Capacity and Mutual Information of Soft and Hard Decision Output M-Ary PPM over UWB Channels

The performance of impulse radio is investigated for frequency-selective ultra-wideband (UWB) channels and orthogonal M-ary pulse position modulation (PPM) in terms of the maximum achievable data rate, where the outputs of the M-ary correlation receiver implemented through the rake structure with conventional maximal ratio combining undergo either hard or soft decisions. The major difference observed between the soft and hard decision output systems is that at low code rates increasing the constellation size, M, requires an increase in the minimum signal-to-noise ratio (SNR) per communicated bit for the system with hard decisions. It is demonstrated that independent of the type of decision making, achievable rates in UWB channels are low compared to those in additive white Gaussian noise channels, as the frequency-selectivity of the UWB channel destroys the orthogonality of the transmitted PPM signals. The interference from the other users and the constellation size put additional constraints on the achievable data rates at high values of SNR.