Splitting Precoding Architecture in Massive MIMO

• Splitting Precoding Architecture is a multi-stage MIMO technique that decomposes transmit-side processing into an AAS subspace selection and a BBU digital refinement stage.
• It employs efficient algorithms (GS-MRT, MRT, DFT-beam selection) to select the optimal channel subspace and reduce computational and quantization overhead.
• The design minimizes fronthaul and power constraints while improving spectral efficiency, making it ideal for next-generation massive MIMO deployments.

A splitting precoding architecture is a class of multi-stage precoding schemes in multi-antenna wireless systems, in which the overall transmit-side spatial processing is structurally decomposed across two or more physically or logically distinct nodes, each handling a different aspect of the signal manipulation. The unifying principle is to divide the precoding function into (typically) a subspace selection or dimension-reduction stage and a finetuning digital (often quantized) refinement stage, in order to address bottlenecks such as fronthaul capacity, digital quantization, power or hardware limitations, or computational complexity. With careful design, splitting precoding architectures can substantially outperform conventional monolithic (one-stage, fully-digital) precoders under these practical constraints, particularly in massive MIMO systems where fronthaul and quantization are limiting factors (Khorsandmanesh et al., 2 Jan 2026).

1. Mathematical Structure and System Model

In the canonical setting, a massive-MIMO base station consists of $M$ antennas equipped with an advanced antenna system (AAS), connected to a physically separate baseband unit (BBU). The downlink precoder is decomposed as

$\mathbf{W} = \mathbf{P}_a\,\mathbf{P}_{\text{BBU}}$

where $\mathbf{P}_a \in \mathbb{C}^{M\times N}$ is the subspace selector (implemented in the AAS) and $$\mathbf{P}_{\text{BBU}} \in \mathbb{C}^{N \times K}$$ is the quantized digital refinement (computed by the BBU and transmitted over the fronthaul) (Khorsandmanesh et al., 2 Jan 2026).

The system model operates over a block fading channel, with the received signal for $K \le M$ users as

$$\mathbf{y} = \mathbf{H}\, \mathbf{P}_a\, \mathbf{P}_{\text{BBU}} \, \mathbf{s} + \mathbf{n}$$

where $\mathbf{H}\in\mathbb{C}^{K\times M}$ is the channel matrix, $\mathbf{s}\in\mathbb{O}^K$ is the data symbol vector, and $$\mathbf{n}\sim \mathcal{CN}(0, \sigma_0^2 \mathbf{I}_K)$$ is the noise.

The fronthaul signaling overhead is governed by the bit-budget for transmitting the digital refinement precoder. Crucially, splitting architectures allow the digital precoder to be lower-dimensional and quantized with higher per-entry precision compared to one-stage approaches, directly reducing quantization noise and overhead.

2. Subspace Selection at the AAS

The first stage, implemented at the AAS, seeks a semi-unitary subspace selector $\mathbf{P}_a$ satisfying $\mathbf{P}_a^H \mathbf{P}_a = \mathbf{I}_N$, selecting the most relevant $N$-dimensional channel subspace for transmission. The objective is to maximize the projected channel power:

$$\underset{\mathbf{P}_a \in \mathbb{C}^{M \times N}}{\text{maximize}}\; \operatorname{tr}(\mathbf{P}_a^H \mathbf{H}^H \mathbf{H} \mathbf{P}_a)\qquad\text{subject to}\;\,\mathbf{P}_a^H\mathbf{P}_a = \mathbf{I}_N$$

(Khorsandmanesh et al., 2 Jan 2026).

Three practical algorithms are provided:

• GS-MRT: Gram-Schmidt orthonormalization of maximum ratio transmission (MRT) vectors per user.
• MRT: Non-orthogonal selection of normalized MRT vectors, rescaling $\mathbf{P}_{\text{BBU}}$ for power.
• DFT-Beam selection: Selects DFT matrix beams with the largest projected $\ell_2$-norm, efficient via FFT.

Complexity for the AAS stage depends on the algorithm: $O(M N^2)$ for GS-MRT, $O(MN)$ for MRT, $O(M\log M)$ for DFT-beam selection.

3. Quantized Refinement at the BBU

After $\mathbf{P}_a$ is fixed, the effective reduced channel is $$\mathbf{H}_\text{eff} = \mathbf{H} \mathbf{P}_a \in \mathbb{C}^{K\times N}$$, which is then communicated back to the BBU (perfect CSIT assumed) (Khorsandmanesh et al., 2 Jan 2026).

The digital refinement $\mathbf{P}_{\text{BBU}}$ is computed to minimize the sum-MSE under a complex-quantized constraint:

$$\min_{\mathbf{P}_{\text{BBU}}\in \mathcal{P}^{N\times K},\, \| \mathbf{P}_{\text{BBU}} \|_F^2 \leq q} \;\; \mathbb{E}[ \|\mathbf{s} - \mathbf{B} [ \mathbf{H}_\text{eff} \mathbf{P}_{\text{BBU}} \mathbf{s} + \mathbf{n} ] \|^2 ]$$

where $\mathcal{P}$ denotes a mid-rise uniform quantization alphabet with $B = \log_2 L$ bits per real dimension, and $\mathbf{B}$ is a diagonal receiver gain matrix. The mapping is optimized via (columnwise) mixed integer least-squares (SESD), reparameterized as

$$\min_{\mathbf{a} \in \mathcal{P}^N}\, \| \mathbf{e} - \mathbf{R} \mathbf{a} \|_2^2$$

with per-column sphere decoding (or similar).

Optimization over $\mathbf{P}_\text{BBU}$ is the computational bottleneck for the BBU, but the dimension $N$ is much smaller than $M$ in one-stage quantization, producing exponential savings in both signaling and complexity.

4. Fronthaul, Power, and Complexity Tradeoffs

Splitting the precoder yields powerful fronthaul savings: for a fixed bit-budget $C_\text{total}$, the two-stage approach permits larger per-entry quantization $B_\text{split}$ since only $N<K$ columns are transmitted. Precise scaling: $M/N = B_\text{split}/B_\text{one-stage}$ for equal overhead.

Complexity at the BBU reduces from $O(K L^{2\gamma M})$ (one-stage) to $O(K L^{2\gamma N})$ (splitting), where $\gamma\in[0,1]$ is a reduction exponent. At the AAS, all subspace selection algorithms are polynomial ($O(M N^2)$ or less).

Power constraints are efficiently enforced: by having $\mathbf{P}_a$ semi-unitary, the transmit power constraint reduces to $\|\mathbf{P}_\text{BBU}\|_F^2 \leq q$.

5. Spectral Efficiency and Empirical Performance

Empirical results in (Khorsandmanesh et al., 2 Jan 2026) for i.i.d. Rayleigh and mmWave channels (e.g., $M=32$, $K=8$ or $M=128$, $K=8$) demonstrate:

• GS-MRT splitting with 4-bit quantization saturates only at high SNR, outperforming one-stage 1-bit SESD by several bps/Hz in spectral efficiency.
• MRT and DFT-based splitting have lower computational load but saturate earlier due to less effective interference suppression.
• In sparse mmWave (large $M$), DFT-based splitting achieves near-optimal GS-MRT performance at high SNR.
• By increasing both $N$ (dimension) and $B_\text{split}$, the performance gap to infinite-resolution RZF is further closed.

The overall architectural tradeoff is sacrificing limited interference cancellation flexibility at the AAS for a substantial gain in fronthaul quantization, resulting in improved sum-rates under finite fronthaul constraints.

6. Practical Implementation Considerations

The core splitting precoding architecture is readily compatible with standard massive MIMO deployments featuring geographical or structural separation between the antenna array and digital baseband processing. The AAS design can be implemented in analog or mixed-signal hardware. Communication of the effective low-dimensional channel from AAS to BBU is feasible for practical coherence times and subcarrier granularity. The quantized MMSE refinement employs established quantizer design (Lloyd-Max/min-MSE), with parameter tuning performed offline. SESD-based optimization is computationally tractable for small $N$.

The approach synergizes with frequency-selective (OFDM) and frequency-flat systems, and enables low-latency updating of digital precoders as channels evolve. The separation is particularly advantageous for cell architectures with stringent fronthaul or cloud radio access network (C-RAN) limitations.

7. Broader Context and Significance

Splitting precoding is a distinct approach compared to prior fully monolithic digital or analog/hybrid architectures. While hybrid analog/digital designs target RF complexity and power constraints (particularly for mmWave/THz), the splitting architecture directly addresses baseband-to-antenna data movement: specifically, the fronthaul link, quantization loss, and baseband processing (Khorsandmanesh et al., 2 Jan 2026). Importantly, the method preserves much of the array and multiplexing gain of massive-MIMO, avoids severe quantization penalties, and adapts flexibly to various hardware or deployment scenarios.

This class of architectures is expected to be increasingly central for next-generation (beyond 5G, 6G) deployments where scalability, modularity, and energy efficiency are essential, and fronthaul constraints represent a system-level bottleneck.

---

References:

"Splitting Precoding with Subspace Selection and Quantized Refinement for Massive MIMO" (Khorsandmanesh et al., 2 Jan 2026)