---
title: "Need for diversity; maximum ratio combining"
subject: "Wireless Communication"
chapter: 5
key: "semester_7/wireless_communication:diversity-need-mrc"
source: https://www.bctengineer.com/q/semester_7/wireless_communication/diversity-need-mrc
site: BCT Engineering
---

# Need for diversity; maximum ratio combining

Wireless Communication · Chapter 5: Equalization and Diversity

- Asked in: 2080 Bhadra, 2+2 marks
- Video: [Diversity Combining Techniques -  Maximum Ratio combining](https://www.youtube.com/watch?v=KAFWQp9Kk6w) — deva Sena
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/wireless_communication/diversity-need-mrc
- Whole chapter: https://www.bctengineer.com/md/semester_7/wireless_communication/chapter-5

## Question

Why is there a need to implement diversity? Describe the maximum ratio combining space diversity technique.

## Short answer

Diversity counters deep fading by providing independent signal paths, so the probability of simultaneous fade is low. Maximal ratio combining co-phases the signals from M antennas, weights each by its instantaneous SNR, and sums them, yielding output SNR equal to the sum of branch SNRs — the optimal linear combining method.

## Answer

#### Need for diversity
In a fading channel the received signal often falls into deep fades (20–40 dB). Increasing transmit power to cover these fades is costly. **Diversity** sends or receives the signal over two or more independently fading paths; the chance that all paths fade at the same time is very small. It improves the average SNR and reduces the error rate, with low cost and no extra bandwidth (for space diversity).

#### Maximal ratio combining (MRC)
In MRC, the signals from all M antenna branches are **co-phased**, **weighted in proportion to their own signal amplitude (SNR)**, and summed.
```text
 Ant1 ->[x G1]-+
 Ant2 ->[x G2]-+->(Σ)-> output, SNR = Σ γ_i
 AntM ->[x GM]-+
   (co-phased, G_i ∝ r_i/N_i)
```
- Output SNR = sum of the branch SNRs: γ_M = Σ γ_i, the best possible for a linear combiner.
- Gives an acceptable SNR even when no single branch is good.
- Needs a separate receiver and phase tracking per branch, so it is the most complex method.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Why is diversity preferred over simply raising transmit power in a fading channel?
   A. Deep fades of 20-40 dB are costly to cover; independent paths rarely all fade together
   B. Raising power removes ISI completely
   C. Diversity increases the transmit power automatically
   D. Fading never occurs on multiple antennas
   Answer: A. Covering deep fades with power is costly, whereas independent branches are unlikely to fade simultaneously. (Key point: Why diversity)

2. What does MRC do to the signals from M antenna branches?
   A. Picks only the strongest branch
   B. Co-phases them, weights in proportion to their SNR/amplitude and sums
   C. Adds them with equal weights without phase correction
   D. Subtracts the weaker branches from the strongest
   Answer: B. MRC co-phases each branch, weights it by its own strength and sums all. (Key point: MRC processing)

3. What is the output SNR of MRC in terms of branch SNRs gamma_i?
   A. Maximum of gamma_i
   B. Average of gamma_i
   C. Sum of gamma_i
   D. Product of gamma_i
   Answer: C. The MRC output SNR equals the sum of the branch SNRs, the best for a linear combiner. (Key point: MRC output SNR)

4. What is the main drawback of MRC?
   A. It needs extra bandwidth
   B. It uses only one branch
   C. It gives worse SNR than selection
   D. Needs a separate receiver and phase tracking per branch, so it is most complex
   Answer: D. MRC is best in performance but costs the most because every branch needs its own receiver and co-phasing. (Key point: MRC cost)

## Related in Wireless Communication

- [Feedback vs maximum ratio combining diversity](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Afeedback-vs-mrc-diversity) — Wireless Communication, chapter 5
- [Need for diversity; combining techniques](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Adiversity-combining-techniques) — Wireless Communication, chapter 5
- [Diversity techniques and space diversity combining](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Adiversity-space-combining) — Wireless Communication, chapter 5
- [Equalization and diversity; space diversity methods](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Aequalization-diversity-space-methods) — Wireless Communication, chapter 5
- [ISI mitigation and space diversity techniques](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Aisi-space-diversity) — Wireless Communication, chapter 5
- [Space diversity techniques with block diagrams](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Aspace-diversity-block-diagrams) — Wireless Communication, chapter 5

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