The Acoustic Channel and Delay: A Tale of Capacity and Loss

We analyze the capacity of single-input-multi-output (SIMO) acoustic channels with long propagation delays and longterm frequency-dependent properties that are found in acoustic channels. The focus of this paper is on the effects of feedback delay on the achievable rate of the acoustic channel. Four power allocation policies are analyzed within a framework of orthogonal frequency division multiplexing (OFDM): water-filling, statistical water-filling (water-filling based on long-term channel statistics), frequency band selection (uniform power allocated to all carriers within a range of frequencies), and uniform power allocation across all carriers irrespective of the channel (“all-on”). The first three methods show very little difference in rate for average to high SNRs. However, the frequency-band-selection method is robust against feedback delay, requires little overhead and has low complexity, thus making it the method of choice. In mobile systems where the distance between the transmitter and receiver vary significantly, adaptive frequency band selection can deliver a significant gain compared to the “all-on” policy, as it picks the band that is statistically optimal for the given distance. Finally, we show that although water-filling can increase the capacity significantly in SNR-starved systems with perfect channel knowledge at the transmitter, the gain turns into a loss with the long feedback delays associated with underwater acoustic channels.