Theoretical limitations on frequency and time diversity for fading binary transmissions

The purpose of this note is to point out that for either frequency diversity or time diversity, the dependence of required transmitted power on number of branches is quite different than for space diversity. For both frequency- and time-diversity techniques the saving of transmitter power can come only from the first factor above (that is, the averaging of fluctuations), since the total mean received power is a fixed fraction of the scattered power. It will be shown that as a consequence: 1) The minimum required transmitter power for a specified reliability is strictly larger than zero. 2) Both the value of this minimum and the number of diversity branches yielding the minimum depend upon the diversity-combining method used.