Frequency reuse and co-channel reuse ratio

Frequency reuse is the technique of using the same set of radio channels in different cells that are far enough apart, so that co-channel interference stays within a tolerable limit. It lets a cellular system with a limited spectrum serve a very large number of users.

Frequency reuse concept

• The total S duplex channels are divided into N groups. Each cell in a group of N neighbouring cells (a cluster) gets k = S/N channels, so a cluster uses the full spectrum once.
• The cluster is then repeated across the service area. Cells with the same letter (same channel set) are co-channel cells.
• Each base station uses low power and antennas placed so that coverage stays roughly inside its own cell.
• For hexagonal cells, cluster size is N = i² + ij + j² (i, j = 0, 1, 2, …), so N = 1, 3, 4, 7, 9, 12, …
• If the cluster is repeated M times, total capacity is C = M·k·N = M·S. Smaller N means more repetitions and more capacity, but co-channel cells come closer and interference increases.
• The frequency reuse factor is 1/N, since each cell gets 1/N of the channels.

      B   C          B   C
    G   A   D  ...  G   A   D
      F   E          F   E
   cluster 1 (N=7)  cluster 2
  Cell A in both clusters uses the same channel set

Co-channel reuse ratio

The co-channel reuse ratio Q is the ratio of the distance D between the centres of the nearest co-channel cells to the cell radius R:

Q = D / R = √(3N)

• D = R√(3N) for hexagonal geometry, so Q depends only on cluster size.
• Large Q (large N): co-channel cells are far apart, so co-channel interference is low and transmission quality is better, but each cell has fewer channels and capacity is lower.
• Small Q (small N): more channels per cell and higher capacity, but more co-channel interference.
• Q links directly to signal-to-interference ratio. With path loss exponent n and i₀ first-tier interferers: S/I ≈ (√(3N))ⁿ / i₀ = Qⁿ / i₀.

Example: for an S/I requirement of 18 dB with n = 4 and i₀ = 6, N = 7 (Q = 4.58) gives S/I = 4.58⁴/6 ≈ 73.5 = 18.66 dB, which is acceptable.