---
title: Sub-Connected Hybrid Beamforming
url: https://www.emergentmind.com/topics/sub-connected-hybrid-beamforming
type: topic
---

# Sub-Connected Hybrid Beamforming

Sub-connected hybrid beamforming is a hybrid analog-digital beamforming architecture in which each radio-frequency (RF) chain is connected to a disjoint subset of antenna elements rather than to the entire array. In the literature, closely related formulations appear as partially-connected, sub-array-connected, one-stream-per-subarray (OSPS), generalized sub-array-connected (GSAC), unequal sub-connected, dynamic subarray, and tiled hybrid architectures. The common structural feature is a block-diagonal analog network and a composite precoder or combiner of the form $\mathbf{F}=\mathbf{F}_{\rm RF}\mathbf{F}_{\rm BB}$, designed to reduce phase-shifter count, RF-network loss, hardware complexity, and power consumption relative to fully-connected (FC) architectures while preserving much of the achievable rate or spectral efficiency of large-array systems [1806.09246][1810.13161][2012.02889].

## 1. Architectural definition and taxonomy

The canonical sub-connected architecture partitions the antenna array into non-overlapping subarrays, each driven by one RF chain. In FC hybrid beamforming, each RF chain connects to all antennas via phase shifters; in sub-array-connected (SAC) beamforming, each RF chain connects only to one non-overlapping subarray. GSAC generalizes SAC by allowing an arbitrary number of sub-arrays, with each sub-array having an arbitrary number of antennas $N_{{\rm t},i}$ and RF chains $N_{{\rm RF},i}$, and by allowing each RF chain to connect to an arbitrary group of antennas rather than to a uniform grouping [1806.09246].

In the GSAC formulation, both the analog precoder and the digital precoder are block-diagonal,
$$
\mathbf{F}_{\rm RF}=\text{block-diag}(\mathbf{F}_{{\rm RF},1},\ldots,\mathbf{F}_{{\rm RF},N_{\rm sub}})
$$
and
$$
\mathbf{F}_{\rm BB}=\text{block-diag}(\mathbf{F}_{{\rm BB},1},\ldots,\mathbf{F}_{{\rm BB},N_{\rm sub}}).
$$
This structure makes FC and SAC special cases: FC corresponds to a single “sub-array” with all antennas and all RF chains, while SAC corresponds to $N_{\rm sub}=N_{\rm RF}^{\rm t}$ with one RF chain per sub-array [1806.09246].

Later variants refine this basic partitioning. Unequally sub-connected architectures (UESA) permit unequal numbers of antennas in sub-antenna arrays and perform the assignment through a switching network, with all antennas still used but the number per sub-array optimized [1908.10056]. Dynamic-subarray designs allow the antenna-to-RF mapping to vary with channel state information (CSI); one formulation writes the analog beamforming matrix as
$$
\mathbf{F}_{\rm RF}=\tilde{\mathbf{F}}_{\rm RF}\odot \mathbf{X}_{\rm sel},
$$
where $\mathbf{X}_{\rm sel}\in\{0,1\}^{N_t\times K}$ has exactly one nonzero entry per row, so each antenna is exclusively connected to only one RF chain at a given time [2602.07509]. A more hardware-reductive direction shares one phase shifter (PS) among multiple antennas inside each sub-array through an optimized static PS-to-antenna connection matrix, thereby preserving static wiring while still enabling adaptive phase control and digital precoding [2607.02393].

The same architectural principle also appears in tiled receivers for sub-THz links, where each tile or subarray is a phased array performing analog beamforming followed by digital signal processing on tile outputs, and in receiver-side hybrid combining, where unequal subarrays or sub-connected active partitions are used to balance achievable rate and power consumption [2512.06532][1908.10056][2402.11547]. This broad taxonomy shows that “sub-connected hybrid beamforming” denotes not one fixed circuit but a family of constrained analog interconnects centered on disjoint or nearly disjoint analog domains.

## 2. Signal model, block structure, and performance criteria

The standard downlink precoding model uses the effective hybrid precoder $\mathbf{F}=\mathbf{F}_{\rm RF}\mathbf{F}_{\rm BB}$ and the achievable-rate objective
$$
R=\log_2\det\left(\mathbf{I}_{N_r}+\frac{\rho}{N_s\sigma^2}\mathbf{H}\mathbf{F}\mathbf{F}^*\mathbf{H}^*\right).
$$
For GSAC, the block-diagonal structure permits decomposition of the total achievable rate into a sum of sub-rates associated with individual sub-arrays, which is the key algebraic property underlying successive interference cancellation (SIC)-based design [1806.09246].

Receiver-side sub-connected combining admits an analogous decomposition. In the unequal sub-connected receiver architecture, the sum rate at the output of the hybrid combiner is
$$
R=\log_2\det\left(\mathbf{I}_N+\rho\,\mathbf{H}^H\mathbf{W}_A\mathbf{W}_A^H\mathbf{H}\right),
$$
and can be factorized into
$$
R=\sum_{n=1}^{N}\log_2\left(1+\rho\,\mathbf{w}_n^H\mathbf{T}_n\mathbf{w}_n\right),
$$
which enables per-subarray optimization under constant-modulus or quantized phase-shifter constraints [1908.10056].

A central motivation for sub-connected structures is explicit energy-efficiency optimization. In the GSAC framework, total power is modeled as
$$
P_{\rm total}=P_{\rm CO}+N_{\rm RF}^{\rm t}P_{\rm RF}+N_tP_{\rm PA}+N_{\rm PS}P_{\rm PS},
$$
with energy efficiency
$$
\eta=\frac{R}{P_{\rm total}}.
$$
Because the number of phase shifters $N_{\rm PS}$ depends on the subarray configuration, GSAC interpolates between FC and SAC in hardware complexity and power draw [1806.09246]. A related wideband sub-THz tiled architecture uses the hardware model
$$
P_{\mathrm{tot}}\approx 20N+400N_d~\text{mW},
$$
with $20~\text{mW}$ per antenna for LNA and phase shifter and $400~\text{mW}$ per tile for RF chain and ADCs, making tile size and number of tiles explicit design variables [2512.06532].

The same block-structured modeling extends beyond conventional rate maximization. Distortion-aware integrated sensing and communication (ISAC) formulations keep the sub-connected analog beamformer block-diagonal and incorporate nonlinear power-amplifier effects via Bussgang decomposition,
$$
\phi(\mathbf{x})=\mathbf{B}\mathbf{x}+\mathbf{e},
$$
with communication rate and sensing mutual information jointly optimized under total transmit power and unit-modulus constraints [2507.14018]. Near-field rate-splitting multiple access (RSMA) with sub-connected hybrid analog-digital beamfocusing similarly imposes
$$
\mathbf{F}=\mathrm{blkdiag}(\mathbf{f}_1,\ldots,\mathbf{f}_L),\qquad |\mathbf{f}_{l,m}|=1,
$$
and jointly optimizes analog beamfocuser, digital beamfocuser, and common-rate allocation under imperfect CSI and imperfect SIC [2507.11854].

## 3. Core design and optimization methods

A major line of work exploits the sub-rate decomposition induced by block-diagonal structure. In GSAC precoding, the total achievable-rate optimization is decomposed into multiple sub-rate optimization problems and solved sequentially by SIC: for each sub-array, an SVD is performed, the analog beamformer is obtained by extracting the phases of dominant right singular vectors, the digital precoder is computed by least squares, and the residual interference covariance is updated before moving to the next sub-array [1806.09246]. This design targets achievable-rate maximization for a fixed RF-chain and antenna configuration, after which an exhaustive search over integer partitions of RF chains can be used to select the configuration with the best energy efficiency.

Alternating-optimization methods are another dominant paradigm. For partially connected mmWave massive MIMO, weighted minimum mean square error (WMMSE) formulations have been developed for both single-user and multi-user settings, with separate algorithms for full-array-based and sub-array-based processing. In these methods, the digital combiner or precoder admits closed-form updates, whereas analog subarray beamformers are optimized iteratively under power constraints. Lower-complexity subarray-based zero-forcing (ZF) algorithms provide a reduced-complexity alternative, and the reported numerical results are used as upper bounds for lower-complexity methods [2012.02889].

Unequal and dynamic connectivity introduce discrete allocation problems on top of continuous beamforming. In UESA, the antenna-allocation problem is controlled by two analytical rules: a non-decreasing number of antennas per sub-array, $m_1\leq m_2\leq \dots \leq m_N$, and a channel-row ordering that places the rows with largest norms first. Exhaustive search (UESA-ES), reduced exhaustive search (UESA-RES), early termination (UESA-RES-ET), and a greedy Fast-UESA algorithm all optimize an eigenvalue-based objective while balancing complexity and rate [1908.10056]. Dynamic-subarray beamforming in near-space airship-borne communications goes further by jointly learning analog beamforming, antenna selection, and digital beamforming with Transformer encoders; the digital stage embeds a model-driven WMMSE update, while the selection matrix dynamically assigns each antenna to one RF chain based on CSI [2602.07509].

Recent formulations also address hardware nonidealities and new operating regimes. In near-field RSMA-enabled communications, a penalty-based block coordinate descent (BCD) method alternates over auxiliary hybrid variables, the analog beamfocuser, and the digital beamfocuser; the analog update has the closed form
$$
\mathbf{f}^*_{l,m}=e^{-j\angle \psi^H_{l,m}},
$$
and the digital update is an unconstrained least-squares solution,
$$
\mathbf{W}^*=(\mathbf{F}^H\mathbf{F})^{-1}\mathbf{F}^H\mathbf{P}
$$
[2507.11854]. In distortion-aware ISAC, the common strategy is two-stage: first solve an equivalent fully digital non-convex problem by alternating optimization with manifold optimization, then decompose the result into a block-diagonal analog beamformer and a digital beamformer that respect unit-modulus constraints [2507.14018].

Static sparse phase-shifter sharing introduces mixed discrete-continuous optimization over PS-to-antenna connections, sub-array assignment, PS phases, and digital precoders. For a single RF chain, the design becomes an antenna-grouping problem; for multiple RF chains, a QoS-majorization-minimization algorithm alternates digital precoder updates, phase updates on the unit circle, and mixed-integer updates of the connection topology [2607.02393]. This suggests that sub-connected beamforming has evolved from a fixed hardware constraint into a co-design problem where topology itself is an optimization variable.

## 4. Training, feedback, and channel acquisition

Because sub-connected analog networks restrict the observation dimension, training and CSI acquisition are often more consequential than in FC architectures. A limited-feedback GSAC design uses a beamsteering codebook for each sub-array and standard digital codebooks for the smaller digital precoder. Reported simulations show that with 6–8 quantization bits, the codebook-based GSAC scheme achieves almost indistinguishable rate performance from the perfect-CSI case and remains superior to codebook-based SAC [1806.09246].

Beam acquisition for OSPS and related architectures is a distinct problem because subarrays offer lower angular resolution than FC networks. In mmWave MU-MIMO, FC and OSPS were studied jointly over initial beam acquisition and data transmission. The proposed beam acquisition scheme provides higher angular resolution for FC and requires fewer training slots, while OSPS requires 20–30% more training slots to reach similar detection probability; despite that penalty, the two architectures achieve similar sum spectral efficiency, and OSPS is better in hardware complexity and power efficiency [1810.13161].

Wideband beam training has motivated hierarchical codebooks that explicitly exploit subarray structure. One multiuser wideband mmWave algorithm constructs wide sector beams and narrow beams using orthogonal beamformer vectors, trains over codebooks without requiring channel matrix knowledge, and incorporates antenna coupling, element radiation pattern, and beam squint. In the analyzed scenarios, it attains more than 70 percent of the spectral efficiency, corresponding to a 1.5 to 3 dB SNR loss relative to ideal fully-digital beamforming, while maintaining linear dependence on the number of antennas and shorter training overhead [1905.03918]. A concrete example in that study uses $M_{\text{ap}}=32$, $M_{\text{ue}}=32$, $M_{\text{sub}}=8$, and $N_{\text{rf}}=4$, requiring only 77 training transmissions.

Channel estimation under partially connected hybrid beamforming can also be restructured around subarray grouping. A recent uplink channel-estimation method divides the columns of a uniform planar array into groups and assigns each group a narrow beam covering one vertical-angle sub-interval. The analog beam matrix is block diagonal,
$$
\mathbf{F}_a=\operatorname{blkdiag}\left(\widehat{\mathbf{F}_a^1},\ldots,\widehat{\mathbf{F}_a^{N_y}}\right),
$$
and the grouping pattern is optimized offline by an Estimation of Distribution Algorithm using integrated sidelobe level and statistical resolution limit criteria. The resulting GW-SC-VBI estimator achieves nearly the same NMSE as VBI and SC-VBI, but at about one-third of the runtime of regular SC-VBI and about one-fifteenth of the runtime of Turbo-VBI [2506.01043].

Another direction reduces in-band pilot overhead through out-of-band CSI transfer. The SA-MUHBF framework predicts mmWave beamspace from sub-6G channel estimates by a 2D CNN, selects analog beams with a multi-layer graph neural network, and computes digital beamforming by LMMSE on the effective channels. Reported gains over the best baselines are 0.5%, 5.2%, 14.4%, and 22.2% for $K=4,8,16,32$, respectively, and the predicted mmWave beamspace reaches a normalized MSE of 0.0894 on test data [2403.10873]. This suggests that, for sub-connected systems, CSI acquisition is increasingly being treated as a cross-band inference problem rather than solely as a beam-sweeping problem.

## 5. Extensions across mmWave, THz, near-field, RIS, and ISAC

Sub-connected hybrid beamforming is used not only for narrow-beam data transmission but also for broadcast and access procedures. For mmWave and THz initial access, a partially-connected architecture with $M$ subarrays of size $N_s=N/M$ forms complementary beams over sub-arrays to produce instantaneously uniform omnidirectional gain. With $M=2$, the composite pattern
$$
|g(\theta,t)|^2=\frac{|g_1(\theta,t)|^2+|g_2(\theta,t)|^2}{2}
$$
is optimized to satisfy the omnidirectional criterion $|g(\theta,t)|^2=\text{constant}$ for all $\theta$, and numerical results show that the resulting complementary beamforming matches the optimal single-antenna broadcasting BER at all angles while outperforming random beamforming [2205.01098].

RIS-assisted systems have pushed sub-connected beamforming into joint active-passive design. One mmWave point-to-point formulation uses dynamically configured sub-array-connected hybrid beamforming at the base station together with an RIS, twin-resolution phase shifters in each subarray, a SIC-based rate decomposition across subarrays, a greedy phase-shifter configuration rule, and complex-circle-manifold optimization of RIS coefficients [2201.04328]. A related line analyzes hybrid RIS structures with sub-connected active partitions, where a reflecting sub-surface shares one amplification factor across a partition of elements. In that setting, passive RIS yields asymptotic SNR scaling of $\mathcal{O}(N^2)$, while active, SC-active, and hybrid active/passive variants yield $\mathcal{O}(N)$ scaling, thereby exposing an explicit trade-off among capacity, energy efficiency, and the number of active components [2402.11547].

Near-field and wideband regimes have introduced new reasons to prefer sub-connected architectures. In RSMA-enabled near-field communications, sub-connected hybrid analog-digital beamfocusing is used to reduce hardware overhead while coping with imperfect CSI and imperfect SIC. The reported simulations underscore three conclusions: beamfocusing alone is insufficient to fully suppress interference even under perfect CSI, RSMA provides superior interference management over SDMA under imperfect CSI and SIC, and the sub-connected architecture delivers near-optimal digital beamfocusing performance with fewer RF chains [2507.11854]. For wideband sub-THz communication, tiled hybrid beamforming partitions the array into tiles with one RF chain per tile; broadbeam RF weights with quadratic phase,
$$
\phi[n]=\Omega_c n+\frac{\Delta\Omega}{2N}n^2,
$$
are proposed to mitigate beam squint, and realistic tile sizes of $N_a=16$ to $32$ are motivated by RF trace loss considerations [2512.06532].

The architecture has also been coupled to emerging hardware concepts. Movable-antenna-aided hybrid beamforming assigns one movable sub-array to each RF chain and jointly optimizes digital beamformer, analog beamformer, and subarray positions inside finite local regions; with sufficiently large movable regions, the sub-connected movable-array scheme outperforms its fully-connected fixed-position counterpart [2404.00953]. Distortion-aware ISAC and dynamic-subarray Transformer-based beamforming extend the same principle to nonlinear transmitters and energy-constrained airborne platforms, respectively, indicating that sub-connected beamforming is now embedded in broader joint optimization stacks rather than treated as a stand-alone precoder constraint [2507.14018][2602.07509].

## 6. Trade-offs, misconceptions, and research directions

A persistent misconception is that sub-connected hybrid beamforming is simply a low-performance approximation to FC hybrid beamforming. The literature is more specific. In GSAC, the achievable-rate and power-consumption orderings are
$$
R_{\rm SAC}\leq R_{\rm GSAC}\leq R_{\rm FC},\qquad
P_{\rm SAC}\leq P_{\rm GSAC}\leq P_{\rm FC},
$$
and simulations show that an optimized GSAC configuration can achieve a rate very close to the FC architecture while improving energy efficiency over both FC and SAC [1806.09246]. In mmWave MU-MIMO, OSPS and FC have similar sum spectral efficiency, with OSPS better in hardware complexity and power efficiency, at the cost of a slightly longer initial beam-acquisition phase [1810.13161]. These results do not imply equivalence of the architectures; they show that the rate loss can be modest when the analog network, training, and digital stage are co-designed.

A second misconception is that equal-sized subarrays are intrinsic to sub-connected design. UESA explicitly rejects that premise by optimizing unequal antenna counts per sub-array and reports up to 10.5% rate gain over equal subarrays at a marginal increase in power consumption [1908.10056]. Dynamic-subarray methods similarly reject static mapping, and sparse-PS-sharing architectures reject the assumption that each antenna must retain its own dedicated phase shifter. In the latter case, reported PS-count reductions are 37.5% for single-RF-chain systems and 62.5% for multi-RF-chain systems, while avoiding the deep-null and grating-lobe degradations associated with deterministic connection schemes [2607.02393].

A third misconception is that sharper analog beams can eliminate the need for interference management or accurate CSI. Near-field RSMA results state the opposite: beamfocusing alone is insufficient to fully suppress interference even under perfect CSI, and RSMA remains superior to SDMA under imperfect CSI and SIC [2507.11854]. Likewise, the channel-estimation literature for partially connected structures emphasizes that block-diagonal observation models, single-shot pilot constraints, and vertical compression require specialized beam design and Bayesian inference rather than straightforward transplantation of FC methods [2506.01043].

Current research directions therefore cluster around three themes. The first is topology optimization: arbitrary GSAC partitions, unequal subarrays, dynamic antenna-to-RF assignment, and static sparse sharing all treat the analog interconnect as a design variable rather than a fixed constraint [1806.09246][1908.10056][2607.02393]. The second is hardware-awareness: nonlinear power amplifiers, beam squint, twin-resolution phase shifters, switch power, and RF trace loss are now included directly in the objective functions and power models [2507.14018][2201.04328][2512.06532]. The third is inference efficiency: limited feedback, blind codebook training, group-wise narrow-beam estimation, and sub-6G-aided beam prediction all seek to recover much of FC performance without FC acquisition overhead [1806.09246][1905.03918][2403.10873]. A plausible implication is that the modern meaning of sub-connected hybrid beamforming is no longer merely “fewer phase shifters,” but a broader hardware-software co-design framework in which analog connectivity, estimation strategy, and digital processing are optimized jointly.

Source: https://www.emergentmind.com/topics/sub-connected-hybrid-beamforming