g through the same cable bundle and SO on are other sources of interference. Same operator FEXT also adds to the system noise. The received signal power facilitates data communications in the presence of this noise and interference. The higher the SINR, or the cleaner the signal as compared with noise and inter- ference, the higher the transmission rates that can be supported. The interference frequency response behaves similar to that of signal: it is lower at higher frequencies. As path loss increases at higher frequencies both signal and interference become weaker. AWGN however remains at a constant power. This results in transmission rate limitation being a function of mainly interference at lower frequencies but also of noise at higher frequencies. Since a DMT method of modulation is used, different subcarriers experience different capacities as a function of signal, noise and interference power levels at that particular frequency. Example 9.1 What is the maximum downlink capacity of an ADSL2+ system which uses 80% of all avail- able 512 subcarriers, each with an effective bandwidth of 4 kHz, at a distance of 2 km. Assume transmission power is 30 dBm, the receiver noise power is -70 dBm, and path loss follows the table shown. Further assume that FEXT interference level is 20 dB lower than the received power. What is the system's Shannon capacity? Carriers Path loss (dB/km) 1~128 129~256 257~384 385~512 Answer Carriers Rx Signal Rx FEXT Rx Noise Rx SINR Number of Shannon Power Power Power Carriers Capacity (dB/km) (dBm) (dBm) (dBm) (Mbps) 1~128 129~256 257~384 385~512 Total 8.3 Mbps Note that carriers 1-384 capacity is mostly limited by FEXT interference, whereas carriers 385-512 capacity is limited by noise. Clearly interference removal can lead to significant capacity improvement. Vectored DSL While much of additive noise is random and therefore difficult to remove, the crosstalk inter- ference signals are deterministic and therefore it is possible to calculate and remove them from the received signal. Such