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Performance Analysis of a Reduced Rank Spatial Filter for Interference Cancellation

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Abstract

In the interference mitigation context, it has been shown by simulations in Fety et al. (International symposium on wireless communication systems, pp 241–245,2012), the outperformance of the coefficient constraints (CC) versus the power constraint on the channel impulse response, in terms of BER about 1–3 dB. However, no theoretical justification has been introduced. In this paper, we have proved theoretically this result. Moreover, we have investigated an interesting issue of the CC constraint concerning the choice of the coefficient position; we have given a full theoretical framework analysis about this feature. Two substantial propositions have been introduced to this end. Theoretical results were validated by simulations.

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Author information

Authors and Affiliations

  1. Lab. Cedric/Laetitia Cnam, 292 Rue Saint Martin, 75141, Paris Cedex 03, France

    Rabah Maoudj, Ali Dziri & Michel Terre

Authors
  1. Rabah Maoudj

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  2. Ali Dziri

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  3. Michel Terre

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Corresponding author

Correspondence toAli Dziri.

Appendix

Appendix

Equation (27) can be rewritten as,

$$ \hbox{min}_{a} Ra^{2} \backslash a\left( i \right) = 1,\quad 2L < i \le N $$

Define the sub matrix\( \varvec{R}_{i} \in C^{N \times N - 1} \) as the matrixR except theith column vector, the vector\( - \varvec{r}_{i} \in C^{N \times 1} \) theith column vector ofR andai isa vector without the theith component. Therefore,

$$ \varvec{Ra} = \varvec{R}_{i} \varvec{a}_{i} - \varvec{r}_{i} $$

Then the last equation becomes,

$$ \hbox{min}_{{a_{i} }} \left( {R_{i} a_{i} - r_{i} } \right)^{H} \left( {R_{i} a_{i} - r_{i} } \right) $$

By nulling the first derivation with respect toai, thenai is solution of the following linear system,

$$ a_{i} = \arg_{{a_{i} }} R_{i}^{H} R_{i} a_{di} - R_{i}^{H} r_{i} = 0 $$

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Maoudj, R., Dziri, A. & Terre, M. Performance Analysis of a Reduced Rank Spatial Filter for Interference Cancellation.Wireless Pers Commun85, 1635–1651 (2015). https://doi.org/10.1007/s11277-015-2859-3

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