arXiv subjects

Peter Smith

Publications and source records attributed to Peter Smith.

At least 19 recordsLinked to original sources

arXiv2026

SDSS-V Local Volume Mapper (LVM): The Integrated Light and Internal Rotation of Omega Centauri

The SDSS-V Local Volume Mapper (LVM) is a wide-field integral field spectroscopic survey of the Southern Milky Way plane, the Magellanic Clouds, and nearby Local Group galaxies. We use Early Science observations of the whole body of the nearest nuclear cluster, Omega Centauri, to extend the LVM beyond its primary interstellar-medium science case. The wide LVM field allows us to precisely map $\omega$ Cen's line-of-sight rotation out to $\sim 3r_{HL}$ or $15^\prime$, reaching a maximum value of $(8.4 \pm 0.8)$ km s$^{-1}$ at $r \approx 4.7^\prime$. Within the central region, comparisons with existing VLT MUSE oMEGACat data show explicitly that the unresolved-light signal is dominated by a small number of bright stars, with an effective sample size of only $\sim$12 per resolution element. Using Gaia DR3 as an external reference, we verify that the SDSS-V's LVM reduction pipeline recovers integrated stellar fluxes to 1-4 % across six magnitudes of surface brightness. Our resulting total spectrum of $\omega$ Cen is one of the highest S/N integrated spectrum for any globular or nuclear star cluster. We use it to test four widely-used SSP template libraries against resolved age-metallicity ground truth from oMEGACat. All templates recover an old, metal-poor population. But, even at S/N $\sim$1300, the inferred mean ages and mean [Fe/H] vary by $\sim$7 Gyr and $\sim$0.4 dex, respectively, across libraries and wavelength ranges, reflecting a systematic floor for integrated-light studies of old multi-population systems.

astro-ph.GA↗

arXiv2026

A Long Period Stellar-Mass Black Hole Binary in $\omega$ Centauri

Modern simulations of stellar dynamics in globular clusters peg a dominant role for stellar-mass black holes, but direct evidence for black holes in clusters remains limited. We present the discovery of an astrometric stellar-mass black hole--main sequence star binary in $\omega$ Centauri, the most massive Galactic globular cluster, using Hubble Space Telescope data from the oMEGACat project and additional JWST data that span a total of 23 years. The luminous companion to the black hole is a main-sequence turnoff star, and has a period of $94^{+63}_{-42}$ years, a semi-major axis of $31^{+15}_{-12}$ AU, and an eccentricity of $e=0.72^{+0.08}_{-0.13}$. Since we observe the binary during periastron, the mass of the black hole is well-constrained even though we only observe a partial orbit: the inferred black hole mass is $4.46^{+1.22}_{-1.01}$ M$_\odot$. We call this black hole oMEGACat BH-2. This is the first astrometric discovery of a stellar-mass black hole in a globular cluster, and is the longest period black hole binary system yet discovered. The low mass of this black hole is perhaps surprising given the low metallicity of the cluster, and shows that at least some low-mass black holes form at metallicity $Z<10^{-3}$. We find that the binary is almost certainly dynamically formed and is soft, with an expected binary disruption timescale of $\sim$800 Myr. While the total number of black hole binaries in $\omega$ Centauri is uncertain, we show that existing surveys only cover a small area of parameter space, and that the presence of additional detectable black hole binaries is likely.

astro-ph.GA↗

arXiv2025

Constant Modulus Waveforms for IoT-Centric Integrated Sensing and Communications

Integrated sensing and communications (ISAC) is considered a key enabler to support application scenarios such as the Internet-of-Things (IoT) in which both communications and sensing play significant roles. Multi-carrier waveforms, such as orthogonal frequency division multiplexing (OFDM), have been considered as good candidates for ISAC due to their high communications data rate and good time bandwidth property for sensing. Nevertheless, their high peak-to-average-power-ratio (PAPR) values lead to either performance degradation or an increase in system complexity. This can make OFDM unsuitable for IoT applications with insufficient resources in terms of power, system complexity, hardware size or cost. This article provides IoT-centric constant modulus waveform designs that leverage the advantage of unit PAPR and thus are more suitable in resource-limited scenarios. More specifically, several single-carrier frequency and/or phase-modulated waveforms are considered. A comprehensive discussion on their radar sensing and communications performance is conducted based on performance metrics, including the radar ambiguity function, the bandwidth property, the data rate, and the communications receiver complexity.

cs.IT↗

arXiv2025

Stringent Limits on H$_3^+$ Emission from the Hot Jupiters WASP-80b and WASP-69b

Observations of auroras on exoplanets would provide numerous insights into planet-star systems, including potential detections of the planetary magnetic fields, constraints on host-star wind properties, and information on the thermal structures of planets. However, there have not yet been any discoveries of auroras on exoplanets. In this paper, we focus on the search for infrared auroral emission from the molecular ion H$_3^+$, which is common in the atmospheres of solar system planets Jupiter, Saturn, and Uranus. Using Keck/NIRSPEC high-resolution spectroscopy, we search for H$_3^+$ emission from two hot Jupiters, WASP-80b and WASP-69b. We do not see any evidence of emission in the observed spectra when cross-correlating with an H$_3^+$ spectral model or when using an auto-correlation approach to search for any significant features. We therefore place upper limits on the total emission of $5.32 \times 10^{18}$ W for WASP-80b and $1.64 \times 10^{19}$ W for WASP-69b. These upper limits represent the most stringent limits to date and approach the regime of emission suspected from theoretical models.

astro-ph.EP↗

arXiv2025

oMEGACat. VI. Analysis of the overall kinematics of Omega Centauri in 3D: velocity dispersion, kinematic distance, anisotropy, and energy equipartition

Omega Centauri ($\omega$ Cen) is the Milky Way's most massive globular cluster and is likely the stripped nucleus of an accreted dwarf galaxy. In this paper, we analyze $\omega$ Cen's kinematics using data from oMEGACat, a comprehensive catalog of $\omega$ Cen's central regions, including 1.4 million proper motion measurements and 300,000 spectroscopic radial velocities. Our velocity dispersion profiles and kinematic maps are consistent with previous work but improve on their resolution, precision, and spatial coverage. The cluster's 3D dispersion is isotropic in the core, with increasing radial anisotropy at larger radii. The 2D kinematic maps show an elongation of the velocity dispersion field comparable to the flattening observed photometrically. We find good agreement between proper motions and line-of-sight velocity dispersion and measure a kinematic distance of 5494$\pm$61 pc, the most precise kinematic distance to $\omega$ Cen available. The subset of data with precise metallicity measurements shows no correlation between metallicity and kinematics, supporting the picture of well-mixed stellar populations within the half-light radius of $\omega$ Cen. Finally, we study the degree of energy equipartition using a large range of stellar masses. We find partial energy equipartition in the center that decreases towards large radii. The spatial dependence of the radial energy equipartition is stronger than the tangential energy equipartition. Our kinematic observations can serve as a new reference for future dynamical modeling efforts that will help to further disentangle the complex mass distribution within $\omega$ Cen.

astro-ph.GA↗

arXiv2024

Peering into the black box: forward-modeling the uncertainty budget of high-resolution spectroscopy of exoplanet atmospheres

Ground-based high-resolution cross-correlation spectroscopy (HRCCS; R >~ 15,000) is a powerful complement to space-based studies of exoplanet atmospheres. By resolving individual spectral lines, HRCCS can precisely measure chemical abundance ratios, directly constrain atmospheric dynamics, and robustly probe multidimensional physics. But the subtleties of HRCCS datasets -- e.g., the lack of exoplanetary spectra visible by eye and the statistically complex process of telluric removal -- can make interpreting them difficult. In this work, we seek to clarify the uncertainty budget of HRCCS with a forward-modeling approach. We present a HRCCS observation simulator, scope (https://github.com/arjunsavel/scope), that incorporates spectral contributions from the exoplanet, star, tellurics, and instrument. This tool allows us to control the underlying dataset, enabling controlled experimentation with complex HRCCS methods. Simulating a fiducial hot Jupiter dataset (WASP-77Ab emission with IGRINS), we first confirm via multiple tests that the commonly used principal components analysis does not bias the planetary signal when few components are used. Furthermore, we demonstrate that mildly varying tellurics and moderate wavelength solution errors induce only mild decreases in HRCCS detection significance. However, limiting-case, strongly varying tellurics can bias the retrieved velocities and gas abundances. Additionally, in the low-SNR limit, constraints on gas abundances become highly non-Gaussian. Our investigation of the uncertainties and potential biases inherent in HRCCS data analysis enables greater confidence in scientific results from this maturing method.

astro-ph.EP↗

arXiv2024

CRIRES+ and ESPRESSO reveal an atmosphere enriched in volatiles relative to refractories on the ultra-hot Jupiter WASP-121b

One of the outstanding goals of the planetary science community is to measure the present-day atmospheric composition of planets and link this back to formation. As giant planets are formed by accreting gas, ices, and rocks, constraining the relative amounts of these components is critical to understand their formation and evolution. For most known planets, including the Solar System giants, this is difficult as they reside in a temperature regime where only volatile elements (e.g., C, O) can be measured, while refractories (e.g., Fe, Ni) are condensed to deep layers of the atmosphere where they cannot be remotely probed. With temperatures allowing for even rock-forming elements to be in the gas phase, ultra-hot Jupiter atmospheres provide a unique opportunity to simultaneously probe the volatile and refractory content of giant planets. Here we directly measure and obtain bounded constraints on the abundances of volatile C and O as well as refractory Fe and Ni on the ultra-hot giant exoplanet WASP-121b. We find that ice-forming elements are comparatively enriched relative to rock-forming elements, potentially indicating that WASP-121b formed in a volatile-rich environment much farther away from the star than where it is currently located. The simultaneous constraint of ice and rock elements in the atmosphere of WASP-121b provides insights into the composition of giant planets otherwise unattainable from Solar System observations.

astro-ph.EP↗

arXiv2024

The metallicity and carbon-to-oxygen ratio of the ultra-hot Jupiter WASP-76b from Gemini-S/IGRINS

Measurements of the carbon-to-oxygen (C/O) ratios of exoplanet atmospheres can reveal details about their formation and evolution. Recently, high-resolution cross-correlation analysis has emerged as a method of precisely constraining the C/O ratios of hot Jupiter atmospheres. We present two transits of the ultra-hot Jupiter WASP-76b observed between 1.4-2.4 $\mu$m with Gemini-S/IGRINS. We detected the presence of H$_{2}$O, CO, and OH at signal-to-noise ratios of 6.93, 6.47, and 3.90, respectively. We performed two retrievals on this data set. A free retrieval for abundances of these three species retrieved a volatile metallicity of $\left[\frac{\mathrm{C}+\mathrm{O}} {\mathrm{H}}\right]=-0.70^{+1.27}_{-0.93}$, consistent with the stellar value, and a super-solar carbon-to-oxygen ratio of C/O$=0.80^{+0.07}_{-0.11}$. We also ran a chemically self-consistent grid retrieval, which agreed with the free retrieval within $1\sigma$ but favored a slightly more sub-stellar metallicity and solar C/O ratio ($\left[\frac{\mathrm{C}+\mathrm{O}} {\mathrm{H}}\right]=-0.74^{+0.23}_{-0.17}$ and C/O$=0.59^{+0.13}_{-0.14}$). A variety of formation pathways may explain the composition of WASP-76b. Additionally, we found systemic ($V_{sys}$) and Keplerian ($K_{p}$) velocity offsets which were broadly consistent with expectations from 3D general circulation models of WASP-76b, with the exception of a redshifted $V_{sys}$ for H$_{2}$O. Future observations to measure the phase-dependent velocity offsets and limb differences at high resolution on WASP-76b will be necessary to understand the H$_{2}$O velocity shift. Finally, we find that the population of exoplanets with precisely constrained C/O ratios generally trends toward super-solar C/O ratios. More results from high-resolution observations or JWST will serve to further elucidate any population-level trends.

astro-ph.EP↗

arXiv2023

A Combined Ground-based and JWST Atmospheric Retrieval Analysis: Both IGRINS and NIRSpec Agree The Atmosphere of WASP-77A b is Metal-Poor

Ground-based, high-resolution and space-based, low-resolution spectroscopy are the two main avenues through which transiting exoplanet atmospheres are studied. Both methods provide unique strengths and shortcomings, and combining the two can be a powerful probe into an exoplanet's atmosphere. Within a joint atmospheric retrieval framework, we combined JWST NIRSpec/G395H secondary eclipse spectra and Gemini South/IGRINS pre- and post-eclipse thermal eclipse observations of the hot Jupiter WASP-77A b. Our inferences from the IGRINS and NIRSpec data sets are consistent with each other, and combining the two allows us to measure the gas abundances of H$_2$O and CO as well as the vertical thermal structure with higher precision than either data set provided individually. We confirm WASP-77A b's subsolar metallicty ([(C+O)/H]=-0.61$^{+0.10}_{-0.09}$) and solar C/O ratio (C/O = 0.57$^{+0.06}_{-0.06}$). The two types of data are complementary, and our abundance inferences are mostly driven by the IGRINS data while inference of the thermal structure is driven by the NIRSpec data. Our ability to draw inferences from the post-eclipse IGRINS data is highly sensitive to the number of singular values removed in the detrending process, potentially due to high and variable humidity. We also search for signatures for atmospheric dynamics in the IGRINS data and find that propagated ephemeris error can manifest as both an orbital eccentricity or a strong equatorial jet. Neither are detected when using more up-to-date ephemerides. However, we find moderate evidence of thermal inhomogeneity and measure a cooler nightside that presents itself in the later phases after secondary eclipse.

astro-ph.EP↗

arXiv2023

OTFS based Joint Radar and Communication: Signal Analysis using the Ambiguity Function

Orthogonal time frequency space (OTFS) modulation has recently been identified as a suitable waveform for joint radar and communication systems. Focusing on the effect of data modulation on the radar sensing performance, we derive the ambiguity function (AF) of the OTFS waveform and characterize the radar global accuracy. We evaluate the behavior of the AF with respect to the distribution of the modulated data and derive an accurate approximation for the mean and variance of the AF, thus, approximating its distribution by a Rice distribution. Finally, we evaluate the global radar performance of the OTFS waveform with the OFDM waveform.

eess.SP↗

arXiv2023

Confirmation of sub-solar metallicity for WASP-77Ab from JWST thermal emission spectroscopy

We present the dayside thermal emission spectrum of WASP-77Ab from 2.8 -- 5.2 $\mu$m as observed with the NIRSpec instrument on the James Webb Space Telescope (JWST). WASP-77Ab was previously found to have a sub-solar metallicity and a solar carbon-to-oxygen (C/O) ratio from H$_2$O and CO absorption lines detected using high-resolution spectroscopy. By performing atmospheric retrievals on the JWST spectrum assuming chemical equilibrium, we find a sub-solar metallicity [M/H]=$-0.91^{+0.24}_{-0.16}$ and C/O ratio $0.36^{+0.10}_{-0.09}$. We identify H$_2$O and CO and constrain their abundances, and we find no CO$_2$ in the spectrum. The JWST and high-resolution spectroscopy results agree within $\sim1\sigma$ for the metallicity and within 1.8$\sigma$ for the C/O ratio. However, our results fit less well in the picture painted by the shorter wavelength spectrum measured by HST WFC3. Comparing the JWST thermal emission spectra of WASP-77Ab and HD 149026b shows that both hot Jupiters have nearly identical brightness temperatures in the near-infrared, but distinctly different atmospheric compositions. Our results reaffirm high-resolution spectroscopy as a powerful and reliable method to measure molecular abundances. Our results also highlight the incredible diversity of hot Jupiter atmospheric compositions.

astro-ph.EP↗

arXiv2023

Multimass modelling of Milky Way globular clusters -- I. Implications on their stellar initial mass function above 1 M$_{\odot}$

The distribution of stars and stellar remnants (white dwarfs, neutron stars, black holes) within globular clusters holds clues about their formation and long-term evolution, with important implications for their initial mass function (IMF) and the formation of black hole mergers. In this work, we present best-fitting multimass models for 37 Milky Way globular clusters, which were inferred from various datasets, including proper motions from Gaia EDR3 and HST, line-of-sight velocities from ground-based spectroscopy and deep stellar mass functions from HST. We use metallicity dependent stellar evolution recipes to obtain present-day mass functions of stars and remnants from the IMF. By dynamically probing the present-day mass function of all objects in a cluster, including the mass distribution of remnants, these models allow us to explore in detail the stellar (initial) mass functions of a large sample of Milky Way GCs. We show that, while the low-mass mass function slopes are strongly dependent on the dynamical age of the clusters, the high-mass slope ($\alpha_3; m > 1 M_\odot$) is not, indicating that the mass function in this regime has generally been less affected by dynamical mass loss. Examination of this high-mass mass function slope suggests an IMF in this mass regime consistent with a Salpeter IMF is required to reproduce the observations. This high-mass IMF is incompatible with a top-heavy IMF, as has been proposed recently. Finally, based on multimass model fits to our sample of Milky Way GCs, no significant correlation is found between the high-mass IMF slope and cluster metallicity.

astro-ph.GA↗

arXiv2022

The Roasting Marshmallows Program with IGRINS on Gemini South I: Composition and Climate of the Ultra Hot Jupiter WASP-18 b

We present high-resolution dayside thermal emission observations of the exoplanet WASP-18b using IGRINS on Gemini South. We remove stellar and telluric signatures using standard algorithms, and we extract the planet signal via cross correlation with model spectra. We detect the atmosphere of WASP-18b at a signal-to-noise ratio (SNR) of 5.9 using a full chemistry model, measure H2O (SNR=3.3), CO (SNR=4.0), and OH (SNR=4.8) individually, and confirm previous claims of a thermal inversion layer. The three species are confidently detected (>4$\sigma$) with a Bayesian inference framework, which we also use to retrieve abundance, temperature, and velocity information. For this ultra-hot Jupiter (UHJ), thermal dissociation processes likely play an important role. Retrieving abundances constant with altitude and allowing the temperature-pressure profile to freely adjust results in a moderately super-stellar carbon to oxygen ratio (C/O=0.75^{+0.14}_{-0.17}) and metallicity ([M/H]=1.03^{+0.65}_{-1.01}). Accounting for undetectable oxygen produced by thermal dissociation leads to C/O=0.45^{+0.08}_{-0.10} and [M/H]=1.17^{+0.66}_{-1.01}. A retrieval that assumes radiative-convective-thermochemical-equilibrium and naturally accounts for thermal dissociation constrains C/O<0.34 (2$\sigma$) and [M/H]=0.48^{+0.33}_{-0.29}, in line with the chemistry of the parent star. Looking at the velocity information, we see a tantalising signature of different Doppler shifts at the level of a few km/s for different molecules, which might probe dynamics as a function of altitude and location on the planet disk. Our results demonstrate that ground-based, high-resolution spectroscopy at infrared wavelengths can provide meaningful constraints on the compositions and climate of highly irradiated planets. This work also elucidates potential pitfalls with commonly employed retrieval assumptions when applied to UHJ spectra.

astro-ph.EP↗

arXiv2022

A Modified Union Bound on Symbol Error Probability for Fading Channels

In this paper, we propose a new upper bound on the error probability performance of maximum-likelihood (ML) detection. The proposed approach provides a much tighter upper bound when compared to the traditionally used union bound, especially when the number of pairwise error probabilities (PEPs) is large. In fact, the proposed approach tightens the union bound by first assuming that a detection error always occurs in a deep fading event where the channel gain is lower than a certain threshold. A minimisation is then taken with respect to the gain threshold in order to make the upper bound as tight as possible. We also prove that the objective function has a single minimiser under several general assumptions so that the minimiser can be easily found using optimisation algorithms. The expression of the new upper bound under correlated Rayleigh fading channels is derived and several analytical and numerical examples are provided to show the performance of the proposed bound.

cs.IT↗

arXiv2022

Frequency Permutation Subsets for Joint Radar and Communication

This paper focuses on waveform design for joint radar and communication systems and presents a new subset selection process to improve the communication error rate performance and global accuracy of radar sensing of the random stepped frequency permutation waveform. An optimal communication receiver based on integer programming is proposed to handle any subset of permutations followed by a more efficient sub-optimal receiver based on the Hungarian algorithm. Considering optimum maximum likelihood detection, the block error rate is analyzed under both additive white Gaussian noise and correlated Rician fading. We propose two methods to select a permutation subset with an improved block error rate and an efficient encoding scheme to map the information symbols to selected permutations under these subsets. From the radar perspective, the ambiguity function is analyzed with regards to the local and the global accuracy of target detection. Furthermore, a subset selection method to reduce the maximum sidelobe height is proposed by extending the properties of Costas arrays. Finally, the process of remapping the frequency tones to the symbol set used to generate permutations is introduced as a method to improve both the communication and radar performances of the selected permutation subset.

cs.IT↗

arXiv2022

Confirmation of Water Absorption in the Thermal Emission Spectrum of the Hot Jupiter WASP-77Ab with HST/WFC3

Secondary eclipse observations of hot Jupiters can reveal both their compositions and thermal structures. Previous observations have shown a diversity of hot Jupiter eclipse spectra, including absorption features, emission features, and featureless blackbody-like spectra. We present a secondary eclipse spectrum of the hot Jupiter WASP-77Ab observed between $1-5$ $\mu$m with the Hubble Space Telescope (HST) and the Spitzer Space Telescope. The HST observations show signs of water absorption indicative of a non-inverted thermal structure. We fit the data with both a one-dimensional free retrieval and a grid of one-dimensional self-consistent forward models to confirm this non-inverted structure. The free retrieval places a $3\sigma$ lower limit on the atmospheric water abundance of $\log(n_\mathrm{H_2O})>-4.78$ and can not constrain the CO abundance. The grid fit produces a slightly super-stellar metallicity and constrains the carbon-to-oxygen ratio to less than or equal to the solar value. We also compare our data to recent high-resolution observations of WASP-77Ab taken with the Gemini-South/IGRINS spectrograph and find that our observations are consistent with the best-fit model to the high-resolution data. However, the metallicity derived from the IGRINS data is significantly lower than that derived from our self-consistent model fit. We find that this difference may be due to disequilibrium chemistry, and the varying results between the models applied here demonstrate the difficulty of constraining disequilibrium chemistry with low-resolution, low wavelength coverage data alone. Future work to combine observations from IGRINS, HST, and JWST will improve our estimate of the atmospheric composition of WASP-77Ab.

astro-ph.EP↗

arXiv2021

A solar C/O and sub-solar metallicity in a hot Jupiter atmosphere

Measurements of the atmospheric carbon (C) and oxygen (O) relative to hydrogen (H) in hot Jupiters (relative to their host stars) provide insight into their formation location and subsequent orbital migration. Hot Jupiters that form beyond the major volatile (H2O/CO/CO2) ice lines and subsequently migrate post disk-dissipation are predicted have atmospheric carbon-to-oxygen ratios (C/O) near 1 and subsolar metallicities, whereas planets that migrate through the disk before dissipation are predicted to be heavily polluted by infalling O-rich icy planetesimals, resulting in C/O < 0.5 and super-solar metallicities. Previous observations of hot Jupiters have been able to provide bounded constraints on either H2O or CO, but not both for the same planet, leaving uncertain the true elemental C and O inventory and subsequent C/O and metallicity determinations. Here we report spectroscopic observations of a typical transiting hot Jupiter, WASP-77Ab. From these, we determine the atmospheric gas volume mixing ratio constraints on both H2O and CO (9.5$\times 10^{-5}$ - 1.5$\times 10^{-4}$ and 1.2$\times 10^{-4}$ - 2.6$\times 10^{-4}$, respectively). From these bounded constraints, we are able to derive the atmospheric C/H (0.35$^{+0.17}_{-0.10}$ $\times$ Solar) and O/H (0.32 $^{+0.12}_{-0.08}$ $\times$ Solar) abundances and the corresponding atmospheric carbon-to-oxygen ratio (C/O=0.59$\pm$0.08; the solar value is 0.55). The sub-solar (C+O)/H (0.33$^{+0.13}_{-0.09}$ $\times$ Solar) is suggestive of a metal-depleted atmosphere relative to what is expected for Jovian-like planets while the near solar value of C/O rules out the disk-free migration/C-rich atmosphere scenario.

astro-ph.EP↗

arXiv2021

Combined Radar and Communications with Phase-Modulated Frequency Permutations

This paper focuses on the combined radar and communications problem and conducts a thorough analytical investigation on the effect of phase and frequency change on the communication and sensing functionality. First, we consider the classical stepped frequency radar waveform and modulate data using M-ary phase shift keying (MPSK). Two important analytical tools in radar waveform design, namely the ambiguity function (AF) and the Fisher information matrix (FIM) are derived, based on which, we make the important conclusion that MPSK modulation has a negligible effect on radar local accuracy. Next, we extend the analysis to incorporate frequency permutations and propose a new signalling scheme in which the mapping between incoming data and waveforms is performed based on an efficient combinatorial transform called the Lehmer code. We also provide an efficient communications receiver based on the Hungarian algorithm. From the communications perspective, we consider the optimal maximum likelihood (ML) detector and derive the union bound and nearest neighbour approximation on the block error probability. From the radar sensing perspective, we discuss the broader structure of the waveform based on the AF derivation and quantify the radar local accuracy based on the FIM. Extensive numerical examples are provided to illustrate the accuracy of our results.

cs.IT↗