Mode filtering in long multimode transmission lines with random coupling

Effectiveness of mode filtering in multimode waveguides designed for long-distance communication is examined. Based on a general solution to weakly coupled transmission lines having different attenuation coefficients, an expression is derived for the fractional reduction of the average reconverted power by mode filters. It is shown that this improvement depends on the differential attenuation of the parasitic modes along the section of the line between adjacent filters and the attenuation of the parasitic modes in filters. If the latter is increased above about 10dB, it does not result in any improvement in the performance of the system. Further improvement can only be achieved by reducing the filter spacing. The effect of filtering on the delay distribution of the reconverted power is also considered. It is shown that mode filters attenuate echoes with long delay more strongly than those with short delays.