74,012 research outputs found
Cost-effective aperture arrays for SKA Phase 1: single or dual-band?
An important design decision for the first phase of the Square Kilometre
Array is whether the low frequency component (SKA1-low) should be implemented
as a single or dual-band aperture array; that is, using one or two antenna
element designs to observe the 70-450 MHz frequency band. This memo uses an
elementary parametric analysis to make a quantitative, first-order cost
comparison of representative implementations of a single and dual-band system,
chosen for comparable performance characteristics. A direct comparison of the
SKA1-low station costs reveals that those costs are similar, although the
uncertainties are high. The cost impact on the broader telescope system varies:
the deployment and site preparation costs are higher for the dual-band array,
but the digital signal processing costs are higher for the single-band array.
This parametric analysis also shows that a first stage of analogue tile
beamforming, as opposed to only station-level, all-digital beamforming, has the
potential to significantly reduce the cost of the SKA1-low stations. However,
tile beamforming can limit flexibility and performance, principally in terms of
reducing accessible field of view. We examine the cost impacts in the context
of scientific performance, for which the spacing and intra-station layout of
the antenna elements are important derived parameters. We discuss the
implications of the many possible intra-station signal transport and processing
architectures and consider areas where future work could improve the accuracy
of SKA1-low costing.Comment: 64 pages, 23 figures, submitted to the SKA Memo serie
Semiparametric CRB and Slepian-Bangs formulas for Complex Elliptically Symmetric Distributions
The main aim of this paper is to extend the semiparametric inference
methodology, recently investigated for Real Elliptically Symmetric (RES)
distributions, to Complex Elliptically Symmetric (CES) distributions. The
generalization to the complex field is of fundamental importance in all
practical applications that exploit the complex representation of the acquired
data. Moreover, the CES distributions has been widely recognized as a valuable
and general model to statistically describe the non-Gaussian behaviour of
datasets originated from a wide variety of physical measurement processes. The
paper is divided in two parts. In the first part, a closed form expression of
the constrained Semiparametric Cram\'{e}r-Rao Bound (CSCRB) for the joint
estimation of complex mean vector and complex scatter matrix of a set of
CES-distributed random vectors is obtained by exploiting the so-called
\textit{Wirtinger} or -\textit{calculus}. The second part
deals with the derivation of the semiparametric version of the Slepian-Bangs
formula in the context of the CES model. Specifically, the proposed
Semiparametric Slepian-Bangs (SSB) formula provides us with a useful and
ready-to-use expression of the Semiparametric Fisher Information Matrix (SFIM)
for the estimation of a parameter vector parametrizing the complex mean and the
complex scatter matrix of a CES-distributed vector in the presence of unknown,
nuisance, density generator. Furthermore, we show how to exploit the derived
SSB formula to obtain the semiparametric counterpart of the Stochastic CRB for
Direction of Arrival (DOA) estimation under a random signal model assumption.
Simulation results are also provided to clarify the theoretical findings and to
demonstrate their usefulness in common array processing applications.Comment: Submitted to IEEE Transactions on Signal Processing. arXiv admin
note: substantial text overlap with arXiv:1807.08505, arXiv:1807.0893
Performance Bounds for Parameter Estimation under Misspecified Models: Fundamental findings and applications
Inferring information from a set of acquired data is the main objective of
any signal processing (SP) method. In particular, the common problem of
estimating the value of a vector of parameters from a set of noisy measurements
is at the core of a plethora of scientific and technological advances in the
last decades; for example, wireless communications, radar and sonar,
biomedicine, image processing, and seismology, just to name a few. Developing
an estimation algorithm often begins by assuming a statistical model for the
measured data, i.e. a probability density function (pdf) which if correct,
fully characterizes the behaviour of the collected data/measurements.
Experience with real data, however, often exposes the limitations of any
assumed data model since modelling errors at some level are always present.
Consequently, the true data model and the model assumed to derive the
estimation algorithm could differ. When this happens, the model is said to be
mismatched or misspecified. Therefore, understanding the possible performance
loss or regret that an estimation algorithm could experience under model
misspecification is of crucial importance for any SP practitioner. Further,
understanding the limits on the performance of any estimator subject to model
misspecification is of practical interest. Motivated by the widespread and
practical need to assess the performance of a mismatched estimator, the goal of
this paper is to help to bring attention to the main theoretical findings on
estimation theory, and in particular on lower bounds under model
misspecification, that have been published in the statistical and econometrical
literature in the last fifty years. Secondly, some applications are discussed
to illustrate the broad range of areas and problems to which this framework
extends, and consequently the numerous opportunities available for SP
researchers.Comment: To appear in the IEEE Signal Processing Magazin
Asymptotic Signal Detection Rates with 1-bit Array Measurements
This work considers detecting the presence of a band-limited random radio
source using an antenna array featuring a low-complexity digitization process
with single-bit output resolution. In contrast to high-resolution
analog-to-digital conversion, such a direct transformation of the analog radio
measurements to a binary representation can be implemented hardware and
energy-efficient. However, the probabilistic model of the binary receive data
becomes challenging. Therefore, we first consider the Neyman-Pearson test
within generic exponential families and derive the associated analytic
detection rate expressions. Then we use a specific replacement model for the
binary likelihood and study the achievable detection performance with 1- bit
radio array measurements. As an application, we explore the capability of a
low-complexity GPS spectrum monitoring system with different numbers of
antennas and different observation intervals. Results show that with a moderate
amount of binary sensors it is possible to reliably perform the monitoring
task
A Generalized Spatial Correlation Model for 3D MIMO Channels based on the Fourier Coefficients of Power Spectrums
Previous studies have confirmed the adverse impact of fading correlation on
the mutual information (MI) of two-dimensional (2D) multiple-input
multiple-output (MIMO) systems. More recently, the trend is to enhance the
system performance by exploiting the channel's degrees of freedom in the
elevation, which necessitates the derivation and characterization of
three-dimensional (3D) channels in the presence of spatial correlation. In this
paper, an exact closed-form expression for the Spatial Correlation Function
(SCF) is derived for 3D MIMO channels. This novel SCF is developed for a
uniform linear array of antennas with nonisotropic antenna patterns. The
proposed method resorts to the spherical harmonic expansion (SHE) of plane
waves and the trigonometric expansion of Legendre and associated Legendre
polynomials. The resulting expression depends on the underlying arbitrary
angular distributions and antenna patterns through the Fourier Series (FS)
coefficients of power azimuth and elevation spectrums. The novelty of the
proposed method lies in the SCF being valid for any 3D propagation environment.
The developed SCF determines the covariance matrices at the transmitter and the
receiver that form the Kronecker channel model. In order to quantify the
effects of correlation on the system performance, the information-theoretic
deterministic equivalents of the MI for the Kronecker model are utilized in
both mono-user and multi-user cases. Numerical results validate the proposed
analytical expressions and elucidate the dependence of the system performance
on azimuth and elevation angular spreads and antenna patterns. Some useful
insights into the behaviour of MI as a function of downtilt angles are
provided. The derived model will help evaluate the performance of correlated 3D
MIMO channels in the future.Comment: Accepted in IEEE Transactions on signal processin
Parametric channel estimation for massive MIMO
Channel state information is crucial to achieving the capacity of
multi-antenna (MIMO) wireless communication systems. It requires estimating the
channel matrix. This estimation task is studied, considering a sparse channel
model particularly suited to millimeter wave propagation, as well as a general
measurement model taking into account hybrid architectures. The contribution is
twofold. First, the Cram{\'e}r-Rao bound in this context is derived. Second,
interpretation of the Fisher Information Matrix structure allows to assess the
role of system parameters, as well as to propose asymptotically optimal and
computationally efficient estimation algorithms
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