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Telecommunication Systems
Erschienen in: Telecommunication Systems 2/2017

07.09.2016

Performance analysis of ZF receivers with imperfect CSI for uplink massive MIMO systems

verfasst von: Van-Dinh Nguyen, Oh-Soon Shin

Erschienen in: Telecommunication Systems | Ausgabe 2/2017

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Abstract

We consider the uplink of massive multiple-input multiple-output systems in a multicell environment. Since the base station (BS) estimates the channel state information (CSI) using the pilot signals transmitted from the users, each BS will have imperfect CSI in practice. Assuming zero-forcing method to eliminate the multi-user interference, we derive the exact analytical expressions for the probability density function of the signal-to-interference-plus-noise ratio, the corresponding achievable rate, the outage probability, and the symbol error rate (SER) when the BS has imperfect CSI. An upper bound of the SER is also derived for an arbitrary number of antennas at the BS. Moreover, we derive the upper bound of the achievable rate for the case where the number of antennas at the BS goes to infinity, and the analysis is verified by presenting numerical results.
Vorheriger Artikel EIAS-CP: new efficient identity-based authentication scheme with conditional privacy-preserving for VANETs
Nächster Artikel Design and simulation analysis of network-based fully distributed mobility management in flattened network architecture

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Fußnoten
1
Assume that the k-th columns \(\mathbf {h}_{i\ell ,k}\) and \(\mathbf {h}_{j\ell ,k}\) of \(\mathbf {H}_{i\ell }\) and \(\mathbf {H}_{j\ell k}\), respectively, are mutually independent \(M\times 1\) vectors, whose elements are i.i.d. random variables with zero mean and unit variance. From the law of large numbers, we have \(\frac{1}{M}\mathbf {h}_{i\ell ,k}^{\dagger }\mathbf {h}_{i\ell ,k}\mathop {\rightarrow }\limits ^{a.s}1\) and \(\frac{1}{M}\mathbf {h}_{i\ell ,k}^{\dagger }\mathbf {h}_{j\ell ,k}\mathop {\rightarrow }\limits ^{a.s}0\) as \(M\rightarrow \infty \), where \(\mathop {\rightarrow }\limits ^{a.s}\) denotes the almost sure convergence.
 
2
With \(\mathbf {h}_{i\ell ,k}\) and \(\mathbf {h}_{j\ell ,k}\) defined in (29), from Lindeberg–Levy central limit theorem, we have \(\frac{1}{\sqrt{M}}\mathbf {h}_{i\ell ,k}^{\dagger }\mathbf {h}_{j\ell ,k}\mathop {\rightarrow }\limits ^{d.}\mathcal {CN}(0,1)\) as \(M\rightarrow \infty \), where \(\mathop {\rightarrow }\limits ^{d.}\) denotes convergence in distribution.
 
3
Note that \(\alpha _{i\ell }\) and \(\hat{\mathbf {G}}_{\ell \ell }\) in (17) are estimated by \(\alpha _{i\ell }=\mathrm {tr}\bigl (\mathbb {E}[\varvec{\xi }_{i\ell }\varvec{\xi }_{i\ell }^{\dag }]\bigr )\) and (9), respectively.
 
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Metadaten
Titel
Performance analysis of ZF receivers with imperfect CSI for uplink massive MIMO systems
verfasst von
Van-Dinh Nguyen
Oh-Soon Shin
Publikationsdatum
07.09.2016
Verlag
Springer US
Erschienen in
Telecommunication Systems / Ausgabe 2/2017
Print ISSN: 1018-4864
Elektronische ISSN: 1572-9451
DOI
https://doi.org/10.1007/s11235-016-0225-8

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