Hybrid Dynamic Subarrays (HDS)

• Hybrid Dynamic Subarrays (HDS) is an analog-digital array architecture that partitions large antenna arrays into dynamic subarrays for flexible RF chain mapping.
• The approach enables low-complexity spatial processing and fast, high-accuracy direction-of-arrival estimation using RD-MUSIC and IMRD-MUSIC algorithms.
• HDS significantly reduces hardware and computational burdens, making it ideal for scalable 6G THz ultra-massive MIMO systems while preserving performance.

A Hybrid Dynamic Subarray (HDS) is an analog-digital array architecture in which a large set of antennas is partitioned into subarrays, each dynamically and flexibly mapped to a small number of RF chains, typically via an electronically switchable network. HDS architectures are devised for large-scale MIMO systems, including THz ultra-massive MIMO, where reducing the number of high-cost RF chains is essential for power and cost efficiency. By dynamically assigning antenna subarrays, it is possible to maintain a high aperture and array resolution while minimizing front-end hardware complexity. The HDS paradigm enables algorithmic and architectural advances for low-complexity spatial processing, including fast, high-accuracy direction-of-arrival (DOA) estimation, with performance approaching the fully-digital baseline (Tian et al., 30 Jan 2025).

1. HDS Array Architecture and Signal Model

An HDS receiver employs a uniform planar array (UPA) with $N_r = N_x \times N_z$ antennas and $N_{\rm RF} \ll N_r$ RF chains. The array is partitioned into $N_{\rm RF}$ subarrays of size $N_s = N_r/N_{\rm RF}$. Each RF chain is connected to a chosen combination of these subarrays via an electronically controlled switch network. The analog combining matrix is

$$\mathbf W_A = \mathbf M_S \odot \mathbf M_P \in \mathbb{C}^{N_r \times N_{\rm RF}},$$

where $\mathbf M_S$ is a binary subarray-selection matrix and $\mathbf M_P$ a phase-shifter matrix with entries of modulus $1/\sqrt{N_r}$.

Under pilot excitation, the per-subarray signal model ensures that post-combiner phase differences between subarrays are functions of a single angular variable, i.e., either elevation or azimuth. The subarrays can thus be treated as super-elements forming an effective ULA along one axis, decoupling 2D angular estimation and simplifying subsequent processing. The system-level received signal is

$$\tilde{\mathbf Y} = \tilde{\mathbf W}^H \mathbf A_r \mathbf S + \tilde{\mathbf N},$$

where $\tilde{\mathbf W}$ stacks the equivalent analog combiners across RF chains and snapshots, $\mathbf A_r$ is the array manifold, and $\mathbf S$ contains pilot symbols.

2. Reduced-Dimension MUSIC (RD-MUSIC) and GAT Bias Correction

The HDS structure enables a reduced-dimension version of MUSIC (RD-MUSIC) for DOA estimation. The post-processing sample covariance is

$$\mathbf R_y = \frac{1}{N_a} \tilde{\mathbf Y} \tilde{\mathbf Y}^H.$$

Due to the high-dimensional and undersampled setting (small $N_{\rm RF}$, large $N_r$), estimates of eigenvalues and eigenvectors exhibit biases described by Generalized Asymptotic Theory (GAT). The bias corrections involve analytic transformations of the estimated noise floor and signal eigenvalues, crucial for avoiding systematic underestimation of DOA resolution.

The RD-MUSIC approach leverages the HDS array's geometry to perform a dimension reduction: the 2D spectral search in classical MUSIC is replaced by a pair of coupled 1D searches. Using parameterization $u = \sin\phi$, $v = \sin\theta\cos\phi$, the 2D MUSIC pseudo-spectrum becomes

$$V(u, v) = \mathbf a_x^H(v)[\mathbf a_z(u) \otimes \mathbf I_{N_x}]^H \mathbf E_n \mathbf E_n^H [\mathbf a_z(u)\otimes \mathbf I_{N_x}] \mathbf a_x(v),$$

allowing staged solution—first optimizing over $v$ for fixed $u$, then over $u$.

3. Accelerated Estimation: IMRD-MUSIC Algorithm

THz ultra-massive MIMO channels exhibit strong sparsity, which is exploited by the IMRD-MUSIC algorithm. A two-RF-chain configuration is engineered such that their subarrays overlap in a prescribed fashion. The resulting pair of subspace estimates yields generalized eigenvalues whose phases directly yield coarse elevation estimates: $$\tilde\phi_\ell = \arcsin\left(\frac{\angle\beta_\ell\, \lambda N_{\rm RF}}{2\pi d N_z}\right).$$ Subsequent refinement is accomplished via short 1D searches (in the vicinity of these estimates) and least-squares phase retrieval for azimuth estimation. This bypasses a full 2D or even 1D grid search for each path, reducing computational complexity by an order of magnitude compared to RD-MUSIC.

4. Cramér-Rao Lower Bound Analysis and HDS Fundamental Limits

The estimation-theoretic limits of HDS architectures are characterized by explicit Cramér-Rao Lower Bounds (CRLBs) for the vector of unknown DOAs. The Fisher information incorporates the pilot allocation, subarray geometry, and analog combining structure: $$\mathop{\rm CRLB}_\text{HDS} = \frac{\sigma^2}{2} \left[ \Re \left\{ \sum_{n=1}^{N_a} \tilde S^H(n) \tilde B^H \Pi_{\tilde E} \tilde B \tilde S(n) \right\}\right]^{-1}.$$ Crucially, Theorem 2 in (Tian et al., 30 Jan 2025) demonstrates that, under mild random-phase assumptions, all HDS, hybrid fully-connected (HFC), and hybrid subarray (HS) architectures with the same average switch density $\rho$ achieve essentially identical CRLBs. Performance approaches that of the fully-digital reference system as the product $N_{\rm RF} T$ increases, with precise scaling characterized by

$$\mathop{\rm CRLB}_\text{HDS} \approx \frac{N_r T_d}{N_{\rm RF} T} \mathop{\rm CRLB}_\text{FD},$$

where $T_d$ is the number of pilots in the fully-digital array.

5. Computational Complexity and Performance Benchmarks

Analytic and empirical results quantify the trade-offs between architectural complexity, computational load, and estimation performance:

• Complexity: FD-2D-MUSIC requires $$\mathcal O(N_r^2 T N_a + N_r^3 + N_r^2 n_\theta n_\phi)$$. HDS-IMRD-MUSIC reduces the bottleneck to $$\mathcal O(N_{\rm RF}^2 T^2 N_a + N_{\rm RF}^3 T^3 + (N_r^2+N_x^3)\bar n_\phi L)$$, with $\bar n_\phi\ll n_\phi$.
• Accuracy: For $N_r=1024$, $N_{\rm RF}=8$, $T=12$, $L=3$ paths, RMSE for IMRD-MUSIC is $0.03^\circ$ at SNR = 10 dB, matching FD-2D-MUSIC.
• Saturation effects: Doubling either $N_{\rm RF}$ or $T$ beyond modest values yields diminishing returns in RMSE beyond SNR ≈ 0 dB.
• Aperture scaling: Increasing antenna count (e.g., 1024 to 1280) at fixed $N_{\rm RF}$ further reduces error, but phase ambiguities may arise unless either $N_{\rm RF}$ or $T$ is also increased.

A summary table:

Algorithm/Class	Complexity Order	Typical RMSE ($10$ dB SNR, $N_r=1024$)
FD-2D-MUSIC	$$\mathcal O(N_r^2 T N_a + N_r^3 + N_r^2 n_\theta n_\phi)$$	$0.03^\circ$
HDS-2D-MUSIC	$$\mathcal O(N_{\rm RF}^2 T^2 N_a + N_{\rm RF}^3 T^3 + \ldots)$$	$0.03^\circ$
HDS-RD-MUSIC	$\mathcal O(\ldots)$	$0.03^\circ$
HDS-IMRD-MUSIC	$\mathcal O(\ldots)$ < 10× less than RD-MUSIC	$0.03^\circ$

6. Practical Implications and 6G-THz UM-MIMO Applicability

The HDS architecture, when paired with RD-MUSIC or IMRD-MUSIC, yields estimation accuracy comparable to fully-digital systems but with dramatically reduced hardware complexity and computational burden. The explicit CRLB derivations guide the subarray, RF-chain, and pilot design for optimal trade-offs. The finding that random/dynamic subarray mappings with equivalent switch density perform equivalently removes the need for precise deterministic switch patterns, facilitating hardware-friendly implementations.

For practical THz ultra-massive MIMO arrays in 6G wireless, HDS enables scalable, low-power, and real-time DOA estimation and, by extension, efficient beamforming, calibration, and spatial interference management (Tian et al., 30 Jan 2025).