We consider a scenario where signals that can be modeled as finite sums of linearly modulated signals that are non-orthogonal in both time and frequency are observed by a sensor. Under this model, when an antidiagonal slice of the trispectum of the sum of these signals is computed for multiple segments in time and stacked into a frontal symmetric block partitioned tensor (FSBPT) whose factor matrices characterize the received power spectrum and transmission activities of the signals. We propose a new alternating soft thresholding decomposition strategy that is tailored to FSBPTs and, unlike existing BPT decomposition algorithms, simultaneously estimates the factor partitions which is necessary since in our signal model the partitioning is not known a priori. We demonstrate the algorithm's performance via Monte Carlo simulations. We find that our proposed non-blind algorithm is able to estimate the tensor partitions and moderately accurately estimate the factor matrices under a range of factor matrix column collinearity values.

Symmetric block partitioned tensors (SBPT) are a useful structure in signal processing applications, often generated from computing higher-order statistics on observed data. Such tensors often follow the rank-(R-m, R-m, 1) SBPT structure, but in some applications the partitioning of the factor matrices is not known a priori. We propose a both blind and non-blind column-wise SBPT decomposition algorithms that are better scalable to high-dimensional tensors because they avoid large matrix inversions. We apply the algorithms to simulated SBPTs and demonstrate that they estimate factor matrices having high congruence with the originals across a range of collinearity values for the columns of the original factor matrices.

We consider a scenario where a single sensor is observing a bandwidth of the radio spectrum occupied by several signals which are non-orthogonal in both time and frequency. We form a tensor using anti-diagonal slices of the trispectrum and show that it can be modeled by a block-partitioned tensor (BPT) structure. Current BPT decomposition algorithms assume known factor-matrix partitioning which does not apply in our setting. Hence we develop a blind BPT decomposition strategy to estimate each individual signals' power spectrum and activity-in-time. We verify the functioning of the algorithm through Monte Carlo simulations and observe that it can accurately estimate the BPT paritioning and factor matrices. The accuracy of the estimates is a function of the correlation between factor matrix columns and the frequency resolution used.

We consider a model where a single sensor observes a bandwidth of spectrum occupied by several non-orthogonal in both time and frequency signals. The sensor constructs a tensor based on the trispectrum and which can be modeled as a block partitioned tensor (BPT). By decomposing this tensor we can estimate signal activity in both time and frequency. We develop a partition-blind BPT decomposition algorithm using iterative thresholding and parallel coordinate descent. We test the algorithm in simulations and find that it succeeds in estimating received signal PSDs and time activity substantially faster than previous algorithms.

We consider reception of non-persistently excitated radio signals that overlap in time and frequency from a group of transmitters to a single receiver. The signals can be categorized as using a linear modulation or a non-linear modulation that can be approximated as a finite sum of linearly modulated signals. An analysis of a particular slice of the fourth-order cumulant spectra (trispectra) of this signal mixture reveals that the structure of their combined trispectrum can be modeled as a 3-dimensional tensor formed by a sum of rank 1 tensors corresponding to the trispectra of the component signals which fits the Canonical Decomposition/Parallel Factors (CP) tensor model. We develop an algorithm to decompose the trispectrum tensor which allows us to blindly estimate the power spectra, activity (in time) sequences, and number of signals contributing to an approximation of nonlinear signals. We then simulate the algorithm to verify results and quantify performance.

Many modern communications systems use Orthogonal Frequency Division Modulation (OFDM). These systems need to synchronize the receiver and equalize the channel to achieve good performance. The algorithms used to perform timing synchronization and channel estimation/equalization typically are designed without considering whether an adversarial signal could disrupt these subsystems. In typical scenarios, a jammer would not have reliable (or any) knowledge of the channels filtering the target or jamming signals. Thus, in this paper, we consider attack strategies that do not require channel knowledge. We study the efficiency of several jamming strategies targeting each subsystem as measured by the peak and average signal-to-jamming ratio (SJR) required to achieve signal denial for each method and find that jamming the timing can be substantially more efficient than other jamming strategies. We also discuss modifications to the jamming strategies that might be necessary for real-world operation.