Cellular RF Planning & Wireless Propagation Modeling
Okumura-Hata Urban Macro-Cell Path Loss Formula
Calculate Masaharu Hata’s Empirical Urban Macro-Cell Mobile Height Correction a(h_m), Distance Path-Loss Slope 44.9 - 6.55*LOG10(h_b), Total Median Path Loss L_urban (dB), and Cell-Edge Received Signal Power (dBm).
Replace optimistic 20*LOG10(d) free-space loss with Okumura-Hata’s ~32–38 dB/decade urban clutter slope!
Planning terrestrial 700–1500 MHz LTE/5G macro-cells with Friis Free-Space Path Loss (20 dB per distance decade) wildly overstates coverage radius because urban rooftops, street canyons, and ground reflections steepen path attenuation above 30 dB/decade! Masaharu Hata (1980, IEEE Transactions on Vehicular Technology) parameterized Yoshihisa Okumura’s Tokyo field measurements across carrier frequency f_MHz (150–1500 MHz), base-station height h_b (30–200 m), mobile height h_m (1–10 m), and range d_km (1–20 km): a(h_m) = (1.1 * LOG10(f_MHz) - 0.7) * h_m - (1.56 * LOG10(f_MHz) - 0.8), and Urban Median Path Loss L_urban_dB = 69.55 + 26.16 * LOG10(f_MHz) - 13.82 * LOG10(h_b) - a(h_m) + (44.9 - 6.55 * LOG10(h_b)) * LOG10(d_km)!
Verify on a 1,000 MHz Macro Tower—Carrier_Frequency f = 1,000 MHz (LOG10 = 3, B2), Tower_Height h_b = 100 m (LOG10 = 2, B3), Handset_Height h_m = 1.5 m (B4 -> Mobile Correction a(h_m) = 2.6 * 1.5 - 3.88 = 0.02 dB in E2), Cell_Radius d = 10 km (LOG10 = 1, B5), and Sector_EIRP = 60 dBm (B6): Distance Path-Loss Exponent Slope is 44.9 - 6.55 * 2 = 31.80 dB/decade (path-loss exponent n = 3.18 vs 2.0 free-space!, E3); Urban Path Loss L_urban is 69.55 + 78.48 - 27.64 - 0.02 + 31.80 = 152.17 dB (E4); yielding Cell-Edge Received Power = 60 - 152.17 = -92.17 dBm (E5)!
| Okumura-Hata RF Metric (f=1,000 MHz, h_b=100 m, h_m=1.5 m, d=10 km, EIRP=60 dBm) | Formula | Verified Output |
|---|---|---|
| Mobile Antenna Factor a(h_m) | (1.1*LOG10(f)-0.7)*hm - (1.56*LOG10(f)-0.8) | 0.02 dB |
| Distance Slope (dB / decade) | 44.9 - 6.55 * LOG10(h_b_m) | 31.80 dB/dec (n = 3.18 Clutter) |
| Median Urban Path Loss (dB) | 69.55 + 26.16*lg(f) - 13.82*lg(hb) - a + Slope*lg(d) | 152.17 dB (120.37 dB @ d=1 km) |
| Cell-Edge Rx Power (dBm) | Sector_EIRP_dBm - L_urban_dB | -92.17 dBm (-60.37 dBm @ d=1 km) |
Okumura-Hata Urban Macro-Cell Path Loss (dB) Formula
Enforce Hata’s empirical validity bounds: 150 <= f_MHz <= 1500 (above 1500 MHz use COST-231 Hata!), 30 <= h_b <= 200 m, 1 <= h_m <= 10 m, and 1 <= d_km <= 20 km!
=LET(fr_m, B2, hb_m, B3, hm_m, B4, ds_k, B5, IF(OR(fr_m < 150, fr_m > 1500, hb_m < 30, hb_m > 200, hm_m < 1, hm_m > 10, ds_k < 1, ds_k > 20), "Out of Hata Empirical Bounds", LET(lg_f, LOG10(fr_m), lg_b, LOG10(hb_m), a_hm, (1.1 * lg_f - 0.7) * hm_m - (1.56 * lg_f - 0.8), sl_d, 44.9 - 6.55 * lg_b, ROUND(69.55 + 26.16 * lg_f - 13.82 * lg_b - a_hm + sl_d * LOG10(ds_k), 2))))1-Kilometer Reference Ring Check & COST-231 Frequency Guard
Move handset to d = 1 km in B5 (LOG10(1) = 0): Path Loss E4 drops exactly by 31.80 dB to 120.37 dB (Rx Power E5 = -60.37 dBm)! Entering 2,600 MHz triggers "Out of Hata Empirical Bounds"!
=IF(ISTEXT(E4), E4, ROUND(B6 - E4, 2))Try the example
Use the original values or change them to test your understanding.