Patent ID: 8406416

Claim:
An apparatus comprising: a processor configured to obtain an upper bound for a worst-case far-end crosstalk (FEXT) power spectral density (PSD) for a victim line in a plurality of subscriber lines, wherein obtaining the upper bound for the worst-case FEXT PSD comprises determining a 99 percent worst-case FEXT PSD in the victim line from a plurality of disturbing lines FEXT 0,i by FEXT 0,i ( f )≦|10×log 10 ( k×n 0.6 ×f 2 )+(− a−b√{square root over (f)} )|+10×log 10 L 0 , where k is a FEXT coupling constant, n is a quantity of the disturber lines, f is a frequency, a and b are upstream power back-off (UPBO) parameters determined by an operator, and L 0 is a loop length of the victim line: and a transmitter configured to transmit a digital subscriber line (DSL) signal in the victim line according to a reference virtual noise power spectral density (PSD), wherein the reference virtual noise PSD is based on the upper bound.