Bi-Angular Multipath Enhancement

• Bi-angular multipath enhancement is a strategy that exploits both angle-of-arrival and angle-of-departure data to improve sensing, localization, and imaging.
• The approach employs joint AoA–AoD estimation, adaptive beamforming, and optimized array design to utilize multipath signals instead of treating them as interference.
• Empirical results demonstrate reduced angular RMSE and enhanced detection probabilities, benefiting applications in mmWave indoor localization and MIMO radar.

Bi-angular multipath enhancement refers to signal processing, algorithmic, and hardware strategies that jointly exploit both angle-of-arrival (AoA) and angle-of-departure (AoD) diversity to enhance sensing, localization, and imaging performance in multipath-rich environments. Rather than treating multipath as an interfering phenomenon, these methods leverage secondary paths to improve angular resolution, robustness to non-line-of-sight (NLoS) conditions, and the extraction of geometric information from radio frequency, radar, or communication systems. Bi-angular multipath enhancement underpins advances in mmWave indoor localization, MIMO radar, and automotive and urban sensing with architectures ranging from hybrid beamforming to sparse and frequency-diverse arrays (Valecha et al., 14 Mar 2024, Li et al., 16 Jan 2024, Chen et al., 18 Nov 2025, Jia et al., 25 Jul 2024).

1. System Models for Bi-Angular Multipath Scenarios

Bi-angular multipath enhancement models assume that each multipath component (MPC) is parameterized by a tuple $(\theta_\ell, \phi_\ell, \tau_\ell, \alpha_\ell)$, representing the AoA, AoD, delay, and complex amplitude, respectively. For single-input multi-output (SIMO), MIMO, or frequency diverse array (FDA)-MIMO systems, the received signal at a given snapshot is

$$y_{i,t,r}[k] = \sum_{\ell=1}^L \alpha_\ell\, b_t(\phi_\ell)\, b_r(\theta_\ell)\, x[k-\tau_\ell] + \eta[k],$$

where $b_t$ and $b_r$ capture the normalized beampattern gains of the transmit and receive codebook beams, $x[\cdot]$ is a known probing sequence, and $\eta[k]$ is AWGN. For MIMO radar, the channel model incorporates both direct and indirect (multipath) returns; critically, MPCs may exhibit non-equal transmit and receive angles, breaking the direct-path $\theta=\phi$ symmetry inherent in classical virtual array models (Valecha et al., 14 Mar 2024, Li et al., 16 Jan 2024, Chen et al., 18 Nov 2025).

Joint AoA–AoD representation (a bi-angular image) forms the basis for setting up estimation, detection, and beamforming algorithms, using either received signal strength (RSS), matched-filtered waveforms, or array covariance matrices.

2. Algorithmic Frameworks for Joint AoA–AoD Estimation

Bi-angular multipath methods perform joint estimation of $(\theta, \phi)$ by directly searching the two-dimensional angular manifold. In the RSS-based beamforming approach, codebook beam sweep data $P_{Rx}(t,r)$ across all transmit and receive beam indices are recorded. The dominant $(\hat\theta, \hat\phi)$ is extracted by maximizing the two-dimensional fit

$$f(\theta,\phi) = \frac{| \sum_{t,r} P_{Rx}(t,r) b_t(\phi) b_r(\theta) |^2}{\sum_{t,r}|b_t(\phi) b_r(\theta)|^2},$$

via grid search or continuous optimization (Valecha et al., 14 Mar 2024). In compressive or Bayesian radar, sparse representations over a two-dimensional grid $(\theta_t, \theta_r)$ are constructed. Structured priors, such as the cross-sparsity Ising prior, are leveraged for multi-target multipath environments, where first-order reflections induce off-diagonal elements in the $\mathbf{x}$ vector: direct paths at $(i,i)$, first-order multipaths at $(i,j),\,i\neq j$ (Chen et al., 18 Nov 2025).

Structured Fast Turbo Variational Bayesian Inference (SF-TVBI) enables efficient inference over this high-dimensional, loopy graphical model by integrating two-timescale EM, message passing, and gradient methods restricted to active grid supports.

3. Array Design and Beampattern Optimization for Bi-Angular Enhancement

Sparse linear array (SLA) designs address bi-angular enhancement by explicitly optimizing transmit and receive array element positions to minimize the two-dimensional peak sidelobe level (PSL) and ensure distinctiveness of virtual array positions. The optimization problem includes angular resolution constraints

$$\delta_{\rm t}\le \delta_1,\quad \delta_{\rm r} \le \delta_2,$$

and a distinct-virtual-positions constraint

$L > \sigma MN,$

where $L$ is the number of unique virtual array positions, $M$ and $N$ are array sizes, and $\sigma$ controls the allowed multiplicity (Li et al., 16 Jan 2024).

A cyclic coordinate descent algorithm alternates optimization of transmit and receive element positions. Empirically, optimized SLAs reduce PSL (e.g., $-6.84$ dB vs $-5.8$ dB), yield narrower main lobes in both DOD and DOA, and increase the directivity factor compared to classical Minimum Redundancy (MRA) and Nested Arrays (NA).

4. Multipath Identification, Enhancement, and Suppression Mechanisms

These systems enhance or discriminate multipath components by extracting multi-peak bi-angular fingerprints. Secondary peaks in the bi-angular response map $f(\theta, \phi)$ correspond to NLoS MPCs, and can be algorithmically separated using thresholding or clustering. In RSS-driven or covariance-based methods, the distribution of $(\theta, \phi)$ pairs representing direct and indirect paths provides a rich geometric signature (Valecha et al., 14 Mar 2024, Jia et al., 25 Jul 2024).

FDA-MIMO radars use carrier increments across transmit elements to break range-angle ambiguities. After range compensation, only direct-path returns align along the $\theta_t=\theta_r$ diagonal in the joint spectrum, while multipath returns are off-diagonal. Algorithmic steps include joint optimization of transmit/receive weights and frequency increment $\Delta f$ to suppress multipath by minimizing output power or maximizing SINR under angular constraints (Jia et al., 25 Jul 2024).

5. Performance Metrics, Experimental Platforms, and Quantitative Results

Key metrics include angular RMSE for AoA/AoD, peak sidelobe level (PSL), directivity factor (DF), maximum error CDF, and detection probability. In RSS-LS2D estimation with mm-FLEX at 60 GHz, compound CDFs show that $<10^\circ$ error is achieved in over $90\%$ of cases for both AoA and AoD; RMSE is $2{-}3\times$ lower for LS2D versus single-angle search. Importantly, robust performance persists under LoS blockage due to NLoS MPC exploitation (Valecha et al., 14 Mar 2024).

Cross-sparsity-enabled Bayesian approaches yield $1{-}2$ dB RMSE reduction over non-cross-structured VBI at low SNR, with detection probability increases from $0.7$ to $0.9$ at $\mathrm{SNR}=-5$ dB (Chen et al., 18 Nov 2025). FDA-MIMO radar with compensation reduces first-order multipath peak power by $\sim 10$ dB and maintains correct target identification along the $\theta_t=\theta_r$ diagonal, as demonstrated by spatial spectrum and CA-CFAR statistics (Jia et al., 25 Jul 2024).

System / Array Type	Angular RMSE	PSL (dB)	Detection Probability	Comments
RSS-LS2D (mm-FLEX)	~4°	–	>0.9	Robust in NLoS
SLA$^\star$ (optimized SLA)	–	–6.84	–	Mainlobe at ($\theta_t, \theta_r$)
SF-TVBI (cross-sparsity)	Lowest	–	0.9 at –5 dB SNR	>10% RMSE gain at high NLoS
FDA-MIMO	–	–	–	Multipath peaks –10 to –15 dB

6. Application Domains and System-Level Implications

Bi-angular multipath enhancement is applicable to mmWave indoor localization for 5G NR positioning, automotive radar in urban environments, and smart-city infrastructure monitoring. The ability to separate and localize multiple angular components using RSS-only or hybrid-beamforming architectures facilitates sub-meter positioning without the need for tight TX–RX synchronization or fully digital arrays (Valecha et al., 14 Mar 2024).

In MIMO radar, sparse array and FDA-MIMO configurations provide improved detection in multipath-rich and spectrally complex scenarios, enabling the identification, suppression, or even constructive use of ghost and NLoS returns (Li et al., 16 Jan 2024, Jia et al., 25 Jul 2024). A plausible implication is the transition from multipath suppression to explicit multipath recognition and exploitation in radar receiver chains.

7. Theoretical Insights and Future Directions

Theoretical results bound the loss in directivity factor as a function of virtual position distinctness; empirical evidence shows conservative theoretical loss bounds are rarely approached with optimization (Li et al., 16 Jan 2024). The structured Bayesian cross-sparsity framework demonstrates that the coupling of diagonal (direct-path) and off-diagonal (first-order path) coefficients can bootstrap weak direct-path detection using multipath information, indicating possible generalizations to higher-order multipath exploitation and non-uniform array topologies (Chen et al., 18 Nov 2025).

A plausible direction is the integration of learning-based or data-driven approaches on top of bi-angular physical models to further optimize multipath exploitation. The compatibility with hybrid analog–digital beamforming, low-cost hardware, and real-time processing on platforms such as mm-FLEX points toward scalable deployment for next-generation wireless and sensing applications (Valecha et al., 14 Mar 2024).

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References:

(Valecha et al., 14 Mar 2024) "Angle estimation using mmWave RSS measurements with enhanced multipath information" (Li et al., 16 Jan 2024) "Sparse array design for MIMO radar in multipath scenarios" (Chen et al., 18 Nov 2025) "Cross-Sparsity-Enabled Multipath Perception via Structured Bayesian Inference for Multi-Target Estimation" (Jia et al., 25 Jul 2024) "Multipath Identification and Mitigation with FDA-MIMO Radar"