qfunc

Q function

Syntax

y = qfunc(x)

Description

y = qfunc(x) returns the output of the Q function for each element of the real-valued input. The Q function is (1 – f), where f is the result of the cumulative distribution function of the standardized normal random variable. For more information, see Algorithms.

Examples

Calculate Q Function Value and Plot Results

Calculate the Q function values for a real-valued input vector.

x = -4:0.1:4;
y = qfunc(x);

Plot the results.

plot(x,y)
grid

Calculate QPSK Error Probability Using Q Function

Calculate the QPSK error probability at an ${\mathit{E}}_{\mathrm{b}}/{\mathit{N}}_0$ setting of 7 dB by using the Q function.

Convert the ${\mathit{E}}_{\mathrm{b}}/{\mathit{N}}_0$ in dB to its linear equivalent.

ebnodB = 7;
ebno = 10^(ebnodB/10);

Using the Q function, calculate the QPSK error probability, $$P_b=Q\left(\sqrt{2\frac{E_b}{N_0}}\right)$$.

Pb = qfunc(sqrt(2*ebno))

Pb = 
7.7267e-04

Input Arguments

x — Input

scalar | vector | matrix | array

Input, specified as a real-valued scalar, matrix, or array.

Data Types: double

Output Arguments

y — Q function output

scalar | vector | matrix | array

Q function output, returned as a scalar, matrix, or array. y has the same dimensions as input x. Output values are in the range [0, 1].

Algorithms

For a scalar x, the Q function is (1 – f), where f is the result of the cumulative distribution function of the standardized normal random variable. The Q function is defined as

$$Q(x)=\frac{1}{\sqrt{2\pi }}{\displaystyle \underset{x}{\overset{\infty }{\int }}\exp (-t^2/2)dt}$$

The Q function is related to the complementary error function, erfc, according to

$$Q(x)=\frac{1}{2}\text{erfc}\left(\frac{x}{\sqrt{2}}\right)$$

Version History

Introduced before R2006a