Need for diversity; combining techniques

Need for diversity

In a mobile channel the received signal suffers small-scale (Rayleigh) fading: the envelope can drop 20–40 dB below its average when the mobile moves only a fraction of a wavelength. During such deep fades the bit error rate becomes very high and calls may drop. Raising transmit power to cover the deepest fades is wasteful and causes interference.

Diversity solves this by giving the receiver several independently faded copies (branches) of the same signal:

• The chance that all M branches are in a deep fade at once is roughly pᴹ, which is very small.
• Average SNR improves and, more importantly, the SNR becomes much more stable (fewer deep fades).
• It gives a large BER improvement with no extra bandwidth (space, polarization) and no training overhead.
• It works well together with equalization (for ISI) and channel coding (for remaining errors).

Diversity branches can be obtained by space (antenna separation), polarization, frequency (separation > coherence bandwidth) or time (separation > coherence time). Whatever the source, the branches are then combined by one of the methods below.

Diversity combining techniques

Once the branch signals are available they must be combined. Let γᵢ be the SNR of branch i.

1. Selection combining

• The branch with the largest instantaneous SNR is chosen: γ_out = max(γ₁, …, γ_M).
• Only one demodulator after the switch; simple.
• Mean SNR improvement = Σₖ₌₁ᴹ 1/k times the single-branch mean (e.g. 1.83 for M = 3).

2. Feedback (scanning / switched) combining

• Branches are scanned in order; the first one above a threshold is used until it drops below the threshold.
• Needs only one receiver; slightly poorer than selection.

3. Maximal ratio combining (MRC)

• Each branch is co-phased and weighted by Gᵢ ∝ (signal amplitude)/(noise power), then summed.
• γ_out = Σ γᵢ, so the mean output SNR is M times the single-branch mean; this is the optimum linear combiner.
• Needs channel estimates and a receiver on each branch; used in RAKE receivers and modern base stations.

4. Equal gain combining (EGC)

• Branches are co-phased and summed with equal (unity) weights.
• Performance close to MRC (within about 1 dB), but simpler because only phase must be estimated.

  r1 --[co-phase, ×G1]--+
  r2 --[co-phase, ×G2]--+--(Σ)--> detector
  ...                   |
  rM --[co-phase, ×GM]--+
  MRC: Gi ∝ amplitude/noise   EGC: Gi = 1
  Selection: switch to max SNR branch only

Example: with three branches each having mean SNR Γ, selection combining gives a mean output SNR of Γ(1 + 1/2 + 1/3) = 1.83Γ (about 2.6 dB), while MRC gives 3Γ (about 4.8 dB). The real benefit is larger at low outage probabilities, where diversity can save 10 dB or more of fade margin.