mathbf{w}_i s_i + \mathbf{v}, \quad \mathbf{v} \sim \mathcal{CN}(\mathbf{0},\mathbf{V}),$$

where $\mathbf{v}$ serves as both artificial noise and an energy-bearing signal (Ng et al., 2013).

The information-theoretic multicast model in (Wu et al., 2018) is deliberately more abstract. A single transmitter encodes a common message $W$ into a length-$C_O(\mathbf{B}) = C(\mathbf{B})$0 codeword $C_O(\mathbf{B}) = C(\mathbf{B})$1 and multicasts it to $C_O(\mathbf{B}) = C(\mathbf{B})$2 receivers over independent channels. Reliability is required simultaneously over all channels, and each receiver must receive at least $C_O(\mathbf{B}) = C(\mathbf{B})$3 energy per channel use on average: $C_O(\mathbf{B}) = C(\mathbf{B})$4 The same-signal constraint is central: the encoder does not adapt per receiver or per channel realization (Wu et al., 2018).

Later system models add architectural constraints. In the millimeter-wave hybrid precoding setting (Hao et al., 2020), a base station with $C_O(\mathbf{B}) = C(\mathbf{B})$5 antennas and $C_O(\mathbf{B}) = C(\mathbf{B})$6 RF chains serves $C_O(\mathbf{B}) = C(\mathbf{B})$7 single-antenna users with one multicast stream and $C_O(\mathbf{B}) = C(\mathbf{B})$8 unicast streams. The analog RF precoder $C_O(\mathbf{B}) = C(\mathbf{B})$9 is selected from a codebook, while users perform power splitting with ratio $C_n(\mathbf{B}) = n C_1(\mathbf{B})$0 between information decoding and energy harvesting. With Layered Division Multiplexing, each user decodes the multicast first, treating all unicast as interference, then cancels it and decodes its own unicast (Hao et al., 2020).

In the cell-free massive MIMO formulation (Tan et al., 2020), $C_n(\mathbf{B}) = n C_1(\mathbf{B})$1 distributed access points, each with $C_n(\mathbf{B}) = n C_1(\mathbf{B})$2 antennas, jointly serve $C_n(\mathbf{B}) = n C_1(\mathbf{B})$3 single-antenna UEs partitioned into $C_n(\mathbf{B}) = n C_1(\mathbf{B})$4 disjoint multicast groups. Layered-division multiplexing superposes group-common multicast streams and user-specific unicast streams, while each UE applies power splitting and decodes multicast before unicast. The received signal at UE $C_n(\mathbf{B}) = n C_1(\mathbf{B})$5 is

$C_n(\mathbf{B}) = n C_1(\mathbf{B})$6

and the information branch is

$C_n(\mathbf{B}) = n C_1(\mathbf{B})$7

(Tan et al., 2020).

The IoT scheduling model in (Kim et al., 2023) is slotted rather than continuously beamformed. One hybrid access point serves $C_n(\mathbf{B}) = n C_1(\mathbf{B})$8 sensors participating in $C_n(\mathbf{B}) = n C_1(\mathbf{B})$9 multicast tasks. In each slot, the controller selects either a multicast task or a unicast sensor and also selects an integrated-receiver-compatible modulation, ARSK or ADSK. At most one stream is scheduled per slot: $N_T$0 This makes IDEM a joint scheduling problem over service mode, target group or sensor, and modulation (Kim et al., 2023).

The holographic formulations (Huang et al., 2024, Huang et al., 7 Jul 2025) move from discrete arrays to continuous or densely sampled apertures. In H-IDET, the transmitter is a continuous holographic aperture $N_T$1 carrying tri-polarized current density $N_T$2, and the electromagnetic field is computed using the dyadic Green’s function: $N_T$3 The multicast specialization treats a single common data-bearing current distribution together with optional energy-only beams (Huang et al., 2024). In the circular H-MIMO multicast formulation (Huang et al., 7 Jul 2025), the transmitter uses $N_T$4 antennas, $N_T$5 RF chains, a propagation matrix $N_T$6, and a diagonal analog beamformer $N_T$7, with received signal

$N_T$8

3. Performance objectives, constraints, and trade-offs

Across IDEM formulations, the objective function depends on which system aspect is primary. In (Ng et al., 2013), the design objective is total transmit power minimization: $N_T$9 subject to multicast QoS for premium and basic users, energy-harvesting constraints for idle receivers, and a probabilistic secrecy constraint for passive eavesdroppers. The dual role of $k \in \{1,\ldots,K\}$0 is explicit: it supplies RF power to EH receivers and acts as artificial noise to degrade eavesdroppers’ SINR (Ng et al., 2013).

The EH constraint in that model is

$k \in \{1,\ldots,K\}$1

or, in matrix form for idle receiver $k \in \{1,\ldots,K\}$2,

$k \in \{1,\ldots,K\}$3

(Ng et al., 2013). This formulation makes explicit the power trade-off between information delivery, RF energy delivery, and secrecy.

In the capacity-energy formulation (Wu et al., 2018), the trade-off is encoded in the feasible set of input distributions. Tightening any $k \in \{1,\ldots,K\}$4 shrinks the feasible set and can lower the achievable common rate because the objective is $k \in \{1,\ldots,K\}$5. For AWGN channels with Gaussian input and output-power harvesting,

$k \in \{1,\ldots,K\}$6

(Wu et al., 2018). The tightest energy constraint sets the minimum feasible power, while the weakest SNR sets the common rate.

In mmWave hybrid SWIPT (Hao et al., 2020), the central objective is energy efficiency,

$k \in \{1,\ldots,K\}$7

subject to transmit power, minimum harvested energy, power splitting, and analog precoder constraints (Hao et al., 2020). The multicast and unicast SINRs both depend on $k \in \{1,\ldots,K\}$8, so receiver-side power splitting directly controls the rate–energy trade-off.

The cell-free massive MIMO counterpart (Tan et al., 2020) also uses an EE objective, but augments it with pilot overhead, backhaul power, AP activation, and nonlinear energy harvesting: $k \in \{1,\ldots,K\}$9 Constraints include multicast QoS, unicast QoS, EH constraints $j \in \{1,\ldots,J\}$0, backhaul capacity, and per-AP power budgets (Tan et al., 2020). This yields a significantly more coupled optimization than classical SWIPT beamforming.

The IoT integrated-receiver formulation (Kim et al., 2023) instead maximizes a weighted sum of average unicast service throughput and harvested energy: $j \in \{1,\ldots,J\}$1 subject to minimum average multicast throughput, unicast throughput, and harvested energy. The long-term averages are

$j \in \{1,\ldots,J\}$2

(Kim et al., 2023). Here the IDEM trade-off is controlled not by beamforming alone but by slot-wise scheduling and modulation choice.

A recurring theme across all formulations is that energy delivery is not merely an add-on constraint. It changes the geometry of the feasible set, the optimal signaling distribution, or the spatial structure of beamforming. This suggests that multicast design under IDEM cannot be reduced to conventional multicast plus a separate WPT layer without performance loss.

4. Solution methodologies

The secure layered multicast problem in (Ng et al., 2013) is formulated as a non-convex optimization because of the probabilistic secrecy constraint and rank-one beamforming structure. The key tractability step is the replacement of the non-convex chance constraint by a convex deterministic bound. With

$j \in \{1,\ldots,J\}$3

a sufficient condition for

$j \in \{1,\ldots,J\}$4

is

$j \in \{1,\ldots,J\}$5

(Ng et al., 2013). The problem then becomes a convex semidefinite program after semidefinite relaxation. The paper also states sufficient conditions for SDR tightness and proposes two suboptimal recovery schemes: principal-eigenvector projection plus convex scaling, and Gaussian randomization plus convex scaling (Ng et al., 2013).

The information-theoretic paper (Wu et al., 2018) uses coding theorems rather than numerical optimization. Achievability treats IDEM as a compound channel with constrained input set, and the converse uses Fano’s inequality receiver-wise, followed by minimization over receivers and restriction to feasible input distributions. The main technical contribution is the proof that the nth-letter multicast capacity-energy function single-letterizes for DMCs (Wu et al., 2018).

The mmWave hybrid SWIPT problem (Hao et al., 2020) combines fractional programming, codebook-based analog beam selection, and successive convex approximation. The fractional EE objective is transformed into a subtractive form using a Dinkelbach-type parameter $j \in \{1,\ldots,J\}$6, with outer-loop bisection because the optimal value function $j \in \{1,\ldots,J\}$7 is strictly decreasing and convex in $j \in \{1,\ldots,J\}$8. The inner problem uses variable substitutions such as $j \in \{1,\ldots,J\}$9 and $L$0, first-order Taylor lower bounds for quadratic terms, and convex upper bounds for bilinear terms. A lower-complexity alternative fixes unicast directions using zero forcing and optimizes powers, multicast beam, and splitting ratios (Hao et al., 2020).

The cell-free massive MIMO framework (Tan et al., 2020) is more elaborate. It introduces auxiliary multicast rate variables to replace the nonsmooth group minimum, smooths indicator functions via $L$1, lower-bounds nonconcave rate terms with concave quadratics, and convexifies the nonlinear EH constraints by using the pseudo-inverse of the nonlinear harvesting function together with a first-order lower bound on the received RF power. The resulting quasi-convex SCA subproblem is then solved using a Dinkelbach transform and a dual first-order method with closed-form primal updates for $L$2, $L$3, and $L$4. An accelerated first-order algorithm replaces plain dual gradient with Nesterov-type momentum (Tan et al., 2020).

The IoT scheduler (Kim et al., 2023) uses Lagrangian duality and stochastic optimization. Dual variables $L$5, $L$6, and $L$7 are associated with multicast throughput, unicast throughput, and harvested-energy constraints. Given these dual variables and a channel realization, the per-slot problem decomposes into a discrete comparison between the best multicast metric

$L$8

and the best unicast metric

$L$9

for each modulation $$\mathbf{x} = \sum_{i=1}^L \mathbf{w}_i s_i + \mathbf{v}, \quad \mathbf{v} \sim \mathcal{CN}(\mathbf{0},\mathbf{V}),$$0 (Kim et al., 2023). The dual variables are updated by stochastic subgradients with diminishing step sizes.

The holographic IDET framework (Huang et al., 2024) combines block coordinate descent, Fourier-domain functional approximation, and WMMSE/SCA. The continuous current distribution is expanded in a finite Fourier basis,

$$\mathbf{x} = \sum_{i=1}^L \mathbf{w}_i s_i + \mathbf{v}, \quad \mathbf{v} \sim \mathcal{CN}(\mathbf{0},\mathbf{V}),$$1

so the field integrals become finite-dimensional bilinear forms (Huang et al., 2024). For the unicast sum-rate problem, the paper exploits the equivalence between SINR and MSE and alternates over receiver combiners, WMMSE weights, and transmit currents. The multicast specialization is described through a max–min formulation with a common current distribution and energy-only beams, solvable by SCA in the Fourier domain (Huang et al., 2024).

The circular H-MIMO paper (Huang et al., 7 Jul 2025) adopts a different decomposition. It first derives an asymptotically optimal fully-digital beamformer using spatial orthogonality, then approximates that beamformer by a constrained hybrid factorization $$\mathbf{x} = \sum_{i=1}^L \mathbf{w}_i s_i + \mathbf{v}, \quad \mathbf{v} \sim \mathcal{CN}(\mathbf{0},\mathbf{V}),$$2 through alternating optimization. The digital step is least squares,

$$\mathbf{x} = \sum_{i=1}^L \mathbf{w}_i s_i + \mathbf{v}, \quad \mathbf{v} \sim \mathcal{CN}(\mathbf{0},\mathbf{V}),$$3

while the analog step is an elementwise projection under one of three metasurface control modes: amplitude only, binary amplitude, or Lorentzian-constrained phase (Huang et al., 7 Jul 2025). Scaling schemes enlarge the effective analog feasible set and are then mapped back through normalization.

5. Architectural variants and receiver models

A major source of diversity in IDEM research is receiver architecture. Classical SWIPT formulations in (Hao et al., 2020) and (Tan et al., 2020) use power splitting. In the mmWave setting, the harvested energy per user is

$$\mathbf{x} = \sum_{i=1}^L \mathbf{w}_i s_i + \mathbf{v}, \quad \mathbf{v} \sim \mathcal{CN}(\mathbf{0},\mathbf{V}),$$4

while the information-decoding branch experiences both RF noise and ID-chain noise (Hao et al., 2020). In cell-free massive MIMO, the splitting factor also appears in the denominator of both multicast and unicast SINRs through $$\mathbf{x} = \sum_{i=1}^L \mathbf{w}_i s_i + \mathbf{v}, \quad \mathbf{v} \sim \mathcal{CN}(\mathbf{0},\mathbf{V}),$$5, yielding a closed-form balance between rate and energy (Tan et al., 2020).

The integrated receiver architecture in (Kim et al., 2023) departs from power splitting and time switching. It uses a double half-wave rectifier with two diode-capacitor branches producing a positive DC amplitude $$\mathbf{x} = \sum_{i=1}^L \mathbf{w}_i s_i + \mathbf{v}, \quad \mathbf{v} \sim \mathcal{CN}(\mathbf{0},\mathbf{V}),$$6 and a negative DC amplitude $$\mathbf{x} = \sum_{i=1}^L \mathbf{w}_i s_i + \mathbf{v}, \quad \mathbf{v} \sim \mathcal{CN}(\mathbf{0},\mathbf{V}),$$7, and information decoding is performed by detecting a scalar function of these rectified outputs. The paper considers Amplitude Ratio Shift Keying,

$$\mathbf{x} = \sum_{i=1}^L \mathbf{w}_i s_i + \mathbf{v}, \quad \mathbf{v} \sim \mathcal{CN}(\mathbf{0},\mathbf{V}),$$8

and Amplitude Difference Shift Keying,

$$\mathbf{x} = \sum_{i=1}^L \mathbf{w}_i s_i + \mathbf{v}, \quad \mathbf{v} \sim \mathcal{CN}(\mathbf{0},\mathbf{V}),$$9

(Kim et al., 2023). Harvested power is proportional to the square of the DC voltage difference over the load,

$\mathbf{v}$0

This design explicitly removes local oscillators and mixers in the information-decoding path.

Another axis of variation is the relationship between data and energy receivers. In (Ng et al., 2013), idle legitimate receivers harvest energy while active receivers decode layered multicast video; energy and secrecy are coupled through artificial noise. In (Wu et al., 2018), every receiver simultaneously imposes reliability and energy constraints on the same common-message channel. In (Huang et al., 7 Jul 2025), data users and energy users are distinct, and the transmitter maximizes the minimum rate of data users while guaranteeing $\mathbf{v}$1 for energy users.

Holographic systems add electromagnetic modeling as an architectural feature. In (Huang et al., 2024), energy harvesting is modeled through the Poynting vector and a nonlinear rectifier map $\mathbf{v}$2, while in (Huang et al., 7 Jul 2025) the harvested energy uses a baseband-linear proxy,

$\mathbf{v}$3

The first is closer to full-wave EM modeling, while the second is closer to conventional communication-theoretic beamforming.

A plausible implication is that the term IDEM encompasses both “same-message same-waveform” systems and “common data plus differentiated receiver roles” systems. The literature does not impose a single receiver model; instead, it adapts IDEM to the hardware or analytical regime under study.

6. Near-field and holographic IDEM

Near-field holographic work reframes IDEM as an electromagnetic aperture-synthesis problem. "Holographic Integrated Data and Energy Transfer" treats the transmitter as a continuous aperture capable of generating arbitrary vector surface current distributions. The electromagnetic field obeys

$\mathbf{v}$4

and is represented through the dyadic Green’s function without Fresnel or Fraunhofer truncation (Huang et al., 2024). This allows energy focusing in both angle and distance and interference shaping through field orthogonality and polarization.

For a data user $\mathbf{v}$5, after polarization combining by $\mathbf{v}$6, the SINR is

$\mathbf{v}$7

and for an energy user $\mathbf{v}$8, the RF power through a small aperture is

$\mathbf{v}$9

(Huang et al., 2024). The nonlinear EH constraint is imposed through $W$0.

The multicast specialization replaces user-specific data beams by a common current distribution $W$1 plus optional energy-only beams $W$2, with multicast SINR

$W$3

(Huang et al., 2024). This is structurally close to artificial-noise-aided secure multicast, except that the energy beams are designed through a continuous EM model rather than standard array beamforming.

The circular H-MIMO paper (Huang et al., 7 Jul 2025) develops a more explicit near-field IDEM theory for circular apertures. It defines the resolution function

$W$4

and derives a closed form in terms of Bessel functions: $W$5 (Huang et al., 7 Jul 2025). The dependence on range through $W$6 distinguishes near-field resolution from purely angular far-field beam patterns.

The same paper proves asymptotic spatial orthogonality: $W$7 for distinct points, and then

$W$8

for full channels (Huang et al., 7 Jul 2025). This leads to an asymptotically optimal fully-digital multicast beamformer,

$W$9

where the data-user weights equalize rates and the energy-user weights satisfy EH constraints (Huang et al., 7 Jul 2025).

These holographic results indicate that IDEM in the near field is governed not only by array gain but by 3D focusing resolution. This suggests that, as apertures become larger and more continuous, IDEM increasingly overlaps with electromagnetic inverse design rather than conventional finite-dimensional beamforming.

7. Empirical findings, interpretations, and open directions

Several consistent empirical patterns recur across the cited works. In the secure layered multicast system (Ng et al., 2013), total transmit power increases with the number of receivers and decreases with the number of transmit antennas, and the proposed suboptimal schemes perform close to the SDR upper bound while achieving significant power savings over MRT with isotropic energy signal generation. Harvested energy increases with the number of receivers because the QoS constraints force greater total power, but baseline schemes can appear to harvest more energy only because they transmit excessive RF power (Ng et al., 2013).

In the information-theoretic model (Wu et al., 2018), receiver segmentation can improve common rates when the full receiver set is heterogeneous. Grouping similar receivers reduces the worst-case bottleneck, and the segmentation performance can be characterized either through worst-group capacity or through the same-signal loss metric $C_O(\mathbf{B}) = C(\mathbf{B})$00 (Wu et al., 2018). This gives a conceptual counterpart to practical user grouping in beamformed systems.

In the mmWave hybrid SWIPT architecture (Hao et al., 2020), energy efficiency increases with $C_O(\mathbf{B}) = C(\mathbf{B})$01 and then saturates, subarray structures often achieve the highest EE because they reduce circuit power, and higher EH requirements reduce EE once more power must be diverted to energy harvesting. The ZF-based inner loop converges in about five iterations, whereas the SCA-based inner loop requires about fifty but achieves slightly higher spectral efficiency (Hao et al., 2020).

In the cell-free massive MIMO setting (Tan et al., 2020), EE is flat at low multicast-rate targets and low energy requirements, then degrades as the multicast requirement or EH threshold grows. The accelerated first-order method roughly halves the iterations of the non-accelerated method while maintaining near-optimal EE, and the reported performance is within approximately $C_O(\mathbf{B}) = C(\mathbf{B})$02 of global BRB at much lower computational cost (Tan et al., 2020). This supports the scalability of first-order IDEM optimization in massive-access systems.

In the IoT integrated-receiver scheduler (Kim et al., 2023), ARSK generally yields higher harvested energy but lower throughput, while ADSK yields higher throughput but less harvested energy. As the energy weights $C_O(\mathbf{B}) = C(\mathbf{B})$03 increase, the modulation-selection ratio shifts toward ARSK, sum harvested energy increases monotonically, and sum unicast throughput decreases monotonically. Under heterogeneous QoS and energy constraints, the proposed UMSM scheduler satisfies both throughput and energy requirements while outperforming fixed-modulation baselines (Kim et al., 2023).

Near-field holographic studies report especially strong gains for nearby energy users. In (Huang et al., 2024), the full electromagnetic dyadic Green’s model improves near-field focusing and harvested energy relative to traditional channel models, especially when energy users are close to the transmitter. In (Huang et al., 7 Jul 2025), the closed-form resolution function matches exact summation well except very close to the array, circular arrays maintain consistent multi-point focusing over azimuth angles, and scaled analog beamforming schemes approach high-rate performance with a single RF chain (Huang et al., 7 Jul 2025).

Several limitations recur. Linear EH models remain common in secure multicast and circular H-MIMO formulations (Ng et al., 2013, Huang et al., 7 Jul 2025), whereas nonlinear models appear in cell-free massive MIMO and holographic IDET (Tan et al., 2020, Huang et al., 2024). Perfect CSI or known near-field channels are often assumed. Passive eavesdropper modeling via safe chance constraints is conservative (Ng et al., 2013). Holographic formulations typically idealize continuous apertures and metasurface control (Huang et al., 2024, Huang et al., 7 Jul 2025). The IoT scheduler assumes fitted rate–energy maps for IR-compatible modulations (Kim et al., 2023).

Open directions identified across the literature include nonlinear harvesting in broader IDEM settings (Ng et al., 2013), constructive code design and subblock energy constraints (Wu et al., 2018), multi-group multicast and fairness-aware extensions (Hao et al., 2020), robust scheduling under CSI uncertainty (Kim et al., 2023), and robust or quantized-control holographic beamforming (Huang et al., 2024, Huang et al., 7 Jul 2025). A plausible implication is that future IDEM research will increasingly unify electromagnetic aperture design, nonlinear rectification models, and cross-layer control, rather than treating data multicast and energy transfer as separable subsystems.