A MULTIPLE UNIT STEERABLE ANTENNA 403 



By definition, diversity in fading occurs when the fading of the 

 two branches is not synchronous. If all degrees of asynchronism are 

 equally probable the diversity is random. This is the case considered. 

 In Fig. 38 five stages in the cycle of variation from synchronous to 

 asynchronous fading are used for calculation. In each of these, fading 

 curves corresponding to the two assumed waves are shown displaced 

 from each other by 0, 30, 60, 90, and 180 degrees. With "ideal" 

 automatic gain control, the two receiver gains, always equal, will be 

 proportional to the reciprocal of the resultant of bsa and csb- For 

 "ideal" linear detectors the noise output of the receivers will be pro- 

 portional only to the gain. The noise curves plot the noise variation 

 on this basis. Two cases of signal addition are considered— voltage 

 and power addition. The corresponding noise curves differ only as the 

 reciprocals of the resultant signal curves dififer. These noise curves are 

 averaged (with a planimeter) and the resulting average signal-to-noise 

 ratios are used to plot the improvement curves shown in the figure. 

 The improvement curve for power addition of signal is located on the 

 improvement axis so that zero improvement is shown for synchronous 

 fading. The curve for voltage addition of signal is located three 

 decibels higher at synchronous fading. These curves are again aver- 

 aged over the cycle from synchronism to asynchronism (by averaging 

 noise voltage). The improvements are 2.0 decibels and 4.9 decibels. 



Power addition of the two signals corresponds in practice to the case 

 in which the delay is unequalized and sufficient to cause the audio out- 

 puts of each branch to combine on a power basis like noise. The 

 two-decibel improvement might appropriately be called the primary 

 improvement since it is due solely to the diversified fading. The addi- 

 tional improvement of 2.9 decibels found with voltage addition of the 

 signals is due to favorable discrimination in the addition of signal and 

 of noise and might be called the secondary improvement. The 

 secondary improvement occurs in reception with the MUSA; it has 

 already been included in the 10 log iV^ decibel improvement calculation. 



In practice, it would be undesirable to use the "ideal" automatic 

 gain control assumed in the above analysis; the action must be 

 smoothed out with, for instance, a capacitance-resistance network. 

 The effect of this is to reduce the primary gain since the noise peaks, 

 whose avoidance by diversity action results in the primary improve- 

 ment, are reduced. An analysis of diversity action without automatic 

 gain control was made. In this case the signal was averaged while the 

 noise remained constant. The results are included in the table shown 

 in Fig. 39 which is introduced later. 



