--- title: "Numerical: 10 km link feasibility with Okumura" subject: "Wireless Communication" chapter: 3 key: "semester_7/wireless_communication:okumura-link-feasibility" source: https://www.bctengineer.com/q/semester_7/wireless_communication/okumura-link-feasibility site: BCT Engineering --- # Numerical: 10 km link feasibility with Okumura Wireless Communication · Chapter 3: Radio Wave Propagation in Mobile Networks - Asked in: 2074 Bhadra, 12 marks - Video: [OKUMURA AND HATA MODELS (SOLVED PROBLEMS)](https://www.youtube.com/watch?v=serB4I59bC0) — Prof. Barapate's Tutorials - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_7/wireless_communication/okumura-link-feasibility - Whole chapter: https://www.bctengineer.com/md/semester_7/wireless_communication/chapter-3 ## Question Estimate the feasibility of a 10-km wireless link in suburban area, with one access point and one client radio, using Okumura model for path loss. The median attenuation value is 20 dB and gain due to environment is 13 dB. The height of access point antenna is 100 m and that of client antenna is 10 m: a. Access point is connected to antenna with 5-dBi gain, with a transmitting power of 20-dBm and a receive sensitivity of -80-dBm b. Client is connected to antenna with 20-dBi gain, with a transmitting power of 15-dBm and a receive sensitivity of -75-dBm c. Cables in both systems are short, with a loss of 3-dB at each side at 2.4-GHz frequency of operation. ## Short answer Okumura path loss is 122.61 dB at 10 km. Received power is -83.61 dBm at the client and -88.61 dBm at the access point, both about 8.6 dB below sensitivity. The link is not feasible. ## Answer A link is **feasible** if the received power at each end is at least the receiver sensitivity. Path loss is found from Okumura's model and then a link budget is done for both directions. Given: d = 10 km, f = 2.4 GHz, Amu = 20 dB, GAREA = 13 dB, hte = 100 m, hre = 10 m. #### Step 1: Free space loss ```text λ = 3×10⁸ / 2.4×10⁹ = 0.125 m LF = 20 log(4πd/λ) = 20 log(4π × 10 000 / 0.125) = 120.05 dB ``` #### Step 2: Height gains and median path loss ```text G(hte) = 20 log(100/200) = −6.02 dB G(hre) = 20 log(10/3) = 10.46 dB L50 = LF + Amu − G(hte) − G(hre) − GAREA = 120.05 + 20 + 6.02 − 10.46 − 13 = 122.61 dB ``` #### Step 3: Link budget diagram ```text Access point Client 20 dBm Tx 15 dBm Tx −3 dB cable −3 dB cable +5 dBi ant <---- 122.61 dB ----> +20 dBi ant Rx sens −80 dBm Rx sens −75 dBm ``` #### Step 4: Forward link (AP → client) ```text Pr = 20 − 3 + 5 − 122.61 + 20 − 3 = −83.61 dBm Sensitivity = −75 dBm Margin = −83.61 − (−75) = −8.61 dB (fails) ``` #### Step 5: Reverse link (client → AP) ```text Pr = 15 − 3 + 20 − 122.61 + 5 − 3 = −88.61 dBm Sensitivity = −80 dBm Margin = −88.61 − (−80) = −8.61 dB (fails) ``` | Link | Received power | Sensitivity | Margin | |---|---|---|---| | AP → client | −83.61 dBm | −75 dBm | −8.61 dB | | Client → AP | −88.61 dBm | −80 dBm | −8.61 dB | **Answer: The 10 km link is NOT feasible**; both directions fall about 8.6 dB short of the receiver sensitivity (and there is no fade margin). It could be made feasible by using higher-gain antennas (e.g. a 15 dBi or higher antenna at the AP), lower-loss cables, higher transmit power within limits, or a shorter distance. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. When is the link feasible? A. When path loss exceeds 100 dB B. When received power is at least the receiver sensitivity in both directions C. When transmit powers are equal D. When antenna gains are equal Answer: B. A link works only if Pr is at or above sensitivity at each end. (Key point: Feasibility criterion) 2. L50 = LF + Amu − G(hte) − G(hre) − GAREA gives: A. 102.6 dB B. 122.61 dB C. 142.6 dB D. 120.05 dB Answer: B. 120.05 + 20 + 6.02 − 10.46 − 13 = 122.61 dB. (Key point: Median path loss) 3. AP to client received power is: A. −63.6 dBm B. −73.6 dBm C. −88.6 dBm D. −83.61 dBm Answer: D. 20 − 3 + 5 − 122.61 + 20 − 3 = −83.61 dBm, 8.61 dB below −75 dBm. (Key point: Forward link budget) 4. Client to AP received power and margin are: A. −88.61 dBm, margin −8.61 dB B. −88.61 dBm, margin +8.61 dB C. −83.61 dBm, margin −8.61 dB D. −78.61 dBm, margin +1.4 dB Answer: A. 15 − 3 + 20 − 122.61 + 5 − 3 = −88.61 dBm versus −80 dBm sensitivity. (Key point: Reverse link budget) 5. What is the conclusion? A. Feasible with 8.6 dB margin B. Feasible only forward C. Feasible only reverse D. Not feasible; improve with higher-gain antennas, lower-loss cable, more power or shorter distance Answer: D. Both directions fall about 8.6 dB short of sensitivity. 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