Use of the reference noise method bounds the performance loss due to upstream power backoff

This paper presents mathematical proofs that the performance loss due to using the reference noise method of upstream power backoff is bounded. First, it is shown that when two lines of arbitrary lengths are considered, application of the reference noise method results in an upstream signal-to-noise ratio (SNR) degradation of less than 3 dB relative to when the two loops are the same length and the remote transceivers transmit at the maximum allowed power spectral density. Next, an extension to the reference noise method is introduced, and it is shown that the 3-dB bound holds for an arbitrary number of lines. Finally, the reference noise method is shown to minimize the maximum SNR loss relative to when all lines are the same length and all remote transceivers transmit at the maximum allowed power spectral density. The result is significant for very high-speed digital subscriber line applications because it allows service providers to determine a priori the worst case impact of upstream power backoff on upstream bit rates without consideration of the loop plant topology