Examples of Large-Scale Path Loss Models

Examples of Large-Scale Path Loss Models

Free Space Propagation Model The free space power received by a receiver antenna which is separated from a radiating transmitter antenna by a distance d, is given by the Friis free space equation P r (d) = P tg t G r λ 2 (4π) 2 d 2 L 2

Free Space Propagation Model (continued) In the Friis free space equation of the previous slide P t = transmitted power P r (d) = received power which is a function of the T-R separation G t = transmitter antenna gain G r = receiver antenna gain L = system loss factor not related to propagation (L 1) λ = wavelength in meters 3

Path Loss for the Free Space Model The path loss for the free space model when the antenna gains are included is given by PL(dB) = 10 log P [ ] t G t G r λ 2 = 10 log P r (4π) 2 d 2 When the antenna are assumed to have unity gain, the path loss for the free space model is given by PL(dB) = 10 log P [ ] t λ 2 = 10 log P r (4π) 2 d 2 4

Example: Free Space Model A mobile receiver is located at the cell boundary which is R km from the base station. The base station transmits at the carrier frequency is 2000MHz with 1W power. Transmitting antenna gain G t = 1.64 and receiving antenna gain G r = 1. Assume the speed of propagation for electromagnetic waves = 3 10 8 m/s, miscellaneous loss is equal to 1 and minimum power required by the mobile to operate is -90dBm. The heights of the transmitting and receiving antennas are 50m and 1.5m, respectively. Please find the cell radius, R (km), when path loss obeys the Free Space model. 5

Ground Reflection (2-Ray) Model At large values of d, the received power is where P r (d) = P tg t G r h 2 th 2 r d 4 h t = transmitter antenna height h r = receiver antenna height 6

Path Loss for the 2-Ray Model The path loss for the 2-ray model (with antenna gains) can be expressed in db as P L(dB) = 10 log P t P r P t = 10 log h P t G t G 2 t h2 r r d 4 d = 10 log 4 G t G r h 2 th 2 r = 40 log d 10 log (G t G r ) 20 log (h t h r ) Comments: Both Free Space and 2-ray models are based on theory 7

Example: 2-Ray Model A mobile receiver is located at the cell boundary which is R km from the base station. The base station transmits at the carrier frequency is 2000MHz with 1W power. Transmitting antenna gain G t = 1.64 and receiving antenna gain G r = 1. Assume the speed of propagation for electromagnetic waves = 3 10 8 m/s and minimum power required by the mobile to operate is -90dBm. If the heights of the transmitting and receiving antennas are 50m and 1.5m, respectively, please find the cell radius R km, when the path loss obeys 2-ray model. 8

Log-distance Path Loss Model It indicates that average received signal power decreases logarithmically with distance PL(d) = PL(d 0 ) + 10n log d d 0 n = path loss exponent which indicates the rate at which the path loss increases with distance In free space n = 2, in urban areas n = 2.7 4 d 0 = close-in reference distance which is determined from measurements close to the transmitter d = T-R separation distance 9

Limitations of Previous Path Loss Models The previous models ignore the fact that the surrounding environment clutter may be vastly different at two different locations having the same T-R separation distance 10

Log-normal Shadowing Model This model takes into account the fact that at any value of d, the path loss PL(d) at a particular location is random and distributed log-normally (normal in db) about the mean distance dependent value According to this model path loss at a T-R separation distance d is expressed as PL(d)[dB] = PL(d) + X σ = PL(d 0 ) + 10n log d + X σ d 0 X σ N (0, σ), i.e. X σ is a zero-mean Gaussian distributed random variable (in db) with standard deviation σ (also in db) 11

Received Signal under Log-normal Shadowing The received signal for this model is expressed as P r (d) = = P t PL(d) [ P t PL(d 0 ) 10n log d ] d 0 X σ = P r (d) + X σ Comments: P r (d) N ( P r (d), σ ) 12

QoS at Distance d The probability that the received signal level at distance d will exceed a certain value (threshold) γ can be calculated as Prob[P r (d) > γ] = Q γ P r(d) σ 13

Example: Log-normal Shadowing The base station transmits at the carrier frequency is 2000MHz with 1W The speed of propagation for electromagnetic waves = 3 10 8 m/s The heights of the transmitting and receiving antennas are 50m and 1.5m, respectively Transmitting antenna gain G t = 1.64 and receiving antenna gain G r = 1 The measured power at reference distance d 0 = 0.1 km from the base station follows the Free Space model At distance d > d 0, the mean of the received power is proportional to 1/d 4 and lognormally distributed with standard deviation 10dB Minimum power required by the mobile to operate is -90dBm, which must be guaranteed at the cell boundary with probability 0.75 Please find the radius, R, of the cell 14

Conclusions of Today s Class As the environment becomes challenging, for a given transmitted power, the cell coverage area reduces To handle the above situation, the transmitter power should be adjusted based on the environment and the target coverage area 15