Bandwidth Scaling for Fading Channels

The issue of bandwidth scaling has always caused some confusion for channels subject t.o additive white Gaussian noise plus multipath fading. On the one hand, there is an old result (see, for example, section 8.6 of [I]) saying that the capacity of the channel (under 2 power constraint but no bandwidth constraint) is the same as the infinite bandwidth capacity of the non-fading additive noise channel with the same average received power as the fa,?ing channel. On the other hand, it appears intuitively that when a CDMA system is spread t-oo widely in bandwidth, it become~ increasingly difficult for a, rake receher t;) measure the channel and ccrrcspoadiEgEy d!Ec take p!;ece. Eere we fool; at a particuiariy simpic p11~0de1 of the fading channel, but the ~inei-hodn! tendabie to more general models. available bandwidth into small slices much sma!lea than !,he r:oberei