"Active Reflection Coefficient" in Phased Arrays

Hi,

Recently I was working on a paper from Pozar [1] in which he analyzed arrays of rectangular microstrip patches using moment method.

The problem I encountered was the definition below for "Active Reflection Coefficient":

R= (Zin(theta, phi) - Zin(0,0)) / (Zin(theta, phi) + Zin*(0,0))

where, theta and phi are the array's scan angles. Pozar says it assumes the array is conjugate matched to broadside scan. (This definition has been repeated through many publications even in "Microstrip Antenna Design Handbook" by R. Garg in pg.740)

Contrary to the above, I think it should be: R= (Zin - Zin*(0,0)) / (Zin + Zin*(0,0)) ; i.e. the Zin(0,0) term in the nominator must be conjugated.

Anyone can explain the difference?

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[1] D. Pozar, "Finite phased arrays of rectangular microstrip patc," IEEE Trans. Antennas Propag., vol. 34, pp. 658-665, 1986.