Capacity of M-ary PPM ultra-wideband communications over AWGN channels

We compute the channel capacity of M-ary pulse position modulation (PPM) ultra-wideband (UWB) communications over the additive white Gaussian noise channel. The computation extends the known capacity of PPM orthogonal signals to incorporate UWB-specific constraints. The constraints are the power spectrum density limitation under FCC Part 15 rules and a specified spreading ratio. The UWB capacity is expressed as a function of range demonstrating a fundamental trade-off in UWB system design. UWB capacity is also compared to the capacity of M-ary phase shift keying (PSK) direct sequence spread spectrum (DS-SS). It is shown that for the same power constraint,. both systems have similar capacity at high signal to noise ratio (SNR). At low SNR, UWB has a significant advantage for multilevel modulations with M>4, while for M=2,4, DS-SS has a slight advantage