Let W1 and W2 be independent n×n complex central Wishart matrices with m1 and m2 degrees of freedom respectively. This paper is concerned with the extreme eigenvalue distributions of double-Wishart ...matrices (W1+W2)−1W1, which are analogous to those of F matrices W1W2−1 and those of the Jacobi unitary ensemble (JUE). Defining α1=m1−n and α2=m2−n with m1, m2≥n, we derive new exact distribution formulas in terms of (α1+α2)-dimensional matrix determinants, with entries involving derivatives of Legendre polynomials. This provides a convenient exact representation, while facilitating a direct large-n analysis with α1 and α2 fixed (i.e., under the so-called “hard-edge” scaling limit). The analysis is based on new asymptotic properties of Legendre polynomials and their relation with Bessel functions that are here established. Specifically, we present limiting formulas for the smallest and largest eigenvalue distributions as n→∞ in terms of α1- and α2-dimensional determinants respectively, which agrees with expectations from known universality results involving the JUE and the Laguerre unitary ensemble (LUE). We also derive finite-n corrections for the asymptotic extreme eigenvalue distributions under hard-edge scaling, giving new insights on universality by comparing with corresponding correction terms derived recently for the LUE. Our derivations are based on elementary algebraic manipulations and properties of Legendre polynomials, differing from existing results on double-Wishart and related models which often involve Fredholm determinants, Painlevé differential equations, or hypergeometric functions of matrix arguments.
Wireless sensor networks deployed within metallic cavities are known to suffer from a very severe fading, even in strong line-of-sight propagation conditions. This behavior is well-captured by the ...Two-Wave with Diffuse Power (TWDP) fading distribution, which shows great fit to field measurements in such scenarios. In this paper, we address the joint estimation of the parameters K and Δ that characterize the TWDP fading model, based on the observation of the received signal envelope. We use a moment-based approach to derive closed-form expressions for the estimators of K and Δ, as well as closed-form expressions for their asymptotic variance. Results show that the estimation error is close to the Cramer-Rao lower bound for a wide range of values of the parameters K and Δ. The performance degradation due to a finite number of observations is also analyzed.
This paper shows that the recently proposed ι -μ shadowed fading model includes, besides the ι -μ model, the η-μ fading model as a particular case. This has important relevance in practice, as it ...allows for the unification of these popular fading distributions through a more general, yet equally tractable, model. The convenience of new underlying physical models is discussed. Then, we derive simple and novel closed-form expressions for the asymptotic ergodic capacity in ι -μ shadowed fading channels, which illustrate the effects of the different fading parameters on the system performance. By exploiting the unification here unveiled, the asymptotic capacity expressions for the ι -μ, η-μ, and Rician shadowed fading models are also obtained in closed form as special cases.
A frequency locked loop (FLL) for phase noise reduction of wideband voltage controlled oscillators is proposed. The key building block of the system is a low noise (−160 dBV/Hz) and high sensitivity ...(22 V/GHz) delay line frequency discriminator with 5–8 GHz coverage, which makes use of a high performance multilayer hybrid. The authors derive closed-form, universal design equations for the maximum noise reduction and stability of the FLL circuitry. Application of the proposed technique to a state-of-the-art voltage controlled oscillator operating in the 5–8 GHz band yields a phase noise reduction of 8–10 dB at 100 kHz and 5 dB at 1 MHz off the carrier, which shows the results are in good agreement with the simulated results; so phase noise better than −107 dBc/Hz at 100 kHz and better than −123.5 dBc/Hz at 1 MHz is obtained.
This paper is concerned with the largest eigenvalue of the Wishart-type random matrix <inline-formula> <tex-math notation="LaTeX">\mathbf {{W}}=\mathbf {{X}}\mathbf ...{{X}}^\dagger</tex-math></inline-formula> (or <inline-formula><tex-math notation="LaTeX">\mathbf {{W}}=\mathbf {{X}}^\dagger \mathbf {{X}}</tex-math> </inline-formula>), where <inline-formula><tex-math notation="LaTeX">\mathbf {{X}}</tex-math></inline-formula> is a complex Gaussian matrix with unequal variances in the real and imaginary parts of its entries, i.e., <inline-formula> <tex-math notation="LaTeX">\mathbf {X}</tex-math></inline-formula> belongs to the noncircularly symmetric Gaussian subclass. By establishing a novel connection with the well-known complex Wishart ensemble, we here derive exact and asymptotic expressions for the largest eigenvalue distribution of <inline-formula><tex-math notation="LaTeX">\mathbf {{W}}</tex-math></inline-formula>, which provide new insights on the effect of the real-imaginary variance imbalance of the entries of <inline-formula><tex-math notation="LaTeX">\mathbf {X}</tex-math></inline-formula>. These new results are then leveraged to analyze the outage performance of multiantenna systems with maximal ratio combining subject to Nakagami-<inline-formula><tex-math notation="LaTeX">q</tex-math></inline-formula> (Hoyt) fading.
This paper proposes a novel approach to the statistical characterization of non-central complex Gaussian quadratic forms (CGQFs). Its key strategy is the generation of an auxiliary random variable ...that replaces the original CGQF and converges in distribution to it. This technique is valid for both definite and indefinite CGQFs and yields simple expressions of the probability density function (PDF) and the cumulative distribution function (CDF) that only involve elementary functions. This overcomes a major limitation of previous approaches, where the complexity of the resulting PDF and CDF does not allow for further analytical derivations. Additionally, the mean square error between the original CGQF and the auxiliary one is provided in a simple closed-form formulation. These new results are then leveraged to analyze the outage probability and the average bit error rate of maximal ratio combining systems over correlated Rician channels.
A Tractable Product Channel Model for Line-of-Sight Scenarios Fernandez-Plazaola, Unai; Moreno-Pozas, Laureano; Lopez-Martinez, F. Javier ...
IEEE transactions on wireless communications,
2020-March, 2020-3-00, 20200301, Letnik:
19, Številka:
3
Journal Article
Recenzirano
Odprti dostop
We present a general and tractable fading model for line-of-sight (LOS) scenarios, which is based on the product of two independent and non-identically distributed κ-μ shadowed power envelopes. ...Simple closed-form expressions for the probability density function, cumulative distribution function and moment-generating function are derived, which are as tractable as the corresponding expressions derived from a product of Nakagami-m random variables. This model simplifies the challenging characterization of LOS product channels, as well as combinations of LOS channels with non-LOS ones. We leverage these results to analyze performance measures of interest in the contexts of wireless powered and backscatter communications, where both forward and reverse links are inherently of LOS nature, as well as in device-to-device communications subject to composite fading. In these contexts, the proposed model shows a higher flexibility when fitting field measurements with respect to conventional approaches based on product distributions with deterministic LOS, together with a more complete physical interpretation of the underlying propagation characteristics.
In this paper, a novel frequency-locked loop (FLL) architecture for phase-noise reduction of wideband voltage-controlled oscillators (VCO) is presented. The circuit makes use of a phase-shifterless ...frequency discriminator, which completely avoids the use of any control circuitry to keep the loop in its quadrature condition, highly simplifying the loop. The FLL circuit, which can be operated in a completely transparent way, can be easily interchangeable with the original VCO. An FLL prototype, based on a commercial state-of-the-art VCO, has been fabricated and measured exhibiting a phase-noise reduction higher than 9 and 5.5 dB up to 100-kHz and 1-MHz offset from carrier, respectively, in the complete 4.6-9-GHz band. Absolute phase noise results of -106.5 and -124 dBc/Hz at 100-kHz and 1-MHz offset from carrier have been obtained, showing lower phase noise than other wideband FLLs in the literature.
We provide some comments and subsequent corrections to a paper recently published in this Journal (see ibid., vol. 33, no. 1, pp. 111-119, Jan. 2015). More precisely, we show that the pdf for the κ-μ ...shadowed fading model given by S.L. Cotton cannot be obtained from the underlying statistical model proposed therein. To support this observation, we present a detailed mathematical analysis as well as some Monte Carlo simulations. We also demonstrate that by simply adopting the underlying statistical model for the κ-μ shadowed fading distribution proposed in an earlier and independent work by J.F. Paris enables the κ-μ shadowed pdf later presented by S.L. Cotton to be obtained.
This paper shows that the proposed Rician shadowed model for multi-antenna communications allows for the unification of a wide set of models, both for multiple-input multiple-output (MIMO) and ...single- input single-output (SISO) communications. The MIMO Rayleigh and MIMO Rician can be deduced from the MIMO Rician shadowed, and so their SISO counterparts. Other more general SISO models, besides the Rician shadowed, are included in the model, such as the κ-μ, and its recent generalization, the κ-μ shadowed model. Moreover, the SISO η-μ and Nakagami-q models are also included in the MIMO Rician shadowed model. The literature already presents the probability density function (pdf) of the Rician shadowed Gram channel matrix in terms of the well-known gamma- Wishart distribution. We here derive its moment generating function in a tractable form. Closed- form expressions for the cumulative distribution function and the pdf of the maximum eigenvalue are also carried out.
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