The calculation of the cell radius in 5G from the Physical Random Access CHannel (PRACH) format is similar to LTE technologies, but there are some differences due to the higher frequency bands used in 5G and the use of beamforming and Massive MIMO techniques. The following steps can be followed to calculate the cell radius from the PRACH format in 5G:
1.Determine the frequency band used by the cell. 5G uses frequency bands in the range of 600 MHz to 52.6 GHz, with higher frequency bands providing higher data rates but shorter coverage distances.
2.Calculate the wavelength of the signal using the formula: λ = c/f, where c is the speed of light and f is the frequency. In 5G, the wavelength is much shorter than in previous cellular technologies due to the use of higher frequency bands.
3.Find the duration of the PRACH preamble in seconds, which can be obtained from the 5G NR (New Radio) specifications. The PRACH preamble duration varies depending on the configuration, but it is typically in the range of a few microseconds.
4.Determine the propagation speed of the radio waves in the medium between the mobile device and the base station. This depends on the type of medium, such as air or a building material, and can be estimated or measured. In 5G, the propagation speed is affected by the higher frequency bands, which can cause more attenuation and reflection of the signals.
5.Calculate the cell radius using the formula: R = (c * T * √(n^2 – 1)) / (2 * n * f), where R is the cell radius, T is the duration of the PRACH preamble, n is the refractive index of the medium, and f is the frequency. In 5G, the calculation of the cell radius may also take into account the beamforming and Massive MIMO techniques used to increase the coverage and capacity of the network. Beamforming allows the base station to focus the signal towards the mobile device, which can increase the received signal power and reduce interference. Massive MIMO uses multiple antennas at the base station to improve the spatial efficiency of the communication, which can increase the capacity and coverage of the network.
Note that the refractive index of the medium can affect the propagation speed of the radio waves and should be taken into account in the calculation. It is also important to note that the cell radius in 5G may vary depending on the configuration of the network, the type of antenna used, and the interference level. The calculation provides an estimate of the cell radius, but the actual cell coverage may be affected by various factors such as terrain, obstacles, and mobility of the mobile devices.