---
title: "Non-linear effect in FDMA; channels numerical"
subject: "Wireless Communication"
chapter: 7
key: "semester_7/wireless_communication:fdma-nonlinear-channels"
source: https://www.bctengineer.com/q/semester_7/wireless_communication/fdma-nonlinear-channels
site: BCT Engineering
---

# Non-linear effect in FDMA; channels numerical

Wireless Communication · Chapter 7: Multiple Access in Wireless Communication

- Asked in: 2080 Baisakh, 3+2 marks
- Video: [5CS5-11 WC - UNIT 2 LECTURE 3 (TOPIC: FDMA CAPACITY & NON LINEAR EFFECTS) BY DEEPAK SHARMA](https://www.youtube.com/watch?v=ZU_VpKHArrQ) — MITRC LECTURE
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/wireless_communication/fdma-nonlinear-channels
- Whole chapter: https://www.bctengineer.com/md/semester_7/wireless_communication/chapter-7

## Question

Explain the non-linear effect in FDMA. If the total spectrum allocation is 25 MHz, the guard band allocated at the edge of the spectrum is 100 KHz, and the channel bandwidth is 200 KHz, find the number of channels available in an FDMA system.

## Short answer

In FDMA, many carriers share a common amplifier run near saturation; nonlinearity creates intermodulation products that interfere with other channels. With 25 MHz total, 100 kHz guard at each edge, and 200 kHz channels, N = (25,000,000 - 200,000)/200,000 = 124 channels.

## Answer

#### Non-linear effect in FDMA

In FDMA the base station transmits many carriers at once through a **common power amplifier**. To get high efficiency, the amplifier is run near saturation, where it is **non-linear**. A non-linear device produces **intermodulation (IM) products**: with carriers f₁ and f₂, third-order products at 2f₁ − f₂ and 2f₂ − f₁ fall inside the band, on other users' channels.

- IM products act as interference in other channels, and also spread the signal spectrum (spectral regrowth).
- Effects: lower signal-to-interference ratio and adjacent channel interference.
- Remedies: back off the amplifier into its linear region (lower efficiency), use linearisation, choose carrier frequencies so IM products do not fall on used channels, or use separate amplifiers per carrier.

#### Number of channels

**Given:** B_t = 25 MHz, B_guard = 100 kHz (at each edge), B_c = 200 kHz.

```text
 N = (B_t − 2·B_guard) / B_c
   = (25×10⁶ − 2 × 100×10³) / (200×10³)
   = (25 000 000 − 200 000) / 200 000
   = 24 800 000 / 200 000
   = 124
```

**Answer: N = 124 channels** (this is the GSM-900 case: 25 MHz band with 200 kHz carriers).

## Check yourself

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

1. Why does non-linear effect occur in FDMA base stations?
   A. Many carriers share a common power amplifier run near saturation
   B. Each carrier has its own linear amplifier
   C. Guard bands are too wide
   D. The channels are too narrow for mixers
   Answer: A. A common PA near saturation is non-linear and produces intermodulation. (Key point: Cause of non-linearity)

2. For carriers f1 and f2, which third-order products fall in band?
   A. 2f1 - f2 and 2f2 - f1
   B. f1 + f2 only
   C. f1 - f2 only
   D. 3f1 and 3f2
   Answer: A. These land near the carriers and interfere with other users' channels. (Key point: IM products)

3. Which is a remedy for IM interference?
   A. Back off the amplifier into its linear region
   B. Run it into saturation
   C. Remove guard bands
   D. Add more carriers
   Answer: A. Backoff, linearisation, careful frequency choice or separate amplifiers reduce IM. (Key point: Remedy)

4. With Bt = 25 MHz, Bg = 100 kHz at each edge and Bc = 200 kHz, N = ?
   A. 124
   B. 125
   C. 123
   D. 128
   Answer: A. (25000 - 200)/200 = 124. (Key point: Calculation)

## Related in Wireless Communication

- [Numerical: FDMA channels (12.8 MHz)](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Afdma-channels-12-8mhz) — Wireless Communication, chapter 7, asked 2×
- [Numerical: FDMA channels (12.5 MHz)](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Afdma-channels-12-5mhz) — Wireless Communication, chapter 7
- [Numerical: cellular vs non-cellular voice channels](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Acellular-vs-noncellular-channels) — Wireless Communication, chapter 2
- [CCI/ACI, reuse ratio proof and channels per cell](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Acci-aci-reuse-duplex-channels) — Wireless Communication, chapter 2
- [Numerical: 12-cell system capacity at 2% GOS](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Acellular-capacity-12-cell-system) — Wireless Communication, chapter 2
- [Numerical: 32-cell system area and channels](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Acellular-32-cells-capacity) — Wireless Communication, chapter 2

## Related in other subjects

- [FM numerical: 10 kHz baseband, 100 MHz carrier, 75 kHz deviation](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Afm-10khz-100mhz-75khz) — Communication Systems, chapter 3
- [FM numerical: 5cos(18849.55t), 9 kHz/V, 25 V, 88.7 MHz (five parts)](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Afm-5cos18849-five-parts) — Communication Systems, chapter 3, asked 3×
- [FM numerical: 102.4 MHz carrier, 75 kHz deviation](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Afm-102-4mhz-75khz) — Communication Systems, chapter 3
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