Power Allocation for OFDM Over Multi-Scale Multi-Lag Channels

Underwater acoustic (UWA) signal is wideband in nature and suffers doubly selective fading in time and frequency. In the presence of relative motion, a typical UWA channel can be described by a multiscale multilag (MSML) model. To compensate the scaling effect of UWA channels, many UWA communication systems employ a signal-resampling operation by a single scale at the front end of the receiver. For orthogonal frequency division multiplexing systems, since the path scales are different from each other, the resampling can alleviate but not clean out the intercarrier interference (ICI) resulting from the MSML channel. In this paper, we first describe the resampled signal by an equivalent MSML model with residual time scales, which are much smaller than that of the original MSML channel. With the given statistical parameters of the equivalent MSML channel, the closed-form expressions of the average subchannel gains and ICI coefficients are derived. Based on the ICI coefficients, we derive the analytical expression of a lower bound on the average achievable rate of the system as a function of the power allocation. We then investigate the power allocation to improve the lower bound on the achievable rate. Our key idea is that, on subcarriers whose ICIs dominate the additive noise, nothing is transmitted to avoid low energy efficiency. After proving that the ICI coefficient increases monotonically as the subcarrier frequency rises, we propose an ON-OFF uniform power allocation method, in which subcarriers with odd indices keep inactive starting from a certain index to avoid ICI. The performance of the proposed power allocation is evaluated via numerical simulations, whose results show that the proposed method outperforms the existing methods when the residual time scales cannot be neglected.