235 research outputs found
Novel Complex Adaptive Signal Processing Techniques Employing Optimally Derived Time-varying Convergence Factors With Applicatio
In digital signal processing in general, and wireless communications in particular, the increased usage of complex signal representations, and spectrally efficient complex modulation schemes such as QPSK and QAM has necessitated the need for efficient and fast-converging complex digital signal processing techniques. In this research, novel complex adaptive digital signal processing techniques are presented, which derive optimal convergence factors or step sizes for adjusting the adaptive system coefficients at each iteration. In addition, the real and imaginary components of the complex signal and complex adaptive filter coefficients are treated as separate entities, and are independently updated. As a result, the developed methods efficiently utilize the degrees of freedom of the adaptive system, thereby exhibiting improved convergence characteristics, even in dynamic environments. In wireless communications, acceptable co-channel, adjacent channel, and image interference rejection is often one of the most critical requirements for a receiver. In this regard, the fixed-point complex Independent Component Analysis (ICA) algorithm, called Complex FastICA, has been previously applied to realize digital blind interference suppression in stationary or slow fading environments. However, under dynamic flat fading channel conditions frequently encountered in practice, the performance of the Complex FastICA is significantly degraded. In this dissertation, novel complex block adaptive ICA algorithms employing optimal convergence factors are presented, which exhibit superior convergence speed and accuracy in time-varying flat fading channels, as compared to the Complex FastICA algorithm. The proposed algorithms are called Complex IA-ICA, Complex OBA-ICA, and Complex CBC-ICA. For adaptive filtering applications, the Complex Least Mean Square algorithm (Complex LMS) has been widely used in both block and sequential form, due to its computational simplicity. However, the main drawback of the Complex LMS algorithm is its slow convergence and dependence on the choice of the convergence factor. In this research, novel block and sequential based algorithms for complex adaptive digital filtering are presented, which overcome the inherent limitations of the existing Complex LMS. The block adaptive algorithms are called Complex OBA-LMS and Complex OBAI-LMS, and their sequential versions are named Complex HA-LMS and Complex IA-LMS, respectively. The performance of the developed techniques is tested in various adaptive filtering applications, such as channel estimation, and adaptive beamforming. The combination of Orthogonal Frequency Division Multiplexing (OFDM) and the Multiple-Input-Multiple-Output (MIMO) technique is being increasingly employed for broadband wireless systems operating in frequency selective channels. However, MIMO-OFDM systems are extremely sensitive to Intercarrier Interference (ICI), caused by Carrier Frequency Offset (CFO) between local oscillators in the transmitter and the receiver. This results in crosstalk between the various OFDM subcarriers resulting in severe deterioration in performance. In order to mitigate this problem, the previously proposed Complex OBA-ICA algorithm is employed to recover user signals in the presence of ICI and channel induced mixing. The effectiveness of the Complex OBA-ICA method in performing ICI mitigation and signal separation is tested for various values of CFO, rate of channel variation, and Signal to Noise Ratio (SNR)
Towards Unified All-Neural Beamforming for Time and Frequency Domain Speech Separation
Recently, frequency domain all-neural beamforming methods have achieved
remarkable progress for multichannel speech separation. In parallel, the
integration of time domain network structure and beamforming also gains
significant attention. This study proposes a novel all-neural beamforming
method in time domain and makes an attempt to unify the all-neural beamforming
pipelines for time domain and frequency domain multichannel speech separation.
The proposed model consists of two modules: separation and beamforming. Both
modules perform temporal-spectral-spatial modeling and are trained from
end-to-end using a joint loss function. The novelty of this study lies in two
folds. Firstly, a time domain directional feature conditioned on the direction
of the target speaker is proposed, which can be jointly optimized within the
time domain architecture to enhance target signal estimation. Secondly, an
all-neural beamforming network in time domain is designed to refine the
pre-separated results. This module features with parametric time-variant
beamforming coefficient estimation, without explicitly following the derivation
of optimal filters that may lead to an upper bound. The proposed method is
evaluated on simulated reverberant overlapped speech data derived from the
AISHELL-1 corpus. Experimental results demonstrate significant performance
improvements over frequency domain state-of-the-arts, ideal magnitude masks and
existing time domain neural beamforming methods
Efficient Covariance Matrix Reconstruction with Iterative Spatial Spectrum Sampling
This work presents a cost-effective technique for designing robust adaptive
beamforming algorithms based on efficient covariance matrix reconstruction with
iterative spatial power spectrum (CMR-ISPS). The proposed CMR-ISPS approach
reconstructs the interference-plus-noise covariance (INC) matrix based on a
simplified maximum entropy power spectral density function that can be used to
shape the directional response of the beamformer. Firstly, we estimate the
directions of arrival (DoAs) of the interfering sources with the available
snapshots. We then develop an algorithm to reconstruct the INC matrix using a
weighted sum of outer products of steering vectors whose coefficients can be
estimated in the vicinity of the DoAs of the interferences which lie in a small
angular sector. We also devise a cost-effective adaptive algorithm based on
conjugate gradient techniques to update the beamforming weights and a method to
obtain estimates of the signal of interest (SOI) steering vector from the
spatial power spectrum. The proposed CMR-ISPS beamformer can suppress
interferers close to the direction of the SOI by producing notches in the
directional response of the array with sufficient depths. Simulation results
are provided to confirm the validity of the proposed method and make a
comparison to existing approachesComment: 14 pages, 8 figure
Communications-Inspired Projection Design with Application to Compressive Sensing
We consider the recovery of an underlying signal x \in C^m based on
projection measurements of the form y=Mx+w, where y \in C^l and w is
measurement noise; we are interested in the case l < m. It is assumed that the
signal model p(x) is known, and w CN(w;0,S_w), for known S_W. The objective is
to design a projection matrix M \in C^(l x m) to maximize key
information-theoretic quantities with operational significance, including the
mutual information between the signal and the projections I(x;y) or the Renyi
entropy of the projections h_a(y) (Shannon entropy is a special case). By
capitalizing on explicit characterizations of the gradients of the information
measures with respect to the projections matrix, where we also partially extend
the well-known results of Palomar and Verdu from the mutual information to the
Renyi entropy domain, we unveil the key operations carried out by the optimal
projections designs: mode exposure and mode alignment. Experiments are
considered for the case of compressive sensing (CS) applied to imagery. In this
context, we provide a demonstration of the performance improvement possible
through the application of the novel projection designs in relation to
conventional ones, as well as justification for a fast online projections
design method with which state-of-the-art adaptive CS signal recovery is
achieved.Comment: 25 pages, 7 figures, parts of material published in IEEE ICASSP 2012,
submitted to SIIM
Implicit differentiation of variational quantum algorithms
Several quantities important in condensed matter physics, quantum
information, and quantum chemistry, as well as quantities required in
meta-optimization of machine learning algorithms, can be expressed as gradients
of implicitly defined functions of the parameters characterizing the system.
Here, we show how to leverage implicit differentiation for gradient computation
through variational quantum algorithms and explore applications in condensed
matter physics, quantum machine learning, and quantum information. A function
defined implicitly as the solution of a quantum algorithm, e.g., a
variationally obtained ground- or steady-state, can be automatically
differentiated using implicit differentiation while being agnostic to how the
solution is computed. We apply this notion to the evaluation of physical
quantities in condensed matter physics such as generalized susceptibilities
studied through a variational quantum algorithm. Moreover, we develop two
additional applications of implicit differentiation -- hyperparameter
optimization in a quantum machine learning algorithm, and the variational
construction of entangled quantum states based on a gradient-based maximization
of a geometric measure of entanglement. Our work ties together several types of
gradient calculations that can be computed using variational quantum circuits
in a general way without relying on tedious analytic derivations, or
approximate finite-difference methods.Comment: 13 pages, 8 figures. The code and data for the article is available
at https://github.com/quantshah/quantum-implicit-differentiatio
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