Path Loss Models and Link Budget

Transcription

1 Path Loss Models and Link Budget

2 A universal path loss model P r dbm = P t dbm + db Gains db Losses Gains: the antenna gains compared to isotropic antennas Transmitter antenna gain Receiver antenna gain

3 Losses: path loss large scale path loss (path loss on average) Reflection, diffraction, scattering, or shadowing losses (if you know these specifically) imperfect matching small scale fading loss (receive power variation over very short distance. This is random, we have to prepare for deep fading. So we d have a fading margin.) other margins

4 Path loss models Theoretical: 1. Free Space path loss, 2. Exponential Decay Empirical: 3. Path loss exponent model

5 1. Free Space Path Loss Friis Equation 2 λ P r = P t G t G r = P 4πd t G t G r /L p P r dbm = P t dbm + G t db + G r db L p db P r is the received power, not average received power P t is the transmit power G t is the transmitter antenna gain. Effective Isotropic Radiated Power (EIRP) is P t G t G r is the receiver antenna gains. 4πd L p db = 20log 10 is the free space path loss λ λ is the wavelength. Wavelength λ = c where c = 3 f 10 8 m/s is the speed of light, and f is the frequency.

6 Free Space Path Loss Friis Equation 2 λ P r = P t G t G r = P 4πd t G t G r /L p P r dbm = P t dbm + G t db + G r db L p db Why P r is proportional to d 2? Why P r is proportional to λ 2? Space communications, satellite communications

7 Received Power Reference In some cases, the antenna gains and mismatches and transmit power are not known, while the received power at the certain distance d 0 can be measured λ d0 d 0 P r = P t G t G r = P 4πd 0 d 0 d d P r dbm = P 0 dbm 20log 10 λ 2 where P 0 = P t G t G r, is the received power at 4πd 0 the reference distance d 0. Keep in mind this is the actual received power, not on average. d 0

8 Antenna gain Isotropic radiator Antenna gain G is 1 (linear terms) or 0 db in all directions. Does not exist in practice Any antenna that is not isotropic is directive dbi: Gain compared to isotropic radiator Directivity D = P r(maximum) P r (isotropic) where P r (maximum) is the maximum received power (at the same distance but max across angle)

9 Half-wave dipole antenna Antenna gains referred to dipole: dbd: Gain compared to a half-wave dipole antenna. The 1/2 wave dipole has gain 1.64 (linear) or 2.15 db, so dbi is 2.15 db greater than dbd.

10 Antenna mismatches Γ t and Γ r. Both are 1, and only one if there is a perfect impedance match and no loss.

11 2. Exponential Decay P r = P t G t G r λ 4πd 2 10 αd/10 due to its propagation through certain medium that absorbs the power for example, at 60 GHz, at which oxygen molecules absorb RF radiation, or due to rain at 30 GHz

12 3. Path Loss Exponent Model d P r dbm = P 0 dbm 10nlog 10 d 0 find the parameter n from measurements

13 Path Loss Exponent Model d P r dbm = P 0 dbm 10nlog 10 d 0 For some situations, P 0 is not available or the measurement at d 0 varies significantly over a very short distance (much shorter than d 0 ), such as an indoor environment, what to do? Recall that P 0 (intercept) and n (slope) both are parameters of a linear function of P r dbm with respect to 10log 10 (d/d 0 ). Given sufficient number of measurements over different distance d, both P 0 and n can be calculated. The math tool is linear fit (linear regression).

14 Link budgeting Accounting the gains and losses that occur in a radio channel between a transmitter and receiver. For a given required S/N ratio (SNR), some valid questions are: What is the required base station (or mobile) transmit power? What is the maximum coverage (i.e., path length)? What is the effect of changing the frequency of operation? S/I, S/N, C/N (carrier to noise ratio), P r /P N

15 Link Budget S N db = P r dbw P N dbw = P t dbw + db Gains db Losses P N dbw P N : noise power Receiver sensitivity: required S N + P N dbw.

16 Thermal noise P N = FkT 0 B k is Boltzmann s constant, k = J/K. The units are J/K (Joules/Kelvin) or W s/k (1 Joule = 1 Watt second). T 0 is the ambient temperature, typically taken to be K. If not given, use 294 K, which is 70 degrees Fahrenheit. B is the bandwidth, in Hz (equivalently, 1/s). F is the (unitless) noise figure, which quantifies the gain to the noise produced in the receiver. The noise figure F = SNR out /SNR in 1.

17 In db terms, P N dbw = F db + k dbws/k + T 0 dbk + B(dBHz) k dbws/k = 10 log J/K = dbws/k

18 Noise figure and noise temperature of a receiver Equivalent noise temperature of receiver T e the level of available noise power introduced by a receiver Input Signal S Input Noise N i Temperature T 0 F = SNR out /SNR in = 1 + T e Gain G Receiver Noise N e Noise Temp. T e T 0 Output Signal GS Output Noise G(N i +N e )

19 Relationship among link budget variables

20 Example Assume two wireless sensors 1 foot above ground need to communicate over a range of 30 meters. They operate the standard (DS-SS at 2.4 GHz). Assume the log-distance model with reference distance 1m, with path loss at 1 m is Π 0 = 40dB, and path loss exponent 3 beyond 1m. Assume the antenna gains are both 3.0 dbi. The transmitter is the TI CC2520, which has max P t = 1 mw, and its spec sheet gives a receiver sensitivity of -98 dbm. What is the fading margin at a 30 meter range?

21 Solution Margin is the difference between the expected receive power and the receiver sensitivity (P N (dbm) plus the required S/N(dB) S N db = P r dbm P N dbm = P t dbm + db Gains db Losses P N dbm Receiver Sensitivity = S N db + P N dbm = P t dbm + db Gains db Losses = P t dbm + G t db + G r db L p db Margin(dB)

22 Margin(dB) = P t dbm + G t db + G r db L p db Receiver Sensitivity 1. P t dbm = 0dBm. 2. G t db = G r db = 3. d 3. L p db = Π nlog 10 = 40 + d log 10 = 84.3dB 1 4. Receiver Sensitivity = 98dBm Margin(dB)=19.7dB