In this paper, Compressive Sensing (CS) methods for Direct Sequence Spread Spectrum (DSSS) signals are
introduced. DSSS signals are formed by modulating the original signal by a Pseudo-Noise sequence. This
modulation spreads the spectra over a large bandwidth and makes interception of DSSS signals challenging.
Interception of DSSS signals using traditional methods require Analog-to-Digital Converters sampling at very
high rates to capture the full bandwidth. In this work, we propose CS methods that can intercept DSSS
signals from compressive measurements. The proposed methods are evaluated with DSSS signals generated
using Maximum-length Sequences and Binary Phase-Shift-Keying modulation at varying signal-to-noise and
In this paper, compressive detection strategies for FHSS signals are introduced. Rapid switching of the carrier
frequency among many channels using a pseudorandom sequence makes detection of FHSS signals challenging.
The conventional approach to detect these signals is to rapidly scan small segments of the spectrum sequentially.
However, such a scanner has the inherent risk of never overlapping with the transmitted signal depending on
factors such as rate of hopping and scanning. In this paper, we propose compressive detection strategies that
sample the full spectrum in a compressive manner. Theory and simulations are presented to illustrate the benefits
of the proposed framework.
Traditional compression involves sampling a signal at the Nyquist rate, then reducing the signal to its essential
components via some transformation. By taking advantage of any sparsity inherent in the signal, compressed
sensing attempts to reduce the necessary sampling rate by combining these two steps. Currently, compressive
sampling operators are based on random draws of Bernoulli or Gaussian distributed random processes. While
this ensures that the conditions necessary for noise-free signal reconstruction (incoherence and RIP) are fulfilled,
such operators can have poor SNR performance in their measurements. SNR degradation can lead to poor reconstruction despite using operators with good incoherence and RIP. Due to the effects of incoherence-related signal
loss, SNR will degrade by M/K compared to the SNR of the fully sampled signal (where M is the dimensionality
of the measurement operator and K is the dimensionality of the representation space).
We model an RF compressive receiver where the sampling operator acts on noise as well as signal. The signal
is modeled as a bandlimited pulse parameterized by random complex amplitude and time of arrival. Hence, the
received signal is random with known prior distribution. This allows us to represent the signal via Karhunen-Loeve expansion and so investigate the SNR loss in terms of a random vector that exists in the deterministic KL basis. We are then able to show the SNR trade-off that exists between sampling operators based on random
matrices and operators matched to the K-dimensional basis.
In this paper, compressive sensing strategies for interception of Frequency-Hopping Spread Spectrum (FHSS)
signals are introduced. Rapid switching of the carrier among many frequency channels using a pseudorandom
sequence (unknown to the eavesdropper) makes FHSS signals dicult to intercept. The conventional approach to
intercept FHSS signals necessitates capturing of all frequency channels and, thus, requires the Analog-to-Digital
Converters (ADCs) to sample at very high rates. Using the fact that the FHSS signals have sparse instanta-
neous spectra, we propose compressive sensing strategies for their interception. The proposed techniques are
validated using Gaussian Frequency-Shift Keying (GFSK) modulated FHSS signals as dened by the Bluetooth
We consider direct minimum mean-squared error (MMSE) reconstruction of difference images without explicit
reconstruction of the two images at the two time instants. We first derive the MMSE reconstruction operator
and show that it depends on the cross-correlation between the two images taken at different times. We then
consider the reconstruction performance of different strategies for measuring linear spatial projections of the two
images. Performance is evaluated by using measured video imagery of an urban intersection as the input into a
simulation that models the linear projections.
We describe a novel method to track targets in a large field of view. This method simultaneously images multiple,
encoded sub-fields of view onto a common focal plane. Sub-field encoding enables target tracking by creating
a unique connection between target characteristics in superposition space and the target's true position in real
space. This is accomplished without reconstructing a conventional image of the large field of view. Potential
encoding schemes include spatial shift, rotation, and magnification. We briefly discuss each of these encoding
schemes, but the main emphasis of the paper and all examples are based on one-dimensional spatial shift encoding.
Simulation results are included to show the efficacy of the proposed sub-field encoding scheme.