--- title: "Okumura vs Hata; delay spread numerical" subject: "Wireless Communication" chapter: 3 key: "semester_7/wireless_communication:okumura-hata-delay-spread" source: https://www.bctengineer.com/q/semester_7/wireless_communication/okumura-hata-delay-spread site: BCT Engineering --- # Okumura vs Hata; delay spread numerical Wireless Communication · Chapter 3: Radio Wave Propagation in Mobile Networks - Asked in: 2081 Bhadra, 4+6 marks - Video: [Outdoor Propagation Model Okumura - Mobile Radio Propagation - Mobile Communication System](https://www.youtube.com/watch?v=GqploKEmD3w) — Ekeeda - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_7/wireless_communication/okumura-hata-delay-spread - Whole chapter: https://www.bctengineer.com/md/semester_7/wireless_communication/chapter-3 ## Question Compare Okumura model with Hata model. Calculate mean excess delay, rms delay spread and maximum excess delay for the multipath profile Pr(τ) given as: Pr(τ) = (-20 dB, -10 dB, -10 dB, 0 dB) for τ = (0, 1, 2, 5) second. Also estimate 50% coherence bandwidth. ## Short answer Okumura uses measured curves, Hata gives closed-form formula with narrower range. For the profile, mean excess delay is 4.38 µs, rms delay spread 1.37 µs, maximum excess delay (10 dB) 5 µs, and 50% coherence bandwidth about 146 kHz. ## Answer #### Okumura vs Hata model | Point | Okumura model | Hata model | |---|---|---| | Basis | Measurements in Tokyo, given as curves | Empirical formula fitted to Okumura's curves | | Form | LF + Amu − G(hte) − G(hre) − GAREA | Closed-form equation in fc, hte, hre, d | | Frequency | 150–1920 MHz (to 3 GHz) | 150–1500 MHz | | Distance | 1–100 km | 1–20 km | | hte | 30–1000 m | 30–200 m | | Use in software | Hard (needs graph reading) | Easy | | Environments | Urban, suburban, open with corrections | Urban formula + suburban/rural corrections | | Accuracy | About 10–14 dB std. deviation | Very close to Okumura for d > 1 km | #### Delay spread calculation The delays are taken as **µs**, the usual unit for such a profile. (If they really are in seconds, the numbers are the same but every time is in s and Bc is in Hz.) | τ (µs) | Pr (dB) | Pr (linear) | |---|---|---| | 0 | −20 | 0.01 | | 1 | −10 | 0.1 | | 2 | −10 | 0.1 | | 5 | 0 | 1 | ```text ΣP = 0.01 + 0.1 + 0.1 + 1 = 1.21 ``` **Mean excess delay** ```text τ̄ = Σ P(τk)τk / ΣP = (0.01×0 + 0.1×1 + 0.1×2 + 1×5) / 1.21 = 5.3/1.21 = 4.38 µs ``` **Second moment** ```text τ²̄ = (0.01×0 + 0.1×1 + 0.1×4 + 1×25) / 1.21 = 25.5/1.21 = 21.07 µs² ``` **RMS delay spread** ```text στ = √(τ²̄ − τ̄²) = √(21.07 − 4.38²) = √(21.07 − 19.19) = 1.37 µs ``` **Maximum excess delay (10 dB)** By definition, τmax(X dB) = τX − τ0, where τ0 is the first arriving component and τX is the largest delay at which a component is within X dB of the strongest one. The strongest component is 0 dB at 5 µs, so τX = 5 µs; the first arrival is at τ0 = 0. ```text τmax(10 dB) = 5 − 0 = 5 µs ``` **50% coherence bandwidth** ```text Bc ≈ 1/(5στ) = 1/(5 × 1.374 µs) = 145.5 kHz ≈ 146 kHz ``` **Answer: τ̄ = 4.38 µs, στ = 1.37 µs, τmax(10 dB) = 5 µs, Bc(50%) ≈ 146 kHz.** ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Compared with Okumura, the Hata model: A. Needs graphs B. Covers 100 km C. Is a closed-form formula fitted to Okumura curves, easier in software D. Uses more curves Answer: C. Hata has a smaller range but is easy to code. (Key point: Okumura vs Hata) 2. The mean excess delay of the profile is: A. 4.38 us B. 5.3 us C. 2.0 us D. 1.37 us Answer: A. Sum P*tau = 5.3, sum P = 1.21, so 4.38 us. (Key point: Mean excess delay) 3. RMS delay spread is computed as: A. Mean of tau B. Max delay minus min C. Sum of P D. sqrt(mean of tau^2 - (mean tau)^2) Answer: D. sigma = sqrt(21.07 - 19.19) = 1.37 us. (Key point: RMS delay spread) 4. 50% coherence bandwidth is approximately: A. 730 kHz B. 14.6 kHz C. 1.46 MHz D. 146 kHz Answer: D. 1/(5*1.374 us) = 145.5 kHz. 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