Maximum Free Distance Binary to $M$-ary Convolutional Codes for Pseudo Chaotic Type Time Hopping PPM Impulse Radio UWB

The topic of spectral line suppression is of major interest in the design of pulse position modulated time hopping impulse radio ultra wideband communications systems. Previously pseudo-chaotic time hopping (PCTH) has been introduced to eliminate spectral lines and improving bit error rates (BER). In this letter, new binary to M-ary maximum free distance convolutional codes are introduced showing similar power spectral density characteristics as those obtained with PCTH and better BER for hard and soft decision decoding

I. Introduction

In one of its early forms, time hopping impulse radio (TH–IR) ultra wideband (UWB) systems used pulse position modulation (PPM) for the transmission of information. The method has low cost and is simple to implement but leads to “spectral lines” within its power band. Spectral lines in PPM TH–IR UWB systems can be reduced using pseudo chaotic time hopping (PCTH) [1], which can be interpreted as the concatenation of a convolutional encoder (which resembles the dynamics of Bernoulli shift and tent maps) with -ary PPM based UWB. PCTH can be seen as a set of rate 1 binary to -ary convolutional encoders with constraint length , used in conjunction with -ary orthogonal PPM (OPPM) UWB. PCTH's useful spectral line reduction characteristics can be explained by its Markov chain (MC) model, [1], [2], therefore there exists the possibility of finding binary to -ary convolutional encoders with better bit error rate (BER) performance and similar spectral characteristics to those obtained with PCTH.