A priori probability calculation for UWB systems using correlated PPM and polarity modulation

In pulsed ultrawideband (UWB) systems, pulse position modulation (PPM) allows information to be conveyed by delaying the pulse position inside a pulse repetition period (PRP). In addition, polarity (antipodal positions) allows the transmission of one more bit per pulse, at low implementation cost. The contribution of one pulse to the received signal is the composite channel response (CCR), which is the convolution of the emitted pulse shape and the impulse channel response. The demodulator can be simply a bank of correlators using delayed versions of the estimated CCR, as templates. For a soft-input bitwise channel decoding, the A priori probability (APP) per bit is then calculated using the correlators' output values, and processed by a channel decoder. In this paper, assuming perfect synchronisation, a perfect CCR estimation, and no inter symbol interference (ISI), we investigate the effect of the correlation between the delayed CCRs on the APP calculation. Proof is given for N-PPM and polarity modulation that there is no need to consider the correlation values in the APP calculation. Simulation results shows the APP distribution for different signal-to-noise ratio (SNR) and correlation values, the influence of the max log approximation on the BER performance is also presented.