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

In this paper 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 specific 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.