--- title: "Equalization fundamentals and RAKE receiver" subject: "Wireless Communication" chapter: 5 key: "semester_7/wireless_communication:equalization-fundamentals-rake" source: https://www.bctengineer.com/q/semester_7/wireless_communication/equalization-fundamentals-rake site: BCT Engineering --- # Equalization fundamentals and RAKE receiver Wireless Communication · Chapter 5: Equalization and Diversity - Asked in: 2070 Magh, 4+4 marks - Video: [Rake Receiver (Principle, Construction and Working)- CDMA,WCDMA, Fading in Wireless Communication](https://www.youtube.com/watch?v=sC_Hx_SwMsk) — All About Education - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_7/wireless_communication/equalization-fundamentals-rake - Whole chapter: https://www.bctengineer.com/md/semester_7/wireless_communication/chapter-5 ## Question Describe the fundamentals of equalization with respect to communication system. Explain with block diagram the function of RAKE receiver. ## Short answer Equalization removes inter-symbol interference (ISI) caused by multipath or band-limited channels using an adaptive filter that approximates the channel inverse. The RAKE receiver in CDMA uses multiple correlators ('fingers') aligned to different multipath delays, weights each by its strength, and combines them for maximal ratio combining, turning multipath into diversity gain. ## Answer #### Fundamentals of equalization **Equalization** is a receiver technique that removes **inter-symbol interference (ISI)** caused by multipath delay spread or band-limited channels. ISI appears when the delay spread is comparable to the symbol period, so symbols overlap and the error rate becomes high. - The equalizer is a filter whose response is the inverse of the channel: F(f)·H_eq(f) = 1, i.e. f(t) * h_eq(t) = δ(t), giving an overall flat, ISI-free response. - Since the mobile channel is unknown and time-varying, the equalizer is **adaptive**: 1. **Training mode:** a known training sequence is sent; the error e(k) = d(k) − d̂(k) is used to set the taps. 2. **Tracking mode:** detected data symbols are used as the reference to follow channel changes. - Basic structure: a **transversal (tapped delay line) filter**, d̂(k) = Σ wₙ·y(k − n). - Types: linear (transversal, lattice) and non-linear (decision feedback equalizer, MLSE). - Algorithms: zero forcing, LMS, RLS. ```text y(k)->[T]->[T]->...->[T] | | | | w0 w1 w2 ... wN (adapted by LMS/RLS) +----+----+----------+--(Σ)--> d^(k) -> decision ``` #### RAKE receiver A **RAKE receiver** is used in CDMA to collect the energy of several multipath copies instead of suffering from them. Paths that arrive more than one chip apart are resolvable because the PN code has low autocorrelation away from zero shift. ```text +------------+ +----+ w1 +--->| Correlator |-->|Z1 |--(x)--+ | | code c(t) | +----+ | | +------------+ | r(t) | +------------+ +----+ w2 v +-------+ ------>+--->| Correlator |-->|Z2 |--(x)-(+)->|Integr.| | | c(t - τ2) | +----+ ^ | & dec.| | +------------+ | +-------+ | +------------+ +----+ wM | | +--->| Correlator |-->|ZM |--(x)--+ v | c(t - τM) | +----+ data bits +------------+ (one "finger" per resolvable multipath) ``` **Function** 1. *M* correlators ("fingers") each despread the received signal using the PN code delayed to match one strong multipath delay τₖ. 2. A searcher finds the path delays and amplitudes and assigns fingers. 3. Finger outputs Zₖ are weighted by wₖ (proportional to path strength) and summed: Z′ = Σ wₖZₖ (maximal-ratio combining). 4. The sum is integrated over the bit period and a decision gives the data. So multipath, which causes ISI in narrowband systems, is turned into **time diversity**, raising SNR and reducing fading in IS-95 and WCDMA. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What problem does an equalizer remove? A. Co-channel interference B. Inter-symbol interference from delay spread or band-limiting C. Thermal noise D. Doppler shift Answer: B. Equalization removes ISI that appears when delay spread is comparable to the symbol period. (Key point: Purpose of equalization) 2. In the training mode of an adaptive equalizer, what is used to set the taps? A. Detected data symbols B. The PN code C. The error between a known training sequence and the output D. The channel bandwidth Answer: C. A known training sequence gives e(k) = d(k) - d^(k), which adapts the taps; tracking mode later uses detected symbols. (Key point: Training vs tracking) 3. Which multipath components can a RAKE receiver resolve? A. Those arriving less than a chip apart B. Only the strongest path C. Paths with identical delays D. Those arriving more than one chip apart, because PN autocorrelation is low away from zero shift Answer: D. Low PN autocorrelation at non-zero shifts lets paths separated by more than one chip be despread separately. (Key point: RAKE resolvability) 4. How are RAKE finger outputs combined? A. Weighted in proportion to path strength and summed (maximal-ratio combining) B. Multiplied together C. Averaged with equal weights only D. Only the first finger is used Answer: A. Z' = sum of w_k Z_k with weights proportional to path strength is maximal-ratio combining. (Key point: Finger weights) 5. What does the RAKE receiver turn multipath into? A. Frequency diversity at the transmitter B. Additional ISI C. Time diversity that raises SNR D. Higher Doppler spread Answer: C. Multipath copies are collected and combined, giving time diversity instead of fading loss. (Key point: Multipath as diversity) ## Related in Wireless Communication - [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× - [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 - [Short note: RAKE receiver](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Arake-receiver-note) — Wireless Communication, chapter 5 - [ISI, RAKE and linear transversal equalizer](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Aisi-rake-linear-transversal-equalizer) — Wireless Communication, chapter 5 - [MLSE equalization](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Amlse-equalization) — Wireless Communication, chapter 5 ## Related in other subjects - [Block diagram of digital communication system](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Ablock-diagram-digital-comm) — Data Communication, chapter 1, asked 8× - [Communication system and block diagram](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Acomm-system-block-diagram) — Basic Electronics Engineering, chapter 5, asked 7× - [Modulation; analog communication system block diagram](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Amodulation-analog-block-diagram) — Communication Systems, chapter 1, asked 3× - [Block diagram of analog communication system](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aanalog-comm-block-diagram) — Communication Systems, chapter 1, asked 2×