Nishant Mehrotra

Reliable detection and localization of humans through structural obstructions is critical for time-sensitive applications such as disaster response. This paper presents a novel ultra-wideband (UWB) radar-based framework for multi-person localization and breathing rate estimation in obstructed environments. To overcome the challenges posed by signal attenuation, multipath interference, and limited spatial resolution, we propose a synthetic aperture radar (SAR) system that combines linear translation and on-axis rotation of a single radar. By fusing intensity maps from multiple radar viewpoints, the system achieves enhanced localization of human targets. A signal quality assessment pipeline, including SNR-based filtering, dominance ratio analysis, and periodicity checks, is used to extract clean respiratory signals from selected range bins. The estimates are further integrated into a spatial breathing-rate matrix, which is fused with radar motion maps to suppress false detections and improve reliability. The proposed algorithm is validated experimentally under line-of-sight, through-wall, and emulated rubble conditions. Results demonstrate significant improvements in localization accuracy and robustness of respiration-based human presence detection. The proposed post-processing filtering algorithms reduce the 80^th percentile Chamfer distance by 1.53×, while the maximum Chamfer distance is reduced by $\sim 3\times$. The estimated breathing rate correlates strongly with ground truth while achieving a Pearson correlation of 0.79.

Orthogonal signaling or Nyquist signaling limits the number of information symbols transmitted in bandwidth $B$ and time $T$ to be $BT$, the time-bandwidth product. Transmitting more than $BT$ symbols leads to loss of orthogonality. The standard approach is to reduce the symbol interval and resolve the resulting inter-symbol interference. This requires changing the sampling frequency and possibly the sampling clock. This paper shows that it is possible to improve spectral efficiency on doubly spread channels without changing the sampling frequency. The idea is to superimpose the information symbols using mutually unbiased bases (MUB) while maintaining the original spacing. We carry this out in the delay-Doppler domain using Zak-transform based orthogonal time frequency space (Zak-OTFS) modulation as it allows construction of MUB. We also construct a precoder that mitigates the effect of the doubly-spread channel. This simplifies receiver processing to detection in Gaussian noise since each basis appears to the other as Gaussian noise. This reduction makes it possible to use trellis coded modulation to further improve the bit-error performance. Numerical results demonstrate that the proposed signaling scheme using MUB achieves good bit-error performance.

Zak-OTFS provides a framework for integrated sensing & communication (ISAC) in high delay and Doppler spread environments. Pulse shaping filter design enables joint optimization of sensing and communication performance. For sensing, a localized pulse shaping filter enables input-output (I/O) relation estimates close to the physical scattering channel. For communication, orthogonality of the pulse shape on the information lattice prevents inter-symbol interference, and no time and bandwidth expansion enables full spectral efficiency. A filter simultaneously meeting all three objectives is ideal for ISAC. Existing filter designs achieve two, but not all three objectives. In this work, we design pulse shaping filters meeting all three objectives via the Isotropic Orthogonal Transform Algorithm. The proposed filters have improved spectral efficiency, data detection and sensing performance over existing filter choices.

There is significant recent interest in designing new modulation schemes for doubly-selective channels with large delay and Doppler spreads, where legacy modulation schemes based on time-frequency signal representations underperform. Multiple modulation schemes, e.g., in the delay-Doppler, chirp, time-sequency, and other domains, have been proposed in the literature for this purpose, with varying implementation details. In this letter, we establish that all previously proposed modulation schemes for doubly-selective signaling are instances of a single family of complex Hadamard-modulated pulse trains. When the delay and Doppler spread of the doubly-selective channel is limited to a certain support, all modulation schemes in this waveform family offer equivalent, full diversity achieving performance with no symbol fading and low channel estimation overhead. The existence of this waveform family also enables flexible, multi-waveform co-existence – allowing a common transceiver architecture to generate multiple waveforms in the family, that may each be flexibly allocated to different users and services.

Polarimetry, which is the ability to measure the scattering response of the environment across orthogonal polarizations, is fundamental to enhancing wireless communication and radar system performance. In this paper, we utilize the Zak-OTFS modulation to enable instantaneous polarimetry within a single transmission frame. We transmit a Zak-OTFS carrier waveform and a spread carrier waveform mutually unbiased to it simultaneously over orthogonal polarizations. The mutual unbiasedness of the two waveforms enables the receiver to estimate the full polarimetric response of the scattering environment from a single received frame. Unlike existing methods for instantaneous polarimetry with computational complexity quadratic in the time-bandwidth product, the proposed method enables instantaneous polarimetry at near-linear complexity in the time-bandwidth product. Via numerical simulations, we show ideal polarimetric target detection and parameter estimation results with the proposed method, with improvements in computational complexity and greater clutter resilience over comparable baselines.

Zak-transform based orthogonal time frequency space (Zak-OTFS) is a delay-Doppler (DD) domain modulation scheme in which the signal processing is carried out in the DD domain. The channel when viewed in the DD domain is predictable. However, even with Zak-OTFS, pilots need to be sent periodically, albeit at a lower rate. In this paper, we propose a differential communication scheme for Zak-OTFS systems that alleviates the need for periodic pilot transmission. Towards this, we analytically show that the detected data can be used as a pilot and that the channel estimate obtained from the detected data can enable further detection enabling the “differential” aspect of the communication. Specifically, we leverage the prediction capability of the DD channel in Zak-OTFS to use the channel estimate (obtained from detected data symbols treated as pilots) in the previous instant to detect data in the next instant and propagate this forward. The advantages are two fold. First, it allows the data symbols to enjoy higher energy since the energy that would otherwise be required for pilot symbols can also be allocated to data symbols. Second, it allows for full spectral efficiency compared to point or embedded pilots. Comparison with the full spectral efficiency achieving spread pilot scheme shows that the proposed method achieves better bit-error rate at lower complexity.

Radars are widely adopted for autonomous navigation and vehicular networking due to their robustness to weather conditions as compared to visible light cameras and lidars. However, radars currently struggle with differentiating static vs tangentially moving objects within a single radar frame since both yield the same Doppler along line-of-sight paths to the radar. Prior solutions deploy multiple radar or visible light camera modules to form a multi-“look” synthetic aperture for estimating the single-frame velocity vectors, to estimate tangential and radial velocity components of moving objects leading to higher system costs. In this paper, we propose to exploit multi-bounce scattering from secondary static objects in the environment, e.g., building pillars, walls, etc., to form an effective multi-“look” synthetic aperture for single-frame velocity vector estimation with a single multiple-input, multiple-output (MIMO) radar, thus reducing the overall system cost and removing the need for multi-module synchronization. We present a comprehensive theoretical and experiment evaluation of our scheme, demonstrating a $4.5 \times$ reduction in the error for estimating moving objects' velocity vectors over comparable single-radar baselines.

Zak-OTFS (orthogonal time frequency space) modulation is a communication framework that parameterizes the wireless channel in the delay-Doppler (DD) domain, where the parameters map directly to physical attributes of the scatterers that comprise the scattering environment. As a consequence, the channel can be efficiently acquired and equalized. The Zak-OTFS carrier is a pulse in the DD domain, and the Zak transform converts it to a pulse train modulated by a tone (pulsone) in the time domain. The pulsone waveform is localized rather than spread, and it suffers from high peak-to-average power ratio (PAPR). We describe how to transform the orthonormal basis of Zak-OTFS pulsones into an orthonormal basis of spread carrier waveforms with low PAPR (only 6.58 dB) that support communication in the presence of mobility and delay spread. This transformation is realized by a unitary transform based on the discrete affine Fourier transform. Unlike other spread modulations that achieve low PAPR by spreading information across a wider bandwidth (thus reducing the spectral efficiency), the proposed spread carrier-based Zak-OTFS achieves full spectral efficiency like pulsone-based Zak-OTFS, with 5.6 dB lower PAPR per basis element. We demonstrate uncoded bit error rate (BER) similar to pulsone-based Zak-OTFS, and improved BER performance over competing methods based on OFDM and OTFS in high mobility & delay spread environments.