Cell footprint and interference tier

Cell footprint

The cell footprint is the actual geographical area over which a base station's signal is strong enough for reliable service (above the minimum usable level). The real footprint is irregular because of terrain, buildings and antenna patterns; it is modelled as a hexagon for planning, since hexagons tile the area without gaps or overlaps and approximate a circle closely.

Interference tier

Co-channel cells around a given cell are arranged in rings called tiers:

• First tier: the 6 nearest co-channel cells, each at distance D = R√(3N) from the centre cell.
• Second tier: the next ring of 12 co-channel cells, six at √3·D and six at 2D, and so on (the third tier has 18 cells, at about 2.6D to 3D).

              (I)          (I)
                  \       /
         (I) ──── [ Serving ] ──── (I)     I = first-tier
                  /   cell  \           co-channel cell
              (I)          (I)          at distance D

Because received power falls as d⁻ⁿ (n = 2 to 4), each second-tier cell contributes only (1/√3)ⁿ to (1/2)ⁿ of a first-tier cell's interference (1/9 to 1/16 for n = 4). Therefore, in practice, only the first tier is considered:

S/I = R⁻ⁿ / Σ(i=1..i₀) Dᵢ⁻ⁿ ≈ (D/R)ⁿ / i₀ = (√(3N))ⁿ / i₀

with i₀ = 6 for omni antennas, 2 for 120° sectoring and 1 for 60° sectoring (roughly). Example: N = 7, n = 4 gives S/I = 4.583⁴/6 = 73.5 ≈ 18.66 dB.