Proper vs improper handoff; cellular concept N = 7

Improper vs proper handoff

A handoff starts when the signal from the serving base station falls to the handoff threshold Pr,handoff, which is kept above the minimum usable level Pr,min by a margin Δ.

 Signal  BS1                          BS2
   │ \                                /
   │   \ A: Pr,handoff reached     /
   │     \                  ____/
   │.......\ B: Pr,min ....../...........
   │  (improper: call drops at B)
   │  (proper: transferred to BS2 at C, before B)
   └───────────────────────────────── distance

Too large a Δ is also bad: it gives unnecessary handoffs and loads the MSC.

Cellular concept for N = 7

In the cellular concept, the service area is divided into small hexagonal cells, each served by a low-power base station. The total S channels are divided among N = 7 cells forming a cluster, so each cell gets S/7 channels. The cluster is repeated across the area (frequency reuse).

        ___
    ___/ 2 \___
   / 7 \___/ 3 \
   \___/ 1 \___/
   / 6 \___/ 4 \
   \___/ 5 \___/
       \___/

• N = 7 is obtained with i = 2, j = 1 (N = i² + ij + j² = 4 + 2 + 1).
• Reuse ratio Q = √(3×7) = 4.58, so co-channel cells are 4.58R apart.
• With n = 4 and six interferers, S/I = 4.58⁴/6 ≈ 73.5 = 18.7 dB, which meets the 18 dB needed by AMPS. That is why N = 7 is the classic choice.
• Frequency reuse factor = 1/7.