Pathloss and Link Budget From Physical Propagation to Multi-Path Fading Statistical Characterization of Channels. P r = P t Gr G t L P

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1 Path Loss I Path loss L P relates the received signal power P r to the transmitted signal power P t : P r = P t Gr G t L P, where G t and G r are antenna gains. I Path loss is very important for cell and frequency planning or range predictions. I Not needed when designing signal sets, receiver, etc. 2018, B.-P. Paris ECE 732: Mobile Communications 7

2 Received Signal Power I Received Signal Power: P r = P t Gr G t L P L R, where L R is implementation loss, typically 2 3 db. 2018, B.-P. Paris ECE 732: Mobile Communications 8

3 Noise Power I (Thermal) Noise Power: P N = kt 0 B W F, where I k Boltzmann s constant ( Ws/K), I T 0 temperature in K (typical room temperature, T 0 = 290 K), I ) kt 0 = W/Hz = mw/hz = 174 dbm/hz, I B W signal bandwidth, I F noise figure, figure of merit for receiver (typical value: 5dB). 2018, B.-P. Paris ECE 732: Mobile Communications 9

4 Signal-to-Noise Ratio I The ratio of received signal power and noise power is denoted by SNR. I From the above, SNR equals: SNR = P r P N = P t G r G t kt 0 B W F L P L R. I SNR increases with transmitted power P t and antenna gains. I SNR decreases with bandwidth B W, noise figure F, and path loss L P. 2018, B.-P. Paris ECE 732: Mobile Communications 10

5 E s /N 0 I For the symbol error rate performance of communications system the ratio of signal energy E s and noise power spectral density N 0 is more relevant than SNR. I Since E s = P r T s = P r and N 0 = kt 0 F = P N /B W, it follows that R s E s N 0 = SNR BW R s, where T s and R s denote the symbol period and symbol rate, respectively. I The ratio R S B W is called the bandwidth efficiency; it is a property of the signaling scheme. 2018, B.-P. Paris ECE 732: Mobile Communications 11

6 E s /N 0 I Thus, E s /N 0 is given by: E s N 0 = P t G r G t kt 0 R s F L P L R. I in db: ( E s N 0 ) (db) = P t(dbm) + G t(db) + G r(db) (kt 0 ) (dbm/hz) R s(dbhz) F (db) L R(dB). 2018, B.-P. Paris ECE 732: Mobile Communications 12

7 Receiver Sensitivity I All receiver-related terms are combined into receiver sensitivity, S R : I in db: S R = E s N 0 kt 0 R s F L R. S R(dBm) = ( E s N 0 ) (db) +(kt 0 ) (dbm/hz) + R s(dbhz) + F (db) + L R(dB). I Receiver sensitivity indicates the minimum required received power to close the link. 2018, B.-P. Paris ECE 732: Mobile Communications 13

8 Exercise: Receiver Sensitivity Find the sensitivity of a receiver with the following specifications: I Modulation: BPSK I bit error rate: 10 4 I data rate: R s = 1 Mb/s I noise figure: F = 5 db I receiver loss: L R = 3 db Error Probability E s /N 0 (db) Bit error probability for BPSK in AWGN 2018, B.-P. Paris ECE 732: Mobile Communications 14

9 Exercise: Maximum Permissible Pathloss I A communication system has the following specifications: I Transmit power: P t = 1W I Antenna gains: G t = 3 db and G R = 0 db I Receiver sensitivity: S R = 98 dbm I What is the maximum pathloss that this system can tolerate? 2018, B.-P. Paris ECE 732: Mobile Communications 15

10 Path Loss I Path loss modeling may be more an art than a science. I Typical approach: fit model to empirical data. I Parameters of model: I d - distance between transmitter and receiver, I f c - carrier frequency, I h b, h m - antenna heights, I Terrain type, building density,... I Examples that admit closed form expression: free space propagation, two-ray model 2018, B.-P. Paris ECE 732: Mobile Communications 16

11 Example: Free Space Propagation I In free space, path loss L P is given by Friis s formula: L P = 4pd l c 2 = 4pfc d c 2. I Path loss increases proportional to the square of distance d and frequency f c. I In db: L P(dB) = 20 log 10 ( c 4p )+20 log 10(f c )+20 log 10 (d). I Example: f c = 1 GHz and d = 1 km L P(dB) = 146 db db + 60 db = 94 db. 2018, B.-P. Paris ECE 732: Mobile Communications 17

12 Example: Two-Ray Channel I Antenna heights: h b and h m. I Two propagation paths: 1. direct path, free space propagation, 2. reflected path, free space with perfect reflection. I Depending on distance d, the signals received along the two paths will add constructively or destructively. 2018, B.-P. Paris ECE 732: Mobile Communications 18

13 Example: Two-Ray Channel I For the two-ray channel, path loss is approximately: L P = 1 4 4pfc d c 2 1 sin( 2pf ch b h m cd )! 2. I For ld h b h m, path loss is further approximated by: L P d 2 h b h m 2 I Path loss proportional to d 4 is typical for urban environment. 2018, B.-P. Paris ECE 732: Mobile Communications 19

14 Example: Two-Ray Channel Path Gain (db) Distance (m) 2018, B.-P. Paris ECE 732: Mobile Communications 20

15 Exercise: Maximum Communications range I Path loss models allow translating between path loss P L and range d. I A communication system can tolerate a maximum path loss of 131 db. I What is the maximum distance between transmitter and receiver if path loss is according to the free-space model. I How does your answer change when path loss is modeled by the two-ray model and h m = 1 m, h b = 10 m. 2018, B.-P. Paris ECE 732: Mobile Communications 21

16 Okumura-Hata Model for Urban Area I Okumura and Hata derived empirical path loss models from extensive path loss measurements. I Models differ between urban, suburban, and open areas, large, medium, and small cities, etc. I Illustrative example: Model for Urban area (small or medium city) where L P(dB) = A + B log 10 (d), A = log 10 (f c ) log 10 (h b ) a(h m ) B = log 10 (h b ) a(h m ) = (1.1 log 10 (f c ) 0.7) h m (1.56 log 10 (f c ) 0.8) 2018, B.-P. Paris ECE 732: Mobile Communications 22

17 Simplified Model I Often a simpler path loss model that emphasizes the dependence on distance suffices. I Simplified path loss model: in db: L P = K d d 0 g L P(dB) = 10 log 10 (K )+10g log 10 ( d d 0 ). I Frequency dependence, antenna gains, and geometry are absorbed in K. I d 0 is a reference distance, typically 10m - 100m; model is valid only for d > d 0. I Path loss exponent g is usually between 3 and 5. I Model is easy to calibrate from measurements. 2018, B.-P. Paris ECE 732: Mobile Communications 23

18 Shadowing I Shadowing or shadow fading describes random fluctuations of the path loss. I due to small scale propagation effects, e.g., blockage from small obstructions. I Path loss becomes a random variable Y db. I Commonly used model: log-normal shadowing; path loss Y db in db is modeled as a Gaussian random variable with: I mean: P L(dB) (d) - deterministic part of path loss I standard deviation: s Y - describes variation around P L(dB) ; common value 4dB 10dB. I When fitting measurements to an empirical model, s Y captures the model error (residuals). 2018, B.-P. Paris ECE 732: Mobile Communications 24

19 Outage Probability I As discussed earlier, the received power must exceed a minimum level P min so that communications is possible; we called that level the receiver sensitivity S R. I Since path loss Y db is random, it cannot be guaranteed that a link covering distance d can be closed. I The probability that the received power P r(db) (d) falls below the required minimum is given by: Pr(P r(db) (d) apple S R )=Q( P t + G t + G R P L(dB) (d) S R s Y ). I The quantitity P t + G t + G R P L(dB) (d) S R is called the fade margin. 2018, B.-P. Paris ECE 732: Mobile Communications 25

20 Exercise: Outage Probability I Assume that a communication system is characterized by: I Transmit power: P t = 1W I Antenna gains: G t = 3 db and G R = 0 db I Receiver sensitivity: S R = 98 dbm I Path loss according to the two-ray model with h m = 1 m, h b = 10 m. I Communications range: d = 1 km Querstion: What is the outage probability of the system when the shadowing standard deviation s Y = 6 db? I Question: For a channel with s Y = 6 db, how much fade margin is required to achieve an outage probability of 10 3? 2018, B.-P. Paris ECE 732: Mobile Communications 26

21 Cell Coverage Area I Expected percentage of cell area where received power is above S R. I For a circular cell of radius R, cell coverage area is computed as: C = 1 pr 2 Z 2p 0 Z R 0 Q( S R (P t P L(dB) (r)) s Y )drdq. 2018, B.-P. Paris ECE 732: Mobile Communications 27

22 Cell Coverage Area I For the simplified (range only) path loss model g L P = K this can be computed in closed form: d d0 where: C = Q(a)+exp( 2 2ab b 2 ) Q( 2 ab ) b a = S R (P t 10 log 10 (K ) 10g log 10 (R/d 0 )) s Y and b = 10g log 10(e) s Y. 2018, B.-P. Paris ECE 732: Mobile Communications 28