--- title: "ISI and two practical methods to minimize it" subject: "Communication Systems" chapter: 6 key: "semester_6/communication_systems:isi-practical-methods" source: https://www.bctengineer.com/q/semester_6/communication_systems/isi-practical-methods site: BCT Engineering --- # ISI and two practical methods to minimize it Communication Systems · Chapter 6: Baseband Digital Data Transmission - Asked in: 2069 Chaitra (CS II), 2+6 marks - Video: [Inter Symbol Interference - ISI Explained | Basics, Bandwidth, and Mitigation Techniques](https://www.youtube.com/watch?v=zfF0R2yUn1k) — Engineering Funda - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/communication_systems/isi-practical-methods - Whole chapter: https://www.bctengineer.com/md/semester_6/communication_systems/chapter-6 ## Question What is ISI? Explain two practical methods of minimizing ISI. ## Short answer ISI is interference from neighbouring symbols due to pulse spreading. Raised cosine pulse shaping satisfies Nyquist zero-ISI criterion with roll-off factor α, providing fast tail decay. Adaptive equalisation (e.g., transversal filter) adjusts tap coefficients to cancel channel distortion, minimising ISI. ## Answer #### ISI **Intersymbol interference (ISI)** is the interference caused at the sampling instant of a symbol by the spread-out tails of neighbouring symbols. A band-limited, dispersive channel stretches each pulse beyond its own interval, so the sample becomes $$ y(kT_b) = \mu a_k + \mu\sum_{n\ne k}a_n\,p\big((k-n)T_b\big) + n(kT_b) $$ The sum term is ISI; it reduces the eye opening and causes errors even without noise. #### Method 1: Pulse shaping with raised cosine filters The transmit and receive filters are designed so that the overall pulse satisfies the Nyquist criterion, $p(nT_b) = 0$ for $n \ne 0$. The ideal sinc pulse is not realizable, so the **raised cosine** spectrum is used: - Roll-off factor $\alpha$ ($0 \le \alpha \le 1$); bandwidth $B_T = \frac{R_b}{2}(1 + \alpha)$. - $p(t) = \text{sinc}(t/T_b)\dfrac{\cos(\pi\alpha t/T_b)}{1 - 4\alpha^2t^2/T_b^2}$ has zeros at all other sampling instants. - Tails decay as $1/t^3$, so small timing errors cause little ISI. - It is usually split into root raised cosine filters at the transmitter and the receiver (which also gives matched filtering). Example: $R_b = 9600$ bps with $\alpha = 0.5$ needs $B_T = 4800 \times 1.5 = 7200$ Hz. #### Method 2: Equalization An **equalizer** is a filter at the receiver whose response cancels the channel distortion, so that the channel plus equalizer is close to a Nyquist pulse. The usual form is the **transversal (tapped delay line) equalizer**: ```text x(t)->[Tb]--->[Tb]--->[Tb]---> ... | | | | c-N c-N+1 ... cN (tap gains) | | | | +------+---(sum)-------+---> y(t) to detector ``` $$ y(kT_b) = \sum_{n=-N}^{N} c_n\,x\big((k-n)T_b\big) $$ - **Zero-forcing equalizer:** the $2N+1$ taps are chosen so that $y = 1$ at $k = 0$ and $y = 0$ at the $N$ nearest sampling points on each side ($2N$ points in all), forcing ISI to zero there. - **Adaptive equalizer:** the taps are adjusted continuously (LMS algorithm) using a training sequence or past decisions, so it tracks time-varying channels such as telephone and mobile links. (Other methods: correlative coding such as duobinary, and choosing the best sampling instant from the eye pattern.) ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What is intersymbol interference at the sampling instant? A. Interference from the spread-out tails of neighbouring symbols, even with no noise B. Interference from thermal noise added by the channel C. Interference from other users on the same carrier D. Loss of signal power due to channel attenuation Answer: A. A band-limited dispersive channel stretches pulses beyond their interval, so tails of other symbols add to the sample, causing errors even without noise. (Key point: Meaning of ISI) 2. What condition must the overall pulse p(t) satisfy to give zero ISI? A. p(t) = 0 for all t except t = 0 B. p(nTb) = 0 for n not equal to 0 C. p(nTb) = 1 for every n D. p(t) must be a rectangular pulse of width Tb Answer: B. The pulse must be zero at all other sampling instants so neighbouring symbols do not contribute to the sample. (Key point: Nyquist criterion) 3. For a raised cosine filter with roll-off alpha and bit rate Rb, the transmission bandwidth is A. BT = Rb(1 + alpha) B. BT = (Rb/2)(1 - alpha) C. BT = (Rb/2)(1 + alpha) D. BT = Rb/(2 alpha) Answer: C. Bandwidth is the ideal Rb/2 plus the excess set by the roll-off: (Rb/2)(1+alpha). For 9600 bps and alpha = 0.5 this is 7200 Hz. (Key point: Raised cosine bandwidth) 4. What does a transversal equalizer do? A. Increases the transmit power to overcome noise B. Removes ISI by widening the channel bandwidth C. Filters out noise by averaging over many symbols D. Uses tap gains on a delayed signal so channel plus equalizer approximates a Nyquist pulse Answer: D. The tapped delay line sums weighted delayed copies of the received signal so that the channel distortion is cancelled. (Key point: Role of equalizer) ## Related in Communication Systems - [ISI in baseband systems; ideal and practical solutions](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aisi-ideal-practical-solutions) — Communication Systems, chapter 6, asked 2× - [ISI, Nyquist zero-ISI conditions and practical constraints](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aisi-nyquist-zero-isi-constraints) — Communication Systems, chapter 6 - [Correlative coding; minimizing error in duobinary](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Acorrelative-coding-duobinary-error) — Communication Systems, chapter 6 - [ISI; solutions for zero ISI; duobinary with precoder](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aisi-zero-isi-duobinary-precoder) — Communication Systems, chapter 6 - [Nyquist criteria for zero ISI; duobinary difficulties](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Anyquist-zero-isi-duobinary-difficulties) — Communication Systems, chapter 6 - [Practical factors in sampling; sampling interval for X1(t)X2(t)](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Asampling-practical-x1x2) — Communication Systems, chapter 4 ## Related in other subjects - [Hydropower intake sketch; minimizing head loss](https://www.bctengineer.com/question.md?key=semester_7%2Fhydropower_engineering%3Ahydropower-intake-sketch-minimise-headloss) — Hydropower Engineering, chapter 5 - [Practical IA characteristics; optical isolation](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Aia-practical-characteristics-optical) — Advanced Electronics, chapter 4