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Table 1 Distribution of variables for the considered channel model

From: Spatial modulation based on reconfigurable antennas: performance evaluation by using the prototype of a reconfigurable antenna

Variable Distribution PDF Range
β k Gaussian CN(0,1) \((-\infty,\infty)\)
θ k Truncated Laplacian [22] \(f_{\theta }(\theta) = C_{L} \exp \left (-\frac {\sqrt {2}\mid \theta - \theta _{0}\mid }{\sigma _{L}} \right) \sin (\theta)\),  
   \(C_{L} =\times \frac {2+{\sigma ^{2}_{L}}}{2\sqrt {2}\sigma _{L}\sin (\theta _{0}) + 2{\sigma ^{2}_{L}}\exp \left (-\frac {\pi }{\sqrt {2}\sigma _{L}}\right)\cosh \left (\frac {\sqrt {2}(\frac {\pi }{2}-\theta _{0})}{\sigma _{L}}\right)}\) (0,π]
ϕ k Von-Mises [22] \(f_{\phi }(\phi) = \frac {\exp (\kappa \cos (\phi -\mu))}{2\pi I_{0}(\kappa)}\) (−π,π]
  Truncated Gaussian [23] \({f_{\phi } }(\phi) = {C_{G}}\exp \left ({ - {{\left ({\frac {{\phi,- {\phi _{0}}}}{{\sqrt 2 {\sigma _{G}}}}} \right)}^{2}}} \right)\)  
   \({C_{G}} = \frac {1}{{\sqrt {2\pi } {\sigma _{G}} {\Phi \left ({\frac {{\pi }}{{{\sigma _{G}}}}} \right)} }},\Phi (x) = \frac {1}{2}\left ({1 + {\text {erf}} (x/\sqrt 2)} \right)\)  
  Uniform [23] \(\phantom {\dot {i}\!}{f_{\phi }}({\phi })={\begin {array}{ll}{{\frac {1}{b-a}}}&\text {for}\, a\leq \phi \leq b,\\ 0&\text {otherwise} \end {array}}\)