Alpha max plus beta min algorithm
Encyclopedia
Square root
In mathematics, a square root of a number x is a number r such that r2 = x, or, in other words, a number r whose square is x...
of the sum of two squares. That is to say, it gives the approximate absolute magnitude of a vector given the real
Real number
In mathematics, a real number is a value that represents a quantity along a continuum, such as -5 , 4/3 , 8.6 , √2 and π...
and imaginary
Imaginary number
An imaginary number is any number whose square is a real number less than zero. When any real number is squared, the result is never negative, but the square of an imaginary number is always negative...
parts.
The algorithm avoids the necessity of performing the square and square-root operations and instead uses simple operations such as comparison, multiplication and addition. Some choices of the α and β parameters of the algorithm allow the multiplication operation to be reduced to a simple shift of binary digits that is particularly well suited to implementation in high-speed digital circuitry.
The approximation is expressed as:
Where
is the maximum absolute value of I and Q and 
is the minimum absolute value of I and Q.For the closest approximation, the optimum values for
and 
are 
and 
, giving a maximum error of 3.96%.  |
 |
Largest error (%) | Mean error (%) |
|---|---|---|---|
| 1/1 | 1/2 | 11.80 | 8.68 |
| 1/1 | 1/4 | 11.61 | 0.65 |
| 1/1 | 3/8 | 6.80 | 4.01 |
| 7/8 | 7/16 | 12.5 | 4.91 |
| 15/16 | 15/32 | 6.25 | 1.88 |
 |
 |
3.96 | 1.30 |