arXiv subjects

Saulo Queiroz

Publications and source records attributed to Saulo Queiroz.

12 recordsLinked to original sources

arXiv2026

Computation-Limited Signals in Practice: A Throughput Anomaly in Software-Defined O-RAN PHY Layers

We formalize a performance anomaly in software-based wireless physical-layer (PHY) implementations, a key enabling technology for Open Radio Access Network (O-RAN) systems. For a fixed offered load, the number of PHY symbols required to transmit the load decreases as the nominal bit rate increases because each symbol conveys more bits. Shorter bursts, however, provide fewer opportunities to exploit pipelined modulation, transmission, and demodulation. Processing latency therefore represents a larger fraction of the total delivery time and may cause a nominally faster PHY configuration to deliver lower effective throughput. We call the operating condition in which computational latency governs effective throughput the computation-limited regime. Its most pronounced manifestation occurs when the offered load fits in a single symbol: intersymbol pipelining cannot be exploited, and modulation and demodulation latencies cannot be amortized. Their combined latency may exceed the symbol duration even when transmitter and receiver processing independently meet their real-time deadlines. Because PHY processing complexity often scales superlinearly with the resources allocated to each symbol, a higher-rate configuration may consequently deliver lower throughput than a slower one. We validate this anomaly using processing-latency measurements reported for established software-defined PHY implementations. The results show that PHY processing latency should be incorporated into link-adaptation algorithms for very-high-throughput services in future 6G wireless networks.

eess.SP↗

arXiv2026

Pre-Characterization of Electromagnetic Side-Channel Leakage Using Publicly Available Information: A Case Study on E-Voting Interfaces

In this work, we study the interface of the Brazilian e-Voting Machine (BVM) in the context of electromagnetic side-channel threats commonly referred to as TEMPEST attacks. In a TEMPEST attack against video displays, an eavesdropper uses Software-Defined Radios (SDRs) to recover sensitive information by intercepting electromagnetic emanations generated during video signal transmission. We emulate the BVM using a VGA monitor by leveraging publicly available information disclosed by the electoral authority, including technical specifications, operational rules of the system, and the official BVM interface. Based on this setup, we investigate whether the BVM interface gives rise to a distinctive spectral signature observable through its unintended electromagnetic emissions. Our findings show that design characteristics relevant to a nationwide electoral process -- such as high image contrast, minimal on-screen information, and the prohibition of other electronic devices within the polling station -- result in a simple and highly distinctive spectral signature that can be observed even through a wall in our experiments. Although our experiments do not involve actual BVM hardware, the results raise concerns regarding the system's susceptibility to TEMPEST attacks and highlight the need for further research on protective countermeasures. In this context, our findings may support the design of automatic jammers capable of adaptively targeting compromising frequencies. To the best of our knowledge, this is the first study investigating TEMPEST attacks in the context of an electronic voting system officially adopted by a country.

cs.CR↗

arXiv2025

Fast Compressed-Domain N-Point Discrete Fourier Transform: The "Twiddless" FFT Algorithm

In this work, we present the \emph{twiddless fast Fourier transform (TFFT)}, a novel algorithm for computing the $N$-point discrete Fourier transform (DFT). The TFFT's divide strategy builds on recent results that decimate an $N$-point signal (by a factor of $p$) into an $N/p$-point compressed signal whose DFT readily yields $N/p$ coefficients of the original signal. However, existing compression-domain DFT analyses have been limited to computing only the even-indexed DFT coefficients. With TFFT, we overcome this limitation by efficiently computing both \emph{even- and odd-indexed} DFT coefficients in the compressed domain with $O(N \log N)$ complexity. TFFT introduces a new recursive decomposition of the DFT problem, wherein $N/2^i$ coefficients of the original input are computed at recursion level $i$, with no need for twiddle factor multiplications or butterfly structures. Additionally, TFFT generalizes the input length to $N = c \cdot 2^k$ (for $k \geq 0$ and non-power-of-two $c > 0$), reducing the need for zero-padding and potentially improving efficiency and stability over classical FFTs. We believe TFFT represents a \emph{novel paradigm} for DFT computation, opening new directions for research in optimized implementations, hardware design, parallel computation, and sparse transforms.

cs.CC↗

arXiv2025

Fast Computation of the Discrete Fourier Transform Rectangular Index Coefficients

In~\cite{sic-magazine-2025}, the authors show that the square index coefficients (SICs) of the $N$-point discrete Fourier transform (DFT) -- that is, the coefficients $X_{k\sqrt{N}}$ for $k = 0, 1, \ldots, \sqrt{N} - 1$ -- can be losslessly compressed from $N$ to $\sqrt{N}$ points, thereby accelerating the computation of these specific DFT coefficients accordingly. Following up on that, in this article we generalize SICs into what we refer to as rectangular index coefficients (RICs) of the DFT, formalized as $X_{kL}, k=0,1,\cdots,C-1$, in which the integers $C$ and $L$ are generic roots of $N$ such that $N=LC$. We present an algorithm to compress the $N$-point input signal $\mathbf{x}$ into a $C$-point signal $\mathbf{\hat{x}}$ at the expense of $\mathcal{O}(N)$ complex sums and no complex multiplication. We show that a DFT on $\mathbf{\hat{x}}$ is equivalent to a DFT on the RICs of $\mathbf{x}$. In cases where specific frequencies of $\mathbf{x}$ are of interest -- as in harmonic analysis -- one can conveniently adjust the signal parameters (e.g., frequency resolution) to align the RICs with those frequencies, and use the proposed algorithm to compute them significantly faster. If $N$ is a power of two -- as required by the fast Fourier transform (FFT) algorithm -- then $C$ can be any power of two in the range $[2, N/2]$ and one can use our algorithm along with FFT to compute all RICs in $\mathcal{O}(C\log C)$ time complexity.

eess.SP↗

arXiv2024

Computational Complexity-Constrained Spectral Efficiency Analysis for 6G Waveforms

In this work, we present a tutorial on how to account for the computational time complexity overhead of signal processing in the spectral efficiency (SE) analysis of wireless waveforms. Our methodology is particularly relevant in scenarios where achieving higher SE entails a penalty in complexity, a common trade-off present in 6G candidate waveforms. We consider that SE derives from the data rate, which is impacted by time-dependent overheads. Thus, neglecting the computational complexity overhead in the SE analysis grants an unfair advantage to more computationally complex waveforms, as they require larger computational resources to meet a signal processing runtime below the symbol period. We demonstrate our points with two case studies. In the first, we refer to IEEE 802.11a-compliant baseband processors from the literature to show that their runtime significantly impacts the SE perceived by upper layers. In the second case study, we show that waveforms considered less efficient in terms of SE can outperform their more computationally expensive counterparts if provided with equivalent high-performance computational resources. Based on these cases, we believe our tutorial can address the comparative SE analysis of waveforms that operate under different computational resource constraints.

eess.SP↗

arXiv2024

Fast Computation of the Discrete Fourier Transform Square Index Coefficients

The $N$-point discrete Fourier transform (DFT) is a cornerstone for several signal processing applications. Many of these applications operate in real-time, making the computational complexity of the DFT a critical performance indicator to be optimized. Unfortunately, whether the $\mathcal{O}(N\log_2 N)$ time complexity of the fast Fourier transform (FFT) can be outperformed remains an unresolved question in the theory of computation. However, in many applications of the DFT -- such as compressive sensing, image processing, and wideband spectral analysis -- only a small fraction of the output signal needs to be computed because the signal is sparse. This motivates the development of algorithms that compute specific DFT coefficients more efficiently than the FFT algorithm. In this article, we show that the number of points of some DFT coefficients can be dramatically reduced by means of elementary mathematical properties. We present an algorithm that compacts the square index coefficients (SICs) of DFT (i.e., $X_{k\sqrt{N}}$, $k=0,1,\cdots, \sqrt{N}-1$, for a square number $N$) from $N$ to $\sqrt{N}$ points at the expense of $N-1$ complex sums and no multiplication. Based on this, any regular DFT algorithm can be straightforwardly applied to compute the SICs with a reduced number of complex multiplications. If $N$ is a power of two, one can combine our algorithm with the FFT to calculate all SICs in $\mathcal{O}(\sqrt{N}\log_2\sqrt{N})$ time complexity.

cs.DS↗

arXiv2023

Computation-Limited Signals: A Channel Capacity Regime Constrained by Computational Complexity

In this letter, we introduce the computational-limited (comp-limited) signals, a communication capacity regime in which the signal time computational complexity overhead is the key constraint -- rather than power or bandwidth -- to the overall communication capacity. We present the Spectro-Computational (SC) analysis, a novel mathematical framework that enhances classic concepts of information theory -- such as throughput, spectral efficiency and capacity -- to account for the signal processing computational complexity overhead. We consider a specific Shannon regime under which capacity is expected to get arbitrarily large as channel resources grow. Under that regime, we identify the conditions under which the time complexity overhead causes capacity to decrease rather than increasing, thereby creating the case for the comp-limited regime. We also provide examples of the SC analysis and show the OFDM waveform is comp-limited unless the lower-bound computational complexity of the $N$-point DFT problem verifies as $\Omega(N)$, which remains an open challenge.

cs.IT↗

arXiv2022

Is FFT Fast Enough for Beyond-5G Communications?

In this paper, we study the impact of computational complexity on the throughput limits of the {\color{black}fast Fourier transform (FFT)} algorithm for {\color{black}orthogonal frequency division multiplexing(OFDM)} waveforms. Based on the spectro-computational {\color{\corcorrecao}complexity} (SC) analysis, {\color{\corcorrecao} we verify that the complexity of an $N$-point FFT grows faster than the number of bits in the OFDM symbol.} Thus, we show that FFT nullifies the OFDM throughput on $N$ unless the $N$-point discrete Fourier transform (DFT) problem verifies as $Ω(N)$, which remains a "fascinating" open question in theoretical computer science. Also, because FFT demands $N$ to be a power of two $2^i$ ($i>0$), the spectrum widening leads to an exponential complexity on $i$, i.e. $O(2^ii)$. To overcome these limitations, {\color{\corcorrecao} we consider the alternative frequency-time transform formulation of vector OFDM (V-OFDM), in which an $N$-point FFT is replaced by $N/L$ ($L$$>$$0$) smaller {\color{\corcorrecao}$L$-point} FFTs to mitigate the cyclic prefix overhead of OFDM. Building on that, we replace FFT by the straightforward DFT algorithm to release the V-OFDM parameters from growing as powers of two and to benefit from flexible numerology (e.g., $L=3$, $N=156$). Besides, by setting $L$ to $Θ(1)$, the resulting solution can run linearly on $N$ (rather than exponentially on $i$) while sustaining a non null throughput as $N$ grows. }

eess.SP↗

arXiv2020

Optimal Mapper for OFDM with Index Modulation: A Spectro-Computational Analysis

In this work, we present an optimal mapper for OFDM with index modulation (OFDM-IM). By optimal we mean the mapper achieves the lowest possible asymptotic computational complexity (CC) when the spectral efficiency (SE) gain over OFDM maximizes. We propose the spectro-computational (SC) analysis to capture the trade-off between CC and SE and to demonstrate that an $N$-subcarrier OFDM-IM mapper must run in exact $Θ(N)$ time complexity. We show that an OFDM-IM mapper running faster than such complexity cannot reach the maximal SE whereas one running slower nullifies the mapping throughput for arbitrarily large $N$. We demonstrate our theoretical findings by implementing an open-source library that supports all DSP steps to map/demap an N-subcarrier complex frequency-domain OFDM-IM symbol. Our implementation supports different index selector algorithms and is the first to enable the SE maximization while preserving the same time and space asymptotic complexities of the classic OFDM mapper.

eess.SP↗

arXiv2020

Maximal Spectral Efficiency of OFDM with Index Modulation under Polynomial Space Complexity

In this letter, we demonstrate a mapper that enables all waveforms of OFDM with Index Modulation (OFDM-IM) while preserving polynomial time and space computational complexities. Enabling all OFDM-IM waveforms maximizes the spectral efficiency (SE) gain over the classic OFDM but, as far as we know, the computational overhead of the resulting mapper remains conjectured as prohibitive across the OFDM-IM literature. We show that the largest number of binomial coefficient calculations performed by the original OFDM-IM mapper is polynomial on the number of subcarriers, even under the setup that maximizes the SE gain over OFDM. Also, such coefficients match the entries of the so-called Pascal's triangle (PT). Thus, by assisting the OFDM-IM mapper with a PT table, we show that the maximum SE gain over OFDM can be achieved under polynomial (rather than exponential) time and space complexities.

eess.SP↗

arXiv2018

The Hidden Binary Search Tree:A Balanced Rotation-Free Search Tree in the AVL RAM Model

In this paper we generalize the definition of "Search Trees" (ST) to enable reference values other than the key of prior inserted nodes. The idea builds on the assumption an $n$-node AVL (or Red-Black) requires to assure $O(\log_2n)$ worst-case search time, namely, a single comparison between two keys takes constant time. This means the size of each key in bits is fixed to $B=c\log_2 n$ ($c\geq1$) once $n$ is determined, otherwise the $O(1)$-time comparison assumption does not hold. Based on this we calculate \emph{ideal} reference values from the mid-point of the interval $0..2^B$. This idea follows `recursively' to assure each node along the search path is provided a reference value that guarantees an overall logarithmic time. Because the search tree property works only when keys are compared to reference values and these values are calculated only during searches, we term the data structure as the Hidden Binary Search Tree (HBST). We show elementary functions to maintain the HSBT height $O(B)=O(\log_2n)$. This result requires no special order on the input -- as does BST -- nor self-balancing procedures, as do AVL and Red-Black.

cs.DS↗

arXiv2016

Breaking Through the Full-Duplex Wi-Fi Capacity Gain

In this work we identify a seminal design guideline that prevents current Full-Duplex (FD) MAC protocols to scale the FD capacity gain (i.e. 2x the half-duplex throughput) in single-cell Wi-Fi networks. Under such guideline (referred to as 1:1), a MAC protocol attempts to initiate up to two simultaneous transmissions in the FD bandwidth. Since in single-cell Wi-Fi networks MAC performance is bounded by the PHY layer capacity, this implies gains strictly less than 2x over half-duplex at the MAC layer. To face this limitation, we argue for the 1:N design guideline. Under 1:N, FD MAC protocols 'see' the FD bandwidth through N>1 orthogonal narrow-channel PHY layers. Based on theoretical results and software defined radio experiments, we show the 1:N design can leverage the Wi-Fi capacity gain more than 2x at and below the MAC layer. This translates the denser modulation scheme incurred by channel narrowing and the increase in the spatial reuse offer enabled by channel orthogonality. With these results, we believe our design guideline can inspire a new generation of Wi-Fi MAC protocols that fully embody and scale the FD capacity gain.

cs.NI↗