Chapter 4: Selection Diversity Improvement

📉 The Problem: Multipath Fading

Wireless signals bounce off obstacles, arriving at the receiver via multiple paths. These signals interfere constructively or destructively, causing severe power fluctuations known as fading.

Key Challenge

If a single antenna experiences a "deep fade" (signal power drops significantly), communication fails entirely.

Signal Strength (t)

Deep Fade ↓

⚡ The Solution: Selection Diversity

Instead of one antenna, we use \(M\) independent branches. The receiver monitors all branches and simply selects the best one (highest Instantaneous SNR).

Single Branch

Prob. of Failure: High

M Branches

Prob. of Simultaneous Failure: Very Low

Mathematical Model

Single Branch Outage Probability:

\[ P(\gamma) = 1 - e^{-\gamma/\Gamma} \]

M-Branch Outage Probability:

\[ P_M(\gamma) = \left( 1 - e^{-\gamma/\Gamma} \right)^M \]

Diversity Gain Analysis

Outage Probability vs. Normalized SNR

Interactive

Insight: At -10 dB SNR, a single antenna fails ~9.5% of the time. With 4 antennas, failure drops to ~0.008%. That's a 3 order of magnitude improvement.

Average SNR Improvement

Diversity improves average signal quality, not just reliability.

\[ \overline{\gamma} = \Gamma \sum_{k=1}^{M} \frac{1}{k} \]

Diversity Gain

Technique: Selection

Outage curve gets steeper. Fights fading probability.

Array Gain

Technique: MRC

Curve shifts left. Combats noise power directly.

Conceptual Array Gain

Unlike Selection Diversity, coherent combining techniques like MRC provide Array Gain. This manifests as a pure power shift to the left. The slope of the curve remains identical, but performance improves due to higher average SNR.

Gain(dB) = 10 log₁₀(M)