Question

Question 4: Four RX power measurements were taken at distances of 100m, 200m, 1km and 3km from a TX and the measured RX power levels are OdBm, -20dBm, -35dBm and 70dBm, respectively. Assume the path loss obeys the log-distance model. Find the path loss exponent n that minimizes mean square error (MSE) between measuredand modeled values. (Hint: Use Log distance Path Propagation Model)

Answer 1

oln: Measured power at distance lcom, 200m, 1km, 3km respectively od Bm, -20dBm , - 35dBm, – 70dBm. Distance from bransmitter Tx Received power 10om o dom 200 m - 20dBm - 35 dom 1000 m 3000m - 70 dBm Pr (do) = odom. Log distance propagation path model is written as Prld) = Prldo) - lon log (est) Pr (200m) - o - lon log (200) - - 3.0] n Po clocom) - o-lon log (4000) = -ion Pr (3000m) - 0 - lon log ( 3our) - - 14.971 Mean Square error is wiitten as MSE = √ {(P; _P:)? Pi = actual power measured value ê, - estimated power values. no of sampling peint- as / 22/ REDMI NOTE 8 AI QUAD CAMERA

Distance Measured valuese paver indom estimated values of powe indom 100m 200m - 3.012 1000 m -lon 3ooom - 14.77n MSE = V CO-O)2 +(-20-(-3.01n))2+(-35-(-10n)) +(-70-C-14.748)2 MSE - 327.21 m2 - 2888.2 n +6525 Minimizing the fuutim mith respect to n Ms&2 = 327.21n2, 2888.20 + 6525 Jakief deszivative with respect ton we have, 2 HansF) 654.421- 2888.2 dn . d(MSE) 327.210 - 1444 1 =0 = 327.21 din n = 4.41 44 OO REDMI NOTE 8 C AI QUAD CAMERA