Performance of multiuser TAS/MRC-MIMO systems over Rayleigh fading channels with exponential correlation

Subadar, Rupaban; Mudoi, Rajkishur

doi:10.1109/edcav.2015.7060560

Cited by 2 publications

(1 citation statement)

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“…Also, the correlation matrix R is assumed to be exponential, i.e. (R) i,j = ρ |i−j| with |ρ| < 1 [37][38][39]. A thorough study has been performed by considering multiple combinations of ρ, k and the number of branches, P , which are varied over a large range of SNR.…”

Section: Numerical Resultsmentioning

confidence: 99%

A New Approach to the Statistical Analysis of Non-Central Complex Gaussian Quadratic Forms With Applications

Ramírez-Espinosa

Moreno-Pozas

Paris

et al. 2019

IEEE Trans. Veh. Technol.

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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 (RV) that replaces the original CGQF and converges in distribution to it. The 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 3 or equivalently, the characteristic function, to obtain an approximation of the PDF of CGQFs [13][14][15]. Some works apply different series expansions to the characteristic function to allow such inversion [13,14], while the work by Biyari and Lindsey considers a specific non-central CGQF and inverts its MGF by solving some convolution integrals [15]. All these works present approximations for the PDF of non-central CGQFs in terms of double infinite sum of special functions. In particular, the PDF of positive-definite non-central CGQFs is given in terms of a double infinite sum of modified Bessel functions in [13], while the PDF of indefinite non-central CGQFs is expressed in terms of a double infinite sum of incomplete gamma functions [14] and of a double infinite sum of Laguerre polynomials [15]. Taking into account the limitations of direct inversion methods, since the solutions provided for the PDF and the CDF of non-central CGQFs are difficult to compute and not suitable for any further insightful analysis, very recently, Al-Naffouri et al. presented a different approach. They applied a transformation to the inequality that defines the CDF of non-central CGQFs, yielding a problem in which the well-known saddle point technique allows expressing the CDF as the solution of a differential equation [10].This paper proposes a completely different approach to the statistical analysis of indefinite noncentral CGQFs, which leads to simple expressions that approximate both the PDF and CDF of CGQFs. It is based on appropriately perturbing the non-zero mean components of the Gaussian vectors that build the quadratic form. This yields an auxiliary CGQF, denoted as confluent CGQF, which converges in distribution to the original quadratic form and whose analysis is surprisingly simpler. Specifically, this novel approach offers the following advantages over the recently proposed work in [10] and the other approaches given in the literature [13][14][15]:• The probability functions, namely PDF and CDF, are given as a linear combination of elementary functions (exponentials and powers) in a very tractable form.• Simple closed-form expression for the mean squared error (MSE) between the CGQF and the auxiliary one is provided, allowing the particularization of the auxiliary variable in order

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Section: Numerical Resultsmentioning

confidence: 99%