Table 1 Proposed TR algorithm

i

Set number of subcarriers \(N\), allowed data rate loss \(R_{f}\) and maximum allowed \({\text{PAPR}}_{\max }\)

ii

Generate OFDM signal \({\mathbf{x}}\) and calculate PAPR

iii

If calculated PAPR \(< {\text{PAPR}}_{\max }\), transmit \({\mathbf{x}}\) and terminate program, else got to step (iv)

iv

Calculate clipping threshold \(x_{{{\text{th}}}} = \sqrt {{\text{PAPR}}_{\max } E\left\{ {\left| {x\left( n \right)} \right|^{2} } \right\}}\)

v

Generate desired peak-reduction signal \({\mathbf{d}}\)

vi

Generate IFFT submatrix \(\hat{Q} \in {\mathbb{C}}^{N \times L}\)

vii

Use interior-point method to minimize \(||\hat{Q}{\hat{\mathbf{C}}} - {\mathbf{d}}||_{\infty }\) and solve for PRCs vector \({\hat{\mathbf{C}}}\)

viii

Compute peak-reduction vector \({\mathbf{c}} = \hat{Q}{\hat{\mathbf{C}}}\)

ix

Compute \({\mathbf{s}} = {\mathbf{x}} - {\mathbf{c}}\) and transmit

x

End