Hata Model is applied for GSM Link Budget,here i write about its formula and Cell Size Estimation.

**Hata´S Empirical Formula**

PL = 69.55 +26.6log_{10}f_{c }– 13.82log_{10}h_{b} + (44.9 – 6.55log_{10}h_{b})log_{10}R – a(h_{m}) -CF

Where ,

f_{c} – Frequency in MHZ

h_{b} – Transmitter antenna height

h_{m} – Receiver antenna height

R – Radius in Km

a(h_{m}) is the correction factor for effective mobile antenna height

**Solving backwards the cell radius is given by**

log_{10}R = MAPL +CF – 69.55 +26.6log_{10}f_{c }+ 13.82log_{10}h_{b }+ a(h_{m}) / (44.9 – 6.55log_{10}h_{b})

**Cell Size/Count Estimation**

- Once the Maximum allowable path loss is known, the achievable cell size can be evaluated.
- Cell radius is calculated using MAPL and Hata’s empirical formula.
- Cell radius is the distance from base station where the path loss equals MAPL. Beyond this radius, the signal is too weak to be acceptable.
- Each area has a different correction factor.
- Also the coverage objectives are usually different for Urban, Suburban and Rural areas.
- Therefore MAPL has to be calculated for each area and then cell size determined separately.
- Once the cell radius is calculated, cell count estimates can be made.
- Once the cell radius for each area is calculated, then the minimum number of cells required to provide coverage can be determined.
- For each area

**A = 2.6R ^{2}**

Where,

- R – radius of cell
- A – Area of the corresponding hexagon.

- Cell count = Urban Area(Km2) + Suburban area(Km2) + RuralArea(Km2)
- Cell Count = A
_{urban}(Km^{2}) + A_{suburban}(Km^{2}) + A_{rural}(Km^{2})