The Cramér-Rao bound (CRB), a well-known lower on the performance of any unbiased parameter estimator, has been used to study wide variety problems. However, obtain CRB, requires an analytical expression for likelihood measurements given parameters, or equivalently precise and explicit statistical model data. In many applications, such is not available. Instead, this work introduces novel appro...

Despite an increased interest in complex independent component analysis (ICA) during the last two decades, a closed form expression for the Cramér-Rao bound (CRB) for the demixing matrix is not known yet. In this paper, we fill this gap by deriving a closed-form expression for the CRB of the demixing matrix for instantaneous noncircular complex ICA. It contains the CRB for circular complex ICA ...

In many practical parameter estimation problems, such as coefficient of polynomial regression, the true model is unknown and thus, a selection step performed prior to estimation. The data-based affects subsequent particular, oracle Cramér-Rao bound (CRB), which based on knowledge model, inappropriate for post-model-selection performance analysis system design outside asymptotic region. this pap...

We consider the problem of sampling clock synchronization and channel estimation for Orthogonal Frequency Division Multiplex (OFDM) systems. In such systems, when the number of subcarriers is large, a sampling clock frequency mismatch between the transmitter and the receiver dramatically degrades the performance. So far, the literature proposes ad-hoc estimation algorithms. However, a complete ...

In this paper, we derive the Cramér-Rao bound (CRB) for blind channel estimation in redundant block transmission systems, a lower bound for the mean squared error of any blind channel estimators. The derived CRB is valid for any full-rank linear redundant precoder, including both zero-padded (ZP) and cyclic-prefixed (CP) precoders. A simple form of CRBs for multiple complex parameters is also d...

These review notes serve as a guide for myself to some bounds of interest in the estimation theory and learning theory, including Cramér-Rao Bound (CRB), concentration inequalities, Vapnic-Chervonenkis (VC) theory, probably approximately correct (PAC) learning, and the Johnson-Lindenstrauss (JL) lemma.

In an orthogonal-frequency-division multiplex (OFDM) system, the problem of sampling clock synchronization and channel estimation is analyzed. In such systems, when the number of sub-carriers is large, a sampling clock frequency mismatch between the transmitter and the receiver dramatically degrades the performance. Obviously, the channel-impulse response is unknown at the receiver and also nee...

A Cramer-Rao bound (CRB) study is developed in onedimensional (1D) space which sheds fundamental insight onto the information about multiply scattering point-like scatterers that is contained in scattering field data corresponding to transmissive, reflective, and combined transmissive plus reflective sensing geometries, and singleand multi-frequency measurements.

In this paper, we analyze the impact of compression with complex random matrices on Fisher information and the Cramér-Rao Bound (CRB) for estimating unknown parameters in the mean value function of a complex multivariate normal distribution. We consider the class of random compression matrices whose distribution is right-unitarily invariant. The compression matrix whose elements are i.i.d. stan...

Direction-of-arrival (DOA) estimation is one of the most demanding tasks for millimeter wave (mmWave) communication massive multiple-input multiple-output (MIMO) systems with hybrid beamforming (HBF) architecture. In this paper, we focus on optimization HBF matrix receiving pilots to enhance DOA performance. Motivated by fact that many existing algorithms can achieve Cram\'{e}r-Rao bound (CRB),...