dipole antena design for radio purpose

I want design an antena for radio receiver. I have an LNA with 50 ohm input impedance and i want to design a dipole antena connected to it.
I can easily design a half wavelength dipole antena for it. I read that the impedance is about 75 ohm for half wavelength dipole antena, so it does not match my LNA input impedance. What should i do with it?

You need to match the 75 ohms dipole impedance to 50 ohms, and also you need a balun transformer from balanced to unbalanced (assuming you are using a single-ended input LNA).

Impedance matching between a dipole antenna and a low-noise amplifier is rarely so important to treat it in theory.
The best way to utilize the low noise figure of the amplifier to improve receiver performance is to locate the low-noise amplifier immediately to the dipole, and connect it with as short connections as possible.
If you use the balun described above, you can make sure that dipole radiation pattern will be better symmetrical, but this is all. Even by connecting one dipole terminal to LNA ground and the other to the "live" input the effect will be good.
If you plan to process only a narrow-band signal, you can use a half/wavelength phasing loop as described in any antenna handbook.

The impedance mismatch like in your case, between a 75 Ohm dipole and a 50-Ohm coaxial line, can cause more problems if a longer line is used between the dipole and a load on the other side. Directly connecting LNA to dipole makes all this irrelevant and your receiver will gain from the low noise figure.