Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.02843

On the Optimality of OFDM for Aperiodic Ranging

Yifeng Xiong·Fan Liu·Ya-Feng Liu·Shi Jin·Jianhua Zhang
View original source ↗Read source document ↗Export metadata ↓

Abstract

We study the expected aperiodic autocorrelation sidelobes of random communication symbols transmitted through a unitary modulation matrix. We consider proper sub-Gaussian constellations, namely those with fourth absolute moment $μ_4<2$ and zero pseudo-variance, including the commonly used uniform square quadrature amplitude modulation (QAM) and uniform phase-shift keying (PSK) constellations. For every prescribed lag, we determine the exact minimum expected sidelobe level (ESL) and a unitary modulation attaining it by applying a normalized inverse discrete Fourier transform (IDFT) separately on each chain of sample indices spaced by that lag. The full orthogonal frequency division modulation (OFDM) modulation attains this minimum if and only if the lag divides the block length $N$. Combining this criterion with the complete characterization of the minimizers at lag one, we show that a unitary modulation minimizes the ESL simultaneously over the first $r$ positive lags, called the prefix $\{1,\ldots,r\}$ with $1\le r<N$, if and only if every lag in that prefix divides $N$. In particular, simultaneous optimality over all positive lags is impossible for $N\ge 3$. We also prove that OFDM globally minimizes the partial expected integrated sidelobe level (EISL), defined as the sum of the ESLs over a selected subset of positive lags, for every such prefix. This also resolves the full EISL conjecture when $r=N-1$.

Explore related subjects

eess.SPcs.ITmath.IT

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Yifeng Xiong, Fan Liu, Ya-Feng Liu, Shi Jin, Jianhua Zhang. 2026-10-02. On the Optimality of OFDM for Aperiodic Ranging. https://arxiv.org/abs/2610.02843

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

LatentWave: JEPA Pretraining for Wireless Foundation Models

Wireless foundation models have emerged as a promising alternative to building separate models for each wireless task. However, existing approaches rely on masked input reconstruction, which can bias representations toward low-level signal details. In this paper, we propose LatentWave, a wireless foundation model pretrained using a Joint-Embedding Predictive Architecture (JEPA) on diverse wireless spectrograms and channel state information (CSI). By predicting masked regions in latent space, LatentWave learns representations that are more transferable out of the box across diverse downstream tasks. The proposed architecture employs per-channel patch embeddings with stochastic channel sampling during pretraining, allowing it to process variable antenna counts and improving usability across heterogeneous wireless configurations. We evaluate LatentWave on four downstream tasks: RF signal classification, 5G NR positioning, beam prediction, and LoS/NLoS classification, comparing against a masked-modeling baseline (WavesFM) pretrained on the same data. Additionally, we show that the masking geometry introduces a task-dependent inductive bias: frequency masking strongly favors channel-related tasks such as positioning and beam prediction, while region masking better preserves discriminability for signal classification.

eess.SP↗
arXiv2026

Pinching-Antenna Differential Spatial Modulation with RSSI-Assisted Selection and Low-Complexity Detection: Methods and Performance Analysis

Pinching antenna (PA) systems provide macroscopic spatial reconfigurability by enabling signal radiation from favorable locations along a dielectric waveguide. Exploiting this flexibility, however, typically requires channel knowledge for PA configuration, which can introduce substantial overhead in dynamic propagation environments. This paper proposes PA-assisted differential spatial modulation (PA-DSM), enabling data transfer with spatial index selection and non-coherent data detection without instantaneous channel state information (CSI) at the receiver. To exploit PA reconfigurability while preserving this CSI-efficient operation, we introduce a slow-timescale received signal strength indicator (RSSI)-assisted selection strategy that identifies a favorable subset of PAs from scalar power measurements. We further specialize a two-stage low-complexity maximum-likelihood (LC-ML) detector to phase shift keying (PSK) signaling, obtaining closed-form symbol decisions that remove the joint modulation-combination search while preserving the minimizer of exhaustive differential detection. Furthermore, a moment generating function (MGF)-based pairwise error analysis and the corresponding bit error probability (BEP) bound are developed under normalized common-K Rician fading, revealing how the difference rank and spectrum, number of receive antennas, and previous-state-dependent line-of-sight (LoS) alignment affect the error performance. Numerical results across representative indoor-office, indoor-factory, and street-canyon sixth-generation (6G) Frequency Range 3 (FR3) scenarios validate the analytical trends and quantify when PA-DSM outperforms coherent benchmark schemes whose channel estimates age between pilot transmissions.

eess.SP↗
arXiv2026

Quantized Transformers for Massive MIMO Precoding with Automatic Resolution Tuning

Deep learning precoders, particularly those based on Transformer architectures, offer superior spectral efficiency for Massive MIMO systems but may incur high computational cost. While existing mixed-precision quantization studies on convolutional neural networks establish important energy baselines, traditional discrete search methods fail to scale to the large parameter spaces of modern Transformers. To bridge this gap, we apply a differentiable precision learning technique to massive MIMO precoding. This approach autonomously and jointly optimizes weights, activations, quantization step sizes, and layer-wise bit-widths in a single training loop, directly optimizing for energy efficiency. We further expand this approach by incorporating Neural Architecture Search across various Transformer model sizes and evaluating the impact of random versus floating-point trained initializations on resolution tuning. Ultimately, we demonstrate that the proposed training method enables the deployment of highly compact Transformer precoders, improving energy efficiency by up to 288\(\times\) compared to the classical Weighted Minimum Mean Square Error algorithm at equal sum-rate performance in a dense downtown environment.

eess.SP↗