---
title: "Short note: Adaptive equalization"
subject: "Wireless Communication"
chapter: 5
key: "semester_7/wireless_communication:adaptive-equalization-note"
source: https://www.bctengineer.com/q/semester_7/wireless_communication/adaptive-equalization-note
site: BCT Engineering
---

# Short note: Adaptive equalization

Wireless Communication · Chapter 5: Equalization and Diversity

- Asked in: 2074 Magh, 5 marks
- Video: [Wireless Technology | Adaptive Equalizer](https://www.youtube.com/watch?v=04ltaflxFB8) — RANJI RAJ
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/wireless_communication/adaptive-equalization-note
- Whole chapter: https://www.bctengineer.com/md/semester_7/wireless_communication/chapter-5

## Question

Write a short note on adaptive equalization.

## Short answer

Adaptive equalization automatically updates filter taps to cancel time-varying ISI. Training mode uses a known sequence to set taps optimally; tracking mode then uses receiver decisions for continuous updating. Common algorithms include LMS and RLS, and structures are linear transversal, decision-feedback, and MLSE equalizers.

## Answer

**Adaptive equalization** is equalization in which the filter coefficients are adjusted automatically to track a time-varying channel, so that inter-symbol interference (ISI) is removed even as the mobile moves.

**Why adaptive:** the mobile radio channel is unknown and changes with time (Doppler, moving scatterers), so a fixed equalizer cannot stay matched to it.

```text
 x(k)   +-------------------+ d^(k)   +----------+
 ------>| Transversal filter|-------->| Decision |--> d~(k)
        | taps w0..wN       |    |    +----------+   |
        +-------------------+    |                   |
               ^                 v                   |
               |     e(k)=d(k)-d^(k)  <-- d(k) ------+
               +---- adaptive algorithm (LMS/RLS)
     d(k): training sequence, or decided symbol later
```

**Two modes of operation**

1. **Training mode** – The transmitter sends a known, fixed-length **training sequence** (e.g. a PN sequence or the GSM midamble). The receiver knows d(k), computes the error e(k) = d(k) − d̂(k), and the algorithm sets the tap weights to near optimum.
2. **Tracking (decision-directed) mode** – After training, user data follows. The detector's own decisions d̃(k) are used as the reference to keep updating the taps as the channel slowly changes.

Training is repeated periodically (for TDMA, in every burst/time slot).

**Algorithms**
- **Zero forcing (ZF)** – forces ISI to zero; amplifies noise at spectral nulls.
- **LMS** – w(k+1) = w(k) + μ·e(k)·x(k); simple (2N+1 operations per iteration), slow convergence.
- **RLS** – faster convergence, more computation.

**Structures:** linear transversal equalizer, decision feedback equalizer (DFE), and MLSE (Viterbi) equalizer.

**Performance factors:** rate of convergence, misadjustment, computational complexity and numerical stability.

## Check yourself

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

1. Why can a fixed equalizer not be used in a mobile channel?
   A. The channel is unknown and time-varying
   B. The channel is perfectly known
   C. Fixed equalizers cannot be built
   D. The mobile has no processor
   Answer: A. Doppler and moving scatterers change the channel. (Key point: Why adaptive)

2. Which describes the two modes?
   A. Training uses decisions; tracking uses known sequence
   B. Training uses a known sequence; tracking uses the detector's decisions
   C. Both use known sequence
   D. Both use random data
   Answer: B. Decision-directed mode follows slow channel changes after training. (Key point: Training and tracking)

3. Which is the LMS update?
   A. w(k+1) = w(k) - mu x(k)
   B. w(k+1) = mu w(k)
   C. w(k+1) = w(k) + mu e(k) x(k)
   D. w(k+1) = e(k)/x(k)
   Answer: C. Weights move by step size times error times input. (Key point: LMS update)

4. What is the drawback of zero forcing?
   A. Is too slow to converge
   B. Needs M^L states
   C. Cannot reduce ISI
   D. Amplifies noise at spectral nulls
   Answer: D. Forcing ISI to zero boosts noise where the channel has nulls. (Key point: Zero forcing drawback)

## Related in Wireless Communication

- [Interleaving and adaptive equalization of ISI](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Ainterleaving-adaptive-equalizer) — Wireless Communication, chapter 5
- [Adaptive equalization algorithms (any two)](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Aadaptive-equalization-algorithms) — Wireless Communication, chapter 5