Theoretical analysis of the energy capture in strictly bandlimited ultra-wideband channels

The frequency selectivity of wireless communication channels can be characterized by the delay spread D_s of the channel impulse response. If the delay spread is small compared to the bandwidth W of the input signal, that is, D_sW ¿ 1, the channel appears to be flat fading. For D_sW ¿ 1, the channel appears to be frequency selective, which is usually the case for wideband signals. In the first case, small scale synchronization with a precision much higher than the sampling time T = 1/W is crucial to guarantee the maximum capture of energy at the receiver. In this paper, it is shown by analytical means that this is different in the wideband regime. Here synchronization with a precision of T is sufficient and small scale synchronization cannot further increase the captured energy at the receiver. Simulation results show that this effect already occurs for W ¿ 50MHz for the IEEE 802.15.4a channel model.