Power-law shot noise and its relationship to long-memoryα-stable processes

We consider the shot noise process, whose associated impulse response is a decaying power-law kernel of the form t^β/2-1 . We show that this power-law Poisson model gives rise to a process that, at each time instant, is an α-stable random variable if β<1. We show that although the process is not α-stable, pairs of its samples become jointly α-stable as the distance between them tends to infinity. It is known that for the case β>1, the power-law Poisson process has a power-law spectrum. We show that, although in the case β<1 the power spectrum does not exist, the process still exhibits long memory in a generalized sense. The power-law shot noise process appears in many applications in engineering and physics. The proposed results can be used to study such processes as well as to synthesize a random process with long-range dependence     

Blind two-input-two-output FIR channel identification based onfrequency domain second-order statistics

We present an analytical solution to the two-input-two-output blind crosswise mixture identification based on eigenvalue decomposition of second-order spectra correlations. The sources are independent and non-white, but otherwise, we consider their statistics to be unknown. We show that the cross channels cannot be uniquely determined by the analysis of the frequency domain covariance alone due to the unknown eigenvector permutations. However, the problem can be attacked with the help of two invariant indices that are immune to these permutations. Using these indices together with standard reconstruction-from-phase techniques, we show that the channels can be uniquely determined. Our theoretical results lead to a novel frequency domain second-order algorithm that identifies the unknown channels     

System reconstruction from higher order spectra slices

We consider the problem of system reconstruction from higher order spectra (HOS) slices. We establish that the impulse response of a complex system can be reconstructed up to a scalar and a shift based on any pair of HOS slices, as long as the distance between the two slices satisfies a certain condition. One slice is sufficient for the reconstruction in the case of a real system. We propose a cepstrum-based method for system reconstruction. We also propose a new method for the reconstruction of the system Fourier phase based on the phase of any odd-indexed bispectrum slice. Being able to choose the slices to be used in the reconstruction allows us to avoid bispectrum regions dominated by noise     

Extending network lifetime for ALLIANCES

ALLIANCES is a newly proposed wireless MAC protocol that exploits the cooperation of source nodes and relay nodes to resolve collisions and further improve throughput. Until now, ALLIANCES did not consider energy, which is the most precious commodity of mobile communications. In this paper, we propose an energy-conserving version of ALLIANCES that introduces a sleep state. Our analytical results show that the energy-conserving model can save at least 54% of energy consumption when compared to the original energy model (referred to as the basic energy model in this paper). Because a relay selection scheme is a significant piece of ALLIANCES, directly affecting the throughput and the energy distribution, we also propose an energy-aware relay selection scheme (ERS). ERS maintains the performance benefits of the previously proposed location relay selection scheme (LRS), but more evenly distributes the amount of energy remaining throughout the network. We implement our energy-conserving model and ERS in the popular network simulator (NS-2) to evaluate and compare the energy remaining at each node and the network’s throughput when using LRS and ERS. Simulation results show that the energy-conserving model can save up to 80% of energy without nodes taking longer to communicate. In addition, using the energy-conserving model, ERS provides 23.3% longer lifetime of the network than LRS, without noticeable throughput degradation.     

MIMO Radar Using Compressive Sampling

A multiple-input multiple-output (MIMO) radar system is proposed for obtaining angle and Doppler information on potential targets. Transmitters and receivers are nodes of a small scale wireless network and are assumed to be randomly scattered on a disk. The transmit nodes transmit uncorrelated waveforms. Each receive node applies compressive sampling to the received signal to obtain a small number of samples, which the node subsequently forwards to a fusion center. Assuming that the targets are sparsely located in the angle-Doppler space, based on the samples forwarded by the receive nodes the fusion center formulates an $ell_{1}$ -optimization problem, the solution of which yields target angle and Doppler information. The proposed approach achieves the superior resolution of MIMO radar with far fewer samples than required by other approaches. This implies power savings during the communication phase between the receive nodes and the fusion center. Performance in the presence of a jammer is analyzed for the case of slowly moving targets. Issues related to forming the basis matrix that spans the angle-Doppler space, and for selecting a grid for that space are discussed. Extensive simulation results are provided to demonstrate the performance of the proposed approach at difference jammer and noise levels.      

Blind channel estimation using fractional sampling

We consider the problem of blind estimation of a communication channel based on the oversampled channel output. We propose a nonparametric approach that, based on the cyclic spectrum of the output, finds the channel phase response without neither the need of phase unwrapping nor channel length information. For band-limited channels, the cyclic spectrum has limited support. For this case, we propose an approximation for the discretized phase of the cyclic spectrum that, under certain conditions, results in a simpler channel estimation method. The proposed approach is applied to simulated data and real recordings and is compared to existing methods.     

Blind MIMO FIR channel identification based on second-order spectra correlations

We consider a problem of identifying a multiple-input multiple-output (MIMO) finite impulse response (FIR) system excited by colored inputs with known statistics. We propose a new, nonlinear optimization-based method that involves the power spectra and cross-spectra of the system output. The proposed algorithm is tested for the case of cyclostationary inputs (CDMA scenario) and stationary inputs (SDMA scenario). Simulation results indicate that the proposed scheme works well, even for large order systems, and is robust to noise and channel length mismatch.     

Cross-spectrum based blind channel identification

A novel cross-correlation based framework is proposed for the problem of blind equalization in communications. We assume that we have access to two observations obtained either by sampling, at the symbol rate, the outputs of two sensors or by oversampling, by a factor of two, the output of a single sensor. In either case, the two observations correspond to the outputs of two channels excited by the same input. The channels are estimated using the theory of signal reconstruction from phase only. The phase used is the phase of the cross spectrum of the observations filtered through their minimum phase equivalent filters. We provide an analytical study of the propagation of noise effects in the phase estimate. Comparisons with existing methods indicate that the proposed approach is robust to noise and, at low signal-to-noise ratio (SNR), leads to significantly smaller channel estimation errors. Besides robustness to noise, the proposed method does not require knowledge of channel lengths, which are determined via an iterative procedure     

On modeling biomedical ultrasound RF echoes using a power-law shot-noise model

We propose a new model for the RF ultrasound echo, namely the power-law shot-noise process. Based on this model, the in-phase and quadrature components of the echo are shown to exhibit 1/f^β -type spectral behavior, in a sense that is defined in the paper. The envelope also exhibits this type of spectral behavior, but with a different exponent. This result explains the experimental observations by other researchers of the power-law trend of the RF echo spectrum. Although the shot-noise model has been used in the past for modeling the RF echo, this is the first time that a power-law impulse response filter is used and that the resulting 1/f^β-type spectral behavior of the RF echo has been investigated. The model parameters are linked to tissue characteristics, such as scatterer density and attenuation; thus, they have the potential to be used as tissue characterization features. The validity of the proposed model is tested based on a database of 100 clinical ultrasound images of the breast