Continuous Phase Modulation with Chaotic Interleaving for Different OFDM Versions

Abstract

In this paper, we propose a chaotic interleaving scheme for efficient data transmission with continuous-phase modulation orthogonal frequency-division multiplexing (CPM-OFDM) systems over fading channels. The idea of chaotic maps randomization (CMR) is exploited in this scheme. CMR generates permuted sequences from the sequences to be transmitted with lower correlation among their samples, and hence a better symbol error rate (SER) performance can be achieved. The performance of the proposed approach is tested on the conventional Fast fourier transform OFDM (FFT-OFDM), discrete wavelet transform OFDM (DWT–OFDM), and discrete cosine transform OFDM (DCT–OFDM). The proposed (FFT/DCT/DWT)-CPM-OFDM system with interleaving combines the advantages of frequency diversity and power efficiency from CPM-OFDM and performance improvement from chaotic interleaving. The SER performance of the (FFT/DCT/DWT)-CPM-OFDM system with and without chaotic interleaving is evaluated by computer simulations. Also, a comparison between chaotic interleaving and block interleaving is performed. Simulation results show that the chaotic interleaving scheme can greatly improve the performance of (FFT/DCT/DWT)-CPM-OFDM systems. Furthermore, the results show also that, the (FFT/DCT/DWT)-CPM-OFDM system provides a good trade-off between system performance and bandwidth efficiency.

Appendix: Channel Model

Channel ${\text{C}}_{\text{f}}$ has an exponential delay power spectral density:

$$ \upsigma_{{\upalpha_{\text{l}} ,{\text{C}}}}^{2} = \left\{ {\begin{array}{*{20}l} {{\text{C}}_{{{\text{C}}_{\text{f}} }} {\text{e}}^{{ -\uptau_{\text{l}} /2\,\upmu{\text{s}}}} } \hfill & {0 \le\uptau_{\text{l}} \le 8.75\,\upmu{\text{s}}} \hfill \\ 0 \hfill & {\text{otherwise}} \hfill \\ \end{array} } \right. $$

(13)

where ${\text{C}}_{{{\text{C}}_{\text{f}} }}$ is the normalization constant and given by,

$$ {\text{C}}_{{{\text{C}}_{\text{f}} }} = {\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 {\sum\nolimits_{{{\text{l}} - 0}}^{35} {\exp \left( { - \frac{{\uptau_{\text{l}} }}{{2{\text{e}}^{ - 6} }}} \right) = 0.1188} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${\sum\nolimits_{{{\text{l}} - 0}}^{35} {\exp \left( { - \frac{{\uptau_{\text{l}} }}{{2{\text{e}}^{ - 6} }}} \right) = 0.1188} }$}}. $$

(14)

The effective double-sided bandwidth of the message signal ${\text{x}}\left( {\text{t}} \right)$ is defined as ${\text{W}} = {\text{K}}/{\text{T}}$ Hz. According to Eq. (12), the bandwidth of ${\text{s}}_{\text{I}} \left( {\text{t}} \right)$ is at least W, where the ${\text{n}} = 0$ term contains no information, and thus has zero bandwidth, the ${\text{n}} = 1$ term is the message signal and has bandwidth ${\text{W}},$ the ${\text{n}} = 2$ term has a bandwidth $2{\text{W}}$, and so on. As a result, due to the ${\text{n}} = 1$ term, the bandwidth of ${\text{s}}_{\text{I}} \left( {\text{t}} \right)$ is at least ${\text{W}}$. Depending on the modulation index ${\text{h}}_{\text{in}}$, the effective bandwidth can be greater than ${\text{W}}$. The bandwidth efficiency in CPM-based systems η can be expressed as

$$ \upeta = \frac{\text{R}}{\text{BW}} = \frac{{{ \log }_{2} {\text{M}}}}{{{ \hbox{max} }\left( {2\uppi{\text{h}}_{\text{in}} ,1} \right)}}\,{\text{bps}}/{\text{Hz}} $$

(15)