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In this section the same radar equation factors are grouped differently to create different constants as is used by some authors.

In the last section, we had the basic radar equation given as equation [6] and it is repeated as equation [1] in the table below.

In section 4-4, in order to maintain the concept and use of the one-way space loss coefficient, α1 , we didn't cancel like terms which was done to form equation [6] there. Rather, we regrouped the factors of equation [5]. This resulted in two minus α1 terms and we defined the remaining term as Gσ, which accounted for RCS (see equation [8] & [9]).

Some authors take a different approach, and instead develop an entirely new single factor α2 , which is used instead of the combination of α1 and Gσ.

If equation [1] is reduced to log form, (and noting that f = c/λ) it becomes:

10log Pr = 10log Pt + 10log Gt + 10log Gr - 20log (fR2) + 10log σ + 10log (c2/(4π)3)      [2]

We now call the last three terms on the right minus α2 and use it as a single term instead of the two terms α1 and Gσ. The concept of dealing with one variable factor may be easier although we still need to know the range, frequency and radar cross section to evaluate α2. Additionally, we can no longer use a nomograph like we did in computing α1 and visualize a two-way space loss consisting of two times the one-way space loss, since there are now 3 variables vs two.

Equation [2] reduces to: 10log Pr = 10log Pt + 10log Gt + 10log Gr - "2 (in dB)      [3]

Where α2 = 20log (f1R2) - 10log σ + K3 and where f1 is the MHz or GHz value of frequency

and K3 = -10log (c2/(4π)3) + 20log (conversion for Hz to MHz or GHz)+ 40log (range unit conversions if not in meters) - 20log (RCS conversions for meters to feet)

The values of K3 are given in the table above.

Comparing equation [3] to equation [10] in Section 4-4, it can be seen that α2 = 2α1 - Gσ.