34 research outputs found
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
On the Impact of Phase Noise on Monostatic Sensing in OFDM ISAC Systems
Phase noise (PN) can become a major bottleneck for integrated sensing and
communications (ISAC) systems towards 6G wireless networks. In this paper, we
consider an OFDM ISAC system with oscillator imperfections and investigate the
impact of PN on monostatic sensing performance by performing a misspecified
Cram\'er-Rao bound (MCRB) analysis. Simulations are carried out under a wide
variety of operating conditions with regard to SNR, oscillator type
(free-running oscillators (FROs) and phase-locked loops (PLLs)), 3-dB bandwidth
of the oscillator spectrum, PLL loop bandwidth and target range. The results
provide valuable insights on when PN leads to a significant degradation in
range and/or velocity accuracy, establishing important guidelines for hardware
and algorithm design in 6G ISAC systems
Massive MIMO is a Reality -- What is Next? Five Promising Research Directions for Antenna Arrays
Massive MIMO (multiple-input multiple-output) is no longer a "wild" or
"promising" concept for future cellular networks - in 2018 it became a reality.
Base stations (BSs) with 64 fully digital transceiver chains were commercially
deployed in several countries, the key ingredients of Massive MIMO have made it
into the 5G standard, the signal processing methods required to achieve
unprecedented spectral efficiency have been developed, and the limitation due
to pilot contamination has been resolved. Even the development of fully digital
Massive MIMO arrays for mmWave frequencies - once viewed prohibitively
complicated and costly - is well underway. In a few years, Massive MIMO with
fully digital transceivers will be a mainstream feature at both sub-6 GHz and
mmWave frequencies. In this paper, we explain how the first chapter of the
Massive MIMO research saga has come to an end, while the story has just begun.
The coming wide-scale deployment of BSs with massive antenna arrays opens the
door to a brand new world where spatial processing capabilities are
omnipresent. In addition to mobile broadband services, the antennas can be used
for other communication applications, such as low-power machine-type or
ultra-reliable communications, as well as non-communication applications such
as radar, sensing and positioning. We outline five new Massive MIMO related
research directions: Extremely large aperture arrays, Holographic Massive MIMO,
Six-dimensional positioning, Large-scale MIMO radar, and Intelligent Massive
MIMO.Comment: 20 pages, 9 figures, submitted to Digital Signal Processin
Scaling up MIMO Radar for Target Detection
This work focuses on target detection in a colocated MIMO radar system. Instead of exploiting the »classical' temporal domain, we propose to explore the spatial dimension (i.e., number of antennas M) to derive asymptotic results for the detector. Specifically, we assume no a priori knowledge of the statistics of the autoregressive data generating process and propose to use a mispecified Wald-type detector, which is shown to have an asymptotic Ï-squared distribution as M â â. Closed-form expressions for the probabilities of false alarm and detection are derived. Numerical results are used to validate the asymptotic analysis in the finite system regime. It turns out that, for the considered scenario, the asymptotic performance is closely matched already for M â„ 50
Massive MIMO radar for target detection
Since the seminal paper by Marzetta from 2010, the Massive MIMO paradigm in communication systems has changed from being a theoretical scaled-up version of MIMO, with an infinite number of antennas, to a practical technology. Its key concepts have been adopted in the 5G new radio standard and base stations, where 64 fully-digital transceivers have been commercially deployed. Motivated by these recent developments, this paper considers a co-located MIMO radar with MT transmitting and MR receiving antennas and explores the potential benefits of having a large number of virtual spatial antenna channels N=MTMR. Particularly, we focus on the target detection problem and develop a robust Wald-type test that guarantees certain detection performance, regardless of the unknown statistical characterization of the disturbance. Closed-form expressions for the probabilities of false alarm and detection are derived for the asymptotic regime Nââ. Numerical results are used to validate the asymptotic analysis in the finite system regime with different disturbance models. Our results imply that there always exists a sufficient number of antennas for which the performance requirements are satisfied, without any a-priori knowledge of the disturbance statistics. This is referred to as the Massive MIMO regime of the radar system
Non-Bayesian Post-Model-Selection Estimation as Estimation Under Model Misspecification
In many parameter estimation problems, the exact model is unknown and is
assumed to belong to a set of candidate models. In such cases, a predetermined
data-based selection rule selects a parametric model from a set of candidates
before the parameter estimation. The existing framework for estimation under
model misspecification does not account for the selection process that led to
the misspecified model. Moreover, in post-model-selection estimation, there are
multiple candidate models chosen based on the observations, making the
interpretation of the assumed model in the misspecified setting non-trivial. In
this work, we present three interpretations to address the problem of
non-Bayesian post-model-selection estimation as an estimation under model
misspecification problem: the naive interpretation, the normalized
interpretation, and the selective inference interpretation, and discuss their
properties. For each of these interpretations, we developed the corresponding
misspecified maximum likelihood estimator and the misspecified
Cramr-Rao-type lower bound. The relations between the
estimators and the performance bounds, as well as their properties, are
discussed. Finally, we demonstrate the performance of the proposed estimators
and bounds via simulations of estimation after channel selection. We show that
the proposed performance bounds are more informative than the oracle
Cramr-Rao Bound (CRB), where the third interpretation
(selective inference) results in the lowest mean-squared-error (MSE) among the
estimators.Comment: This work has been submitted to the IEEE for possible publication.
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Massive MIMO is a reality - What is next? Five promising research directions for antenna arrays
Massive MIMO (multiple-input multiple-output) is no longer a âwildâ or âpromisingâ concept for future cellular networksâin 2018 it became a reality. Base stations (BSs) with 64 fully digital transceiver chains were commercially deployed in several countries, the key ingredients of Massive MIMO have made it into the 5G standard, the signal processing methods required to achieve unprecedented spectral efficiency have been developed, and the limitation due to pilot contamination has been resolved. Even the development of fully digital Massive MIMO arrays for mmWave frequenciesâonce viewed prohibitively complicated and costlyâis well underway. In a few years, Massive MIMO with fully digital transceivers will be a mainstream feature at both sub-6 GHz and mmWave frequencies. In this paper, we explain how the first chapter of the Massive MIMO research saga has come to an end, while the story has just begun. The coming wide-scale deployment of BSs with massive antenna arrays opens the door to a brand new world where spatial processing capabilities are omnipresent. In addition to mobile broadband services, the antennas can be used for other communication applications, such as low-power machine-type or ultra-reliable communications, as well as non-communication applications such as radar, sensing and positioning. We outline five new Massive MIMO related research directions: Extremely large aperture arrays, Holographic Massive MIMO, Six-dimensional positioning, Large-scale MIMO radar, and Intelligent Massive MIMO
An Approximate MSE Expression for Maximum Likelihood and Other Implicitly Defined Estimators of Non-Random Parameters (extended version)
An approximate mean square error (MSE) expression for the performance
analysis of implicitly defined estimators of non-random parameters is proposed.
An implicitly defined estimator (IDE) declares the minimizer/maximizer of a
selected cost/reward function as the parameter estimate. The maximum likelihood
(ML) and the least squares estimators are among the well known examples of this
class. In this paper, an exact MSE expression for implicitly defined estimators
with a symmetric and unimodal objective function is given. It is shown that the
expression reduces to the Cramer-Rao lower bound (CRLB) and misspecified CRLB
in the large sample size regime for ML and misspecified ML estimation,
respectively. The expression is shown to yield the Ziv-Zakai bound (without the
valley filling function) when it is used in a Bayesian setting, that is, when
an a-priori distribution is assigned to the unknown parameter. In addition,
extension of the suggested expression to the case of nuisance parameters is
studied and some approximations are given to ease the computations for this
case. Numerical results indicate that the suggested MSE expression not only
predicts the estimator performance in the asymptotic region; but it is also
applicable for the threshold region analysis, even for IDEs whose objective
functions do not satisfy the symmetry and unimodality assumptions. Advantages
of the suggested MSE expression are its conceptual simplicity and its
relatively straightforward numerical calculation due to the reduction of the
estimation problem to a binary hypothesis testing problem, similar to the usage
of Ziv-Zakai bounds in random parameter estimation problems