The radio frequency spectrum is currently congested due to the advancement in wireless communication systems. For these system, low noise-figure linear amplifier is crucially needed to design the front-end receiver and amplify very low-power received signals without significantly degrading their qualities. Gallium Nitride (GaN) High Electron Mobility Transistor (HEMT) has wider linear dynamic range and thus represents an excellent alternative for designing highly linear Low Noise Power Amplifier (LNA). Also, GaN as a wide bandgap material could be very optimistic to work in harsh and noisy environment such as earth space for satellite communications. In this work, global optimization technique-based noise-models are presented and then used to design LNAs. An extensive review of state-of-the-art GaN HEMT based low noise amplifier is given in this paper. Then different topologies of the low noise amplifier are explored. The techniques of bandwidth enhancement are also reviewed. The design of low noise amplifiers using the developed GaN HEMT model is done at X and K bands of frequencies. The performances of the designed LNAs are compared with state-of-the-art reported LNAs in terms of the Noise Figure (NF), gain and bandwidth. The paper presented very interesting results for the cascade, which exhibited the best NF of 1.6-2 dB and a gain of 14.5-16.4 dB within a bandwidth of 9 to 11 GHz. The highest gain of 25-27 dB was achieved by the quadrature cascode LNA with slightly higher NF of 2.1-2.5 at an operating frequency of 8-12 GHz.