Hybrid Beamforming via Programmable Unitary RF Networks

Abstract

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.

Figures (3)

• Figure 1: System diagram of the proposed hybrid transmitter with an interlaced programmable unitary RF network. The analog stage is the first $r$ columns of an $N\times N$ programmable unitary processor.
• Figure 2: Narrowband average sum-rate versus depth $M$ at injected power $P_T=0$ dBm for $N=512$ and $S=r=16$. The proposed architecture is shown for continuous phases and for $2$-, $4$-, and $6$-bit phase quantization followed by greedy local discrete refinement; the FC1 and FC2 baselines are shown with continuous phases only, and the Butler/DFT baseline uses adaptive beam selection within a fixed Fourier basis. The proposed continuous-phase and $6$-bit curves saturate near $M\approx 2S=32$.
• Figure 3: Narrowband average sum-rate versus injected power $P_T$ (in dBm) for $M=32$, $N=512$, and $S=r=16$. The proposed architecture is shown for continuous phases and for $2$-, $4$-, and $6$-bit phase quantization followed by greedy local discrete refinement; the FC1 and FC2 baselines are shown with continuous phases only, and the Butler/DFT baseline uses adaptive beam selection within a fixed Fourier basis. In this $S=16$ setting, the continuous-phase and $6$-bit realizations of the proposed architecture are nearly indistinguishable from the fully-digital benchmark across the entire injected-power range.

Theorems & Definitions (10)

• Remark 1: Interpretation of injected power and PA placement
• Remark 2: Notation convention
• Proposition 1: Power preservation of the proposed analog stage
• Remark 3: Connection to lossless multiport networks
• Corollary 1: Exact recovery under subspace containment
• Corollary 2: MMSE equivalence under channel-subspace containment
• Remark 4: Quantization preserves RF efficiency
• Proposition 2: Stream-aware DoF guideline (dimension-counting, necessary)
• Remark 5: Interpretation and limitations
• Remark 6: RF-chain count and comparison axes