Hybrid Digital–MiLAC Architecture

• Hybrid Digital–MiLAC architecture is a design paradigm that partitions signal processing between a low-complexity digital front end and a reconfigurable analog microwave network for real-time linear computations.
• It shifts intensive operations like matrix inversion and beamforming from the digital baseband to the analog MiLAC core, drastically reducing power consumption and hardware complexity.
• This architecture achieves near-digital performance in ultra-massive MIMO systems, making it ideal for scalable 6G and gig-antenna applications while lowering RF chain requirements.

A hybrid digital–MiLAC (microwave linear analog computer) architecture is a transmitter or receiver design paradigm that partitions signal processing tasks between a low-complexity digital front end and a highly reconfigurable analog microwave network. The MiLAC core executes linear algebraic computations such as matrix-vector multiplication, beamforming, and matrix inversion instantaneously in the analog domain, enabling hardware- and computation-efficient realization of ultra-massive (gigantic) MIMO systems with antenna counts in the thousands. By minimizing the number of radio-frequency (RF) chains and shifting the most numerically intensive operations out of digital baseband, this architecture achieves performance nearly identical to fully digital systems using drastically reduced power, hardware, and computational resources (Nerini et al., 10 Apr 2025, Nerini et al., 9 Apr 2025, Nerini et al., 6 Jun 2025, Wu et al., 15 Jan 2026).

1. System Organization and Block Structure

A hybrid digital–MiLAC system comprises both digital and analog stages, with a concrete partitioning of responsibilities:

• Digital Front End:
  • Generates and preprocesses K data streams $s\in\mathbb{C}^{K}$ (at the transmitter, K = number of users; at the receiver, K = number of data streams).
  • Computes normalization coefficients, simple per-block baseband precoders $V$, and downloads matrix parameters required to configure the MiLAC.
  • Interfaces to the analog domain via $K$ DACs (or ADCs), each carrying a single data stream and typically operating at low bit resolution (e.g., 2–4 bits) due to the reduced requirements of per-stream processing.
• MiLAC Analog Core:
  • Realizes a reconfigurable $(K+N_t)$-port (or $(K+N_r)$-port at the receiver) passive microwave network.
  • Executes the main linear transformations (e.g., zero-forcing, discrete Fourier transform, LMMSE) via physical wave scattering determined by a tunable admittance matrix $Y$.
  • Outputs the beamformed or processed waveforms directly at antenna ports or to downstream ADCs.

The digital and analog stages are tightly coupled via periodic digital-to-analog parameter updates based on channel state information or other higher-layer control, but operate independently on a symbol-by-symbol basis with zero per-symbol digital overhead (Nerini et al., 10 Apr 2025, Nerini et al., 9 Apr 2025).

2. Mathematical and Physical Model

The MiLAC module acts as a programmable linear operator. For an input voltage $u$ at $K$ ports and a $(K+M)$-port microwave network with admittance matrix $Y$, the network realizes a digital-to-analog mapping based on the P-matrix formalism:

$$v = P^{-1}\tilde{u}, \quad P = Y/Y_0 + I_{P}, \quad \tilde{u} = [u; 0_M]$$

Partitioning $P$ appropriately yields an output $v_2$ which matches the desired linear transformation (e.g., for MMSE or ZF precoding):

$$v_2 = (P_{22})^{-1}P_{21}(P_{12}P_{22}^{-1}P_{21}-P_{11})^{-1} u$$

For MIMO beamforming, the relevant block choices of $P$ permit the implementation of precoders and matrices such as $H^H(HH^H + \lambda I)^{-1}$ for R-ZF, or more generally arbitrary full-rank transformations $A$ (Nerini et al., 10 Apr 2025, Nerini et al., 9 Apr 2025).

3. Beamforming Flexibility and Hybrid Decomposition

The hybrid digital–MiLAC architecture achieves the full beamforming flexibility of digital architectures when the number of RF chains equals the number of data streams ($N_{RF} = K$), but with half the RF chains required by conventional hybrid digital–analog phase-shifter architectures. Explicitly, any matrix $W \in \mathbb{C}^{N_t \times K}$ with $\|W\|_F^2 \leq P_T$ can be decomposed as $W = F V$ where $F$ is the analog MiLAC matrix ($\|F\|_2 \leq 1$) and $V$ implements digital power/stream allocation. This property is enforced via a linear matrix inequality or via explicit SVD-based decomposition. The MiLAC constraints arise from its realization as a lossless, reciprocal passive microwave network whose submatrix $F$ is required to have $\|F\|_2 \leq 1$ (Wu et al., 15 Jan 2026).

In the MU-MISO downlink, the architecture enables per-user weights $w_k = F v_k$ and transforms the sum-rate maximization into a joint optimization over digital and analog components, subject to the physical constraints induced by the passive microwave network (Wu et al., 15 Jan 2026).

4. Optimization and Algorithmic Techniques

The classical weighted minimum mean squared error (WMMSE) algorithm is adapted for the hybrid digital–MiLAC architecture. The nonconvex joint optimization over the analog matrix $F$ and the digital matrix $V$ is formulated as:

$$\max_{F, V} \quad \sum_{k=1}^K \log_2(1 + \text{SINR}_k), \quad \|F\|_2 \leq 1, \quad \text{tr}(V V^H) \leq P_T$$

where $$\text{SINR}_k = |h_k^H (F v_k)|^2 / (\sum_{j\ne k} |h_k^H (F v_j)|^2 + \sigma^2)$$.

• Alternating minimization techniques update receiver weights and equalizers in closed form, digital precoder $V$ via water-filling–type solutions, and analog matrix $F$ via projected-gradient methods.
• The MiLAC constraint is enforced either through spectral norm projection or a convex linear matrix inequality.
• Reduction to a low-dimensional subspace (via rowspace of $H^H$) enables efficient optimization for large $N_t$.

The per-iteration complexity is $O(\max(N_t K^2, K^3))$, and offline design cost is drastically lower than the $O(N_t^3)$ per-symbol complexity of full digital architectures (Wu et al., 15 Jan 2026).

5. Hardware Complexity and Implementation Considerations

Hybrid digital–MiLAC systems minimize component counts and operational energy by:

• Reducing RF chains to the number of data streams ($K$), which is the minimum required for any full multiplexing.
• Employing low-resolution DACs/ADCs since each chain carries a single symbol stream, not a weighted sum.
• Using a $(N_t + K)$-port MiLAC with $(N_t + K)^2$ tunable (purely reactive) admittance elements, programmed only once per coherence block rather than per symbol.
• Replacing expensive, power-hungry matrix-multiplies and inversions in baseband with one-time analog parameter updates and physical wave scattering.

For giga-antenna MIMO, MiLAC-aided implementations drop computational requirements by several orders of magnitude compared to digital, e.g., block cost of $6N_t K$ real operations vs. $8(N_t K^2 + K^3/3)$ digital (Nerini et al., 10 Apr 2025). Bandwidth and dynamic range constraints are met by careful design of matching networks, periodic calibration, and selection of high-Q tunable elements to maintain lossless operation (Nerini et al., 9 Apr 2025, Wu et al., 15 Jan 2026).

6. Capacity, Performance, and Scalability

MiLAC-aided beamforming achieves identical sum-rate and mutual information as full digital beamforming under practical lossless and reciprocal constraints, with the following qualitative and quantitative outcomes:

• Capacity Achievement: Under optimal analog precoder and combiner design, MiLAC-aided systems null inter-stream interference and match the information-theoretic capacity of fully digital MIMO (Nerini et al., 6 Jun 2025).
• Flexibility: The hybrid digital–MiLAC achieves digital flexibility with $K$ RF chains, surpassing conventional analog/phase-shifter based hybrid schemes (Wu et al., 15 Jan 2026).
• Numerical Results: Large-scale simulations show 98–100% of digital sum-rate for $N_t=64$ and $K=4$; as $N_t$ increases, any gap due to MiLAC’s semi-unitary constraint vanishes ($<2\%$ for $N_t=512$).
• Complexity Scaling: The cubic dependence of matrix inversion cost per block in conventional architectures is replaced by $O(N_t K)$ parameter setup and $O(1)$ per-symbol complexity in MiLAC-aided systems.

A summary of resource scaling is as follows:

Architecture	RF Chains	DAC Resolution	Per-Symbol Digital Cost	MiLAC Core Complexity
Fully Digital	$N_t$	High	$O(N_t K)$	N/A
Phase-Shifter Hybrid	$K$	High	$O(K^2)$	$N_t K$ phase shifters
Hybrid Digital–MiLAC	$K$	Low	0	$(N_t+K)^2$ admittances

Table: Comparison of architectures for MIMO beamforming in terms of hardware complexity and digital computation, constructed from (Wu et al., 15 Jan 2026, Nerini et al., 10 Apr 2025).

7. Applications and Future Directions

Hybrid digital–MiLAC architectures are particularly suited for settings requiring extremely large antenna arrays—so-called “gigantic” MIMO, as envisioned in 6G wireless and beyond. Key application domains include:

• Downlink MU‐MISO with thousands of antennas and fully loaded user populations (Wu et al., 15 Jan 2026, Nerini et al., 10 Apr 2025).
• Instantaneous matrix inversion and linear filtering for high-speed control (e.g., Kalman filters) in analog-centric, high-bandwidth systems (Nerini et al., 9 Apr 2025).
• Discrete transforms (DFT), matched filtering, and direct implementation of LMMSE estimators in the analog domain.

A plausible implication is that further research may explore:

• Hierarchical or block-diagonal MiLAC compositions to support networks with $10^3$–$10^4$ ports without linear scaling in tuning resources (Nerini et al., 9 Apr 2025).
• Adaptive, self-calibrating MiLAC cores robust to hardware impairments.
• Cross-layer design integrating MiLAC programming with upper layer (e.g., MAC) optimization in dynamic spectrum environments.

• (Nerini et al., 9 Apr 2025) G. Colavolpe et al., "Analog Computing for Signal Processing and Communications -- Part I: Computing with Microwave Networks."
• (Nerini et al., 10 Apr 2025) G. Colavolpe et al., "Analog Computing for Signal Processing and Communications -- Part II: Toward Gigantic MIMO Beamforming."
• (Nerini et al., 6 Jun 2025) Z. Wu et al., "Capacity of MIMO Systems Aided by Microwave Linear Analog Computers (MiLACs)."
• (Wu et al., 15 Jan 2026) S. Yang et al., "Microwave Linear Analog Computer (MiLAC)-aided Multiuser MISO: Fundamental Limits and Beamforming Design."