A Narrowband Fully-Analog Multi-Antenna Transmitter

TL;DR

The paper tackles the challenge of synthesizing arbitrary per-antenna complex excitations in a narrowband multi-antenna transmitter using a single RF tone. It introduces a split-then-phase, unitary, fully-analog architecture that yields a closed-form, $O(N)$ programming rule to realize any unit-norm direction $\mathbf{c}$ by mapping $\mathbf{e}_1$ through a magnitude-tree $\mathbf{V}_{\mathrm{mag}}(\boldsymbol{\alpha})$ and a per-antenna phase bank $\mathbf{P}(\boldsymbol{\vartheta})$, achieving exact synthesis in the ideal lossless model. The contributions include a parameter-minimal 2N-1 degrees-of-freedom design, an explicit exact-state-preparation algorithm, an idealized hardware mapping, and a non-ideal normalization framework with RF-front-end power comparisons that show substantial DC-power savings versus a fully-digital baseline for $N\le16$. The work provides a proof-of-concept for low-power, symbol-wise reconfigurable analog beamforming, with practical relevance to narrowband wireless systems and potential extensions to wideband or mmWave implementations through hardware validation and further architectural refinements.

Abstract

This paper proposes a narrowband fully-analog $N$-antenna transmitter that emulates the functionality of a narrowband fully-digital $N$-antenna transmitter. Specifically, in symbol interval $m$, the proposed fully-analog transmitter synthesizes an arbitrary complex excitation vector $\bm x[m]\in\mathbb{C}^N$ with prescribed total power $\|\bm x[m]\|_2^2=P$ from a single coherent RF tone, using only tunable phase-control elements embedded in a passive interferometric programmable network. The programmable network is excited through one input port while the remaining $N - 1$ input ports are impedance matched. In the ideal lossless case, the network transfer is unitary and therefore redistributes RF power among antenna ports without dissipative amplitude control. The synthesis task is posed as a unitary state-preparation problem: program a unitary family so that $\bm V(\bm\varphi)\bm e_1=\bm c$, where $\bm c=\bm x/\sqrt{P}$ and $\|\bm c\|_2=1$. We provide a constructive realization and a closed-form programming rule: a binary magnitude-splitting tree allocates the desired per-antenna magnitudes $|c_n|$ using $N -1$ tunable split ratios, and a per-antenna output phase bank assigns the target phases using $N$ tunable phase shifts. The resulting architecture uses $2N-1$ real tunable degrees of freedom and admits a deterministic $O(N)$ programming procedure with no iterative optimization, enabling symbol-by-symbol updates when the chosen phase-control technology supports the required tuning speed. Using representative COTS components, we model the RF-front-end DC power of the proposed fully-analog transmitter and compare it against an equivalent COTS fully-digital array. For $N\le 16$, the comparison indicates significant RF-front-end power savings for the fully-analog architecture. The results in this paper are intended as a proof-of-concept for a narrowband fully-analog transmitter.

Figures (3)

• Figure 1: Fanout-mode interferometric splitter implementing $\bm U(\alpha)=\bm U_{\mathrm{MZI}}(2\alpha)$ with one input matched and unexcited (incident wave $0$). Two fixed $3$ dB couplers form an MZI whose differential control $\delta=2\alpha$ sets the power split. The fixed $\pm 90^\circ$ branch convention of the MZI (\ref{['eq:mzi_matrix']}) is compensated by the per-antenna output phase bank $\bm P(\bm\vartheta)$.
• Figure 2: Balanced binary-tree programmable distributor (conceptual block diagram, $N=2^L$). Each internal node is a tunable $2\times2$ interferometric splitter Cell$_{\ell,i}$ controlled only by $\delta_{\ell,i}=2\alpha_{\ell,i}$ (sets the split). The idle input of every cell is terminated in $Z_0$ to enforce the zero-incident-wave condition implied by Lemma \ref{['lem:zero_input_property']}. After $L$ layers, the $N$ leaf outputs pass through a per-antenna output phase bank $e^{j\vartheta_n}$ implementing $\bm P(\bm\vartheta)$, producing the desired antenna excitations $x_1,\dots,x_N$.
• Figure 3: Total RF-front-end DC power versus number of antennas $N$ at sub-6 GHz (fixed per-antenna conducted power $p_{\mathrm{ant}}=0.2$ W, so $P_{\mathrm{ant,tot}}=Np_{\mathrm{ant}}$). Curves compare the compute-excluded fully-digital RF-front-end model against the fully-analog transmitter parameterized by the stress-case $L_{\mathrm{net}}(N)$ entries in Table \ref{['tab:joint_rate_power_summary']}.

Theorems & Definitions (15)

• Remark 1
• Remark 2
• Definition 1: $2\times 2$ splitter cell
• Lemma 1: Lossless splitting on an input $(a,0)$ with a known branch phase offset
• Lemma 2: Zero-input property at each level
• Definition 2: Right-branch count $w_n$
• Lemma 3: Phase-offset decomposition of the magnitude-tree output
• Theorem 1: Exact split-then-phase state preparation
• Corollary 1
• Remark 3: Degrees of freedom