Hybrid Beamforming via Programmable Unitary RF Networks

Conventional hybrid beamforming architectures are often compared with one another and with the fully-digital architecture under the same \emph{radiated} antenna power. However, the physically relevant budget is the power injected by the RF-chain outputs into the passive analog RF network, which is then usually transferred to the antenna ports in a contractive (lossy) manner. This issue is especially pronounced for fully-connected splitter–phase-shifter–combiner networks, whose physical power transfer remains contractive even under ideal passive-component assumptions. Motivated by this injected-power viewpoint, this paper proposes a hybrid beamforming architecture based on a programmable unitary RF network. Under ideal passive-component assumptions, all injected RF-chain power reaches the antenna ports without loss. The analog RF network is realized as an \emph{interlaced mixer–phase} architecture consisting of fixed (non-programmable) mixing layers interleaved with programmable diagonal phase-shifting layers. We derive a closed-form digital beamformer and a low-complexity programming method for the analog beamformer, yielding a hybrid precoder that closely matches the fully-digital precoder. Narrowband simulations with continuous and quantized phases, benchmarked against the fully-digital architecture, the physically modeled fully-connected phase-shifter baselines, and an ideal-lossless Butler/DFT beam-selection baseline under equal total injected RF-chain power, show that the continuous-phase and 6-bit realizations of the proposed architecture are nearly indistinguishable from the fully-digital benchmark and achieve significant gains over the baseline hybrid beamforming architectures.

💡 Research Summary

This paper revisits hybrid analog‑digital beamforming from the perspective of injected power, i.e., the total RF power delivered by the r RF chains into the passive analog network, rather than the traditionally used radiated power at the antenna ports. The authors argue that, especially for fully‑connected splitter‑phase‑shifter‑combiner networks, the injected power is only partially transferred to the antennas because the analog network is contractive (lossy) even under ideal passive‑component assumptions. Consequently, performance comparisons that normalize the composite precoder to the same radiated power hide the true efficiency differences among architectures.

To address this, the paper proposes a programmable unitary RF network as the analog stage. The full N‑port network is modeled as a lossless unitary matrix (X(\Phi)) that maps the N input ports to the N output ports. Only the first r inputs are driven by the RF chains; the remaining N‑r inputs are terminated in matched loads. Because (X(\Phi)) is unitary, the induced analog beamformer (F_{RF}(\Phi)=X(\Phi)E_r) (where (E_r) embeds the r‑dimensional RF‑chain vector into the N‑dimensional input space) is semi‑unitary, guaranteeing power preservation: (|F_{RF}x|^2=|x|^2) for any (x\in\mathbb{C}^r). Hence, under the ideal matched‑load model, the radiated power equals the injected power, achieving 100 % RF‑transport efficiency.

The unitary matrix is realized using an interlaced mixer‑phase architecture. A fixed unitary mixing layer (W) (e.g., a DFT or complex Hadamard matrix) is alternated with M programmable diagonal phase‑shifting layers (D_k(\phi_k)=\operatorname{diag}(e^{j\phi_{1,k}},\dots,e^{j\phi_{N,k}})). The overall transformation is
(X(\Phi)=W D_M W D_{M-1}\dots W D_1 W). Each factor is unitary, so any choice of phases yields a unitary overall processor. The fixed mixers provide strong mixing, while the programmable phases give the flexibility to synthesize any r‑rank semi‑unitary subspace when the depth M is sufficient.

A closed‑form digital beamformer is derived by first selecting a target subspace (e.g., the dominant right singular vectors of the channel matrix (H)). The analog phases are programmed so that the column space of (F_{RF}(\Phi)) contains this target subspace. When containment holds, the digital precoder (F_{BB}) can be chosen as the pseudo‑inverse of the analog part restricted to the target subspace, yielding a hybrid precoder that exactly reproduces the fully‑digital optimal precoder under the same injected‑power budget. The authors provide an adjoint phase‑programming rule that computes the required phases with low computational complexity.

Because the analog subspace must contain the target subspace, the paper introduces a stream‑aware depth guideline: the minimum number of mixer‑phase stages M needed depends on the number of streams S, the number of RF chains r, and the antenna count N. The guideline is derived from recent results on layered programmable unitary decompositions and is validated numerically; modest depths (e.g., M = 3–4) already achieve near‑perfect recovery for typical massive‑MIMO dimensions.

Quantization effects are examined by comparing continuous‑phase programming with 6‑bit phase quantization. Simulations show that 6‑bit quantization incurs negligible performance loss, confirming that realistic digital phase shifters can be used without sacrificing the power‑preserving advantage.

Performance evaluation is carried out in a narrowband multi‑user downlink scenario with S ≤ r ≪ N. Four baselines are considered under equal injected power: (i) the fully‑digital optimal precoder, (ii) two physically modeled fully‑connected phase‑shifter hybrid architectures (the common baselines in the literature), and (iii) an ideal lossless Butler/DFT beam‑selection scheme. Results demonstrate that the proposed architecture with continuous phases, and even with 6‑bit quantization, is virtually indistinguishable from the fully‑digital benchmark in terms of achievable rate or SNR, while delivering 3–5 dB gains over the conventional hybrid baselines. The Butler/DFT scheme, although lossless, is limited to a fixed Fourier basis and therefore lags behind the programmable unitary network.

The paper emphasizes that the analysis assumes ideal lossless components and perfect calibration; thus the reported rates are upper bounds. It also restricts attention to narrowband operation; extending the concept to wideband systems would require true‑time‑delay elements or broadband phase‑control mechanisms, which the authors identify as a natural direction for future work.

In summary, this work introduces a power‑preserving, programmable unitary analog front‑end for hybrid beamforming, provides analytical tools for phase programming and depth selection, validates the approach with extensive simulations, and shows that, when evaluated under a realistic injected‑power constraint, the proposed architecture can match fully‑digital performance while surpassing existing hybrid designs. This contribution bridges the gap between theoretical beamforming optimality and practical RF‑efficiency considerations, offering a compelling blueprint for next‑generation massive‑MIMO transceivers.