arXiv subjects

Zhang Kuang

Publications and source records attributed to Zhang Kuang.

4 recordsLinked to original sources

arXiv2026

Angle Estimation via WFRFT Spatial-Domain Basis Decomposition: Breaking the Rayleigh Resolution Limit with Structured Waveform Diversity

We propose a MIMO radar angle estimation framework that uses the four-component weighted-type fractional Fourier transform (4-WFRFT) as a spatial-domain waveform diversity mechanism. Unlike conventional fractional Fourier (FrFT) MIMO radar where FrFT serves as a receiver-side time-frequency processing tool, our approach decomposes a data sequence into four WFRFT basis functions,original signal, its Fourier transform, time-reversal, and inverse Fourier transform, and transmits them simultaneously from a four-element uniform linear array. The spatial superposition of these basis functions at each far-field angle creates a unique angle-dependent waveform structure, enabling angle estimation through time-domain matched filtering with known waveforms. We demonstrate that this spatial-domain mixing achieves angular resolution surpassing the Rayleigh diffraction limit by a factor of 1.4$\times$ to 12.8$\times$, with the advantage most pronounced at low SNR where conventional beamforming fails completely. The Cram\'er-Rao bound is derived with a full 3-parameter Fisher information matrix, and the Fisher information is decomposed into geometry and waveform contributions, revealing that the WFRFT waveform structure contributes approximately 3$\times$ more information than array geometry alone. Extension to $M$-element arrays with $M$-component WFRFT demonstrates resolution gain scaling with array size. Simulations with linear chirp base sequences achieve 0\,dB PAPR and validate sub-Rayleigh resolution with a four-element array.

eess.SP↗

arXiv2026

Equation Asymmetry: An Algebraic Framework for Unifying Secrecy and Covertness in Information-Theoretic Security

This paper studies the algebraic structure underlying a broad class of information-theoretic security problems. We define the equation asymmetry degree (EAD) as $\Phi = (n - r)/n$, where $n$ is the signal embedding dimension and $r$ is the effective rank of the adversary's observation matrix. This single parameter is shown to simultaneously govern both secrecy (measured by equivocation $H(M|Y_E)$) and covertness (measured by detection error probability $P_e$). On finite fields $\mathbb{F}_q$, we establish the equivocation lower bound $H(M|Y_E) = \min(k, n - r_E) \log q$ with exact probabilistic conditions (Theorem~1), the secrecy capacity $C_s = (n - r_E) \log q$ with complete achievability and converse proofs (Theorem~2), and a strong converse (Theorem~8). In the continuous Gaussian regime, we derive a differential-entropy equivocation bound (Lemma~1), the high-SNR secrecy capacity asymptotics (Lemma~2), and a 2-Wasserstein distance covertness condition $W_2 \approx \sqrt{r_W} \cdot P / (2N\sigma) \to 0$ (Theorem~5'). The EAD-SDoF equivalence $d_s = n \cdot \Phi$ is established (Theorem~7). Both $\eta_s$ and $\eta_c$ are shown to be monotone functions of $\Phi$ (Theorem~6), with a Pearson correlation of $0.997$ in continuous-domain experiments. Seven existing security schemes -- matrix embedding, MIMO wiretap, secure network coding, FRFT multi-angle transmission, traffic steganography, group-key secure summation, and MDS secure summation -- are unified under the common form $C_s = (n - r) \log q$. Post-quantum security follows from the information-theoretic hardness of underdetermined linear systems (Theorem~9). All numerical experiments are reproducible with open-source code.

cs.IT↗

arXiv2026

WHTDM: Walsh-Hadamard Transform Division Multiplexing for Doubly-Selective Channels

We propose Walsh-Hadamard Transform Division Multiplexing (WHTDM), a multicarrier waveform that replaces the conventional IFFT/FFT pair in OFDM with a real-valued, unitary Walsh-Hadamard transform (WHT). WHTDM inherits the CP-OFDM transceiver structure while eliminating all complex multiplications from the transform stage, yielding a transmitter with zero real multipliers in the core modulation block. For detection under doubly-selective channels, we adopt a cross-domain memory approximate message passing (CD-MAMP) equalizer that operates on the banded structure of the equivalent WHT-domain channel matrix. Simulation results under the 3GPP TDL-C channel model at 28 GHz demonstrate that WHTDM with CD-MAMP significantly outperforms conventional OFDM 1-tap MMSE at high mobility, achieving over an order of magnitude lower BER at 120 km/h. Among the compared CD-MAMP-equalized new waveforms, WHTDM achieves the best BER performance while maintaining a transmitter complexity 2.5 $\times$ lower than OFDM and completely eliminating complex multipliers from the transform stage, making it well-suited for low-power IoT terminals.

eess.SP↗

arXiv2026

WH Statistics: Generalized Pauli Principle for Partially Distinguishable Particles

Traditional statistical mechanics is constrained by the binary paradigms of identical/distinguishable and bosonic/fermionic particle statistics, leading to a fundamental logical gap in describing systems with partial distinguishability. We propose WH Statistics, a unified theoretical framework governed by three key parameters: continuous distinguishability {\lambda}, exclusion weight \k{appa}, and intrinsic exclusivity {\gamma}. By deriving the microstate count and entropy, we show that this framework naturally recovers the Bose-Einstein, Fermi-Dirac, and Maxwell-Boltzmann statistics, while also incorporating anyons and the classical hard-core (Langmuir) limit. We introduce a class of generalized quasiparticles, termed WHons, which exhibit exotic physical phenomena including non-monotonic degeneracy pressure peaks, Schottky-like specific heat anomalies, and tunable interference effects, driven by the interplay between fractional distinguishability and exclusion. This framework bridges the century-old discontinuity between quantum and classical exclusion principles, providing a powerful tool for investigating strongly correlated systems and programmable quantum matter.

cond-mat.stat-mech↗