Optimum Bandwidth Partitioning With Analog-to-Digital Converter Constraints

Abstract

In certain communication channels, such as short copper twisted pairs, it is theoretically possible to perform transmission with very high spectral efficiency using a very wide bandwidth. However, current analog-to-digital converter (ADC) technology limits the allowable sampling rate and resolution, thus severely constraining the transmission speeds. This paper proposes the partitioning of the available bandwidth into multiple bands, each employing an independent ADC. The benefit of such a scheme is the reduction of the sampling rates of the ADCs. An increase in the dynamic range is allowed, thus offering the potential to realize very high spectral efficiencies. An analysis of transmission under ADC constraints is performed, where an expression for the achievable data rate is derived, based on an empirical rule for the tradeoff between the ADC sampling rate and resolution. A bandwidth-partitioning problem is formulated, where the objective is the maximization of the data rate, and the optimization parameters are the frequency-band assignments. Then, a practical example of transmission over category (CAT)-5 cable is considered. The possible impairment factors are outlined, and the essential system elements are described. Using the previously given algorithm, the optimum solution and the corresponding performance are given for two distinct scenarios. These scenarios serve to illustrate the bandwidth-partitioning procedure, and provide useful intuition regarding the application of the proposed method. In particular, it is deduced that it is best to have narrower bands in frequencies where the signal-to-noise ratio (SNR) is relatively high, and wider bands in frequencies where the SNR is relatively low.