Partially-Connected Hybrid Beamforming

• Partially-connected hybrid beamforming is a design strategy that links each RF chain to a subset of antennas, using block-diagonal or sparse analog precoding for efficient signal processing.
• It employs diverse architectural forms—such as fixed, dynamic, and switch-based subarrays—and optimization methods like alternating optimization and manifold projection to meet spectral efficiency goals.
• While offering reduced hardware complexity, lower insertion loss, and energy efficiency, the approach trades off analog-domain flexibility, requiring advanced digital compensation.

Partially-connected hybrid beamforming is a class of hybrid analog–digital beamforming architectures in which each RF chain connects only to a subset of antenna elements, receive apertures, or feed points, so that the analog precoder or combiner is block-diagonal or block-sparse rather than dense. In the literature, this architecture appears in mmWave massive MIMO, OFDM, THz, integrated sensing and communication, dual-function radar-communication, segmented waveguide-enabled pinching-antenna systems, and uplink channel-estimation frameworks. Its central motivation is consistent across these settings: compared with fully-connected hybrid beamforming, partially-connected structures reduce the number of phase shifters, insertion loss, calibration overhead, and power consumption, while sacrificing analog-domain degrees of freedom and shifting more of the burden to digital processing and topology design (Zhao et al., 2020, Sohrabi et al., 2017, Song et al., 2019).

1. Architectural forms and connectivity models

The canonical partially-connected architecture assigns each RF chain to a disjoint subarray. At transmitter side this is commonly written as

$$F_{\mathrm{RF}}=\operatorname{blkdiag}(f_1,f_2,\ldots,f_{N_{\mathrm{RF}}}),$$

with each subarray vector constrained by phase-only hardware, and the same block-diagonal construction appears on the receive side for $W_{\mathrm{RF}}$ (Zhao et al., 2020, Sohrabi et al., 2017). In one widely used interpretation, the architecture is “one-stream-per-subarray” (OSPS): each RF antenna port is connected to a disjoint subarray, and the RF antenna ports are not connected to all antenna elements of the array (Song et al., 2019).

The partially-connected label, however, covers several structurally distinct families. Fixed subarrays are only one case. Dynamic subarrays use a switch network so that each RF chain is adaptively mapped to a non-overlapping subarray rather than to a static partition (Li et al., 2019). Switch-based networks replace phase-shifter weights by a binary connectivity matrix and linear topology constraints, so the analog network is sparse because routing itself is optimized (Nosrati et al., 2019). In SWAN receivers, the paper introduces an interleaved topology in which the subset served by each RF chain is distributed uniformly along the segmented waveguide rather than grouped contiguously, producing a block-sparse combiner with an interleaved support set $S_j$ (Jiang et al., 4 Mar 2026). In receiver-side antenna/RF-chain selection, an LDPC-inspired partially-connected mask is imposed so that information can propagate across clusters despite sparse connectivity (Shen et al., 2022).

Form	Analog structure	Defining feature
Fixed subarray PC-HBF	Block diagonal	Disjoint contiguous subarrays
Dynamic subarray PC-HBF	Sparse with switch reconfiguration	Non-overlapping subarrays change with channel conditions
Switch-based PC-HBF	Binary sparse mask	Routing matrix in $\{0,1\}^{N_t\times k_t}$
Interleaved PC-SWAN	Block-sparse with permuted support	Uniformly distributed segment assignment
LDPC-based PC receiver	Sparse mask with graph constraints	Inter-cluster message reachability

These variants share the same structural principle—restricted RF connectivity—but differ in how sparsity is imposed. This suggests that partially-connected hybrid beamforming is best understood not as a single topology but as a family of sparsity-constrained RF mappings whose performance depends strongly on whether the sparsity is fixed, dynamic, interleaved, graph-structured, or learned.

2. Signal models, constraints, and optimization criteria

A standard narrowband hybrid model writes the transmitted or received signal through the decomposition

$$F = F_{\mathrm{RF}}F_{\mathrm{BB}}, \qquad W = W_{\mathrm{RF}}W_{\mathrm{BB}},$$

with baseband processing performed in a reduced RF-chain dimension and analog processing constrained by phase-shifter hardware (Sohrabi et al., 2017). For OFDM and wideband systems, the analog beamformer is common across subcarriers while the digital beamformer is subcarrier dependent, so $F_{\mathrm{RF}}$ and $W_{\mathrm{RF}}$ are frequency-flat and $F_{\mathrm{BB}}[k],W_{\mathrm{BB}}[k]$ vary with $k$ (Sohrabi et al., 2017, Zhao et al., 2020).

The dominant optimization criteria are spectral efficiency maximization, weighted sum-rate maximization, and minimum mean-square error formulations. In the partially-connected mmWave OFDM framework, the average spectral efficiency is maximized under per-subcarrier power constraints and unit-modulus constraints on the nonzero entries of $F_{\mathrm{RF}}$ and $W_{\mathrm{RF}}$0 (Zhao et al., 2020). In MU-MISO and MU-MIMO formulations, the objective is often

$W_{\mathrm{RF}}$1

with the digital stage handling residual multiuser interference after the analog stage fixes the sparse RF mapping (Majidzadeh et al., 2020, Qi et al., 2023). A key theoretical development is the proof that, for partially-connected architectures, spectral-efficiency maximization can be transformed into a matrix weighted MMSE minimization problem with closed-form digital updates and constrained analog updates (Zhao et al., 2020).

Several papers generalize the basic model by adding hardware or propagation impairments directly into the optimization. In distortion-aware ISAC, the power amplifier output is modeled through Bussgang decomposition,

$W_{\mathrm{RF}}$2

with communication rate and sensing mutual information combined as

$W_{\mathrm{RF}}$3

under a distortion-aware total power constraint (Zhang et al., 18 Jul 2025). In low-resolution THz receivers, quantization is modeled by the additive quantization noise model

$W_{\mathrm{RF}}$4

and the digital combiner is designed against the effective noise covariance induced jointly by analog combining and ADC quantization (Garg et al., 10 Mar 2026). In SWAN tri-hybrid reception, the analog combiner $W_{\mathrm{RF}}$5 is optimized jointly with the digital combiner $W_{\mathrm{RF}}$6 and with pinching-antenna positions $W_{\mathrm{RF}}$7, so the sparse RF topology is embedded in a three-layer digital–analog–pinching architecture rather than a conventional two-layer hybrid model (Jiang et al., 4 Mar 2026).

3. Algorithmic design methodologies

Alternating optimization is the dominant algorithmic template. In the partially-connected WMMSE literature, the digital precoder and combiner are updated in closed form, while the analog block-diagonal matrices are updated either element-wise or by manifold methods adapted to unit-modulus constraints (Zhao et al., 2020, Majidzadeh et al., 2020). For fixed analog variables, the digital step usually reduces to MMSE, ZF, or least-squares updates; for fixed digital variables, the analog step is the nonconvex core.

Two analog-update philosophies recur. The first is element-wise or block-wise phase refinement on the feasible support. In the WMMSE equivalence framework, each nonzero entry of the block-diagonal analog matrix is updated by a one-dimensional search or by explicit phase projection, while preserving the partially-connected sparsity pattern (Zhao et al., 2020). In SWAN’s partially-connected interleaved topology, the manifold step used in the fully-connected case is replaced by element-wise phase calibration,

$W_{\mathrm{RF}}$8

performed only at the nonzero positions of the sparse combiner, precisely to exploit analog sparsity and obtain a stable, low-complexity update (Jiang et al., 4 Mar 2026). A related low-complexity idea appears in multiuser mmWave beamforming: the analog beamformer is first obtained by simple phase alignment to the intended user channel, and only the digital stage solves a WMMSE problem over the effective channels (Qi et al., 2023).

The second philosophy is manifold optimization. In partially-connected DFRC, the analog and digital variables are placed on a Riemannian product manifold composed of a complex circle manifold for the analog phase shifters and a fixed-norm manifold for the digital matrix, and a Riemannian product manifold trust region algorithm is used to approach a near-optional solution (Wang et al., 2021). For partially-connected spectral-efficiency maximization, manifold optimization is also used directly on the product of complex circles, with Euclidean gradients projected to the tangent space and retracted back to unit-modulus feasible points (Zhao et al., 2020).

Other algorithmic families are tied to specific hardware models. Dynamic subarray design under low-resolution phase shifters uses fractional programming with auxiliary variables, a closed-form digital update, and a 0–1 analog mapping problem over the switch network; the reported FP-based algorithm converges in approximately $W_{\mathrm{RF}}$9 iterations and the heuristic dynamic-subarray algorithm in approximately $S_j$0 iterations at $S_j$1 (Li et al., 2019). Switch-based partially-connected beamforming with binary analog matrices uses a rank-constrained subspace reduction and then approximates the solution through norm maximization (SHD-NM) or QR-based majorization (SHD-QRQU) under linear sparsity masks (Nosrati et al., 2019). In the Alt-MaG and MaGiQ framework, the digital target is a fully-digital precoder or combiner defined only up to a unitary matrix, and the analog block-diagonal matrix is obtained by repeated projection of the target onto the feasible partially-connected set (Ioushua et al., 2017).

Wideband THz systems require another layer of algorithmic specialization. There the analog stage is designed in two stages: a frequency-independent sparse or block-diagonal beamformer is first selected, then a few true-time-delay lines per subarray are introduced so that the effective analog beam becomes frequency-dependent and compensates beam-split, after which per-subcarrier digital ZF or MMSE processing is applied under AQNM noise (Garg et al., 10 Mar 2026).

4. Domain-specific realizations

Partially-connected hybrid beamforming is strongly shaped by application domain. In broadband mmWave OFDM, the defining problem is the coexistence of a common analog beamformer with per-subcarrier digital beamformers; the partially-connected version is treated as a block-diagonal analog constraint whose columns correspond to subarrays and whose utility derives from sparse mmWave channels (Sohrabi et al., 2017). In MU-MIMO downlink beamforming, the architecture is often deployed with $S_j$2 and one stream per user, and the reduced-dimensional digital stage performs the interference management that the analog stage can no longer realize because of its block sparsity (Qi et al., 2023).

In THz systems, partially-connected design is motivated not only by hardware efficiency but also by dual-wideband propagation. The analog precoder and combiner are block-diagonal, but the dominant challenge is spatial-wideband beam-squint. The solution reported in the literature is to keep the partially-connected structure while equipping each subarray with a few TTD lines, so that beam-split is compensated without reverting to a fully-connected network (Garg et al., 10 Mar 2026).

In ISAC and DFRC, partially-connected beamforming is embedded in multi-objective optimization rather than pure communication rate maximization. Distortion-aware ISAC jointly maximizes communication rate and sensing mutual information under nonlinear PA distortion, with a block-diagonal $S_j$3 and optional phase quantization during hybrid decomposition (Zhang et al., 18 Jul 2025). In DFRC, the partially-connected analog beamformer is block diagonal with subarray vectors $S_j$4, and the objective minimizes a weighted summation of radar and communication performance relative to communication and radar references, again under constant-modulus and power constraints (Wang et al., 2021).

SWAN broadens the concept further. Its partially-connected analog combiner is not antenna-subarray based in the conventional sense but segment based: each RF chain connects to a subset of segmented waveguide feed points, and the interleaved mapping

$S_j$5

distributes each subarray uniformly along the waveguide (Jiang et al., 4 Mar 2026). The resulting architecture remains partially-connected in the precise sense that the analog combining matrix is block-sparse and each RF chain connects only to allowed entries, yet the geometry of sparsity is tailored to service-area fairness rather than only to PCB or package routing.

Uplink channel estimation provides another specialization. In group-wise narrow beam design for PC-HBF, each RF chain connects to a vertical subarray, the columns of a UPA are divided into groups, and each group is assigned a narrow elevation beam so that a single pilot timeslot realizes an elevation filter bank. The analog combiner takes the structured form

$S_j$6

and the induced group structure is then exploited by a group-wise subspace-constrained variational Bayesian inference algorithm (Zhou et al., 1 Jun 2025).

5. Performance trade-offs, hardware efficiency, and scaling behavior

The principal attraction of partially-connected hybrid beamforming is hardware efficiency. In the ISAC formulation, fully-connected requires $S_j$7 phase shifters in total, while partially-connected reduces the number of phase shifters to $S_j$8 (Zhang et al., 18 Jul 2025). The same count reduction appears in THz block-diagonal arrays and is one reason partially-connected designs are repeatedly described as having lower hardware complexity, lower insertion loss, and improved energy efficiency (Garg et al., 10 Mar 2026). In SWAN, the contrast is especially explicit: the fully-connected structure has $S_j$9 phase shifters, whereas the partially-connected interleaved structure has $\{0,1\}^{N_t\times k_t}$0 phase shifters total (Jiang et al., 4 Mar 2026).

The performance penalty is a loss of analog-domain flexibility. In multiuser mmWave systems, the gap between partially-connected and fully-connected architectures widens as the number of users grows because the partially-connected architecture has fewer analog degrees of freedom (Majidzadeh et al., 2020). In SWAN, the partially-connected structure exhibits a rate gap to the fully-connected structure for the same reason, although the paper reports that the partially-connected structure can strike a good balance between sum rate and energy consumption when the number of segments is large (Jiang et al., 4 Mar 2026).

Reported numerical results nonetheless show that the performance loss is often modest in the regimes that motivated PC-HBF in the first place. In MU-MIMO mmWave with OSPS, the two architectures achieve similar sum spectral efficiency, while the OSPS architecture is advantageous with respect to the fully-connected case in terms of hardware complexity and power efficiency, at the sole cost of a slightly longer BA time-to-acquisition (Song et al., 2019). The same paper quantifies the acquisition penalty: at $\{0,1\}^{N_t\times k_t}$1, OSPS needs about $\{0,1\}^{N_t\times k_t}$2 more beacon slots than the fully-connected architecture to reach detection probability $\{0,1\}^{N_t\times k_t}$3 (Song et al., 2019). In THz wideband MU systems, the proposed two-stage partially-connected transceiver with a few TTD lines delivers a performance improvement of around $\{0,1\}^{N_t\times k_t}$4 in terms of spectral efficiency over existing state-of-the-art techniques (Garg et al., 10 Mar 2026).

Architectural modifications can recover additional performance. Dynamic subarrays with low-resolution phase shifters significantly outperform fixed-subarray baselines; the FP-based algorithm with $\{0,1\}^{N_t\times k_t}$5 approaches the dynamic-subarray scheme that uses double infinite-resolution phase shifters (Li et al., 2019). LDPC-based partially-connected selection shows that sparse but message-passable connectivity can outperform existing fully- and partially-connected benchmarks in operational power and energy efficiency: with $\{0,1\}^{N_t\times k_t}$6, the proposed MARS scheme reports power savings of approximately $\{0,1\}^{N_t\times k_t}$7, $\{0,1\}^{N_t\times k_t}$8, $\{0,1\}^{N_t\times k_t}$9, $$F = F_{\mathrm{RF}}F_{\mathrm{BB}}, \qquad W = W_{\mathrm{RF}}W_{\mathrm{BB}},$$0, and $$F = F_{\mathrm{RF}}F_{\mathrm{BB}}, \qquad W = W_{\mathrm{RF}}W_{\mathrm{BB}},$$1 and energy-efficiency gains of approximately $$F = F_{\mathrm{RF}}F_{\mathrm{BB}}, \qquad W = W_{\mathrm{RF}}W_{\mathrm{BB}},$$2, $$F = F_{\mathrm{RF}}F_{\mathrm{BB}}, \qquad W = W_{\mathrm{RF}}W_{\mathrm{BB}},$$3, $$F = F_{\mathrm{RF}}F_{\mathrm{BB}}, \qquad W = W_{\mathrm{RF}}W_{\mathrm{BB}},$$4, $$F = F_{\mathrm{RF}}F_{\mathrm{BB}}, \qquad W = W_{\mathrm{RF}}W_{\mathrm{BB}},$$5, and $$F = F_{\mathrm{RF}}F_{\mathrm{BB}}, \qquad W = W_{\mathrm{RF}}W_{\mathrm{BB}},$$6 relative to the stated benchmarks (Shen et al., 2022).

The SWAN literature adds a scaling result that is atypical in conventional antenna-array discussions but important for partially-connected designs. For the fully-connected single-chain limit, the maximum rate is non-monotonic in the number of segments and eventually satisfies

$$F = F_{\mathrm{RF}}F_{\mathrm{BB}}, \qquad W = W_{\mathrm{RF}}W_{\mathrm{BB}},$$7

For the partially-connected many-chain limit with digital MRC, the rate increases with the number of segments but is bounded, with

$$F = F_{\mathrm{RF}}F_{\mathrm{BB}}, \qquad W = W_{\mathrm{RF}}W_{\mathrm{BB}},$$8

Accordingly, the achievable rate does not necessarily increase with the number of segments (Jiang et al., 4 Mar 2026). This directly counters the common but inaccurate assumption that adding more sparse apertures or segments is always beneficial.

6. Limitations, misconceptions, and active research directions

A recurring misconception is that partially-connected hybrid beamforming is synonymous with fixed contiguous subarrays. The literature does not support that restriction. Interleaved segment assignments in SWAN, dynamic subarrays with switches, switch-based binary masks, LDPC-based sparse receiver graphs, and flexible subarray mappings in MSE-driven designs are all explicitly partially-connected, yet they differ substantially in hardware abstraction and algorithmic treatment (Jiang et al., 4 Mar 2026, Li et al., 2019, Nosrati et al., 2019, Shen et al., 2022, Ioushua et al., 2017).

A second misconception is that partially-connected structures are intrinsically low-performance approximations. The documented record is more specific. Under perfect CSI, simple RF phase alignment plus digital WMMSE achieves almost the same sum-rate performance as existing schemes but with lower computational complexity in partially-connected millimeter wave massive MIMO (Qi et al., 2023). In OFDM mmWave, the proposed heuristic with practical number of RF chains can already approach the performance of fully-digital beamforming in the MU-MISO case (Sohrabi et al., 2017). In OSPS mmWave MU-MIMO, similar sum spectral efficiency to fully-connected is reported, with better power efficiency (Song et al., 2019). A plausible implication is that performance loss is governed less by connectivity sparsity alone than by whether the sparse architecture is matched to propagation sparsity, interference structure, and hardware impairments.

The main limitations repeatedly emphasized are perfect-CSI assumptions, phase quantization, and sensitivity to hardware nonidealities. Distortion-aware ISAC explicitly lists extension opportunities in robust design under CSI and PA-model uncertainty, explicit phase-quantization-constrained analog design and practical mapping such as switch networks, dynamic subarray partitioning beyond fixed block-diagonal mapping, and joint waveform and beamforming design (Zhang et al., 18 Jul 2025). THz wideband work identifies dynamic blockage and fast time variation, hardware impairments such as nonlinearities, LO phase noise, and frequency-dependent phase-shifter errors, and the joint optimization of TTD placement, phase-shifter quantization, and RF chain counts under power and area constraints as open problems (Garg et al., 10 Mar 2026). Imperfect-CSI multiuser mmWave work adds that user scheduling is needed when $$F = F_{\mathrm{RF}}F_{\mathrm{BB}}, \qquad W = W_{\mathrm{RF}}W_{\mathrm{BB}},$$9 and that multi-antenna users would recouple RF and baseband design (Qi et al., 2023). Channel-estimation work for PC-HBF highlights the need for one-shot, real-time designs compatible with 5G NR SRS and large UPAs, motivating structured group-wise analog beams and reduced-complexity Bayesian inference (Zhou et al., 1 Jun 2025).

The resulting research picture is therefore not one of a settled architecture, but of a mature design space. Partially-connected hybrid beamforming remains defined by the same structural idea—sparse RF connectivity—but current work increasingly treats that sparsity as an optimization variable, a graph, a filter bank, a manifold-constrained object, or a topology co-designed with sensing, wideband compensation, nonlinear hardware mitigation, and channel estimation.