---
title: "ISI, RAKE and linear transversal equalizer"
subject: "Wireless Communication"
chapter: 5
key: "semester_7/wireless_communication:isi-rake-linear-transversal-equalizer"
source: https://www.bctengineer.com/q/semester_7/wireless_communication/isi-rake-linear-transversal-equalizer
site: BCT Engineering
---

# ISI, RAKE and linear transversal equalizer

Wireless Communication · Chapter 5: Equalization and Diversity

- Asked in: 2082 Bhadra, 2+1+4 marks
- Video: [Linear Equalizer](https://www.youtube.com/watch?v=wPZy9PBcFhs) — 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/isi-rake-linear-transversal-equalizer
- Whole chapter: https://www.bctengineer.com/md/semester_7/wireless_communication/chapter-5

## Question

Describe a signal processing operation that minimizes the effects of ISI. What do you understand by RAKE receiver? Explain the structure of linear transversal equalizer with appropriate diagram.

## Short answer

Equalization minimizes ISI by filtering with the inverse channel response. A RAKE receiver correlates each multipath finger in CDMA and combines them for diversity gain. A linear transversal equalizer is a tapped-delay-line FIR filter with adaptive tap weights adjusted by LMS to minimize error.

## Answer

#### Signal processing to minimize ISI
**Equalization** is the signal processing operation that minimizes ISI. An equalizer is a filter at the receiver whose response is roughly the inverse of the channel, so the combined channel + equalizer response is flat. Because the mobile channel changes with time, the equalizer is **adaptive** and tracks the channel using training sequences and decision feedback.

#### RAKE receiver
A **RAKE receiver** is a multi-correlator CDMA receiver. Each correlator ("finger") locks to one multipath component delayed by at least one chip, and the finger outputs are weighted and combined. It turns multipath into diversity gain instead of ISI.

#### Linear transversal equalizer (LTE)
The most common equalizer structure is a **tapped delay line (FIR) filter**. The received signal passes through a chain of delay elements of one symbol period T; each tap output is multiplied by an adjustable complex weight c_n, and all products are summed.
```text
y_k ─┬─[T]─┬─[T]─┬─[T]─┬─ ... ─[T]─┐
     │     │     │     │           │
   (x)c₋N₁ (x)  (x)   (x)  ...   (x)c_N₂
     │     │     │     │           │
     └─────┴─────┴──(Σ)┴───────────┘
                     │
                     v d̂_k ─►[Decision]─► x̂_k
                     │
        x_k (training) ─►(−)─► e_k ─► [Adapt taps]
```
Output:
```text
d̂_k = Σ_(n = −N₁)^(N₂) c_n* y_(k−n)
```
- N₁ = number of taps for future (precursor) samples, N₂ for past (postcursor) samples.
- The error e_k = x_k − d̂_k (or decision − d̂_k in tracking mode) is used by an algorithm such as **LMS** to adjust the taps.
- The minimum MSE of an LTE is:
```text
E[|e|²] = (T/2π) ∫_(−π/T)^(π/T) N₀ dω / (|F(e^jωT)|² + N₀)
```
**Merits:** simple, stable, easy to adapt.
**Limitation:** in channels with deep spectral nulls it boosts noise a lot, so non-linear equalizers (DFE, MLSE) are preferred for severe multipath.

## Check yourself

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

1. Which operation minimizes ISI?
   A. Spreading with a PN code
   B. Increasing the carrier frequency
   C. Gaussian filtering
   D. Equalization, a filter approximating the inverse of the channel
   Answer: D. Combined channel plus equalizer gives a flat response. (Key point: ISI operation)

2. Why are mobile equalizers adaptive?
   A. The channel is time-varying, so taps are set with a training sequence and then tracked
   B. The channel never changes
   C. Tap values are fixed in the factory
   D. They need no training
   Answer: A. Training sets weights; decision feedback tracks changes. (Key point: Adaptive)

3. What is a linear transversal equalizer?
   A. A bank of PN correlators
   B. A tapped delay line (FIR) with adjustable complex weights c_n and summed outputs
   C. An IFFT with a cyclic prefix
   D. A Viterbi trellis
   Answer: B. Delays of one symbol period, weights adapted by e.g. LMS. (Key point: LTE structure)

4. What is a limitation of the LTE?
   A. It is unstable always
   B. It cannot be adapted
   C. In channels with deep spectral nulls it boosts noise
   D. It needs a PN code
   Answer: C. DFE or MLSE are preferred in severe multipath. (Key point: LTE limitation)

## Related in Wireless Communication

- [ISI mitigation and M-branch RAKE receiver](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Aisi-rake-m-branch) — Wireless Communication, chapter 5
- [Diversity and RAKE receiver operation](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Adiversity-rake-operation) — Wireless Communication, chapter 5
- [RAKE receiver and M-branch RAKE](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Arake-m-branch) — Wireless Communication, chapter 5, asked 2×
- [Equalization fundamentals and RAKE receiver](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Aequalization-fundamentals-rake) — Wireless Communication, chapter 5
- [Short note: RAKE receiver](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Arake-receiver-note) — 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